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Multifunctional optical probes for the characterization of microwave and millimeter wave devices

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Multifunctional Optical Probes for the Characterization of
Microwave and Millimeter Wave Devices
by
Ronald M. Reano
A dissertation submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
(Electrical Engineering)
at the University of Michigan
2004
Doctoral Committee
Professor Linda P. B. Katehi, Co-Chair
Associate Research Scientist, John F. Whitaker, Co-Chair
Associate Professor Amir Mortazawi
Professor Stephen Rand
Associate Professor Kim Winick
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UMI Number: 3122033
Copyright 2004 by
Reano, Ronald M.
All rights reserved.
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© Ronald M. Reano 2004
All Rights Reserved
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To my family.
ii
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ACKNOWLEDGEMENTS
This work would not have been possible without the help from a very large number of
people. First, I would like to thank my research advisors, Professor Linda P. B. Katehi
and Dr. John F. Whitaker, for being a tremendous positive influence on me during my
Ph.D. research program. I would also like to thank Professor Amir Mortazawi, Professor
Stephen Rand, and Professor Kim Winick for their critical thinking while participating on
my thesis committee.
Funding support for this dissertation was provided by the Army Research Office
through the Multidisciplinary University Research Initiative on Spatial and Quasi-Optical
Power Combining (Grant DAAG 55-97-0132 under subcontract to Clemson University)
and the Department of Electrical Engineering and Computer Science, University of
Michigan, Ann Arbor through teaching assistantships.
A number of faculty have given me positive boosts and influences along the way. I
wish to thank Professor Fawwaz Ulaby, Professor Kamal Sarabandi, Professor Gabriel
Rebeiz, Professor John Volakis, Professor Stella Pang, Professor Herbert Winful, Dr.
Valdis Liepa, Dr. Adib Nashashibi, and Dr. Leland Pierce. In addition, I would like to
thank Dr. Sean C. Ortiz, formerly of North Carolina State University, Raleigh, for
assistance with the operation and measurements of the Quasi-Optical Power Combining
Array that is discussed in this work.
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I would like recognize department staff in the Department of Electrical Engineering
and Computer Science for their administrative support.
Beth Stalnaker, Karen Lisa,
Mary Eyler, Karla Johnson, Susan Chamley, Karen Kirchner, Serina Brown, Debra
Dieterle, and Tammy Zill have been very helpful with their administrative expertise. I
would also like to thank staff members at the University of Michigan Solid State
Electronics Laboratory for their support with fabrication related issues. In particular, I
would like to thank Brian Vanderelzen, James Kulman, and Tim Brock.
I would like to thank past and present colleagues of the University of Michigan's
Radiation Laboratory, Center for Ultrafast Optical Science, and Electrical Engineering
and Computer Science Department for their friendship, help, support, and patience during
countless interesting discussions about any and all things.
Many thanks to Professor
Dimitris Peroulis, Dr. Alexandras Margomenos, Dr. Lee Harle, Dr. Yongshik Lee,
Farshid Aryanfar, Dr. Mark Casciato, Dr. Werner Thiel, Dr. John David Shumpert, Dr.
Katherine Herrick, Kok Yan Lee, Joseph Burnett, Dr. Kyoung Yang, Dr. Bo Ruffin,
Jason Diebel, Bianca Jackson, Dr. Wei Chen, Helena Chan, Guangyu Li, Yumin Lu, PeiChen Wu, Dr. Ayman Al-Zayed, Reza Azadega, Kevin Buell, Michael Chang, Kaiann
Fu, David Morris, Eray Yasan, Professor Costas Sarris, Professor Bill Chappel, Mike
Reiha, Dr. Abbas Abbspour-Tamijani, Tim Hancock, Yongming Cai, Dr. Guan-Leng
Tang, Dr. Jad Rizk, Dr Bernhard Shoenlinner, Mohammad Abdel Moneum, and Dr. Dan
Lawrence, to name a few.
Finally, I am grateful for my family for being my bedrock foundation: my parents,
Felizardo S. Reano and Herminia M. Reano, my two sisters, Gina and Grace, and my two
nephews Bonjing and Junie.
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TABLE OF CONTENTS
D ED IC A TIO N ...................................................................................................
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A CKNOW LEDGEM ENTS.............................................................................
iii
LIST OF F IG U R E S ...........................................................................................
vii
LIST OF A PPEN D IC ES..................................................................................
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CHAPTERS
1 Introduction.........................................................................................
1
2 Integrated electro/thermal probe.......................................................
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2.1 Electro/thermal concept.......................................................
2.2 Implementation for simultaneous measurements..............
2.3 Characterization....................................................................
2.3.1 Thermal response...............................................
2.3.2 Absolute electric field magnitude.....................
2.3.3 Stabilization of electric field phase...................
2.3.4 Invasiveness........................................................
2.4 Miniaturization.....................................................................
2.5 Conclusion............................................................................
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3 Nonlinear thermo-optic modeling.....................................................
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3.1 Thermo-optic m odel............................................................
3.2 Solution methodology.........................................................
3.3 R esults..................................................................................
3.3.1 Transmission.......................................................
3.3.2 Reflection............................................................
3.3.3 Performance characterization.............................
3.4 Measurement versus simulation.........................................
3.5 Conclusion............................................................................
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4 Polarization-tunable probe for combined E/H-field
measurements.....................................................................................
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4.1
4.2
4.3
4.4
4.5
Hybrid probe concept..........................................................
Implementation for tunable measurements.......................
Isolation characterization.....................................................
Sensitivity enhancement......................................................
Conclusion............................................................................
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5
6
Vector component isolation of arbitrary modulating
electric fie ld .......................................................................................
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5.1 Analysis of field-induced birefringence.............................
5.2 Measurement validation......................................................
5.3 Conclusion............................................................................
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Applications.......................................................................................
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6.1
6.2
6.3
6.4
6.5
6.6
7
Quasi-optical power combining array................................
Patch antenna operating at high pow er...............................
Aperture of V-band horn antenna.......................................
Surface-waves from a microstrip stub discontinuity
RF microelectromechanical switches.................................
Conclusion............................................................................
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Thesis conclusion and future w ork..................................................
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7.1 Thesis conclusion................................................................
7.2 Future w o rk ..........................................................................
7.2.1 Exploration of new material system s...............
7.2.2 Development of post processing for
enhanced spatial resolution...............................
7.2.3 Research into new applications........................
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APPENDICES.............................................................................................................
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BIBLIOGRAPHY......................................................................................................
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LIST OF FIGURES
FIGURE
1.1: First picosecond electro-optic sampling system for electric-field
time-domain transient measurements by Valdmanis et al. (1982)..........
1.2: First harmonic-mixing scheme electro-optic sampling system for
electric-field frequency-domain measurements by Weingarten et al.
(1982)...........................................................................................................
1.3: First ffee-space transient magneto-optic sampling system for THz
detection by Riordan et al. (1997).............................................................
1.4: First fiber-optic instrument for temperature measurement using the
temperature dependence of the bandgap of semiconductors by
Kyuma et al. (1982)....................................................................................
1.5: System design employing the temperature dependence of the
bandgap of GaAs to measure wafer temperatures during molecularbeam-epitaxy growth chambers by Johnson et al. (1991).......................
2.1: The experimental setup for combined electro-thermal measurements.
By separating the electric-field and temperature signals in frequency,
both may be acquired with a single probe. The top beam-line is
implemented for system phase stability. The example RF deviceunder-test in the figure is an MMIC with a microstrip feed....................
2.2: The temperature response of the GaAs probe..........................................
2.3: Cross-sectional view of the configuration used to scale relative
electric-field measurements to absolute units (ie. volts/meter).
The probe is inserted into a rectangular waveguide and analytical
expressions are used to relate the electro-optic signal to the RF
input power..................................................................................................
2.4: Measurement linearity and the minimum detectable electric-field.
Over a 300 ms bandwidth, the EO signal reaches the noise floor
at 1.24 V/m..................................................................................................
2.5: Measured phase drift and demonstration of correction. Any drift
in the measurement of electric-field phase is stabilized via the
implementation of a phase reference channel. The calibrated
phase data, taken over one hour, has a standard deviation of ±3
degrees..........................................................................................................
2.6: The full-wave simulation geometry for the examination of
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invasiveness o f the probe on a device-under-test (DUT).
In this case, the DUT is a coplanar waveguide with lateral
dimensions less than the footprint of the probe........................................
2.7: Simulation results of the spatial extent of the perturbation of the
characteristic impedance, Zo, of the CPW. The presence of the
probe changes Zo by 19% when the bottom edge of the probe
is 25.4 mm above the surface of the transmission line............................
2.8: Sensitivity analysis of invasiveness simulations. Results show
that as the height of the probe becomes less than 50 mm, the
change in Zo and the capacitance per unit length becomes
significant. In practice, there is a tradeoff between invasiveness
and signal-to-noise. The effect of the probe is equivalent to a
lumped shunt capacitor on the order of femtofarads................................
2.9: HP 8510 vector network analyzer time-domain (lowpass)
measurements of probe over CPW. The impulse response
verifies the capacitive loading....................................................................
2.10: SI 1 frequency domain measurements (HP 8510) when probe
is over CPW. The return loss shows that the effect of the probe
is quite minimal...........................................................................................
2.11: Simulated data (HP EEsof Libra) of CPW with an additional
lumped femtofarad shunt capacitor. The simulation is in good
agreement with the measurements of S11 (verifying the order
of the magnitude of the loading capacitance)...........................................
2.12: Aspect-ratio-limited probe fabrication procedure for probe
miniaturization: (a) Probe mask, (b) Wet etch, (c) Mask removal,
(d) Fiber mounting, (e) Acetone release....................................................
2.13: Digital image of fabrication setup...........................................................
3.1: Thermo-optic iterative process flow for solution.....................................
3.2: Optical transmission vs. input optical power...........................................
3.3: Simulated optical power loss in the semiconductor and
corresponding change in probe temperature vs. input optical
power for the transmission case................................................................
3.4: Simulated bandgap of GaAs vs. input optical power for the
transmission case.........................................................................................
3.5: Simulated optical linear power absorption coefficient vs. input
optical power for the transmission case....................................................
3.6: Simulated total reflected optical power vs. input optical power
3.7: Simulated initial change in total reflected optical power with
respect to temperature vs. input optical power.........................................
3.8: Simulated relative change in initial total reflected optical power
with respect to temperature vs. input optical power.................................
3.9: Simulated temperature invasiveness vs. input optical power in the
reflection case..............................................................................................
3.10: Simulated temperature dynamic-range (initial total reflected
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optical power to 10% of final reflected optical power) vs. input
optical power in the reflection case...........................................................
3.11: Measured and simulated response of probe to temperature for
the reflection case........................................................................................
3.12: Electric-field signal vs. temperature signal over measured
temperature range for the reflection case..................................................
3.13: Peak reflected optical power and corresponding peak pulse
power vs. fiber length.................................................................................
4.1: Conceptual schematic of combined electro/magneto-optical probe
with external polarization controls............................................................
4.2: Transmission vs. retardance as a function of Faraday rotation for
theta = 90°....................................................................................................
4.3: The probe consists of a series combination of GaAs (100 um thick)
and TGG (2 mm thick). A quartz tube is used for support.....................
4.4: The experimental setup..............................................................................
4.5: The magnitude of the standing waves on a shorted microstrip
transmission line measured with the combined probe at a height of
2.0 mm above the surface...........................................................................
4.6: The phase of the standing waves on a shorted microstrip
transmission line measured with the combined probe at a height
of 2.0 mm above the surface......................................................................
4.7: Measured and simulated results of the z-component of the
electric-field 2.0 mm above the microstrip line.......................................
4.8: Measured and simulated results of the z-component of the magnetic
field 2.0 mm above the microstrip line......................................................
4.9: Measured peaks in the frequency response of the probe due to the
millimeter-wave field resonating in the probe..........................................
4.10: Finite-element-method simulations confirm the resonant behavior
of the magnetic-field in the probe.............................................................
5.1: Coordinate system, relevant Miller indicies, and orientation, primary
flat, and secondary flat of the gallium arsenide waferof interest
5.2: Normalized field-induced birefringence dependence on modulating
electric-field as a function of optical-polarization angular deviation
delta alpha for an optical path deviation delta psi =0...............................
5.3: Microwave/optical setup for isolation measurements. The RF
electric-field polarization direction at the crystal is varied by
physically rotating the source antenna in the plane transverse to
the boresight direction of the antenna.......................................................
5.4: Measured electro-optic modulation from each RF source. The data
follows the cosine function thereby demonstrating vector component
isolation of the modulating electric-field..................................................
6.1: Measured quasi-optical power combining array.......................................
6.2: Probe and power meter measurement of MMIC......................................
6.3: Probe-only measurements of MMIC.........................................................
6.4: Temperature-calibrated electric-field data................................................
6.5: Simultaneous electric-field and temperature measurementsof MMIC...
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6.6: Measured and simulated magnitude of the z-component (normal)
of the electric-field at a height of 0.5 mm above the surface..................
6.7: Measured and simulated magnitude of the y-component (tangential)
of the magnetic-field at a height of 1.5 mm above the surface...............
6.8: Measured and simulated temperature distribution at a height of
0.5 mm above the surface...........................................................................
6.9: Digital image o f terbium gallium garnet at aperture of V-band
horn antenna................................................................................................
6.10: Measured magnetic-field magnitude as a function of position at
the output of a horn antenna.......................................................................
6.11: Measured magnetic-field phase as a function of position at the
output of a horn antenna. Measured line scans across the aperture
are in good agreement with first-order aperture-antenna theory.............
6.12: Test fixture and probe positioning for measurement of surfacewaves from open microstrip stub discontinuity........................................
6.13: Measured magnitude and phase of surface-wave electric-field
from open microstrip discontinuity...........................................................
6.14: Magnitude and phase of surface-wave electric-field from open
microstrip discontinuity in artificial time representation; the
radiation pattern is also compared with theoretical results.....................
6.15: The RF/optical configuration to measure the RF MEMS capacitive
switch...........................................................................................................
6.16: SEM image o f measured RF MEMS capacitive switch.........................
6.17: Digital image of probe over RF MEMS capacitive switch...................
6.18: Measured temperature rise-times to steady state. The probe height
is 25 micron.................................................................................................
6.19: Measured electric field magnitude in the UP state. The probe
height is 61 micron.....................................................................................
6.20: Measured electric field magnitude in the DOWN state. The probe
height is 61 micron.....................................................................................
6.21: Measured electric field phase in the UP state. The probe height is
61 micron.....................................................................................................
6.22: Measured electric field phase in the DOWN state. The probe
height is 61 micron.....................................................................................
6.23: Measured temperature in the UP state. The probe height is 61 pm
6.24: Measured temperature in the DOWN state. The probe height is 61
micron..........................................................................................................
A. 1: Mask maker................................................................................................
A.2: Wet benches................................................................................................
A.3: Mask aligner...............................................................................................
A.4: SJ-26............................................................................................................
A.5: Sputter coater..............................................................................................
A.6: PECVD.......................................................................................................
A.7: RIE...............................................................................................................
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A.8: Asher...........................................................................................................
A. 9: Spinner station............................................................................................
B. 1: Pump laser for Ti:sapphire mode-locked laser........................................
B.2: Ti:sapphire mode-locked laser..................................................................
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LIST OF APPENDICES
APPENDIX
A: Detailed fabrication procedures...........................................................
B: Optical sources.....................................................................................
C: Optical indicatrix..................................................................................
D: Electromagnetic wave propagation in dispersive nonlinear media....
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CHAPTER 1
Introduction
The application of optical technology towards high-frequency circuit diagnostics has
been driven by the desire to measure temporal and spatial electromagnetic behavior at
internal points of a circuit. In the last two decades, a myriad of creative techniques have
been developed to obtain spatial and temporal electromagnetic field distributions, each
design trading off different aspects of sensitivity, response time, resolution, invasiveness,
dynamic range, accuracy, cost, compatibility, and ease of use.
Methods to measure
electromagnetic fields include probes based on passive detection (monopole /dipole/loop
antennas), modulated scattering, metallic cantilevers (scanning-force-microscopy),
electron beams, and optical waves in crystals (electro-optic/magneto-optic sampling) [1][9]Of emerging interest in the high-frequency, high-power circuit community is RF
induced thermal effects [10]-[12].
The thermal characteristics become especially
important in active antenna arrays and quasi-optical power combining structures where
the generation of heat in such configurations mandates a strong consideration of thermal
dissipation in the overall design [13]-[14],
In addition, the application of
microelectromechanical devices in high power applications raises interesting questions
regarding the effects of RF induced heating on device performance and reliability [15]-
1
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[16].
Methods that exist for observing thermal effects include the use of thermal
cameras, infrared microscopes, bandgap thermometry, thermocouples, and thermistors.
For measuring electric fields, electro-optic sampling provides high spatial resolution,
high bandwidth, low invasivenss, and high contrast [17]. In this technique, an optical
beam is directed into an electro-optic crystal (with low to moderate value of dielectric
constant), which is placed in an electromagnetic field distribution of interest (generated
from a device-under-test). The optical beam experiences a change in polarization state
due to the linear electro-optic (Pockels) effect, the degree of change depending on the
intensity of the electric field (from the device under test) that fringes into the crystal. The
polarization state change is detected, resulting in a measurement of the magnitude and
phase of the electric field (ie. the electric field phasor).
The linear electro-optic effect, first studied by Friedrich Pockels in 1893, is a secondorder nonlinear optical effect mediated by the second-order susceptibility, %(2), as
described through the nonlinear polarization, P,
p(DC+<v)
i nonlinear
n s~\m/i'ho n
i,
2£0zfk (DC, co)E®cE™
( 1.1)
where s0 is the permittivity of free space. The component of electric field with the co
superscript is in the optical frequency range. The DC component of electric field can
extend through the microwave and millimeter wave bands and into THz frequencies.
Equation 1.1 is a phenomenological description of the linear electro-optic effect as long
as the low frequency component remains small relative to optical frequencies [18]. The
nonlinearity produces a birefringence, An, that is proportional to the DC electric field in
the probe, E, and the cube of the index of refraction, n0
( 1.2 )
2
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The proportionality constant depends on geometrical considerations and the strength of
the electro-optic effect of the crystal of choice.
The first picosecond electro-optic sampling system for electric-field time-domain
transient measurements was demonstrated by Valdmanis et al. [7]. As shown in Figure
1.1, this system employs the Pockels effect, mode-locked laser technology, and phasesensitive detection to achieve a temporal resolution of less than 4 ps and a sensitivity of
50 pV.
This system addressed the need for a measurement system with picosecond
accuracy for the characterization of picosecond photodetectors and photoconductive
switches.
CW A rgon Laser
CW M odelocked
Ring Dye Laser
Lithium N iobate
^
C rystal
Lock-In
A m plifier
C om pensator
Analyzer
Delay
Figure 1.1: First picosecond electro-optic sampling system for electric-field time-domain
transient measurements by Valdmanis et al. (1982). {from ref. 7}
3
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The first reference to the use of short pulse lasers in the context of harmonic mixing
for frequency domain electric-field measurements was reported by Kolner et al. [19]. A
system diagram, reported by Weingarten et al. is shown in Figure 1.2 [20]. Frequency
domain measurements are accomplished by setting the microwave synthesizer to an
integer multiple of the optical pulse repetition rate plus a small frequency offset, allowing
for lock-in detection. The magnitude and phase of the microwave electric field inside of
GaAs substrates were measured as a function of position, yielding the standing waves on
an open microstrip transmission line.
When the device-under-test is a planar structure with an electro-optic substrate, such
as gallium arsenide, the optical beam can probe the substrate itself in order to obtain
electric-field information.
electro-optic sampling [19].
This form of electro-optic sampling is called "internal"
"External" electro-optic sampling, on the other hand,
involves the use of small volume electro-optic probe tips that are mounted in close
proximity to the device under test [17]. Crystal probe tips based on electro-optic
Nd:YAG m ode-to ck ed laser
90 p s, 82 MHz, 1.06 pm
M icrow ave
S y n th e s iz e r
0 - 40 GHz
1.5 p s FWHM
Tim ing
S ta b iliz e r
<0.3 p s rm s
jitte r
RF
S y n th e s iz e r
82 MHz
P u ls e
Compressor
M icrow ave Signal
G aA s
P o la riz in g
B e a m sp litte r
I n t e g r a te d C ircu it
10 MHz p u ls e or
p h a s e m o d u latio n
eV ecto
gr
R eceiv er
Slow
P h o to d io d e
Figure 1.2: First harmonic-mixing scheme electro-optic sampling system for electric-field
frequency-domain measurements by Weingarten et al. (1989). {from ref. 20}
4
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materials include the use of lithium tantalate, bismuth silicate, zinc telluride, and gallium
arsenide [18]. Crystals are typically mounted on optically transparent fused silica for
mechanical support and positioning [17]. Electro-optic probes have also been integrated
with optical fibers in order to yield positioning flexibility [21]-[24].
In "external" electro-optic sampling, translation of either the device-under-test or the
probe tip allows for the acquisition of a spatial field-map of the electromagnetic field
distribution. Field mapping of microwave and millimeter wave circuits and radiating
structures such as slot antennas, patch antennas, coupled-line filters, transmission lines,
antenna arrays, and integrated circuits have been demonstrated [25]-[28].
Coupled
radiation, traveling waves, standing waves, and radiating waves can be identified with
spatial field maps [l]-[3], [29]-[31].
An analogous technique to electro-optic sampling, applicable to measuring high-speed
magnetic fields, is magneto-optic sampling.
Free-space magneto-optic sampling was
developed by Freeman, et al. in order to study magnetic dynamics in europium sulfide
films at low temperatures [9]. For magneto-optics, typical sensors exploit the Faraday
effect on an optical probe beam as the sensing methodology [32]. Amorphous glass (SF59) and terbium gallium garnet (TGG) are crystals that have been used in this regard.
These crystals have large bandwidths and are applicable in the THz regime. An example
of a free-space transient magneto-optic sampling configuration for THz detection is
shown in Figure 1.3 [33],
Magneto-optic sampling is based on the Faraday effect [34], In contrast to electro­
optic sampling, which is an electric field induced linear birefringence, magneto-optic
sampling is a magnetic field induced circular birefringence. This circular birefringence
5
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W ollaston
polarizer
^>1 . H
~
s
d etector
MO sen so r
^ T H z b eam j ^ p u m p
em itter
polarizer
probe
Figure 1.3: First free-space transient magneto-optic sampling system for THz detection
by Riordan et al. (1997). {from ref. 33}
results in a rotation of linear optical polarization, though an angle a , in the plane
transverse to the direction of propagation in a material exhibiting the Faraday effect, in
response to an external magnetic field
a
oc
/noH
(1.3)
where p0 is the permeability of free space and H is the low frequency magnetic field
intensity. The proportionality constant depends on geometrical considerations and the
strength of the magneto-optic effect in the material of choice.
In addition to measuring electric and magnetic fields, optical techniques have been
applied to measuring a number of other physical phenomena.
These include both
temperature and pressure. The first system design for measuring temperature using the
temperature dependence of the bandgap of semiconductors was reported by Kyuma et al.
[35].
Bandgap thermometry involves measuring the transparency of materials as a
function of temperature in materials with temperature dependent absorption coefficients.
Due to the temperature dependence of the bandgap of the material, optical power
transmission can be expressed as
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where T0 is the transmission, a is the temperature dependent absorption coefficient, T is
the temperature, and L is the length of the material. As shown in Figure 1.4, an optical
transmitter/receiver system sandwiches a sample of semiconductor coupled via optical
fiber.
The source was an AlGaAs LED (880nm, 150nm spectral width) and the
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semiconductor was either GaAs or CdTe (1 mm x 0.2 mm for GaAs, 1 mm x 0.5 mm
for CdTe).
An accuracy of ±1 °C, response time of 2 seconds, and dynamic range
between -10 °C and 300 °C was reported.
In addition, Johnson et al. in 1995 used the temperature dependence of the bandgap of
GaAs to measure the temperature of GaAs wafers within molecular-beam-epitaxy growth
chambers [36].
Using diffuse reflectance spectroscopy, the absorption spectrum and
temperature of the wafer were obtained. As shown in Figure 1.5, chopped white light
from a tungsten-halogen lamp is focused onto the GaAs wafer and then scattered light is
Optical fibers.
&■
O ptical tra n s m itte r
Optical s e n s o r
/
(a)
O p tic a l rece ive r
S ta in le ss h o ld e r
..- " t
................ 1.................
1..
i.... ;........-,i 1
~J _
1
a b s o rb e r
(b)
Figure 1.4: First fiber-optic instrument for temperature measurement using the
temperature dependence of the bandgap of semiconductors (1982). {from ref. 35}
7
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collected and spectrally analyzed using a monochrometer. Absorption data was collected
through a temperature range covering between 52 °C and 632 °C.
Each technique discussed so far has served one function: to measure quantities such as
electric, magnetic, or thermal fields. The research for this dissertation began with an
observation of temperature corrupted electro-optic data using a fiber coupled gallium
arsenide electro-optic sampling system developed by Yang [37]. When using this system
to measure active devices that heat up due to DC and RF power dissipation, it was
observed that lasing too close to the bandgap produces temperature dependent electro­
optic modulation through bandgap absorption. Rather than tune away from the bandgap,
one can operate in proximity to the band-edge and take advantage of bandgap
thermometry and electro-optic sampling to measure electric field and temperature
simultaneously.
UHV Chamber
Lens
SWindow
WHaJogen —
Lamp
Mirrors
Mono­
iDiffuse Ray
chromator
Cooled
InGaAs
Detector
Chopper
Holder
Wafer
Heater Foils
PBN
Lock-in
Amplifier
Figure 1.5: System design employing the temperature dependence of the bandgap of
GaAs to measure wafer temperatures during molecular-beam-epitaxy growth chambers
by Johnson et al. (1995). {from ref. 36}
8
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The exploration of the concept of multifunctional optical probes (ie. probes that can
measure multiple quantities) for the purpose of characterizing microwave and millimeter
wave devices is the theme of this dissertation. The motivation for such probes stems
from the need to study coupled electro/thermal effects in microwave/millimeter wavedevices, the desire to measure both voltage and current, and the wish to benefit from
techniques that minimize the time, effort, and diagnostic tools required for test and
measurement.
Chapter 2 discusses an integrated electro/thermal probe.
This probe
allows one to simultaneously measure coupled electromagnetic and thermal effects. The
concept, implementation, characterization, and fabrication of such probes are discussed.
Relevant application areas include the measurement of quasi-optical power combining
arrays where electromagnetic performance and thermal management are key drivers in
the overall design, and RF MEMS devices where RF power induced heating is of interest.
Chapter 3 covers nonlinear thermo-optic modeling in electro-optic semiconductors for the
purpose of characterizing the limitations of the electro/thermal probe. The model and
solution methodologies are presented. Modeling results are compared with laboratory
measurements.
In Chapter 4, a polarization-tunable probe for combined electric and
magnetic field measurements is discussed. This probe allows one to measure electric and
magnetic fields with a hybrid probe that can be switched between electric field sensitivity
and magnetic field sensitivity by adjusting external polarization optics. The concept,
implementation, characterization, and limitations are discussed.
A technique for
enhancing magnetic-field sensitivity is also presented, which improves the sensitivity
difference between the electric and magnetic field sensors. Relevant application areas
include point impedance measurements, the characterization of unknown impedance
9
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surfaces (both natural and artificial), and the direct determination of complex
permittivity. Chapter 5 discusses the degree to which isolation occurs between the vector
components of an arbitrary modulating electric field when zincblende crystals are
employed. Analysis of the field-induced birefringence shows that each vector component
can be isolated provided particular orientation angles are maintained. The analysis is
confirmed by measurements.
Chapter 6 presents a number of applications.
These
include measurements of the temperature rise in a quasi-optical power combining array,
the field distributions of a patch antenna operating at high power, the magnetic field at
the aperture of a millimeter wave hom antenna, surface waves from an open microstrip
stub discontinuity, and power induced heating in radio frequency microelectromechanical
switches. Chapter 7 concludes the thesis with an overall conclusion and discussion of
future direction. The appendix provides the fabrication procedures involved in this work,
the background information on the optical sources utilized, a reference derivation of the
index indicatrix, and a derivation of the optical pulse propagation equation in dispersive
nonlinear media that includes nonlinear absorption.
10
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CHAPTER 2
Integrated Electro/Thermal Probe
This chapter presents a method to simultaneously measure electric field and
temperature with a single probe and discusses the full characterization of an
electro/thermal field-mapping system. The Pockels effect is employed within a gallium
arsenide probe to measure electric fields, and the effect of photon absorption due to
bandtail states in the semiconductor is used to determine temperature. This allows for the
combined electro-thermal examination of active microwave and millimeter-wave circuits
and the ability to calibrate electric field data that is corrupted when the probe is placed in
areas where temperature variations are present. Techniques for scaling relative electricfield measurements to absolute units are shown. In addition, a method for stabilizing
electric-field phase drift is also presented.
The probe invasiveness with respect to
electromagnetic fields, due to its value of relative permittivity, is quantified on a planar
transmission line by investigating the change in the characteristic impedance and
capacitance per unit length as the probe is brought into the near-field. Finally, an aspectratio-limited fabrication method for probe miniaturization is discussed. This technique
utilizes secondary-handling of bulk micromachined probes, thereby allowing for
miniaturization since the probes do not need to be handled directly. Relevant application
areas for the electro/thermal probe include the measurement of quasi-optical power
11
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combining arrays where electromagnetic performance and thermal management are key
drivers in the overall design, and RF MEMS devices where RF power induced heating is
of interest.
2.1
Electro/thermal concept
The physical mechanisms employed to measure temperature are the temperature
dependence of the energy bandgap in intrinsic semiconductors and its effect on the
absorption of optical power. A well known equation describing this phenomena has been
established by Varshni [38]
Eg(T) = Eg( 0 ) -
(2 . 1)
T +p
where y and P are material-specific empirical constants, Eg(T) is the bandgap energy at
temperature T, and Eg(0) is the bandgap energy at zero Kelvin. For photon energies in
the bandgap and near the band-edge, the absorption coefficient, a, has been found to
decay exponentially with decreasing photon energy, h v, due to the presence of bandtail
states. The dependence on photon energy is shown to follow [39]
a = A e x p [ ( h v - x 0) / y 0)]
( 2 .2 )
where A, x0, and y0 are constant curve fitting parameters at 300 K. For GaAs at room
temperature ± 50 K, the bandgap and absorption coefficient variation with temperature
can be linearized to within 5%. Linearizing equation (2.1) and (2.2) about a nominal
temperature, T0, and photon energy (hv)0 and noting that
da
da
12
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(2.3)
where £, is a constant on the order of one for the temperature range of interest, the flow of
optical power, P, through the semiconductor is found to obey the following temperature
dependence
— oc 1+ kT
P
where
k
(2.4)
is a constant that depends on the dimension of the semiconductor in the direction
of propagation. Therefore, by monitoring the absorption response of an optical beam that
is directed to propagate through a section of semiconducting material, the change in
temperature can be inferred in a manner that is linear with the inverse of optical power.
To simultaneously measure electric fields, the semiconductor must also be electro­
optic. Due to the Pockels effect, an optical beam propagating through an electro-optic
material exhibits a change in polarization-state when the material is in the presence of an
externally applied, and relatively low-frequency, electric field.
The change in
polarization-state can be made to result in an amplitude modulation of the optical beam
that is proportional to the intensity of the applied electric field. The optical transmission,
T0, through an electro-optic modulator set up for 50% transmission, is given by [34]
T0 = sin 2
rp
n
Erfd
— + 7Z
V
V 2
V _
n
(2.5)
sin(cOrft + $ f )
7
1
Jj
where Erf is the (spatial) average RF electric-field magnitude induced in the probe, <|>rf is
the RF electric-field phase, d is the crystal thickness along the direction of propagation of
the optical beam, corf is the RF frequency, t is time, and V Kis the half-wave voltage of the
electro-optic material. For Erfd « V*, the intensity modulation is linear with the average
RF electric-field induced across the probe.
13
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2.2
Implementation for simultaneous measurements
The experimental setup is shown in Figure 2.1. The probe material is GaAs with a
normal-surface area of 500 pm x 500 pm and a vertical thickness of 200 pm.
A
Ti:Sapphire laser tuned to 895 nm is used to generate a linearly polarized sampling beam
that is coupled to the probe via a section of single-mode optical fiber and a graded-index
lens [24]. Appropriate phase retarders are placed to configure an amplitude modulator
for electric field measurements.
The beamsplitter, polarization control, GaAs crystal, and photodetector arrangement
allows for a "coaxial" arrangement between the incident and reflected beams both to and
from the probe tip. The polarization states for this arrangement have been described for
both free-space and a fiber coupled configurations [20], [37]. From the beamsplitter, a
linearly polarized optical beam passes through a 22.5° oriented quarter-waveplate (with
respect to the axis of the beamsplitter), producing an elliptical polarization. A 33.75°
oriented half-waveplate then rotates the elliptical polarization an additional 22.5° to align
its major axis at 45° to the [011] direction of the GaAs probe tip. The reflected beam
passes back through the waveplates, producing a linear polarization at 45° to the axes of
the polarizing beam-splitter, and the polarization component at 90° orientation is directed
by the beamsplitter onto the photodiode.
To alleviate the need for a fast photodetector, and to provide a method by which the
phase of a signal may also be easily sensed, the device under test is fed via an RF
synthesizer configured for harmonic mixing in order to down-convert the sampled
electric fields to IF frequencies [19]. This is accomplished by mode locking the laser to
produce a train of 80 fs pulses at a pulse repetition rate of 80 MHz and setting the RF
14
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source frequency to an integer multiple of the pulse repetition rate, plus an offset that
corresponds to the IF frequency. The time-domain comb produces a frequency-domain
comb that extends into the THz frequency range. An IF frequency of 3 MHz is used and
was selected based on a tradeoff consideration between signal-to-noise degradation due
to 1/f noise at lower IF frequencies and the loss of sensitivity incurred by selecting higher
IF frequencies. Since the 80-MHz component is not modulated coherently, its amplitude
does not change as it passes through the electro-optic crystal.
A photodiode functions as an envelope detector that transforms the 3-MHz modulation
and the 80-MHz pulse repetition component to electrical signals for detection. The 3MHz signal, denoted
V 3M h z ,
is the modulation signal that provides the electric field
information and the 80-MHz signal, denoted
V so m h z,
is the spectral component that is
monitored for temperature measurements. A high-pass filter that filters as an open-circuit
couples the 80-MHz pulse-repetition component to a spectrum analyzer while the 3-MHz
modulation signal is coupled to a lock-in amplifier with a low pass filter that filters as an
open-circuit for the 80-MHz signal. Such an arrangement allows for the simultaneous
measurement of thermal and electric fields.
2.3
Characterization
2.3.1 Thermal Response
To characterize the thermal properties of the electro-optic sensor, the probe was
mounted in still air approximately four inches above a hotplate. A precision thermistor
with a tolerance of ±0.2°C was positioned adjacent to the probe to monitor the
15
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X/2
R eferen ce
EO Crystal
X/.
Analyzer
£
Photo
Diode
Polarization
Controller
Fiber
C oupler
Polarization
D ep en d en t
B eam
Splitter
F ree
Space
Optical
B eam
Quartz
Ferrule
PhotoDiode
GaAs
P ro b e
High
P ass
Filter
Optical
Isolator
V 80MHz
(Therm al data)
jr
B ragg
x R eflector
MMIC
s.
f . Microstrip
I V IIC I U
77 7 T 7 \ i
IfV v V vT
Low
P ass
Filter
RFD U T
3 MHz
(Electric field data)
Electrical
Switch
P u lsed
L aser
r...
10 MHz
Ref.
S pectrum
Analyzer
Lock-in
Amp
~'i..
3 MHz
External
Ref.
RF
S o u rce
i
i
Figure 2.1: The experimental setup for combined electro-thermal measurements. By
separating the electric-field and temperature signals in frequency, both may be acquired
with a single probe. The top beam-line is implemented for system phase stability. The
example RF device-under-test in the figure is an MMIC with a microstrip feed [58].
temperature variations of the ambient air as the hot plate was turned on and off.
Absorption data from the probe and temperature data from the thermistor were collected
over a fifty minute period as the temperature was varied between 20°C and 60°C. The
results are shown in Figure 2.2 and agree with the theory as described in equation (2.4).
16
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The temperature accuracy and sensitivity of the probe are determined from a linear
regression analysis of the data shown in Fig. 2.2. The accuracy, calculated from the
standard deviation of the data set composed of the absolute value of the deviations from
the linear fit, is calculated to be ±0.5°C. Using the thermistor resistance versus
temperature characteristic and the observed relationship between the measured optical
power and the thermistor resistance, the sensitivity is calculated to be equal to 0.31
mW/°C at 25°C.
2.3.2 Absolute Electric-Field Magnitude
The output of the lock-in amplifier is a DC voltage that is proportional to the first
harmonic rms amplitude of the RF modulation signal. Although this scheme is useful for
relative electric field measurements, scaling the output to electric field units (ie.,
volts/meter) is desirable in order to obtain absolute (spatial) average field measurements
and to characterize the dynamic range of the system. A direct determination of the
5.0x10s '
fl I..I
O)
n
o
4.5x10s -
CL. 4.0x10s -
E
-
o
i= 3.5x10s -
•M
C
d) 3.0x10s c
o
a.
-
E 2.5x10s o
O
N 2.0x10 X
Experimental Data
-
5
o 1.5x10s 00
20
I 1111I
25
30
i
35
i
i 111 I— i— i— r
40
Linear Fit
T 1 I"I 1I"I
45
50
1i 1 1 1 1 i 1
55
60
Tem perature from Precision Therm istor [°C]
Figure 2.2: The temperature response of the GaAs probe [58].
17
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proportionality constant relating the output of the lock-in amplifier and Erfd would allow
the output to be scaled to absolute units.
However, this would require an accurate
characterization of the power mismatches presented by the fiber coupler, the interface
between the fiber and the grin lens, the interface between the grin lens and the GaAs
probe, and the reflectivity of the Bragg reflector.
To circumvent these practical difficulties, an alternative method for scaling the
measured data to absolute units has been developed. This method involves placing the
probe in a region where the absolute value of the electric field distribution is known. The
region inside of a shorted rectangular waveguide enclosure was selected due to the
simplicity of the analytical closed-form field solutions, the confinement of the fields
within a closed structure, and the direct relationship between the power input into the
waveguide and the absolute magnitude of the electric field.
Previous investigators have
scaled electro-optic signals to RF electromagnetic fields associated with open structures
such as microstrip and coplanar waveguide lines in order to determine minimum
detectable signal levels [8], [23].
The method presented here, however, involves a
completely enclosed structure. Relating input RF power to expected fields over an open
structure such as microstrip or CPW leads to inaccuracies due to losses associated with
radiation, losses associated with the coax-to-microstrip/CPW transitions, the sensitivity in
the positioning of the probe above the line (due to exponentially decaying fields), and the
need to rely on non-closed form solutions of the microstrip/CPW fields. The approach
presented in this thesis is also independent of the height of the crystal above a DUT since
the procedure directly scales the amplitude measurement on the RF lock-in with the
induced optical retardation.
18
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The geometry o f the insertion of the probe into the rectangular waveguide is shown in
Figure 2.3. In the absence of the probe, the magnitude of the electric field at a standing
wave peak, |Epeak|, can be related to the input power, P, via the wave-equation and the
Poynting vector as
( 2 .6)
Ep * * h J k a b ’ kz = y » ° £o -
where w is the radian frequency, p0 is the free-space permeability, s0 is the free-space
permittivity, kz is the phase constant along the direction of propagation, A is the length of
the short edge of the rectangular waveguide, and B is the length of the long edge. Since
each quantity on the right hand side of the equation for |Epeak| is measurable, the expected
value for the magnitude of the electric field at a standing wave peak can be determined.
A complication is the distortion of the electric field due to the presence of the probe in
the waveguide. Since the graded-index lens self-focuses the optical beam to a beam-
Q uartz Tube
G RIN Lens
G aA s Probe
Interior o f R ectangular W avegu ide
B
1
Figure 2.3: Cross-sectional view of the configuration used to scale relative electric-field
measurements to absolute units (ie. volts/meter). The probe is inserted into a rectangular
waveguide and analytical expressions are used to relate the electro-optic signal to the RF
input power [58].
19
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waist of less than 10 pm, the field internal to the probe within a 10 pm diameter cylinder
centered between the top and bottom faces of the probe is the region of interest. For
frequencies such that the guide-wavelength is much larger than the probe dimensions, a
quasi-static approximation bounds the electric field inside the probe, Ejnt, to
— EaU<EM <Eea
(2.7)
S rp
where Eext is the field in the absence of the probe, and
is the dielectric constant of the
probe [40], The relation in (2.7) holds because the probe appears as a dielectric object
that is neither a thin slab nor a long thin cylinder. A full-wave finite element method
based simulation based on the geometry in Figure 2.3 was employed to analyze the
expected ratio of Eint to Eext [41]. The average electric-field induced in the probe is found
to be 19% of the electric-field when the probe is absent. This factor is taken into account
when scaling relative measurements to volts/meter via equation (2.6).
The measured results for the probe in the waveguide are shown in Figure 2.4. For this
experiment, a shorted WR-137 waveguide (height A = 15.8 mm, width B = 34.9 mm)
was employed and the operating frequency was set to 6.963 GHz. The waveguide short
was coupled to the RF synthesizer via a coaxial cable and coax-to-waveguide adapter.
An RF power meter was used to measure the input power going into the waveguide from
the coax-to-waveguide adapter. The mismatch at the coax-to-waveguide transition was
characterized via time-domain (bandpass) measurements on a vector network analyzer.
The peak return loss at the coax-to-waveguide transition was -29 dB below the peak
return loss at the waveguide short. Therefore, the transition mismatch can be neglected
with negligible error.
As shown in Figure 2.4, the lock-in voltage can be scaled to
20
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average volts/meter in a linear fashion. By stepping down the input power, the minimum
detectable average electric-field inside of the probe is 1.24 V/m. A measurement error of
±0.06 V/m is estimated from consideration of the measurement error of the power meter,
positioning error of the probe within the waveguide, convergence error associated with
the ratio of Ejnt to E ext, and the error in the linear fit of the data extrapolated to the noise
floor.
To state a sensitivity for the system, knowledge of the system bandwidth is required.
Since a lock-in amplifier is employed in the last stage, the system bandwidth is
determined by the time-constant on the output RC circuit. For the measurements shown
in Figure 2.4, the time constant was 300 ms. Therefore, the sensitivity of the system is
0.68±0.03 V/m/VlHz (assuming 1/1 rolloff). This value is useful as a figure of merit but
should be interpreted with caution. In particular, it is dependent on the intensity of the
input optical beam imposed on the electro-optic crystal. The maximum input power of
the optical beam that
Noise Floor
1.24 [V/m] = Minimum
Detectable Signal
Data
Linear Fit
100
|EJ in probe [V/m]
Figure 2.4: Measurement linearity and the minimum detectable electric-field. Over a 300
ms bandwidth, the EO signal reaches the noise floor at 1.24 V/m [58].
21
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
can be coupled into the fiber is limited to 20 mW in order to avoid 2-photon absorption in
the GaAs. The actual optical power that reaches the probe tip is dependent on the system
optical alignment, which is dominated by the coupling of the free-space beam into the
optical fiber via the fiber coupler. To date, 0.68 V/m/VHz is the highest sensitivity that
this particular system has demonstrated.
2.3.3 Temporal Stabilization of Electric-Field Phase
An external 40-MHz crystal oscillator serves as the master phase synchronization
signal for the entire system. This oscillator is frequency multiplied to 80 MHz to provide
external feedback to the Ti:Sapphire-laser pulse repetition rate and frequency divided by
4 in order to provide a common 10-MHz reference signal for the external 3-MHz lock-in
reference and the RF synthesizer. In principle, the mixed-down electric field modulation
on the 80-MHz pulse train will be phase synchronized with the 3-MHz reference
oscillator allowing phase measurements of the electric field using the quadrature receiver
of the lock-in amplifier.
Observations of the measured phase stability over time,
however, have produced results that demonstrate a consistent phase drift in the system.
In order to correct for the phase drift, a reference electro-optic signal has been
integrated into the system. A key point regarding this method of phase stabilization is that
it corrects for phase drift regardless of the source of phase instability (whether it be due to
a single component of the system or due to a combination of components). As shown in
Figure 2.1, a beam splitter is used to couple 30% of the free space optical beam to a
beam-line consisting of a half-wave plate, an electro-optic probe crystal, a quarter wave
plate, a polarizer, and a second photo-diode.
The optical elements are configured to
produce 50% intensity modulation of the optical beam in response to an RF modulating
22
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signal which is coupled off from the RF source feeding the device-under-test.
An
electrical switch is employed to toggle between the photodiode that collects data from the
device-under-test and the photodiode that collects data from the reference crystal.
By using the phase reference channel, the system phase drift can be calibrated out. A
demonstration of the effect of the phase calibration is shown in Figure 2.5. The reference
electro-optic crystal was bismuth silicate (BSO), although any EO crystal with a
sufficient n3r parameter will suffice, and the modulating signal was imposed on the
crystal via a horn antenna (8.003 GHz RF) for simplicity. The probe was kept stationary
above the device under test while phase data was toggled between photodiode #1 and
photodiode #2 every ten seconds. Over a 60-minute time interval, the uncalibrated phase
data from photodiode #1 happened to drift from 49 degrees to -8 degrees. This data
represents an intermittent system temporal phase instability. The phase data from the
reference channel is seen to drift along with the data from the device under test.
180
135
C alib rated P h a s e D ata
O) 45
^
P h o to d io d e #1
P h o to d io d e #2
-45
-90
-135
RF: 8 .0 0 3 GHz
-180
0
20
40
60
Time [min]
Figure 2.5: Measured phase drift and demonstration of correction. Drift in the E-field
phase is stabilized via the implementation of a phase reference channel. The calibrated
phase data, taken over one hour, has a standard deviation of ±3 degrees [58].
23
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Subtracting the phase drift in the uncalibrated data results in the calibrated data set, which
shows a standard deviation of ±3 degrees over the 60-minute time interval.
2.3.4 Invasiveness
The device-under-test (DUT) that is selected for the study of probe invasiveness is a
coplanar waveguide (CPW) transmission line. The choice of CPW line as the DUT
allows the invasiveness of the probe to be quantified in terms of the characteristic
impedance of the line and the capacitance per unit length. When the probe is placed in
close proximity to the DUT, two undesirable effects occur.
First, the DUT is
electromagnetically perturbed and second, the sampled electric-field present in the probe
is distorted.
The first effect is examined in this thesis. The second effect has been
examined in the time domain where electric-fields generated on a CPW line due to the
propagation of sub-picosecond pulses have been analyzed [42], [43]. It was found that
due to strong dispersion above 0.6 THz, the sampled signal field in the probe can be
significantly different from the unprobed field. In the spectral domain, however, where
the fields are mapped spatially at a single frequency, measurements of the sampled field
inside of the probe have demonstrated spatial measurements that are in good agreement
with both analytical and simulated field solutions [24], [31].
The invasiveness of dielectric probes over transmission lines, in terms of Sn, was
studied via finite-difference-time-domain simulations in [44], by a 2D quasi-static field
analysis based on a TEM-mode assumption in [42], and experimentally in terms of timedelayed pulses in [45]. In this thesis, we quantify invasiveness in terms of the spatial
perturbation in the characteristic impedance and capacitance per unit length of a CPW
line with the probe present via a quasi-static field analysis based on field solutions from
24
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
three-dimensional full-wave fmite-element-method simulations [41].
This method is
applied at 10 GHz and is applicable at low microwave frequencies where the imaginary
part of the characteristic impedance is relatively small.
At higher frequencies, the
imaginary part of the characteristic impedance becomes appreciable due to space and
surface wave radiation [46].
Supporting measurements in the time and frequency
domains follow the simulations.
The geometry of the simulation is shown in Figure 2.6.
Although the transverse
orthogonal refractive indices in the electro-optic probe vary in time with the presence of
an RF electric-field, an index ellipsoid analysis verifies that the change is much less than
a fraction of a percent at breakdown fields. Therefore, with negligible error, the electro­
optic probe is modeled with a constant dielectric permittivity and a linear electromagnetic
simulator is utilized.
Given the electric-field solution in the region of the probe, a quasi-static analysis is
performed to determine the charge per unit length, capacitance per unit length, and
characteristic impedance versus distance along the direction of propagation. This is valid
Graded-index
lens S ri
GaAs probe
Substrate s.
Figure 2.6: The full-wave simulation geometry for the examination of invasiveness of the
probe on a device-under-test (DUT). In this case, the DUT is a coplanar waveguide with
lateral dimensions less than the footprint of the probe [58],
25
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since the phase in any transverse (xy) plane is essentially constant. The charge per unit
length, Qi, along the transmission line can be determined as a function of distance as
QAz) = s $E-d£ [C/m]
c (z )
( 2 . 8)
where the integral is evaluated in the transverse plane and the contour encloses the center
conductor of the transmission line. As long as the contour of integration is selected
sufficiently near the conductor, the longitudinal electric field component will be
sufficiently small compared to the transverse components allowing a charge per unit
length to be evaluated with a line integral. The capacitance per unit length, Ci, and
characteristic impedance of the transmission line, Z0, are obtained from
(2.9)
( 2 . 10)
where V(z) is the voltage between conductors, Z/, is the inductance per unit length, c is
the speed o f light in vacuum, and Q ei=eo, is the capacitance per unit length for a vacuumfilled transmission line.
Simulation results at 10 GHz are shown in Figure 2.7. The CPW center conductor
width is w = 60 pm and the gap width is s = 40 pm. The substrate is modeled after
silicon (srs = 11.7) and the metal is modeled with perfect-electric-conducting surfaces.
The probe dimensions are 500 pm x 500 pm x 200 pm and its relative dielectric constant
is Srp = 12.9 (GaAs). The graded-index lens is patterned after bulk boro-silicate glass (sri
= 2.5) and has a diameter of 1 mm and a length of 2.5 cm. At a height of 25.4 pm (one
26
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
full notch on a physical micrometer knob), Z0 decreases by 19% and the full-width-halfmax of the perturbation is 0.5 mm. Hence, the electromagnetic disturbance is essentially
localized around the probe. Figure 2.8 shows that as the height of the probe decreases the
peak characteristic impedance and the peak capacitance per unit length begin to change
significantly as the probe comes within 50 pm of the CPW.
Since the probe fills the top region of the transmission line with a high-dielectric
constant material, it capacitively loads down the transmission line resulting in a local
change of the capacitance per unit length. Therefore, the effect of the probe can be
modeled with a shunt capacitance across an unloaded line. For RF frequencies such that
the guide-wavelength is much larger than the width of the probe, the average change in
the capacitance per unit length taken over the length of the perturbation provides a value
for a lumped element equivalent circuit shunt capacitance.
The equivalent circuit is
shown in the inset of Figure 2.8 where the shunt capacitance from the probe is denoted
Cprobe-
The magnitude of Cpr0be is on the order of a few femtofarads.
The full-wave simulations were experimentally verified via time domain (low pass)
measurements using an HP 8510C Network Analyzer and 150 pm pitch on-wafer probes.
The measured data for a GaAs probe over a CPW transmission line (400 pm thick silicon
substrate, 1 pm thick gold metallization, 60 pm center conductor, 40 pm gap) is shown in
Figure 2.9. The center perturbation is the response from the probe and it clearly appears
as a shunt capacitance when the probe is 25.4 pm above the line. The two side peaks
represent the response from the 150 pm pitch on-wafer probes.
27
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The effect of the probe on the return loss in the frequency domain is shown in Figure
2.10. The effect of a shunt capacitance is to cause the peaks to alternately shift above and
below the response from an unperturbed transmission line. Figure 2.11 shows simulated
s rp - 12.9, Sf| - 2.5, s rs -1 1 .7
w = 60 pm, s = 40 pm
55
a
, 50
^
45
»***.*♦ •♦S'® »2s9»«»8!8ali
'8
D
N
40
D Probe 25.4 pm above CPW
• No probe present
35
T
4
4 .5
5
5 .5
6
z [m m ]
Figure 2.7: Simulation results of the spatial extent of the perturbation of the characteristic
impedance, Zo, o f the CPW. The presence of the probe changes Zo by 19% when the
bottom edge of the probe is 25.4 mm above the surface of the transmission line [58].
52
50
- Characteristic Impedance
■Capacitance Per Unit Length
□ Probe £ r = 3
• Probe Er = 12.9
0.19
-
48
0.18
£ 46
3
fl
o 44N
^
0.17 3
42
Equivalent Circuit
40
Zo
unloaded
38
20
B
30
40
-LPprobe z 0
-iunloaded
I
50
0.16
B
60
70
80
Height of Probe Above DUT [jam]
Figure 2.8: Sensitivity analysis of invasiveness simulations. Results show that as the
height of the probe becomes less than 50 mm, the change in Zo and the capacitance per
unit length becomes significant. The effect of the probe is equivalent to a lumped shunt
capacitor on the order of femtofarads [58],
28
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
data of a CPW line with an additional lumped femtofarad shunt capacitor [47]. The same
behavior of shifted peaks is observed, thereby verifying the order of magnitude of the
loading capacitance. The return loss changes by 4 dBm at most where it shifts from -34
dBm to -31 dBm. Therefore, the effect of the probe on S 11 is essentially negligible. In
practice, there is a tradeoff between invasiveness and signal-to-noise.
2.4
Miniaturization
While the electric-field spatial resolution is determined by the diffraction of the
optical beam in the crystal, the temperature resolution is dominated by thermal
propagation in the crystal lattice and is therefore dependent on the overall volume of the
probe itself. Bulk micromachining of GaAs allows for the possibility of etching probes
with spatial dimensions approaching tens of microns and therefore provides the capability
of performing electro/thermal measurements on the variety of microstructures developed.
20
Im p u lse R e s p o n s e
L eg en d
Location of
G aA s P robe
-
Shunt C
15 -
w
c
D 10
-
E
S e r ie s L
<D
S e r ie s C —
DC
-10
-
P ro b e H eight = 2 5 .4 p m
No P ro b e P re s e n t
Shunt L —
-1 5
-3 0
0
30
60
90
120
150
T im e [p s e c ]
Figure 2.9: HP 8510 vector network analyzer time-domain (lowpass) measurements of
probe over CPW. The impulse response verifies the capacitive loading [58].
29
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
"60
°o
Probe
Height
= 25.4
Probe
Height
= 25.4
pm (jm
-65 -
••
Probe
removed
from
PW
Probe
farfar
removed
from
C PCW
-70 -L— i— ■
— i— ■
— i— •— i— '— i— ■
— i— ■
— i— >— i
25
30
35
40
5
10
15
20
Frequency [GHz]
Figure 2.10: SI 1 frequency-domain measurements (HP 8510) when probe is over CPW.
The return loss shows that the effect of the probe is quite minimal [58].
-25
-30
-35-40-
CO -45TJ
-50
-5 5 -|
-60
-65
°
c probe = 2.5 [fF]
•
c orob
he = 0 [fF]
-70
10
15
20
25
30
35
40
Frequency [GHz]
Figure 2.11: Simulated data (HP EEsof Libra) of CPW with an additional lumped
femtofarad shunt capacitor. The simulation is in good agreement with the measurements
of SI 1 (verifying the order of the magnitude of the loading capacitance) [58],
Probes with edge dimensions below 500 pm become extremely difficult to mount and
handle directly.
In previous work, free-space probes have been fabricated by first
30
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
bonding a sample of the probe crystal on a fused-silica support and then polishing the
surfaces [8],
Since GaAs can be bulk micromachined by wet chemical etching, a
fabrication procedure has been developed for fiber-mounted sensors that allows for the
micromachining of miniaturized (tens of microns) probes and that is limited only by the
aspect ratio allowed from wet chemical etching. Miniaturization is possible because the
probes do not need to be handled directly.
Figure 2.12 shows the fabrication procedure. There are five essential steps for probe
miniaturization: (a) Probe mask lithography, (b) Wet etch, (c) Mask removal, (d) Fiber
mounting, (e) Acetone release. A cleaved section of double-side-polished GaAs crystal is
mounted on a silicon carrier via clear wax. The probe mask is patterned on the exposed
GaAs surface using 1827 photoresist. The GaAs is then etched using a wet chemical
process and the photoresist mask is removed with a short exposure and subsequent
development. Due to the developer selectivity between SC1827 and clear wax, the probe
mask is removed while the micromachined probes remain on the silicon carrier. The
optical fiber is then mounted on the GaAs probes via UV-cured optical adhesive. After
curing, the adhesive is insensitive to solvents. Therefore, the probe can be released with
a few drops of acetone.
A digital image of the fabrication setup for 125 pm x 125 pm x 100 pm probes
(fabricated by the author) is shown in Figure 2.13. The fiber is vertically mounted on an
xyz translation stage thereby allowing for free positioning over the GaAs sample. The Si
carrier wafer that holds the probes is mounted horizontally on an xyz translation stage to
allow for independent movement. A horizontally mounted microscope allows for
31
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1827 Photoresist
Gallium Arsenide
ear Wax
Silicon carrier
Optical
Fiber
3
UV Cured
j/* Optical
Adhesive
GaAs
(a)
1827 Photoresist
Silicon carrier
GaAs
(d)
Silicon carrier
Optical
Fiber
(b>
GaAs
Bragg
Reflector
y
B rag g reflecto r
if
Silicon carrier
Silicon earner
(e)
Figure 2.12: Fabrication procedure for probe miniaturization: (a) Probe mask, (b) Wet
etch, (c) Mask removal, (d) Fiber mounting, (e) Acetone release [63].
f
'Sir
i-
Figure 2.13: Digital image of fabrication setup.
32
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
magnified viewing of the fiber to probe mounting and alignment. The entire setup is
mounted above a hotplate that is used for hardening of the UV-cured adhesive.
2.5
Conclusion
A method to simultaneously measure electric and thermal fields with a single probe is
presented. The Pockels effect is employed within a gallium arsenide probe to measure
electric fields, and the effect of photon absorption due to bandtail states in the
semiconductor is used to determine temperature. The measured optical power is found to
be inversely related to temperature, in agreement with theory, and experimental results
demonstrate a temperature sensitivity of 0.31 mW/°C at 25°C and an accuracy of ±0.5°C
between 20°C and 60°C. The minimum detectable electric field is 1.24±0.06 V/m using a
300-ms electrical bandwidth. Temporal phase stability of ±3°/hour is achieved through
the implementation of a system phase reference channel. The invasiveness of the probe
is quantified by examining the change in the characteristic impedance and capacitance
per unit length o f a planar transmission line. Measured and simulated data show that the
effect is equivalent to a lumped shunt capacitance on the order of a few femtofarads.
Finally, an aspect-ratio-limited fabrication procedure for the secondary handling of
miniaturized micromachined and fiber-fed gallium arsenide probes is presented.
33
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER 3
Nonlinear Thermo-Optic Modeling
In this chapter, the limitations of the electro/thermal probe are analyzed via numerical
modeling. A nonlinear thermo-optic model is developed to characterize the performance
of electro-optic semiconductors used for the purpose of simultaneously measuring
electric field and temperature. While it would seem advantageous to utilize these probes
with an input optical power as large as possible (with acceptable detection noise) without
inducing optical damage - for example for high electro-optic modulation power and high
temperature resolution/contrast - modeling shows that optical thermal heating in the
semiconductor effectively limits the amount of optical power that can be input into the
system. This limitation of input optical power affects, in turn, the temperature dynamic
range, electro-optic modulation power, temperature responsivity, and temperature
invasiveness. Measurements using gallium arsenide as the sensing element confirm the
modeling results.
3.1
Thermo-optic model
In the optical fiber and in the electro-optic semiconductor probe, optical pulse
propagation can be described analytically through the following pulse propagation
equation
34
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
dA(z,T)
dz
\
^ { z j ) ^ - ^ - \ A { z , T f A(z,T)
/
(3.1)
v
where |A(z,T)|2 represents the optical power in the pulse, z is the spatial coordinate along
the direction of propagation, T is the local time variable in a frame of reference moving
with the pulse at the group velocity, (12 is the group velocity dispersion, oci is the linear
power absorption coefficient, co0 is the center radian frequency of the optical pulse, n2 is
the nonlinear index coefficient, c is the speed of light in vacuum, Aeff is the effective
cross sectional area of the pulse, and a 2 is the two-photon absorption coefficient. In a
region of interest consisting only of optical fiber, the linear power absorption coefficient
and the two-photon absorption coefficient can be neglected because their effects are small
over the relatively short distances used. The pulse propagation equation then reduces to
the nonlinear Schrodinger equation [48].
At the end of the optical fiber, the pulse exits the guiding fiber medium and diffracts
into the semiconductor probe as an unguided optical beam. The linear power absorption
coefficient and the two-photon absorption coefficient dominate in the semiconductor
[49]. Over the short length of the semiconductor, the GVD term and the SPM term of
equation (3.1) can be neglected. The diffraction of the beam into the semiconductor is
modeled with a z dependent effective cross sectional area, Aeff, where the spot size, w(z),
increases in a manner identical to a fundamental Gaussian beam with the minimum waist
located at the fiber/semiconductor interface
f f
A^{z) = nw2
0 1+ —
(3.2)
V %. /
where w0 is the spot size at the fiber/semiconductor interface and z0 is the beam Rayleigh
range. This model is expected to be a good approximation for diffraction as long as the
35
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
propagation distance in the semiconductor is less than a Rayleigh range.
While the
optical beam diffraction can be solved by using, for example, modal expansion of fields,
an approximation for the beam diffraction in this manner allows for the straightforward
inclusion of the spectral absorption that occurs over the bandwidth of the probe-pulse
when propagating in the semiconductor.
In the semiconductor, it is expected that linear and nonlinear optical losses will lead to
heating of the probe. Given the losses, thermal modeling is employed to determine the
change in probe temperature. In general, the three physical mechanisms for macroscopic
heat transfer are conduction, convection, and radiation. In general, since air is a moving
fluid, all three mechanisms needs to be considered [50].
After propagating through the semiconductor, the optical beam reflects off a dielectric
mirror (Bragg reflector) and is redirected back through the semiconductor and then back
into the fiber. The optical power, as a function of z and T, re-received by the fiber is
determined by integrating the beam cross-sectional intensity, I(z,T,r), over the effective
area, Aer, of the optical fiber
,T, r)rdrd(f>
(3.3)
00
(3.4)
8x 2n l cw2
0
(3.5)
K
where PR(z,T) is the optical power re-received by the fiber, r is the radially symmetric
transverse coordinate er is the radiation efficiency, Dr is the directivity of the receiving
fiber aperture, ns/c is the semiconductor index of refraction, and X0 is the free-space
optical wavelength.
36
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3.2
Solution methodology
The input/output optical power relationship of the fiber / semiconductor system is
solved in an iterative manner that includes linear, nonlinear, and thermal effects. An
iterative approach is necessary because the index of refraction of the semiconductor,
linear power absorption coefficient, and two-photon absorption coefficient depend on the
probe temperature, which itself is dependent on the input optical power. The process
flow for solution is shown in Figure 3.1.
The process begins by a specification of the fiber length, Lf,ber, the lasing wavelength,
X 0, the initial probe temperature with no optical power (ambient temperature), Tprobe, the
optical pulsewidth prior to fiber coupling, Tpo, the pulse repetition rate, R, the GVD
parameter, (32, the nonlinear index coefficient, n2, and the length of the semiconductor,
Lprobe- Given the lasing wavelength and the initial probe temperature, the refractive index
of the probe, n(X0,Tpr0be), linear power absorption coefficient, ai(X,0,Tpr0be), and TPA
coefficient, a 2(A,0,Tpr0be) are calculated.
The spectral and temperature dependence of
these parameters were obtained from the literature [51]-[53].
Once the initialization is complete, a loop that marches in optical power is initiated.
Pulse propagation through the optical fiber is solved using the split-step Fourier method
for the solution of the non-linear Schrodinger equation. At the fiber/GaAs interface, the
impedance mismatch results in an interface reflection and transmission. The transmitted
pulse is propagated through the GaAs by solving (3.1) with the Gaussian beam diffraction
assumption.
The optical power re-received by the optical fiber is obtained using the
effective aperture concept.
Multiple reflections within the GaAs section are ignored
since they will be quickly attenuated to intensities much smaller than the first
37
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
S p ecify :
R e -r e c e iv e f r e e - s p a c e b e a m
(Effective aperture m ethod)
ffiben ^o.Tprobei'^poi
R, p j ’ n 2 ’ l-probe
Output:
R e-received power
C o m p ute:
nprobe(^o,Tprobe),
a (^o,Tprobe),a 2(^o,Tprobe)
Input: Pavg =
Compute:
ATprobe due to lo ss in GaA s
(Thermal modeling)
a p
R e-c o m p u te :
nprobe(^o,Tprobe),
(^ •o .T p ro b e X ^ f^ O ’Tprobe)
P ro p a g a te th ro u g h fiber
(split ste p Fourier method)
P ro p a g a te th ro u g h G aA s
(G aussian b eam optics)
Increm ent: P = P aun+ AP
Figure 3.1: Thermo-optic iterative process flow for solution.
transmission/reflection due to the absorption in the material.
For each loop iteration, the time average power loss in the GaAs is computed and is
subsequently entered into a steady-state thermal simulation.
A three-dimensional
conduction/convection finite element method model was employed to solve for the
associated change in temperature [54], For operation in still air at room temperature, the
heat flow is dominated by conduction and natural convection so the radiation term can be
neglected. The recombination lifetime in semi-insulating GaAs is on the order of 1 ns,
whereas the pulse repetition period is 12.5 ns. Therefore, excess carriers photogenerated
in the semiconductor relax between successive optical pulses. The thermal response time
of the probe is on the order of microseconds and the pulsewidth is on the order of 0.1
picoseconds so the probe reaches a steady-state temperature based on the time average
power dissipated in the probe. Given the change in probe temperature, the refractive
index of the probe, n(X0,Tpr0be), linear power absorption coefficient, ai(A.0,Tprobe), and
38
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TPA coefficient, a 2(A,0,Tprobe) are re-calculated and the loop is re-iterated with an
incremental increase in input optical power. At the completion of all of the iterations, a
curve of output time-average optical power (reflected power) versus time-average input
optical power is obtained.
In addition to reflection simulations, transmission simulations are also computed.
Transmission simulations correspond to an optical fiber/semiconductor system where no
Bragg reflector is present. The transmitted optical power is the power that flows from the
semiconductor into the air through the semiconductor/air interface. Both transmission
and reflection simulations are useful for a complete characterization of the device.
Given the input/output optical power relationship, performance characteristics can be
determined by marching in an additional iteration loop where an external excitation is
introduced into the probe thermal simulation in the form of an increment of dissipated
optical power.
This external excitation changes the probe temperature and therefore
represents an increase in the probe temperature due to some device-under-test.
By
marching the loop in external excitation, parameters such as probe responsivity, dynamic
range, and temperature invasiveness are obtained.
3.3
Results
3.3.1 Transmission
Simulated and measured results of output optical power (transmission) versus input
optical power are shown in Figure 3.2. The electro-optic semiconductor is a crystal of
(100) GaAs with transverse cross-sectional dimensions of 125 pm x 125 pm and
thickness of 86 pm. The optical fiber (FS-SN-4224) has an outside cladding diameter of
39
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
125 pm and is 5 m in length. In the transmission configuration, the probe has no end
mirror, therefore output power on transmission corresponds to the output optical power
after propagating through the fiber, into the semiconductor, then into the air where the
optical beam is photodetected. As shown in Figure 3.2, the behavior is nonlinear and
wavelength dependent with the peak output power shifting to higher powers as the
wavelength is increased. At low input optical power, the transmitted power is linear with
input optical power. As the input optical power is increased, optical self-heating occurs
and the power absorption coefficients becomes dependent on the input optical power.
Physically, as the input optical power is increased, the semiconductor absorbs a finite
amount of power based on the linear power absorption coefficient and the two-photon
absorption coefficient. As will be shown below, an appropriate choice of fiber length
minimizes the effect of TPA so that the effects of the linear power absorption dominate.
This power loss leads to nonradiative recombination of electron/hole pairs that results in
,
0.5
I
892.5 nm
-------895.0 nm /
------ 897.5 nm / >'
n5; »0.4
.
O
CL
ro
£
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0.3 H
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_ra
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0.014 ^
a>
■ Data
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A.o“ 895nm
0.012
Lfiber=5m
a>
\ Lprobe = 8 6 Mm
0.010 Q
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0.008 c
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to
s
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1
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£
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yr
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i
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i
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l \■
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0.002 I
,N _
V-’
E
to o.o
0.000 ^
0.0
0.5
1.0
1.5
2.0
2.5
3.0 3.5
4.0
Input Optical Power [mW]
Figure 3.2: Optical transmission vs. input optical power.
40
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
optical self-heating of the probe, which shifts the bandgap of the semiconductor to lower
energies. This in turn increases the linear absorption coefficient as more bandtail states
become available for fundamental absorption. The simulated dissipated optical power in
the probe versus input optical power and the corresponding increase in probe temperature
is shown in Figure 3.3. The ambient temperature in the thermal model is 293 K. As can
be seen, the power loss in the semiconductor leads to increases in the probe temperature
by several tens of degrees Kelvin. The corresponding change in the bandgap and linear
power absorption coefficient is shown in Figure 3.4 and Figure 3.5.
For shorter
wavelengths, the linear power absorption coefficient is higher due to the proximity to the
band-to-band resonance.
Therefore, the losses are higher, and subsequently the
temperature and bandgap change is greater for a given input optical power.
As the input optical power is continuously increased from zero, each incremental
345 O
340 n
<j)
335 o
3
330 ~
<n
325 -o
320 §-
CD
315 H
(V
310 3
. _ _ <D
305 g
300 ^
CD
A m b ie n t T e m p e ra tu re = 2 9 3 K
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
295 3
4.0
Input Optical Power [mW]
Figure 3.3: Simulated optical power loss in the semiconductor and corresponding change
in probe temperature vs. input optical power for the transmission case.
41
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1.4 25 -
— 1.420,gj.
< 1.415ra
(D
4-
o
Q.
1.410-
re
O)
c 1.405ns
CO
■a
1.4000.0
8 9 2 .5 n m
8 9 5 .0 n m
8 9 7 .5 n m
9 0 0 .0 n m
0.5
5
2^0
2^5
3^0
3^5
4^0
Input Optical Power [mW]
Figure 3.4: Simulated bandgap of GaAs vs. input optical power for the transmission case.
increase in input power produces this same dynamic. At some value of input power, an
incremental increase in input power results in zero increase in received power. Further
increases in input power serve to increase the probe temperature further, resulting in ever
decreasing values of received optical power until, eventually, essentially all of the input
power is dissipated in the semiconductor. As the lasing wavelength is tuned away from
the bandgap resonance, the absorption coefficients become smaller, therefore the
temperature increases for a given input optical power are smaller. Therefore, more power
is received for photodetection, and therefore the peak transmission increases with
increasing wavelength.
The simulated results were curve fit to the measured data in Figure 3.2 by using an
effective GaAs convection heat transfer coefficient, heff, as a fitting parameter in the
convection boundary condition of the thermal model. The measured data were obtained
42
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
E 0.28-
A
“
0.24-
<d
892.5 nm
895.0 nm
897.5 nm
900.0 nm
O 0.20-
c
•g. 0.16o
(/>
3
< 0.1 2 <D
V.
0.08-
CL
a>
c
0.04-
- 1 0 .0 0 -
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Input Optical Power [mW]
Figure 3.5: Simulated optical linear power absorption coefficient vs. input optical power
for the transmission case.
at 895 nm. The free-space-to-optical-fiber coupling is estimated to be 45% ± 5% based
on thru measurements of bare optical fiber.
Since the relationship between probe
temperature and dissipated power in the probe is linear, the ratio between radiative and
nonradiative recombination is embedded in this fitting parameter. A convection heat
1 0
transfer coefficient of 211 W-K' -m' yields good agreement between the simulation and
measurements. For the optical fiber, a convection coefficient equal to 418.68 W-K’^m'2
was used [55], For conduction between the semiconductor and the optical fiber, heat
flow was characterized via thermal conductivity. For the fiber, a thermal conductivity of
1.38 W -nf'-K'1 was used (fused silica). For the semiconductor, a thermal conductivity of
46 W-nT'-K'1 was used (GaAs) [56].
3.3.2 Reflection
The results thus far have discussed transmission simulations and measurements. For
reflection simulations/measurements, neglecting interference, the time average optical
43
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
power re-received for photodetection is the sum of the time average power due to the first
reflection from the bottom end mirror on the GaAs probe and the first interface reflection
between the optical fiber and the GaAs probe. All other multiple reflections in the probe
are ignored since they are expected to be quickly suppressed inside the probe.
The
simulated total reflected time-average optical power due to the probe end-mirror
reflection and the fiber/probe interface reflection versus input time-average optical power
is shown in Figure 3.6. The fiber/GaAs first interface reflection is due to the impedance
mismatch between the fiber and the GaAs probe.
For the temperature range in
consideration here, the change in the refractive index of GaAs is on the order of 0.5% so
the first interface reflection is essentially linear with input power.
The input/output
optical power relation in the reflection case is similar to the transmission case discussed
previously, except the first interface reflection produces a pedestal for the 1st probe endmirror reflection.
3.3.3 Performance characterization
The effect of optical self-heating of the probe determines the maximum signal power
that can be received for photodetection, whereas the fiber/GaAs 1st interface reflection
sets the lower bound of the temperature-free-dynamic range. Given the thermo-optical
input/output nonlinear curve, Figure 3.6, a particular choice of input optical power and
lasing wavelength affects the temperature dynamic range, electro-optic modulation
power, temperature responsivity [mW/K], temperature sensitivity [1/K], and temperature
invasiveness.
The responsivity is the initial change in optical power for a given change in probe
temperature (presumably from a device-under-test) for a given input optical power at a
44
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CL
0.88 9 5 .0 n m
0.6-
8 9 7 .5 n m
Q.
9 0 0 .0 n m
9 0 2 .5 n m
- ....... 9 0 5 . 0 n m
0.2-
In te rfa c e
re fle c tio n
0.0
0.0
1.0
2.0
3 .0
4 .0
5 .0
6.0
Input Optical Pow er [mW]
Figure 3.6: Simulated total reflected optical power vs. input optical power.
given lasing wavelength. As shown in Fig. 3.7, the simulated responsivity reaches a
maximum at some input optical power and this maximum shifts to higher input optical
power as the wavelength is increased. Physically, as the input optical power is initially
increased from zero, the change in optical power for a given change in probe temperature
increases linearly, as expected. However, as the input optical power is increased, the
optical self-heating results in an increase in the linear power absorption coefficient and its
first derivative with respect to temperature. In the limit of high input optical power, all of
the power propagating through the semiconductor is absorbed and the responsivity goes
to zero. The shift o f the peak to higher input optical power for longer wavelengths is
consistent with lower optical self-heating for longer wavelengths for a given input optical
power.
The relative change in optical power, a measure of sensitivity, for a change in
temperature is shown in Figure 3.8. At low input optical power, operation at shorter
45
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
wavelengths corresponds to a larger relative responsivity since the change in the
absorption coefficient with temperature is larger at shorter wavelengths. As the input
optical power is increased, however, due to the optical self-heating, the change in the
linear power absorption coefficient with temperature becomes dependent on the input
optical power.
The responsivity peaks and then decreases, as shown in Figure 3.7,
whereas the output power continually increases (in the limit of large input optical power),
as shown in Figure 3.6, due to the sum of the two reflections. Therefore, the sensitivity
falls to zero as the input optical power is increased.
Temperature invasiveness is the temperature of the probe (above ambient temperature)
for a given input optical power with no device-under-test present. It is due to the optical
self-heating of the probe only. As shown in Figure 3.9, the temperature invasiveness
increases for a given input optical power.
It increases more slowly for longer
wavelengths. This is consistent with the loss behavior versus input optical power as a
function of optical wavelength. Depending on the device-under-test, it may be preferable
„ 22^ 20-
- 8 9 5 .0 n m
8 9 7 .5 n m
-
9 0 0 .0 n m
- 9 0 2 .5 n m
- 9 0 5 .0 n m
0.0
2.0
3 .0
4 .0
Input O ptical P o w e r [mW]
5 .0
6.0
Figure 3.7: Simulated initial change in total reflected optical power with respect to
temperature vs. input optical power.
46
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
25.0 -i
8 9 5 .0 n m
8 9 7 .6 n m
9 0 0 .0 n m
*
20.0 -
9 0 2 .5 n m
9 0 5 .0 n m
TJ
15.0-
5.00.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
Input Optical Pow er [mW]
Figure 3.8: Simulated relative change in initial total reflected optical power with respect
to temperature vs. input optical power.
to operate at lower input optical powers, and therefore lower responsivity, so that the
probe itself does not adversely heat up the device-under-test.
As shown in Figure 3.10, the dynamic range is a monotonically decreasing function of
input optical power. There are several reasons for this. First, as the input optical power
is increased, the self-heating of the probe is higher. Second, as the input optical power is
increased, the 1st interface reflection is higher.
These two effects squeeze the
temperature dynamic range to lower values for higher input optical power. Third, at
lower input optical powers, the responsivity is lower. Therefore, the change in optical
power for a given change in temperature is lower so that the temperature dynamic range
is higher.
While operating at lower input optical powers is beneficial for temperature
invasiveness, temperature dynamic range, and depending on the operating wavelength,
for sensitivity, the peak signal power is lower, and therefore the responsivity is lower.
47
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
80-
895.0 nm
897.5 nm
900.0 nm
902.5 nm
905.0 nm
£ 6050 ■
c 40^ 30 Q.
Ambient Temperature = 293 K
0.0
1.0
2.0
3.0
4.0
Input O p tical P o w e r [mW ]
5.0
6.0
Figure 3.9: Simulated temperature invasiveness vs. input optical power in the reflection
case.
Also, for electro-optic detection, the modulation power increases with input optical
power. Therefore, operating at a lower input optical power directly trades electro-optic
modulation power for temperature sensing performance (responsivity being the
exception). The tradeoffs between temperature dynamic range, electro-optic modulation
power, responsivity, and temperature invasiveness need to be considered when choosing
an input optical power and operating wavelength at which to operate for a particular
measurement application. For example, operating shorter than 900 nm at input optical
powers less than 2 mW trades-off temperature dynamic range and electro-optic
modulation
power
for temperature
sensitivity,
contrast,
and
low
temperature
invasiveness.
3.4
Measurement versus simulation
The simulated response of the probe to an external thermal excitation is shown in
48
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
6 0 .0 1
895.0
897.5
- 900.0
• 902.5
■ 905.0
a> 5 0 .0 -
4 0 .0 -
nm
nm
nm
nm
nm
=j 20 . 0 -
10.00.0
0.0
1.0
2.0
3.0
4 .0
5.0
6.0
Input Optical Power [mW]
Figure 3.10: Simulated temperature dynamic-range (initial total reflected optical power to
10% of final reflected optical power) vs. input optical power in the reflection case.
Figure 3.11 for a lasing wavelength of 898 nm and three different input optical powers.
Measured results are also shown where the probe was placed in still-air over a hot-plate
with a precision thermistor employed as a temperature reference. In the measurements,
the input optical power is 1.6 mW. The simulated functional behavior of the optical
response is in good agreement with the measurements. The initial probe temperature is
different between the measured results and the simulated results because the simulated
results include the optical self-heating of the probe. These measurement results serve to
validate the modeling approach discussed above.
In addition to the hot-plate thermal excitation, an RF excitation was simultaneously
introduced by illuminating the probe with 1 Watt of RF power from a hom-antenna at 35
GHz.
Since the electro-optic modulation power is directly proportional to the input
optical power, the change in the received optical power due to temperature effects will
also change the electro-optic modulation power. Figure 3.12 shows that the electro-optic
modulation power scales with the optical absorption so that the measured RF signal can
49
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Simulated Probe Temperature [°C]
42
45
48
51
54
57
60
63
66
69
i ■ i— • i
I n p u t O p tic a l P o w e r
1.8 mW
1.6 mW
1.4 mW
= M easured Data
0.450
0.425
0.400
0.375
0.300
X
0
= 8 9 8 nm
0.275
M e a su re d /S m u a te d A m bient = 297.95 K
25
30
35
40
45
50
Measured Thermistor Temperature [°c]
Figure 3.11: Measured and simulated response of probe to temperature for the reflection
case.
0.10
-
A0 - 898 nm
0.09 - In p u t Optical P o w e r = 1.6 mW
N
X
0.08 - RF = 35 GHz @ 1W
CO
> 0.07
"S
c 0.06
O)
Data
Linear Fit
to 0.05
0)
Lli
0.04 -
4 -f
0.03 -
o
o
_0J
LU 0.02
P ro b e in still air s u s p e n d e d o v er h o t plate
a n d illum inated w ith m illim eter-w ave a n te n n a .
-
1.20
1.35
1.50
1.65
1.80
1.95
T e m p e ra tu re Signal (V sq MHz ) [mV]
Figure 3.12: Electric-field signal vs. temperature signal over measured temperature range
for the reflection case.
50
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
readily be calibrated against temperature effects. The linear relationship between the 80
MHz and the 3 MHz signals is expected to hold as long as the relative change in the
linear electro-optic coefficient, r4 i, due to temperature, remains insignificant.
Finally, the effect of nonlinear absorption from two-photon absorption in the
semiconductor has been minimized in the above analysis by temporal defocusing of the
peak pulse power.
Since the nonlinear absorption is intensity dependent, this can be
accomplished by defocusing the pulse in time in the optical fiber since the combined
action of group velocity dispersion and self-phase modulation over a length of fiber
greater than the dispersion and nonlinear lengths results in an increase in pulse width and
a decrease in peak pulse power. As shown in Figure 3.13, as the fiber length is increased
the pulse power decreases and the peak reflection increases. Beyond a fiber length of 5
m, the point of diminishing returns is reached.
0.92
!_ 0.90-
0)
£
o
Q_
40
CL
_
0.88ra
o
= 905 nm
Q.
°
3
—
<Q
Pe a k Reflection
— ®— P eak P ower
0 .8 6 -
CL
-*—■
2
0-84-
ra
0)
CL
0.82Fiber Length [m]
Figure 3.13: Peak reflected optical power and corresponding peak pulse power vs. fiber
length.
51
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3.5
Conclusion
A nonlinear thermo-optic model for the characterization of electro-optic semiconductor
probes used to simultaneously measure electric-field and temperature is presented.
Optical thermal self-heating of the semiconductor is shown to be the primary limiting
mechanism for temperature dynamic range, electro-optic modulation power, temperature
sensitivity, temperature contrast, and temperature invasiveness. Tradeoff considerations
of these parameters as a function of optical wavelength and input optical power are
discussed. Optical temporal defocusing is shown to minimize the effects of nonlinear
absorption. Simulation results are compared with measurements.
52
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER 4
Polarization-tunable probe for combined electric and magnetic field
measurements
As discussed in the two previous chapters, taking advantage of the electro-optic effect
and bandgap thermometry in electro-optic semiconductors results in a multifunctional
optical probe that can be used to study coupled electro/thermal effects in microwave and
millimeter wave devices. Multifunctional probes reduce the setup time required for test
and measurement, the time required for data acquisition, and the total number of
diagnostic tools.
In addition, they provide the means to study coupled physical
phenomena and non-repeatable effects. In this chapter, this multifunctional concept is
extended to magnetic field measurements. A method to measure the magnitude and phase
of electric and magnetic fields with a hybrid probe is presented. Relevant application
areas include point impedance measurements, the characterization of unknown
impedance surfaces (both natural and artificial), and the possibility of obtaining direct
measurements of complex permittivity. The optically-based probe, consisting of a hybrid
combination of gallium arsenide followed by terbium gallium garnet, employs the
Pockels effect to measure electric fields and the Faraday effect to measure magnetic
fields.
Isolation between the two effects is achieved via external polarization optics,
allowing the probe to be toggled between electric field and magnetic field sensitivity by
53
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switching the input optical polarization between two states. A demonstrated isolation of
22 dB is observed using a shorted microstrip transmission line as a test bed.
4.1
Hybrid probe concept
The two physical phenomena used to measure microwave/millimeter wave electric
and magnetic fields in this work are the Pockels effect and the Faraday effect. The
Pockels effect is an electric-field induced linear birefringence, and the Faraday effect is a
magnetic-field induced circular birefringence [34]. Both effects change the polarization
state of an optical beam. By abutting an electro-optic material against a magneto-optic
material, as shown in Figure 4.1, and using external polarization controls, the probe can
Probe
Optical
beam
Magneto Electro
Optic (mo) Optic (EO) ------- -■
Material Material
Output
polarizer
«“ Hrf
fE rf
Input
polarizer
Figure 4.1: Conceptual schematic of combined electro/magneto-optical probe with
external polarization controls [73].
be toggled between electric field sensitivity and magnetic field sensitivity by switching
the polarization optics between two states.
The degree of isolation between electric field sensitivity and magnetic field sensitivity
can be quantified using Jones calculus to describe the dynamics of the optical
polarization state.
The change in polarization state as the optical beam propagates
through the system can be described via the following cascade of matrices
r
1
1
X '
'1
0
o ' c o s or
0
sin a
- s in a
cos a
..r
cos —
- is m —
2
2
. r
r
- 1sin — c o s —
2
2
7
cos 9
1
—s i n 2 9
(4.1)
sin 2 9
s in 9
54
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In this equation from right to left, the first vector represents the input optical field, which
is set to be polarized along the y-direction. The following matrix represents the input
polarizer, where 0 is the orientation angle of the polarizer relative to the x-axis. The next
matrix represents the optical retardance between two orthogonal eigenwaves polarized at
±45° with respect to the y-axis. The retardance, T, is modulated by the presence of an RF
electric field due to the electro-optic effect. The following matrix represents a vector
rotation through an angle a. The magnitude of this angle is modulated by the presence of
an RF magnetic field due to the Faraday effect. The final matrix represents the output
polarizer, which is aligned along the x-axis.
For 0 equal to 90° the output optical transmission intensity, Ti, of this cascade of
matrices is found to be
f
Tx - (sin2a )iIIcos2—+
2
2
r a « 1
—,
2
(4.2)
This equation shows that a sin-squared modulation curve for pure electro-optic sensitivity
ensues for small angles of Faraday rotation. The transmission is plotted as a function of
retardance, T, for several values of rotation, a, in Figure 4.2.
As shown in Figure 4.2, electro-optic modulation about an optical retardance of 90° is
unaffected by the effects of Faraday rotation for rotation angles much less than 1°. The
expected Faraday rotation due to typical RF magnetic fields of interest is expected to be
much less than one tenth of a degree. For example, as an extreme case, for breakdown
fields in air, the expected Faraday rotation is on the order of 0.1° and the expected
electrooptic retardation is on the order of 6°.
The slope for amplitude modulation
sensitivity at the bias point can be expressed as
55
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1.0 H
Faraday
Rotation a
Input
EO
P olarizer
EO
Birefringent
aY
Birefringent
Axis ,________________ , Axis
O utput
P olarizer
EO-MO
EO Configuration
0,0
0
20
40
60
80
100
120
140
160
180
Retardance r [Degrees]
Figure 4.2: Transmission vs. retardance as a function of Faraday rotation for 0=90° [73].
dT _ sii
dT
(4.3)
For breakdown fields, the slope changes by
0.0003%due to the Faraday effect.
Thus, in
this configuration, to an excellent approximation, the combined probe exhibits only
electro-optic sensitivity.
For 0 equal to tc/4, the electrooptic effect modulates each component equally. Thus,
r=0°, and there is no amplitude modulation.
However, there is phase modulation. The
group velocity of the pulse can be expressed as:
v =
f on
a co n A-1
------ + \oa> c c )
(AAA
(4.4)
which shows the dependence of the index on the group velocity of the pulse. However,
even for electric fields on the order of breakdown fields, the change in the group velocity
56
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is less than a tenth of a percent, implying that the change in the arrival of each pulse is
negligible. The output optical transmission intensity, T 2 , of the cascade of matrices is
found to be
n « T - is in ( 2 « X r = °”
(4.5)
This equation shows that the output transmission depends only on the Faraday rotation
angle and to a good approximation, for 0 equal to tt/4, the hybrid probe exhibits only
magneto-optic sensitivity.
4.2
Implementation for tunable measurements
The electro-optic material used in this study is gallium arsenide (GaAs) and the
magneto-optic material is terbium gallium garnet (TGG). A 1.5 mm2 portion of GaAs
was cleaved from a 100 pm <110> semi-insulating wafer and attached to one face of a 2mm diameter, 2-mm long TGG circular cylinder using UV-cured optical adhesive. RF
reflections at the boundary are minimal due to their similar material parameters (GaAs: sr
= 13.2, TGG: sr = 12.4). Electro-optic sensitivity in GaAs and magneto-optic sensitivity
in TGG have demonstrated pico-second response times and therefore they are expected to
serve as a broadband spectral domain sensors extending to frequencies greater than 100
GHz [20], [33].
The completed probe, supported by a thin quartz tube, is shown in
Figure 4.3.
Each material is primarily sensitive to one component of each respective field-type.
The directional sensitivity of <110> GaAs favors the electric-field component that is
57
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TGG
GaA.
Figure 4.3: The probe consists of a series combination of GaAs (100 um thick) and TGG
(2 mm thick). A quartz tube is used for support [73].
transverse to the direction of optical beam propagation and oriented in the <1-10>
direction [57]. On the other hand, a Faraday effect magneto-optic material such as TGG
is sensitive to the magnetic field component collinear with the direction of optical beam
propagation [34].
The experimental setup is shown in Figure 4.4. A Ti:Sapphire mode-locked laser
tuned to 905 nm is used to generate a linearly polarized sampling beam (80 MHz
repetition rate, 80 fs pulse duration) that is directed through the probe and the
polarization controls via free-space optics.
The device under test is fed via an RF
synthesizer configured for harmonic mixing in order to down-convert the sampled
electric fields to IF frequencies allowing envelope detection with a MHz bandwidth
photodiode [20]. For electric-field measurements, the quarter-waveplate provides the
required 90° of optical bias. For magnetic-field measurements, the quarter-waveplate is
removed.
4.3
Isolation characterization
The isolation between electric and magnetic field sensitivity, and vice-versa, was the
58
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Lock-In
Amp
3 MHz
External
Ref.
RF
Source
10 MHz
Ref.
Pulsed
Laser
Y
A naly zer
X/4
P ro b e
Po arizer
Free
Space
Optical
Beam
Photo-
Diode
-e s s l
Rem ove
for MO
RF DUT
Figure 4.4: The experimental setup [73].
primary focus regarding probe characterization in this study.
A shorted microstrip
transmission line was selected as the test bed. The advantage of this structure is that the
electric and magnetic fields form standing waves with maxima that are displaced by a
quarter-wavelength. The RF frequency was 4.003 GHz at 17.0 dBm and the probe height
was 2.0 mm above the surface. Figures 4.5 and 4.6 show line scans of the magnitude and
phase of the electric and magnetic field standing waves using the combined probe. At x
= 6 mm, the electric field is a maximum and the magnetic field is a minimum. The
isolation at this point is 22 dB.
In order to determine the accuracy of the measurement technique, measured line scans
across the microstrip transmission line were compared with simulation results from fullwave finite-element-method simulations [41]. The width of the microstrip was 3.76 mm.
Figure 4.7 shows simulated and measured results when the combined probe was tuned for
electric-field sensitivity and scanned for the z-component of the electric field.
The
measurement is in excellent agreement with the simulation results. Using the combined
59
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
% 8.0
1
D
c
7.0
°
•
Electric Field (EJ
Magnetic Field (Hy)
6.0
^ 5.0
0
^ 4 .0
UJ
3.0-3
□
S
o
□
•
ft• •
□
_ D
D_
•
D •
•
□
0.5 $2
0.4 a
X
•A
•
0.3
D
•n
1 2.0
m
5
„ o Qn „
»•••-•
□oD0a
Line Scan
y
Jp~X
•D
o
• □
•
a
□
•
•
•
Sc
0.2 5T
c
•
o .i £
• •
1.0-3
0
1
—!—
0.0
10
20
0.0
30
~
40
x [mm] (z= 0 [mm])
Figure 4.5: The magnitude of the standing waves on a shorted microstrip transmission
line measured with the combined probe at a height of 2.0 mm above the surface [73].
m 1 5 0 - loaooooaooonaD00
m
<
D
1_
g> 100
3k
LU
H-i
o Electric Field
• Magnetic Field
100
♦i,
50
<0
-aoooD- 150
D'
50
Q,
0
ffi
oaaooDaDOoanaDaD
nflQix
oD
U
•_
JZ
-5 0
cl
cd
m
w
c
<TJ
Q.
■D
ZT
0)
</)
CD
I
-5 0
T3
(t>
N
D
5 100
-
CD
-100 (Q
-
TO
<t)
2 -1 5 0
CD
CD
-150 </)
'1 I
0
5
10
«"*I'""!""
15 2 0
25
30
35
40
45
50
x [mm] (Z =0 [mm])
Figure 4.6: The phase of the standing waves on a shorted microstrip transmission line
measured with the combined probe at a height of 2.0 mm above the surface [73].
60
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
probe tuned for magnetic-field sensitivity, the probe was scanned for the z-component of
the magnetic field.
As shown in Figure 4.8, the measurement is also in excellent
agreement with the simulation.
4.4
Sensitivity enhancement
As discussed above, probes based on electro-optic and magneto-optic effects can
provide a complete characterization of electromagnetic behavior.
The signal-to-noise
ratio obtained from magneto-optic probes is typically far less than that obtained from
electro-optic probes of similar physical dimensions [58]. A ffequency-domain technique
for magnetic-field sensitivity enhancement is now presented.
By tuning the probe
dimensions to form a resonant cavity at the frequency of interest, the magnetic-field
inside of the probe becomes a magnified representation of the sampled field, thereby
improving the resulting signal-to-noise ratio.
The probe is again a Faraday-effect-based polarization sensitive sensor consisting of a
circular cylinder (length = 2.3 mm, radius = 1 mm) of terbium gallium garnet. Given the
low frequency dielectric constant of 12.4, the length of the probe is approximately two
wavelengths at 75 GHz. The free-space effective length of the probe is less than a halfwavelength at midband thereby allowing spatial field sampling within the Nyquist criteria
without probe deconvolution.
The experimental arrangement is the same as that shown
in Figure 4.4 for magneto-optic sampling. The device-under-test in this section is an
open rectangular waveguide operating in the 55-75 GHz range.
61
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
■
Line Scan
M easurem ent
1200
Simulation
3 .0 -
1000
c/>
2.5 -
Q.
2 .0 600
400
L-
200
0.0
-20
,
-15
,
-10
z [mm] (x=7 [mm])
Figure 4.7: Measured and simulated results of the z-component of the electric-field 2.0
mm above the microstrip line [73].
0.50
=L 0.45
0.40
■
Measurement
—
Simulation
Line Scan
Co
0.35
c_
m
a>
0.30
Jj
CL
0.25
I
N
■n 0.20
aT
c
0.15
0 .1 0 ^
0.05
o.oo 4 ■■■■■i ■ ■ .
-20
-15
-10
Z [mm] (x=18 [mm])
Figure 4.8: Measured and simulated results of the z-component of the magnetic field 2.0
mm above the microstrip line [73].
62
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The frequency response of the probe is shown in Figure 4.9. The average millimeter
wave power was 5 dBm over the frequency band. Two resonant peaks are observed at 60
GHz and 72 GHz. Off resonance, the signal-to-noise ratio is 10:1 whereas on resonance,
this improves to 33:1 corresponding to a 10 dB improvement.
The resonant behavior of the magnetic-field inside the probe is confirmed with finiteelement-method simulations. The simulation results are shown on the graph of Figure
4.10. In this simulation, as in the experiment, the longitudinal dimension of the probe is
along the y-direction. The probe itself is centered at y = 5 mm. As shown, the fieldsolution for the magnetic-field at 60 GHz peaks at a value that is approximately three
times larger than that at 56 GHz and 64 GHz.
Measured frequency-respons# o f probe
^
1;
•fcj
3
1.6
1.4
12
J
1.0
o
0
e o.8
a>
1
0-8'
«
2
0.4
?
■*
'• S \
I
yv*
N oise
0.2
Floor
iz
o.o
55
60
_r_— I------ f
65
1
70
,
r
75
80
Frequency [GHz]
Figure 4.9: Measured peaks in the frequency response of the probe due to the millimeterwave field resonating in the probe [74].
63
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Finite-element-method simulation of magnetic-field inside probe
— 56 GHz
— 60 GHz
—- 64 GHz
0
1
2
3
4
5
6
7
8
9
10
y [mm]
Figure 4.10: Finite-element-method simulations confirm the resonant behavior of the
magnetic-field in the probe [74].
Flence, magneto-optic probes that take advantage of millimeter-wave cavity
resonances can be used to obtain magnetic-field distributions at V-band with enhanced
sensitivity.
When used in conjunction with electro-optic sampling probes, the
complementary probing techniques allow for a complete characterization of the
electromagnetic field.
4.5
Conclusion
A field-tunable probe capable of combined measurements of electric and magnetic
fields is presented. Experimental observations of the response of the probe to electric and
magnetic fields are shown to be consistent with theoretical expectations. The picosecond
64
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
response times o f the materials involved suggest the ability for broadband ffequencydomain measurements in excess of 100 GHz.
Probes with dimensions that take
advantage of cavity resonances can be used to obtain sensitivity enhancement. These
novel measurement techniques can provide a complete electromagnetic diagnosis of the
field behavior of microwave and millimeter-wave structures.
65
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER 5
Vector Component Isolation of Arbitrary Modulating Electric Field
In this chapter, the extent to which there is isolation between the vector components of
an arbitrary modulating electric-field in a zincblende electro-optic probe is investigated.
Field-mapping of each vector component of an arbitrary fringing electric-field is useful
for diagnostic purposes, prototype design, performance validation, and comparisons with
electromagnetic modeling results. For a pre-selected direction of modulating electricfield, the optical path direction and axes of the crossed polarizers are given by Nambda
[57]. For zincblende light modulators used as field probes, however, the direction of the
modulating electric-field is arbitrary.
Several authors have employed electro-optic
sampling using (100) gallium arsenide wafers to "pick-out" the component of the
modulating field that is collinear with the optical beam propagation direction [19], [20],
Probes
machined
from
(llO)-oriented
gallium
arsenide
wafers,
however,
are
geometrically advantageous when it is desirable to measure tangential electrical-fields
near the surface o f planar structures, since the optical probe beam can be brought in
normal to the surface of the device-under-test.
Electro-optic measurements of planar
radiating structures using free-space probes machined from (110) gallium arsenide wafers
suggest that only one orthogonal component of the fringing arbitrary electric-field
tangential to the surface of the device-under-test produces modulation on the optical
66
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
beam [59].
Recently, however, the introduction of the concept of an electro-optic
sensitivity vector has resulted in the claim that the modulating electric-field component
parallel to the [1-10] direction cannot be retrieved from a single electro-optic
measurement using probes machined from (llO)-oriented gallium arsenide wafers [60].
This implies that a single measurement does not yield one vector component of the
arbitrary modulating electric-field that is tangential to the surface of a planar deviceunder-test. In this chapter, the vector component isolation is examined.
5.1
Analysis of field-induced birefringence
Zincblende crystals such as gallium arsenide possess isotropic optical symmetry and
belong to the cubic crystal system in point group 4-3m.
The index ellipsoid for
zincblende crystals is
1
7
1
7
1
7
— x +— y +— z + 2r4]Exy z + 2r4:E x z + 2r4XEzxy = 1,
n
n
n
(5.1)
where x, y, and z define the principal coordinate system, Ex, Ey, and Ez are the respective
components of the modulating electric-field, n is the index of refraction, and r4 i is the
crystal’s electro-optic coefficient [57]. In general, an arbitrary modulating electric field
has non-zero orthogonal vector components (Ex, Ey, Ez). Therefore, it is not obvious that
zincblende crystals can provide measurements of a single vector component with high
isolation from the two remaining components for an arbitrary modulating electric-field.
For this work, the coordinate system and relevant Miller indices are shown in Figure 5.1
along with the orientation, primary flat, and secondary flat of the gallium arsenide wafer
of interest.
67
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Z < 001>
<110>
G aA s
®
< 110>
< 110>
X
Y*
<001>
“ I—
< 110>
< 110 >
Figure 5.1: Coordinate system, relevant Miller indicies, and orientation, primary flat, and
secondary flat of the gallium arsenide wafer of interest.
Assume first that the externally applied modulating electric field is the following
E X - E 5. E y = - E ,9 E * — 0,5
(5.2)
so that the direction of the modulating electric field is in the plane of the GaAs wafer and
along the [11-0] direction. In the x', y', z coordinate system, the intersection of the index
ellipsoid with the y - 0 plane yields an ellipse, which, upon diagonalization through a
counterclockwise rotation of the x', y', z coordinate system about the y' axis by 45
degrees (in order to eliminate mixed terms of x', y', and z) yields
(5.3)
where the rotated x' axis has been relabeled x" and the rotated z axis has been relabeled z'.
For optimal amplitude electro-optic modulation, with the optical propagation in the [1-10] direction, two equal components of a single linearly polarized optical beam should be
oriented along the x" ([11-1-] direction) and z' ([11-1] direction) axes. Therefore, the
input optical polarization should be aligned along the [11-0] direction. This result is
consistent with Namba for light modulators with pre-selected orientation of the
modulating electric field [57].
68
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Now, using the same direction for the optical probe beam path and the same input
optical polarization direction, assume the following modulating electric field
Ex = 0 , E y = 0 , E z =E,
(5.4)
which is orthogonal to the first component considered and still in the plane transverse to
the optical probe beam path. In the x", z' plane, the index ellipse becomes
T-T
2 n ix " + z ')2 + 2 n
(z>~ x ")2 ~ rA\E \ i x " + Z'Y
2
=1•
(5.5)
For input optical polarization along the [11-0] direction, the indices of interest are that for
z'=0 and x"=0. For z'=0,
*" = +
\n
2 ~ rA\
(5.6)
Likewise, for x '-0 ,
z' = ± " T “ r4i —
n
2
(5.7)
Therefore, the index difference z'-x" is identically zero which shows that the orthogonal
component in the plane does not contribute to the birefringence.
For the third orthogonal component of the vector space, assume
E x = E , E = E, E z = 0,
(5.8)
which is orthogonal to both previously considered modulating electric field components
and parallel to the optical probe beam path. In the x', z plane (letting y -0 ), the index
ellipse becomes
(5.9)
n
69
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which is independent of the applied modulating electric field. Since this is the equation
of a circle, there is no field induced birefringence in the x", z' plane. Therefore, the
birefringence, when analyzed for each of the orthogonal components of an arbitrary
modulating electric field, is field-dependent for only one vector component.
The most general case is for an arbitrary modulating electric field with
Ex * 0 , E y * 0 , E z *0.
(5.10)
In the x", z' coordinate system (obtained, as before, from equation (5.1) via rotation of the
x, y, z coordinate system by \\i0 = -45° degrees about the z-axis, followed by a rotation of
a 0 = -45 degrees about the y' axis) the normalized field-induced birefringence is
— y — = sin 2(a0 + Aa \ E x sin(^0 + A y/) + Ey cos(if/0 + A ^)]
H
(5.11)
+ ~ E z sin 2(y/0 + A ^ )c o s2 (« 0 + Aa),
where A\\i and Aa represent angular deviations from vj/0 and a 0. The normalized fieldinduced birefringence is plotted in Figure 5.2 as a function of Aa for Ai|/=0. For Aa = 0,
the birefringence depends only on the component in the [11-0] direction for an arbitrary
modulating field.
Small deviations away from Aa = 0 yields a birefringence that is
dependent on the component of the modulating field in both the [11-0] direction and the
[001] direction. The modulating field component in the [110] direction does not affect
the birefringence for angular deviations away from Aa = 0.
Additionally, the
birefringence is dependent only on the modulating field component in the [001] direction
for Aa = ±45°, however the magnitude is much less there relative to when Aa = 0°.
70
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EX=E, E = -E ,E z=0
Ex=0, Ey=0, EZ=E
-g - 0 . 2 -
^
-0 .4 -
I
-°-6 '
-
0.8
-
1 .0 -
Ex=E. Ey=E. Ez=°
Ex=e , Ey=-E, E jFE
EX=2E, Ey^O, Ez=0
-
40
Ex=2E' Ey=°' Ez=E
-30
-20
-10
0
10
20
30
40
A a [degrees]
Figure 5.2: Normalized field-induced birefringence dependence on modulating electricfield as a function of optical-polarization angular deviation Aa for an optical path
deviation Av|/=0.
5.2
Measurement validation
Measurements to verify these results were performed using an RF radiating source
with known polarization. The measurement setup is shown in Figure 5.3. Once again, a
mode-locked Ti:Sapphire laser tuned to 900 nm is used to generate a linearly polarized
sampling beam (80 MHz repetition rate, 100 fs pulse duration).
Appropriate phase
retarders are configured to yield a 50% transmission intensity modulator for electric field
measurements. The optical polarization incident on the crystal was aligned parallel to the
[11-0] direction (by symmetry, the optical polarization can also be aligned parallel to the
[001] direction). An RF synthesizer configured for harmonic mixing is used to downconvert the sampled electric fields to an IF frequency that allows for demodulation via
71
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
RF
Source
Linearly
polarized
source B 10 MHz
Ref.
(rotated in
transverse
plane)
/
Pulsed
TEM wave
in far-field
<001 >
(rotated in
transverse
EEC
>
\7
Linearly
polarized
source A
I Polarizer
Optical
Beam
<110>
TEM wave
in far-field
3 MHz
External
<1 1 0 >
Lock-in
Amp
Photo
Diode
X/A Crossed
analyzer
Figure 5.3: Microwave/optical setup for isolation measurements. The RF electric-field
polarization direction at the crystal is varied by physically rotating the source antenna in
the plane transverse to the boresight direction of the antenna.
low-frequency electronics [20]. The electro-optic probe was placed in the far-field of an
X-band horn antenna where the radiation is linearly polarized with greater than 30 dB of
transverse cross-polarization isolation, and the longitudinal component of the RF field
tends to zero.
The RF electric-field polarization direction at the crystal is varied by
physically rotating the antenna in the plane transverse to the boresight direction of the
antenna.
The electro-optic modulation from RF source A and RF source B is shown in Figure
5.4 as a function of rotation angle. The 0 degree angle orientation corresponds to the
source antenna oriented such that the RF source polarization was aligned parallel to the
[11-0] direction of the GaAs crystal. The angular dependence of the modulation follows
72
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■ data from source A
a data from source B
— coane function
0 & m o d u la tin g
electric-field a lig n e d
p arallel to G aA s
[11 -0] d ire c tio n
Average Noise Floor
-20 -10
0
10 20 30 40 50 60 70 80 90 100
A n gle [D egrees]
Figure 5.4: Measured electro-optic modulation from each RF source. The data follows
the cosine function thereby demonstrating vector component isolation of the modulating
electric-field.
the cosine function. This is consistent with the modulation being influenced only by the
RF electric-field vector component in the direction of [11-0] with isolation from the two
other orthogonal components. The demonstrated measured isolation is 17 dB for RF
electric-fields in the plane tangential to the direction of the optical path. For RF electricfields in the plane normal to the direction of the optical path (longitudinal direction), the
demonstrated isolation is 31 dB. The relatively low isolation in the former case (relative
to the latter) can be attributed to the sensitivity of the field-component isolation to
alignment error between the optical polarization direction and the [11-0] direction
resulting in a small nonzero value of angular deviation Aa. From equation (5.11), it can
be shown that nonzero values of A\|/ result in a contribution to the birefringence from the
modulating component parallel to [110]. However, for this optical setup, the angular
73
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
deviation Ay is minimized to a negligible value since the beam is required to reflect back
past mirror M l.
5.3
Conclusion
Analysis of the field-induced linear birefringence in zincblende crystals shows that
one can obtain complete isolation of a single vector component of an arbitrary
modulating electric-field. For an optical probe beam path aligned parallel to the [110]
direction and optical probe beam polarization aligned parallel to the [ 1 1 -0 ] direction, the
field-induced birefringence occurs only for the component of the modulating electricfield aligned parallel to the [11-0] direction. Measurements using a modulating electricfield with known polarization and electro-optic probes machined from ( 1 1 0 ) gallium
arsenide wafers demonstrate an alignment-limited isolation between orthogonal
modulating electric-field components of 17 dB.
74
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CHAPTER 6
Applications
This chapter discusses a number of applications of measuring electric, magnetic, and
thermal fields using the techniques that were discussed over the first five chapters of this
thesis. First, the temperature rise in a quasi-optical power-combining array is measured.
This measurement demonstrates simultaneous measurements of electric-field and
temperature. It also illustrates the calibration of electric-field data that is corrupted by the
presence of temperature gradients. Next, the electric, magnetic, and thermal fields of a
patch antenna operating at high power are measured.
Two-dimensional field maps
illustrate the usefulness of measuring all three quantities.
This is followed by the
measurement o f the magnetic fields on the aperture of a horn antenna operating in Vband. Measurements are compared with first order aperture theory. Next, the surfacewaves from a microstrip stub discontinuity are measured.
The radiation pattern is
compared with theoretical results. Finally, power induced heating in RF MEMS switches
is measured. The temperature rise-time to steady state and electro/thermal behavior in
the up and down states are shown.
6.1
Quasi-optical power combining array
To demonstrate the usefulness of the electro-thermal probe, the thermal and electric
75
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fields of a single MMIC cell within an X-band quasi-optical power-combining array was
examined. A horn antenna fed an RF signal to an array of patch antennas, which coupled
power to a set of amplifying MMICs via microstrip line. The output of each MMIC was
re-radiated via an array of patch antennas allowing free-space power-combining to be
accomplished. The probe employed was <100> GaAs with a normal-surface area of 500
pm x 500 pm and a vertical thickness of 200 pm.
As illustrated in Figure 6.1, the probe was mounted near the output of the MMIC and
less than 0.5 mm above the microstrip substrate. For comparison purposes, a power
meter was mounted in the far-field of the array in order to independently monitor its
output performance. To isolate the MMIC under test, the input and output patch antennas
for all the other MMICs were covered with copper tape. The bias and RF for the array
was switched on at time zero.
Figure 6.2 clearly shows that there is a substantial
difference between the behavior of the measured electric field data obtained from the
probe and the measured power from the independent power meter. The explanation for
the discrepancy is shown in Figure 6.3 as the absorption data from the probe is seen to
/
/
X-Band Q O Amp
NCSU
Unit Cell:
Patch -> microstrip -> MMIC -> microstrip -> Patch
Figure 6 .1: Measured quasi-optical power combining array.
76
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Probe [V]
i i i i |"i
i »
t
-j i i i i | i i i i | v i
i i | i i r r - 1— r — i ■■ i i | i i i i | 1 1
i i | i i i i | i i i i
-
8.0x1 O'7 -i
E-Field
Data from
7.0x107
Uncalibrated
0.20
0 .1 5
6.0x10'
5.0x10’;
s a.
-
0.10
4.0x10'7 d
3.0x10 j
2.0x10" d
_D_
0 .0 5
E|e c tro.Therm al Probe
— • — Pow er Meter
Independent Power Meter Signal [V]
9.0x107:
1 .0 x 1 0
T im e [min]
Data from
6 .5 x 1 0
- 0 .0 2 5
6.0x10-
V .
x
\
5.5x10-
5 .0 x 1 0
4 .5 x 1 0
^
X\
0 .0 2 4
X
"
\
\
— -V
d 0 .0 2 3
X]
E le c tric -F ie ld D a ta
o 022
- • — A b s o r p tio n D a ta
3
4
5
6
''V
7
8
9
10
11
T im e [min]
Figure 6.3: Probe-only measurements of MMIC [58].
77
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Probe [V]
E-Field
- 0 .0 2 6
Data from
Uncalibrated
7 .0 x 1 0
Absorption
Probe [V]
Figure 6.2: Probe and power meter measurement of MMIC [58].
9 .0 x 1 0
0.20 o.
a>
"O
<D
a)
XI 8 .0 x 1 0 oi—
OL
13
CL
7 .0 x 1 0 '
E
0
-*-=«
-7
- • - • -=8- • - » =" -fl =■ ~g - a -8 - a = 0 .1 5 S
*
-
"0
rc
a 5 .0 x 1 0 7 “
-I 0 .1 0 ®
4= 6 .0 x 1 0
o
(0
-I—I
at
m) 4 .0 x 1 0
0
(D
Ll
1
HI 3 .0 x 1 0
-O
Q)
■J5 2 .0 x 1 0
.a
i s 1 .0 x 1 0
0 .0 5 ^
(Q
3
0)
— D— Calibrated Probe Data
— • — Pow er Meter
7
-
o
T im e [min]
Figure 6.4: Temperature-calibrated electric-field data [58].
decrease with time along with the electric field data. The change in the absorption signal
is consistent with the expected increase in temperature in the vicinity of the biased MMIC
due to the dissipation o f heat.
Calibration of the temperature effects of the probe on the electric-field measurements
is possible since the absorption signal is linearly proportional to the electric-field signal.
Knowledge o f the deviation of the absorption signal with time,
A V so m h z,
allows for the
compensation of the modulation signal for temperature effects according to
V'5MHz -
/ dV
u y 1MHz
A
dV
VgQ M flz
■*" ^ 3
MHz
( 6 .1 )
\ u r 80MHz J
where the primed notation denotes temperature-calibrated data. In equation (6.1), V 3 MHZ
denotes the temperature corrupted electric field data. The deviation of the absorption
signal is multiplied by the differential change in the corrupted electric field data with
78
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
respect to the differential change in absorption signal.
The product is added to the
corrupted data to yield the temperature corrected electric field data. The results of this
calibration method are shown in Figure 6.4. The calibrated electric-field data is now in
excellent agreement with the independent power-meter measurements. The calculated
standard deviation is 1.3%.
Figure 6.5 illustrates the results from the simultaneous data collected from the probe.
Knowledge of the initial room temperature, the optical-power/temperature relationship,
and the deviation of the 80-MFIz component with time allow for the scaling of the 80MHz component to degrees celsius. The region neighboring the output of the MMIC is
seen to increase by 7°C in 11 minutes.
This measurement example illustrates the advantages of using a multifunctional probe
when studying coupled electro/thermal effects. The alternative to using an integrated
9.0x10
0
34
JQ
O 8.0x10'
32
7
30
Ll 4.0x10 i
1
26
c—t
24
=4*
o
3
0
LD
T3 3.0x107 ^
0
-7
0
0
0
0
0
3
TJ
28 0—i
tj
i_
JO 2.0x10
ro
O 1.0x10
</)
c
-I
Q.
E 7.0x10
o
4=
■7
« 6.0x10
15
0 5.0x107 ~
-4—
*
0
0
— D— Calibrated E-Field Data from Probe
— • — Temperature from Probe [°C]
1 1 11
1
■1 1 1 ■1 1 1 1 1 1 ■i 1 1 1 1 1 1 1 1 1 1
2
3
4
5
6
111
' I 1 1 1 ' I 1 ' tt-T
8
9 10
22
20
11
o
cr
0
O
O
T im e [min]
Figure 6.5: Simultaneous electric-field and temperature measurements of MMIC [58].
79
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
probe is to use two separate probes: one for electric field measurements and one for
temperature.
However, there are disadvantages to using multiple probes when
conducting an experiment. First, integrating multiple diagnostic probes into a deviceunder-test inherently perturbs the experiment. Second, a true measurement of the electric
field and temperature at a point cannot be achieved in a single experiment with two
probes that are physically separated.
Third, both probes must be positioned
independently. This is significant because for densely packed integrated circuits with
sub-millimeter-scale dimensions, the act of precisely positioning the probe is often the
most time consuming aspect of the measurement. In addition, unlike thermocouples and
thermistors, the integrated electo/thermal probe consists of no heavy metals. The probe
consists entirely of a dielectric - a fact that is important for minimum invasiveness and
measurement
accuracy
when
studying
electronic
circuits
where
time-varying
electromagnetic fields are present.
6.2
Patch antenna operating at high power
To illustrate the usefulness of measuring electric, magnetic, and thermal fields, the near
field of a microstrip patch antenna operating at high RF power was measured.
Measurements are compared with simulations. The probes employed were <100> GaAs
with a normal-surface area of 500 pm x 500 pm and a vertical thickness of 200 pm and
terbium gallium garnet with a circular cylinder of length = 2.3 mm and radius = 1 mm.
A patch antenna was fabricated on copper-metallized RT/duroid 6006 (sr = 6.15, tan §
= 0.0027, h = 25 mil). The antenna is fed with a recessed microstrip in conjunction with
a quarter-wave matching section and was operated at resonance (10.403 GHz) with
80
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8
watts of RF input power. The ground plane of the antenna was mounted on a metallic
base in order to allow for heat-sinking. Due to the symmetry of the antenna, it was only
necessary to scan one-half of the desired image.
The measured and simulated z-component of the electric field is shown in Figure
6.6
at
a height of 0.5 mm above the surface. Simulation results were obtained using a finiteelement-method solver [61]. The measured and simulated results are in good agreement
and show that the mode in the dielectric beneath the patch resembles the TMio-mode to z
as described in the cavity model [62].
Measured and simulated results of the y-component of the magnetic field at a height of
1.5 mm are shown in Figure 6.7. Simulation results were once again obtained using
finite-element-method simulations [61]. In the limit of zero height above the surface and
infinite metal conductivity, the y-component of the magnetic field theoretically limits to
the surface current on the metal. In the measured field map, the regions of high magnetic
field are consistent with the presence of large currents, on the top metallization of the
patch, along the non-radiating edges.
The measured temperature profile at a height of 0.5 mm above the patch antenna is
shown in Figure 6 .8 . Once the RF power was turned on, the temperature reached steadystate after approximately one minute, thereby allowing for the imaging of the temperature
distribution. In the measurement, hot spots are observed at the top edge of the antenna
and at the bottom edge in the vicinity of the microstrip feed where the temperature peaks
at forty degrees. This is approximately 20°C above the ambient laboratory temperature.
The temperature distribution is seen to fall away rapidly with lateral distance from the
antenna.
81
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Measured |EZ|
i
Simulated |EZ|
[norm.]
1.0
0.5
0.0
0-0
2,75
5.5
8.25
0.0
11.0
2.75
X (m m ]
5.5
8,25
11.0
X [m m j
Figure 6 .6 : Measured and simulated magnitude of the z-component (normal) of the
electric field at a height of 0.5 mm above the surface [75].
1l0f
Measured |Hy |
Simulated
[norm.]
[norm.]
8.25
I
2.75-
O.Ot
0.0
2,75
5.5
8,25
11.0
0.0
2,75
X [m m ]
4
5.5
8,25
11.0
X [m m J
Figure 6.7: Measured and simulated magnitude of the y-component (tangential) of the
magnetic field at a height of 1.5 mm above the surface [75],
Simulated thermal image
Measured thermal image Temp 0
Tem p
[°q
40.0
0 .0
4 ,5
0 .0
1 3 .5
1 8 .0
0 ,0
4 ,5
9 -0
1 3 .6
1 8 .0
X [m m ]
X [m m ]
Figure 6 .8 : Measured and simulated temperature distribution at a height of 0.5 mm above
the surface [75],
82
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The measurement o f temperature hot spots over metallic surfaces serves to illustrate
the advantages of bandgap thermometry over infrared thermometry based on blackbody
radiation. With infrared cameras, the temperature of the camera itself is imaged onto its
charge-coupled-device (CCD) array due to reflections from test devices that are
composed of metallic surfaces. Additionally, in order to obtain high resolution images,
the infrared camera is required to employ a high magnification microscope objective
which implies a short focal length. Therefore, there is an inherent tradeoff with infrared
cameras between spatial resolution and invasiveness.
The measured thermal image from the electro/thermal probe was compared with
simulations in order to obtain insight from the results. In order to obtain the simulated
temperature distribution o f the patch antenna, a flnite-difference-time-domain technique
was applied to both the electromagnetic problem and to the thermal problem.
The
numerical simulations for the thermal comparison was developed and performed by Thiel
[16]. In a preceding electromagnetic simulation, the dissipated power in the conductor
and in the lossy substrate was calculated. For an accurate modeling of the skin effect in
the conductor, an effective complex conductivity was introduced [64]. The resulting
dissipated power was the basis for a subsequent heat analysis where a forward-time
centered-space (FTCS) scheme was applied to the conductive heat equation [65], [6 6 ]. In
this approach, thermal radiation and convection in the computational domain were not
taken into account. The domain was terminated by boundary conditions that modeled the
heat sink underneath the substrate and the convection on the boundary above the patch.
The measured and simulated temperature profiles are in good agreement except in two
areas. The first is the hot spot at the tip of the patch, which shows up in the measurement
83
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
but not in the simulation. The second is the difference in peak temperature. The first
difference between the measured and simulated temperature profiles can be attributed to
the surface contact between the heat sink and the patch antenna ground plane.
Experimentally, this was accomplished via double-sided tape, which was not modeled in
the simulation. The small air gap allowed for less than ideal conduction into the heat
sink, thereby providing for a greater proportion of heat flow in the direction opposite to
the heat sink, ultimately changing the temperature distribution above the patch. The
difference in peak temperatures can be attributed to the lack of modeling convection in
the computational domain. In the absence of convection, the simulation predicts a higher
temperature than expected in measurements because the presence of convection
introduces air-flow across the surface.
Other than these two exceptions, the thermal
measurement is in good agreement with the simulation.
It is interesting to note that the two hot spots observed in the measured temperature
distribution correlate in location with the maxima of the electric field mode supported in
the dielectric between the patch and the ground plane. This is contrary to an initial
expectation that the temperature distribution should map according to the location of the
currents on the patch. In the structure, however, there are two primary loss mechanisms:
( 1 ) loss in the metal due to the finite conductivity, and (2 ) loss in the dielectric due to
conductivity loss and dielectric damping [67]. Since the temperature measurements show
that the hot spots correlate with the mode in the dielectric where the electric field peaks
and not with the current distribution where the magnetic field peaks, it is concluded that
dielectric loss dominates the temperature profile.
84
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6.3
Aperture of V-band horn antenna
A two-dimensional magnetic-field map of a horn antenna aperture was obtained at 60
GHz by raster scanning a V-band horn antenna with an xy-translation stage. In the near
field, electric and magnetic field distributions approach their quasi-static solutions and
are therefore decoupled. This example illustrates the use of magneto-optic sampling for
magnetic field measurements in the millimeter wave band. Line scans of these maps are
shown in Figure 6.9. The field was imaged in a plane approximately 1.5 mm above the
antenna using a step size of 2 mm. The measurements are in good agreement with firstorder aperture-antenna theory [6 8 ]. The probe employed was terbium gallium garnet
consisting of a circular cylinder of length = 2.3 mm and radius = 1 mm.
Figure 6.9: Digital image of TGG at aperture of V-band horn antenna [74].
M a g n itu d e {H y}
a
M e a su re m e n t
- F irst-o rd er theory
[norm .]
. -
0 6
cs
0 .2 0.0
15
0
x [mm]
10
20
30
40
y [mm] (x = 14 [mm])
Figure 6.10: Measured magnetic-field magnitude as a function of position at the output of
a horn antenna [74].
85
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Phase
180 o
{H y }
42-
0
[Dea.1
M easurem ent
First order theory
135-
-
-1 8 0
0
15
0
30
10
20
30
40
y [m m ] (x = 14 [m m ])
x [mm]
Figure 6.11: Measured magnetic-field phase as a function of position at the output of a
horn antenna. Measured line scans across the aperture are in good agreement with firstorder aperture-antenna theory [74].
6.4
Surface-waves from a microstrip stub discontinuity
Radiation losses from open microstrip discontinuities are known to take on two forms:
space and surface-wave loss [69].
Surface-wave radiation propagates as a bounded
cylindrical wave on a grounded substrate and therefore has the potential to significantly
cause undesireable electromagnetic coupling between elements on a common substrate.
Space-wave radiation nulls along the dielectric substrate and is therefore less of a
detriment with respect to coupling in two-dimensional topologies.
In this section,
surface-waves from a microstrip stub discontinuity are field-mapped. The measurement
of surface-waves requires sensitivity to the field-component normal to the surface of the
substrate. A number of field probes satisfy this criteria (ie. monopole probes, coaxial
field probes). Electro-optic sampling is a good option because of its low invasiveness (all
dielectric), high resolution, and selectivity for one component of an arbitrary electric
field.
8 6
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The test fixture is a microstrip-stub printed on a circular-disk grounded-substrate [69].
As shown in Figure 6.12, the microstrip stub was fed via a coax-to-microstrip transition
and the edges of the substrate were machined with a taper in order to minimize
refelections at the substrate-to-air interface. The disk radius is 7.6 cm. The substrate
thickness is 2.54 mm and the dielectric constant is 10.2. The RF frequency is 7.763 GHz.
These values allow only the dominant surface-wave mode (TM0) to propagate.
This
mode is polarized with its electric field in the direction perpendicular to the substrate.
The probe employed was <100> GaAs with a normal-surface area of 500 pm x 500 pm
and a vertical thickness of 2 0 0 pm.
Coax-to-microstrip
transition
Probe
Tapered
substrate
RF
Synthesizer
Microstrip stub
Figure 6.12: Test fixture and probe positioning for measurement of surface-waves from
open microstrip stub discontinuity.
The measured magnitude and phase of the normal component of the electric-field is
shown in Figure 6.13. The probe was positioned at a height of 1 mm and the lateral stepsize was 500 pm.
The magnitude data clearly shows radiation from the end of the
microstrip stub. The progression of the phase indicates that this radiation is of a traveling
87
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• Amplitude Az(x,y) [norm.]
• Phase <Dz(x,y) [Degrees]
Figure 6.13: Measured magnitude and phase of surface-wave electric-field from open
microstrip discontinuity.
Radiation Pattern
Theory
Exp
Figure 6.14: Magnitude and phase of surface-wave electric-field from open microstrip
discontinuity in artificial time representation; the radiation pattern is also compared with
theoretical results.
wave nature. The magnitude and phase data in an artificial time representation is shown
in Figure 6.14. In this representation, the wave nature of the propagation is more clear as
this represents the traveling wave at one instant of time. The measured radiation pattern
is compared with theoretical results in Figure 6.14.
The theoretical results are from
88
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moment-method numerical simulations developed and executed by Harokopus [69]. The
measurements compare well with the theoretical results. There are two primary sources
of error. First, radiation from the coax-to-microstrip transition is also present. This was
minimized to some extent by placing absorber at the transition. Second, the simulated
results are for a semi-infinite substrate. The finite substrate effect, limited to some extent
by tapering the substrate, allows for multiple reflections within the test fixture.
6.5
RF microelectromechanical switches
The study of RF microelectromechanical switches (RF MEMS) is an area of current
research and development interest.
In particular, the reliability of these devices is
vigorously being studied. RF MEMS switches are electromechanical devices based on
thin-film technology that have the potential to provide RF switching functions with low
power consumption, high linearity, and high isolation.
Applications of these devices
include power limiters, tunable matching networks for broadband amplifiers, and low
loss phase shifters for phased array radars. Due to various loss mechanisms in the device,
RF induced heating occurs. Temperature dependent material and device parameters such
as the Youngs modulus, Poisson ratio, and biaxial residual stress can therefore potentially
have an impact on device characteristics. In this section, electro/thermal measurements
are performed on a capacitive RF MEMS switch in order to demonstrate the usefulness of
measuring coupled electro/thermal effects and to investigate the degree of RF induced
heating on the membrane due to RF power.
Probes with 125 pm x 125 pm x
8 6
pm dimensions have been fabricated for these
measurements. An edge length of 125 pm was selected to match the diameter of the
89
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
optical fiber. The RF MEMS measurement setup is shown in Figure 6.15. Since this
particular measurement configuration contains a few unique aspects (when compared
with the four previous examples), the setup is now described in some detail. The output
of a 20 mW RF synthesizer operating at 17.4815 GHz is fed into a self-biased frequency
doubler whose output (@ 34.963 GHz) is subsequently used to source a Ka-band
traveling-wave tube (TWT) amplifier capable of amplifying the RF signal to several
watts. The coaxial cable from the TWT is terminated with on-wafer probes which serve
as the input port for the switch-shunted co-planar waveguide. A second on-wafer probe
serves as the output port whose output passes through a 20 dB coupler. The thru port is
10 MHz
Ref.
P u lse d
L aser
10 MHz
Ref.
O ptical
B eam
P h o to
D iode
i r
5 MHz
LPF
Lock-in
Amp
3 MHz
External
Ref.
2 5 /9 0
MHz
B PF
Lock-in
Amp
8 0 MHz
External
Ref.
Beam
Splitter
Fiber
Coupler
RF
S o u rc e
M atch ed
Load
\T W T /
\
/
Fiber -*
O n -w afer
p ro b e s
Polarization
Controller
2 0 dB
C oupler
P ow er
M e ter
GaAs
Probe"*1 fr, Bragg
R e fle c to r I
- DC
In F^l
CPW
3 G nd
C a p a c itiv e Sw itch
Figure 6.15: The RF/optical setup to measure the RF MEMS capacitive switch.
90
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terminated in a high-power matched load and the coupled port is terminated in a power
meter. A 50 V DC source provides electrostatic switch actuation via DC contact probes
placed on on-wafer DC pads.
The electrothermal probe is mounted on an
electromechanical x-y translation stage with 1 pm step resolution. A manual translation
support provides movement of the probe in the vertical direction.
A horizontally
mounted low-power-objective microscope allows for the vertical positioning of the probe
above the switch with ± 1 0 pm accuracy.
The output of the photodiode is connected to two lock-in amplifiers for simultaneous
measurement of electric-field and temperature via a coaxial tee. A 5 MHz low pass filter
routes the 3 MHz modulation
measurements.
to the first lock-in amplifier
for electric-field
A bandpass filter routes the 80 MHz signal to the second lock-in
amplifier for temperature measurements. The time constant of the lock-in was placed at
1 0 0
ms, which sets the upper limit on the temporal resolution of the measurement system.
The switch under investigation, fabricated by the author, is shown in Figure 6.16. The
switch design and fabrication procedures are based on the work of Pacheco and Peroulis
[70], [71]. The switch shown here differs primarily in the anchoring, which produces a
consistent gap height. The switch dimensions are 240 pm x
780 pm x1 pm. The switch
membrane (Au) was fabricated with internal stresses conducive to conformal contact in
the DOWN state. The dielectric layer is composed of 2000 angstroms of silicon nitride.
The substrate is 400 mm Si with a resistivity of 2000 Q-cm.
From vector network
analyzer measurements, the measured return loss in the up state is -10.7 dB.
The
insertion loss in the up state configuration is -0.56 dB. In the down state, the measured
91
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return loss is -0.02 dB and the insertion loss is -22.1 dB. A digital image of the probe
over the switch is shown in Figure 6.17.
Non-contact point measurements with the probe 25 +
6
pm above the switch were
performed first. For these measurements, the ambient temperature of the lab was 21 °C.
The air between the switch and the probe forms a moving conductive medium for
convective heat transfer. The temperatures measured are not that of the switch itself but
of the air as measured by the probe at the height above the switch. The rise and fall times
of the switch in the UP state is shown in Figure 6.18. The probe was placed 25 pm
Figure 6.16: SEM image of measured RF MEMS capacitive switch.
Figure 6.17: Digital image of probe over RF MEMS capacitive switch.
92
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directly over the center of the switch and the input RF power was varied between 100
mW and 1 W. These are the input powers at the switch determined by considering the
CPW line loss (2.3 dB/cm) and the on-wafer probe insertion loss (0.72 dB). No self­
actuation due to high RF power was observed at any point.
This is consistent with
previously reported findings [70]. Data acquisition commenced with the RF off for 40
seconds, the RF on for 60 seconds, and the RF off for 40 seconds. The temperature of the
probe shows a rise time, computed between the 10 % and 90 % points, at 1 W input RF,
of 0.32 ± 0.5 sec. The measured temperature change between on and off RF powers is
9.3 ± 0.7 °C at 1 W input RF.
Since the switch reaches a steady state temperature, it is possible to perform line scans
of the field distributions to obtain the spatial behavior. Line scans of the electric field
Temperature Rise and Fall Times
40
RF On
eO
Ifl
£Z
O)
W
30
RF Off
RF Off
2 0
N
o
03
Power at
Switch Input
Switch: Up-State, RF: 34.963 GHz
Probe Height: 25 +- 6 um
1 0
100 mW
500 mW
1W
Probe: <100> GaAs (125 pm)
CPW Loss: 2.3 dB/cm
2 0
40
60
80
1 0 0
120
140
160
Time [sec]
Figure 6.18: Measured temperature rise-times to steady state. The probe height is 25 pm.
93
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Electric-Field Line Scan Along CPW
Switch: Up-State, RF: 34.963 GHz @ 1W, h=61 pm +- 6 pm
1.0 n
o
c
ro
\■
I
0.8
c
O)
00
N
!•
■
\ T
■
i
0.6
;
>L
X
co 0.4
O)
ro
Probe: <100> GaAs
Step Size: 125 pm
5 0.2
aj
L_i
Sample time: 1 sec
Time Constant: 100 ms
LXJ
CPW Loss: 2.3 dB/cm
On-wafer probes embedded
Switch Location
0.0
0.0
0.2
0.4
0.6
0.8
1.0
x [cm ]
Figure 6.19: Measured electric field magnitude in the UP state. The probe height
is 61 pm.
Electric-Field Line Scan Along CPW
Switch: Down-State, RF: 34.963 GHz @ 1W, 61 pm +-
6
pm
E
o
“
0 .8
-
75
c
O)
W
0.6-
CPW Loss: 2.3 dB/cm
N
X
s
G 0.4 D)
On-wafer probes embedded
ro
0 .2
Switch Location
-
<D
Ll_
w
0.0
0.0
0.2
0.4
0.6
0.8
1.0
x [cm ]
Figure 6.20: Measured electric field magnitude in the DOWN state. The probe height
is 61 pm.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
magnitude are shown in Figure 6.19 for the UP state and in Figure 6.20 for the DOWN
state. The phase data are shown in Figures 6.21 and 6.22. The probe was raised to 61
pm above the surface in order to avoid accidentally driving the probe into the circuit
surface. The RF power at the switch was 1 W. In the UP state, the electric field is seen
to drop by approximately 14% across the switch indicating that the switch is performing
the function of passing power through.
This is supported by the slope in the phase
measurements which is indicative of traveling waves. In the DOWN state, the electric
field drop is approximately 90% which shows that the switch is performing a blocking
function for the RF power.
This is supported by the flat slope of the phase
measurements, which is indicative of standing waves on the input side of the switch.
Simultaneous temperature line scans using 1 W input RF power for the switch in the
UP/DOWN states are shown in Figures 6.23 and 6.24. When the RF is on, a peak is
present in the UP state where the switch is physically located. Away from the switch, the
transmission line has increased in temperature when compared with the temperature with
the RF off. This is due to CPW line loss. The peak indicates that heat is confined to the
membrane in the up state. The peak is absent in the down state. This is consistent with
the hypothesis of efficient conductive heat transfer between the membrane and the
substrate in the DOWN position. In the DOWN state with the RF on, the temperature is
higher along the CPW when compared against the DOWN state with the RF off. In
addition, the temperature is slightly higher on the side of the input RF power. This is
consistent with the presence of a large standing wave on the input side of the switch in
the DOWN state and substrate heating from the switch. There is a slight slope in the RF-
95
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Electric-Field Line Scan Along CPW
Switch: Up-State, RF: 34.963 GHz @ 1W, 61 pm +- 6 pm
180
05
<L> 150 Q 120
-
90
6030-
05
05
N
X
s
0 CO
0)
-3 0 05
ro
sz
-60
CL
-9 0 -
Switch
«D 1 2 0
U_I
LU -150 -
-
/
Location
-1800.2
0
0.4
0.6
0.8
1.0
x [cm]
Figure 6.21: Measured electric field phase in the UP state. The probe height is 61 pm.
Electric-Field Line Scan Along CPW
Switch: Up-State, RF: 34.963 GHz @ 1W, 61 pm +- 6 pin
180
05 150
^
<L>
a
120
O)
CO
a* -30
ir>
« -60
-90
1 -120
IS -150
Switch Location
-180
0.0
0.2
0.4
0.6
0.8
1.0
x [cm]
Figure 6.22: Measured electric field phase in the DOWN state. The probe height
is 61 pm.
96
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Temperature Line Scan Along CPW
n
1------ 1------ 1------ T
Switch: Up-State, RF: 34.963 GHz @ 1W
Probe Height: = 61 pm +- 6 pm
40
O
c
o
j
Ll_
w
75
c 20
a)
o
30
X
N
traveling wave
CO
"'**• ‘i ■*n«~n
-
JO
CO
N
X
10
oo
Uniform Heating
consistent with
Switch Location
30
40
—
RF On
—
R F Of f
n
O
3
10
O
jQ
-
r— i
o
Probe: <100> GaAs
Step Size: 125 pm
CO
0.0
0.2
CPW Loss: 2.3 dB/cm
On-wafer probes embedded
0.4
0.6
x
0.8
1.0
[cm ]
Figure 6.23: Measured temperature in the UP state. The probe height is 61 pm.
Temperature Line Scan Along CPW
-------1------ ■
------ 1------- ■
------ 1—
—i------ ■
Switch: Down state, RF: 34.963 GHz @ 1W
50
oO
Probe Height: = 61 pm +-
6
50
pm
40
40
Switch Location
O
N
CO
30 ■
(Q
3
D)
75
c
O)
CO 20 ■
20
N
X
O
CO
o
X
Li­
ar
00
Tl
o
— O— RF On
3
Non-uniform
heating consistent
with standing-wave
RF Off
10
Probe: <100> GaAs
Step Size: 125 pm
o.o
70
10
o
n
T
0.2
0.4
0.6
1.0
x [cm ]
Figure 6.24: Measured temperature in the DOWN state. The probe height is 61 pm.
97
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off measurements due to residual heating from repeated line-scan measurements with the
RF on and the RF off.
6.6
Conclusion
In summary, this chapter has discussed several examples of measuring electric,
magnetic, and thermal fields. Fields associated with a quasi-optical power combining
array, a patch antenna operating at high power, a horn antenna operating at V-band, a
microstrip stub discontinuity, and RF microelectromechanical switches have been
measured. Considerable physical insight can be obtained by probing at internal points
within a circuit and multifunctionality allows this while minimizing the time and effort
required for test and measurement.
98
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CHAPTER 7
Thesis conclusion and future work
This chapter brings the thesis to an end with an overall conclusion and a discussion of
future work. Following a statement of contributions to the field, several promising future
areas are presented that would naturally be pursued from this work.
7.1
Thesis conclusion
This research explored both theoretically and experimentally the concept of
multifunctional optical probes for the purpose of characterizing microwave and
millimeter wave devices. An integrated electro/thermal probe capable of simultaneously
measuring electric and thermal fields, and a polarization tunable probe for combined
measurements of electric and magnetic fields have been presented.
The theoretical
background, concept, fabrication, characterization, and test of these probes were
discussed in detail. A scheme for nonlinear thermo/optic modeling was developed and
utilized in order to characterize the limitations of using electro-optic semiconductors for
the purpose of simultaneously measuring electric field and temperature with a single
probe. Furthermore, a fabrication technique for their miniaturization was developed that
incorporates a scheme for the secondary handling of micromachined electro-optic
99
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semiconductors. For the polarization tunable probe, a Jones calculus formulation was
devised to conceive the isolation characteristics between electric field sensitivity and
magnetic field sensitivity. A novel method for enhanced magnetic field sensitivity was
described, which improves the sensitivity difference between the electric and magnetic
field sensors. For zincblende crystals, the degree of vector component isolation of an
arbitrary modulating electric field was analyzed, quantified, and validated with
measurements. Complete isolation is possible with proper angular orientation. Electric,
magnetic, and thermal field measurements have been demonstrated on a quasi-optical
power-combining array, a patch antenna operating at high power, a horn antenna
operating in the millimeter wave band, a microstrip stub discontinuity, and radio
frequency microelectromechanical switches. This work provides the unique means of
studying coupled electro/thermal effects and measuring electromagnetic fields of
microwave and millimeter wave devices utilizing methods that minimize the time and
effort required for test and measurement.
7.2
Future work
7.2.1 Exploration of new material systems
The electro-optic material used in the hybrid probe is GaAs and the magneto-optic
material is terbium gallium garnet (TGG).
Alternatively, a single crystal of diluted
magnetic semiconductor such as cadmium manganese telluride may be used. Diluted
magnetic semiconductors (DMSs) are semiconductors containing substitutional transition
metal ions [72], Cdi.xMnxTe (0<x<l) is an example of a DMS with a zincblende crystal
structure. The presence of the transition metal ions results in a material that exhibits the
100
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Faraday effect. Since the crystal structure is zincblende, the material is also electro-optic.
Therefore, instead of a hybrid probe, it may be possible to develop a single crystal probe
for the combined measurements of electric and magnetic fields. CdTe also has a higher
electro-optic coefficient than GaAs. Therefore, this material system should provide for
enhanced electric field sensitivity.
7.2.2 Development of post processing for enhanced spatial resolution
Due to the finite thermal conductivity of GaAs, the spatial resolution of the
electro/thermal probe is essentially fixed by the physical dimensions of the probe itself.
Electro/thermal probes on the order of 125 pm have been successfully fabricated but are
still too large to see, for example, localized hot-spots in RF MEMS switches. To measure
localized hot-spots on RF MEMS switches, a thermal resolution on the order of 20-40 pm
is required,
hr order to improve the spatial resolution of the probe with regard to
temperature measurements, the probe can either be miniaturized further or the measured
data can be post-processed.
A possible post processing solution to reduce the spatial resolution is to deconvolve the
probe point-spread function. Due to the large thermal conductivity ratio between GaAs
and air, the point-spread-function of the probe is very nearly a square pulse.
The
measured image, g(r), is the convolution of the real image, f(r), with the probe pointspread-function, h(r), plus noise n(r). By solving this inverse problem, it may be possible
to obtain an approximation of the real image, f(r), with higher spatial resolution.
7.2.3 Research into new applications
The ability to probe both electric and magnetic fields allows for a complete diagnosis of
electromagnetic behavior and provides the means to obtain point-wise characterizations
101
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of field distributions from circuits and radiating structures in terms of point-impedance.
Measuring point-impedance is a paradigm shift away from measuring one of either
electric or magnetic fields.
Measurements of point impedance may open up new
application areas with respect to the characterization of elements such as planar
transmission lines, planar antennas, cavity resonators, and active structures. For example,
one can imagine probing the input of a planar antenna with a single crystal of CdMnTe in
order to determine the input impedance of the structure. In addition, the characterization
of unknown impedance surfaces (both natural and artificial) and the direct determination
of complex permittivity become potential new applications.
102
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APPENDICES
103
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APPENDIX A
Detailed fabrication procedures
This appendix describes the detailed fabrication procedures involved in this thesis.
Fabrication work for this thesis was conducted at the class 100 University of Michigan
clean room. The appendix begins with a discussion of clean room equipment and then
proceeds to a detailed discussion of fabrication steps. Digital images of the clean room
equipment were downloaded from the University of Michigan Solid State Electronics
Lab (SSEL) website and are provided here for reference.
The website is
http://www.eecs.umich.edu/ssel.
A .l
Fabrication equipment
A.1.1 Interserv (model 122135) mask maker
The mask maker selectively exposes small apertures
onto the surface of a photomask based on a user specified
exposure file. The photomask consists of a glass plate (4
in x 4 in for this work) coated with a chrome film and
photoresist.
Figure A.I. Mask maker.
104
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A.1.2. Wet benches
Wet benches are used for wet chemical processing.
In the SSEL cleanroom GaAs bay, hoods exist for
solvent, base, and acid processes.
Interior airflow
provides for protective vapor isolation.
Rinse tanks
provide a steady flow o f D IH 2 O.
Figure A.2. Wet benches.
A.1.3 Karl Suss MJB3 mask aligner
The
mask
aligner
provides
precision
manual
alignment between the photomask and the wafer.
It
employs frontside UV illumination and can handle
wafers pieces from 1 mm square to 3" in diameter. The
UV intensity is typically 20 mW/cm2.
Figure A. 3. Mask aligner.
A, 1.4 SJ-26 electron beam evaporator
The SJ-26 uses an electron beam to evaporate metals
or dielectrics onto a wafer.
The evaporated material
exits a crucible and propagates, essentially collision
free, through an evacuated low pressure chamber to the
sample. For this work, the SJ-26 was primarily used to
evaporate thin films of zince selenide (ZnSe) and
magnesium fluoride (MgF2) onto GaAs in order to form
a dielectric mirror.
Figure A.4. SJ-26.
105
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A.1.5 Enerjet sputter coater
Sputtering involves bombarding a target with high
energy ions in order to free atoms which subsequently
propagate to a substrate to form a thin film. Available
targets include Ti, Au, Cr, Al, SiCr, ITO, and SiC>2 (to
name a few). Due to the randomness of the deposition,
sputtering can produce low stress gold films, which is
Figure A.5. Sputter
coater.
useful for RF MEMS fabrication [76].
A.I.6 Semi-group plasma-enhanced chemical vapor deposition reactor
Plasma
enhanced
chemical
vapor
deposition
(PECVD) involves the reaction of gaseous compounds
to create a material which deposits onto a sample
directly from the gas phase.
•; I n
t
-
Hi
The plasma allows the
reaction to occur at relatively low temperatures
Figure A.6 . PECVD.
(-400 °C).
A.1.7 Semi-group reactive-ion etcher
Reactive ion etching involves the ionization of reactive
gases which are subsequently accelerated in order to etch
a sample via bombardment. The reactive ion etcher is
used, for example, to etch a passivation layer formed
from silicon nitride (deposited via the semi-group
PECVD reactor).
Figure A.7. RIE.
106
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A.1.8 Technics Asher
The asher uses reactive-ion etching with O2 to clean the
-TMKnafc,
surfaces of substrates that may contain organic residues
(from residual photoresist for example).
-
'■ff
1
The resist is
literally burned away (oxidized) - hence the name:
"asher".
$
L
r
The default RF power is 80 watts and the
chamber pressure is typically 250 mT.
Ashing is
performed from 100 to 150 watts.
Figure A.7. Asher.
A.1.9 Solitec spinner station
The spinner station is
spincoat a wafer sample
used in this work to
with photoresist.
The
sample is centered on a vacuum chuck which is
subsequently rotated at a high rate of revolution for
a specified period of time. The RPM and spin time
determine the film thickness and uniformity.
Figure A.8 . Spinner station.
A.I.10 Tousimis Autosamdri 815B critical point dryer
The critical point dryer (CPD) used for this work waslocated in the fabrication lab of
the Radiation Laboratory.
The CPD was necessary inorder to dry MEMS devices after
the removal of the sacrificial layer.
The CPD allows for surface-tension-free liquid
drying. Drying without the CPD results in the "collapse" of free-standing structures due
to the surface tension of the liquid.
107
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A.2
Probe fabrication process
The following is a step-by-step listing of the procedures for the probe fabrication
process described in section 2.4 of this thesis.
A.2.1 GaAs bulk micromachined probes (125 pm x 125 pm x 100pm)
1. Cleave 1 cm x 1 cm sample of 100 pm thick (100) GaAs (probes).
2. Cleave four 1.5 cm x 1.5 cm samples of 500 pm thick Si (carrier wafers).
3. Clean samples (degrease): Acetone (CH 3 COCH3 ; non-polar clean) - 5 min,
Methanol (CH 3 OH; removes acetone) - 5min, IPA (CH 3 CHOHCH 3 ; polar clean)
- 5 min, N 2 dry.
4. Descum with plasma asher: 150 W, 250 mT, 3 min.
5. Dehydrate: 105 °C hotplate, 1 min.
6
. Spincoat HMDS (hexamethyldisilazane) on GaAs sample (for adhesion): 3.5
krpm, 30 sec.
7. Spincoat Shipley SC 1827 photoresist on GaAs sample: 3.5 krpm, 30 sec.
8
. Softbake: 105 °C hotplate, 1 min.
Note: After spin coating, the resist still contains up to 15% solvent and may
contain built-in stresses. The wafers are therefore soft baked to remove solvents
and stress and to promote adhesion of the resist layer to the wafer.
9. Align and expose edge removal photomask: 1 min, 20 mW/cm2.
10. Develop: MF351:DI H20 (1:5), 20-30 sec.
11. DI rinse: 2 min / 2 min.
12. Align and expose probe photomask: 15 sec, 20 mW/cm2.
13. Develop: 351 :DI (1:5), 25 sec.
14. DI rinse: 2 m in /2 min.
108
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15. Examine.
16. Cleave patterned GaAs sample into 4.
17. Place bead of clear wax on Si carrier.
18. Place Si carrier on hotplate: 130 °C, 1 min.
19. Mount patterned GaAs on Si carrier and flatten for no more than 2 minutes on
130 °C hotplate.
20. Cool sample in DI: 5 min.
2 1
. N 2 dry.
21. Examine.
22. Etch GaAs upside down: FLSO^IUC^DI (1:8:1) {Cooled overnight}, 15
min, then in 1 min increments as necessary. Note: the FESO^IUC^DI (1:8:1) wet
etch recipe was adopted from Yang [37].
23. Light N 2 dry.
24. Expose sample: 1 min, 20 mW/cm .
25. Develop: MF351:DI (1:5), 15 sec.
26. Quiet DI rinse: 2 min / 2 min.
27. Air / tissue dry.
28. Examine.
A.2.2 Fiber-to-GaAs Mounting
1. Mount fiber vertically on xyz translation stage.
2. Mount carrier wafer horizontally on xyz translation stage.
3. Mount two microscopes orthogonally in xy plane of carrier wafer.
4. Place a drop of UV cured adhesive on a glass slide.
5. Vertically translate fiber end onto drop of UV cured adhesive.
109
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. Remove excess adhesive by vertically translating fiber tip onto clean slide
(twice).
6
7. Align fiber tip over GaAs probe using microscopes.
8. Vertically translate fiber end onto GaAs probe.
9. Cure 14 minutes (3 left, 3 right, 1 left, then let UV gun cool; repeat).
10. Administer a drop of acetone onto carrier wafer.
11. Vertically translate fiber end to remove mounted probe.
12. Administer a drop of acetone onto probe end to remove excess clear-wax.
13. Heat cure probe at 50°C for 12 hours.
14. Cure 14 minutes (3 left, 3 right, 1 left, then let UV gun cool; repeat).
15. Perform transmission measurements (0.5 mW -> 8 mW @ 900nm).
16. Evaporate bragg reflector with SJ-26 (5 pairs of MgF2 /ZnSe 1406/833
angstroms; note: the MgF2/ZnSe mirror recipe was adopted from Yang [37]).
17. Inspect and test.
A.3
RF MEMS capacitive switch fabrication process
The following is a step-by-step listing of the procedures for the RF MEMS capacitive
switch fabrication process. The switch in chapter
6
was fabricated by the author. The
process and essential design were adopted from Pacheco and Peroulis [70], [71]. The
process is listed here for reference.
1. Cleave 3.5 cm x 3.5 cm sample of 400 pm thick (100) Si (high resistivity 2000 Q cm, double sided polished, 8500 angstrom S i02).
2. Pirania clean: H 2 S0 4 :H2 O2 1:1 (200 ml/200 ml) 10 min.
3. D IH 20 rinse.
110
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4. Thin SiCh to 2000 angstroms with BHF (buffered hydrofluoric acid); etch rate
is -2000 angstroms per minute). Rinse in DI H 2 O.
5. Descum (150 W, 250 mT, 3 min); dehydrate 105 °C 1 min.
6
. Sputter circuit layer (Ti/Au 500 angstroms /1 pm).
7. Spincoat SC 1827 (3.5 krpm, 30 sec).
8
. Softbake (105 °C, 1 min).
9. Align (center) circuit layer mask on wafer and expose (15 sec).
10. Develop MF351:DIH20 1:5 (30 sec).
11. Hardbake (130 °C, 1 min).
12. Descum (100 W, 250 mT, 1 min).
13. Au etch (~ 2 min; spec: 3000 angstroms/min).
14. DI H 2 O rinse (15 min).
15. Ti etch (HF:DI H20 1 :1 0 -4 sec).
16. D IH 2 O rinse.
17. Soak in hot PRS 2000 (overnight).
18. D IH 2 O rinse.
19. Soak Acetone/DPA (2/2 min).
20. Descum (150 W, 250 mT, 3 min).
21. Deposit - 2000 angstroms of Si3 N 4 with PECVD.
SiH4
NH 3
He
N2
100 seem
10 seem
900 seem
990 seem
Deposition pressure: 700 mT, RF power: 100 W,
deposition temperature: 400 °C, deposition rate: -180 angstroms/min.
Preclean: 20 min, postclean: 20 min.
Ill
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22. Clean Acetone/IP A (2/2 min)
23. Spincoat HMDS/Shipley SC1813 (3.5 krpm, 30 sec).
24. Softbake (105 °C, 1 min).
25. Align passivation mask and expose (7 sec).
26. Develop MF351:DI H20 1:5 (20 sec).
27. Hardbake (130 °C, 1 min).
28. Descum (100 W, 250 mT, 1 min).
29. RIE silicon nitride
CF4
0 2
40 seem
1 seem
Pressure: 100 mT, RF power: 100 W, etch rate: ~ 450 angstroms/min.
Preclean: 20 min, postclean: 20 min.
30. Soak in hot PRS 2000 overnight.
31. D IH 20 rinse.
32. Clean Acetone/IPA (2/2 min).
33. Descum (100 W, 250 mT, 1 min).
34. Spincoat HMDS/SCI827 (3.5 krpm, 30 sec) (Sacrificial layer).
35. Softbake (105 °C, 1 min).
36. Align anchor points and expose (18 sec).
37. Develop MF351:DI H20 1:5 (35 sec).
38. D IH 20 rinse.
39. Hardbake (160 °C, 3.5 min).
40. Descum (150 W, 250 mT, 3 min).
41. Sputter switch layer (1 pm Au @ 13 mT pressure).
112
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42. Spincoat SC 1813 (3.5 krpm, 30 sec)
43. Softbake (105 °C, 1 min).
44. Expose switch mask (8.5 sec).
45. Develop MF351:DI H20 1:1 (20 sec).
46. D IH 20 rinse.
47. Hardbake (130 °C, 1 min).
48. Descum (100 W, 250 mT, 1 min).
49. Au etch (~ 2 min).
50. D IH 20 rinse.
51. Soak in hot PRS 2000 overnight.
52. DI H20 rinse.
53. Wet transfer to IPA.
52. CPD release (ethanol soak).
113
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APPENDIX B
Optical sources
The optical source of femtosecond optical pulses used in this dissertation is the SpectraPhysics "Tsunami" mode-locked Ti:Sapphire laser. This appendix provides background
information regarding this optical source and its pump [77], [78].
B.l
Pump for Tirsapphire laser
The pump for the Ti:sapphire laser is the Spectra-Physics "Millennia" Class IV high
power laser. The "Millennia" is a diode-pumped, continuous-wave visible laser that can
produce greater than 5 watts of green 532 nm light.
The gain media is neodymium
yttrium vanadate (Nd:YV 0 4 ). A diode laser bar is used to excite the Nd3+ ions that are
doped in the yttrium vanadate host. Lasing occurs at 1064 nm. A non-criticallly phasematched, temperature tuned lithium triborate (LBO) nonlinear crystal is used to
frequency double the 1064 nm light to 532 nm in order to pump the Ti:sapphire laser in
its absorption band. A schematic of the "Millenia" laser is shown in Figure B.l.
B.2
Tirsapphire mode-locked laser
Titanium-doped sapphire has a broad absorption band in the blue and the green,
extending from 400 nm to 600 nm. The fluorescence band extends from 600 nm to
114
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Photodiode
Output Coupler
90° Polarization
Rotator
Frequency Doubling Arm
532 nm
B eam
Splitter
LBO
Crystal
T elescope
HR M.
Fiber
Bundle
Beam Delivery Arm
Z-Head
Dichroic M.
T elescope
HR M,
Nd:YV04 Gain Media
T elescope
HR M,
Aperture
Dichroic M.
Fiber Bundle
Figure B .l: Pump laser for Ti:sapphire mode-locked laser, {from ref. 77}
T i
greater than 1000 nm. A pump laser in the green excites the Ti
ion in the sapphire host.
In mode-locking, a large number of axial modes within the gain bandwidth are phase
locked by modulating the cavity loss. This produces short pulses with a repetition rate
given by the inverse of the cavity round-trip time. An acouto-optic modulator provides
active loss modulation.
The pulse itself provides for passive mode-locking. Passive
mode-locking is essential for short pulse durations much less than 1 ps. Two prism pairs
are used for management of cavity group velocity dispersion and for spatial wavelength
separation.
A slit aperture is used to select the wavelength range of interest.
The
"Tsunami" is tunable from 690 nm to 1080 nm. However, stable operation requires an
optimized mirror set. For this thesis, a mirror set for tunable operation between 780 and
920 nm is used. The output power at 900 nm is approximately 300 mW. The pulse width
exiting the cavity is approximately 100 femtoseconds. An active feedback loop (Spectra-
115
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physics "Lok-to-clock" option) adjusts the cavity spacing in order to maintain the pulse
repetition rate at 80 MHz with a jitter of less than 100 Hz.
A schematic of the
Ti:sapphire mode-locked laser with the "Lok-to-clock" option is shown in Figure B.2.
The "Tsunami" is a class IV laser.
Fast
Femtosecond System
M5
Pr1
Output
Brewster
Window
Photodiode
M8
Pr4 A0M M10
Pr2 Pr3
Beam
Me
Pump
Beam
Input
Brewster
Window
M3
Splitter
T u n in g
S lit
M9
MLPD
M4
PZT
Model 3955
AOMDriver Electronics
M2
•Residual
Pump
BeamDump
MotorizedM1
LTCPD
PZTErrorDriveSignal
External
Coarse Fine
Timing
Adjust
Level Detector
and Display
Servo
Electronics
Loop
Mon
Variable
Amplifier
Voltage
Controlled
Phase Shift
Photodiode In
Photodiode Out
Phase Detector
Motor
Controller
Internal
80 MHz
Reference
Oscillator
«<*—, Ref In
(BNC)
Frequency
80 MHz Out
Ref - 8
D iv id e r
Model 3930
Ref Out
Figure B.2: Ti:sapphire mode-locked laser, {from ref. 78}
116
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APPENDIX C
Optical indicatrix
The index ellipsoid (a.k.a. optical indicatrix) of zincblende crystals was used in chapter
5. A useful source for its derivation is Optical Waves in Crystals, by Yariv and Yeh [34].
The derivation is provided here for reference.
Gallium Arsenide (GaAs) possesses isotropic optical symmetry and belongs to the
cubic crystal system in point group 43m . The dielectric tensor, e , is:
V
£ - £0
0 0 "
0
n2
0
0
V
(C.l)
0
n2
J
where e0 is the permittivity of free space and n is the index of refraction. The
impermeability tensor,
77
, is defined as:
fj = £0£~X
(C-2)
where s~' is the inverse of the dielectric tensor. In the presence of an external
electric field, E , the impermeability tensor may be expanded in a Taylor series:
(C.3)
117
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(C.4)
where the indicies i, j, k follow the Einstein summation convention.
The
constants r p are the linear (or Pockels) electro-optic coefficients. In a lossless
and optically inactive medium, the dielectric tensor is symmetric.
Therefore,
indicies i and j may be permuted, allowing the use of contracted indicies for the
representation of the third rank tensor, rp . In this notation, the index ellipsoid (a
mathematical construct) takes the general form [34]:
V i j ( E ) x ix J
where
=1
(C.5)
defines the reference coordinate system (i = 1, 2, 3).
In the cubic crystal class, point group 43m, the electro-optic coefficients in
contracted notation are:
(C.6)
0 r4] 0
v °
0
r 41y
The resulting index ellipsoid is:
- j x f +- y
n
n
*2
+
n
+ 2r4XE xx 2x 2 + 2r4XE 2x xx 2 + 2 r4XE 2x xx 2 = 1
118
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(C.7)
APPENDIX D
Electromagnetic wave propagation in dispersive nonlinear media
The derivation o f the pulse propagation equation used in chapter 3 is presented in this
section. This derivation extends the pulse propagation equation found in Agarwal [79] to
include nonlinear absorption.
The wave equation in nonmagnetic source-free media is:
V xV xE = - \ ^ - c2 dt2
ju0^ 4
dt2
(DA)
where E is the electric field, P is the polarization vector, t is time, c is the speed of light
in vacuum, and ju0is the permeability of free-space.
Phenomenologically, far from
resonance, considering nonlinear effects through x ° ] '■
P (r,t) = PL(r,t) + PNL(rA)
(D2)
+CO
PL(r,t) = e„
(D.3)
-00
+C Q
Pn l(r,t) = s 0 JJ jV 3)(t - tx,t - 12,t - 13) IE (r ,tx)E ( r , t2)E ( F , t3)dtxdt2dt3
(DA)
—oo
where the polarization vector has been separated into a linear part, PL, and a nonlinear
part, PNL.
Assuming polarization preserving quasi-monochromatic fields,
119
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(D.6)
PL( r ,t ) = x ^ P L(r ,t)e - ‘-J + A p l\ T , ()«*"•'
= i i / 5« (F ,O e- " - ' + i i p » , (?,<)e+"-'
U>.7)
Hence,
f ) e ‘v e " J d (
(?,<) = *.
(D.8)
Assuming the nonlinear response is instantaneous:
\The envelope is then:
PM(r ,‘) = e . z Z \ \ E ( T , t t f E<r,t)
(£>.10)
Treating /Vz, as a small pertubation on P, the wave equation in Fourier domain becomes:
V '£ (F , o,-
m j + f 1+
(ffl)+ 1 * « l ^ . 0 | ! V„J£ ( F , - a>„) = 0
(£>.11)
+00
E(r,co-coo) - j£ (F , t ) e K“ - <u' ytd t
(D. 12)
—
oo
( a 13)
where k0 = co/c.
Assuming a solution of the form:
E(r,(o-G>0) = F (x,y)A (z, co-<j0o)e p°z
where F(x,y)is themodal distribution in, for example, an optical fiber,
slowly varying pulse
envelope, and
(DAA)
A(z,co-a>0) is the
is the wavenumber, results in the following
separated equations with eigenvalue p :
120
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d
2 F
( x , y )
(
d
2F
( x , y )
|
F
( x , y )
=0
(A 15)
d y 2
J- Pi )2(z,«>- a.) = o
2% 8/l(z’^ ^
(£>•16)
The first of the separated equations can be solved for the modal distribution by
approximating the expression in front of the k 2 with the square of the linear index,
n2(a ) . The eigenvalue fi then corresponds to the propagation constant /3{co) , where
P0 = j3{a>0) , and where the effective mode index is:
{DAI)
n-
Given the modal distribution and the propagation constant, the effect of the nonlinearity
can now be reintroduced into the first of the separated equations. Define:
la
\2
£{(Q) = l F X ^ ( ® ) + - X ^ x\E{r,t)\2 = n +2K
(£>.18)
n = n + n2\E(r ,t) f
(£>•19)
a = a + a ^E (/,t)\
(£>.20 )
where n is the linear index, n2 is the nonlinear index, a is the linear absorption
coefficient, and a 2 is the nonlinear absorption coefficient. The dielectric constant, e((o),
can be written as
s{co) = (n + An)2 « n2 + 2nAn
(£>.2 1)
An - n2\E(r,t)\2 +-^a
2 k„
(£>.22 )
For nonzero An, the first of the separated equations is assumed to continue to yield the
same modal distribution F(x,y) but with a perturbed eigenvalue:
121
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(27. 23)
P (a ) = P(G>) + A/?
+00
KJ
A/7 = -
, y )|2<2«/y
-oo________________
+00
(27.24)
j J|27(x,y)|2r/xr/y
where the nonlinearity is weighted by the modal field distribution. Expanding P(a>) in a
Taylor series about co0 yields:
P(a>) = P(a>0) + {a-co0)
dp
2 (?P
dco2
dco
+
(27. 25)
.
Using this expression in the second separation equation and taking the inverse Fourier
transform yields:
MilO =_ fi SAM
az
where
n
a
,s .
2
af
c 2 Aeff
’ 2
i 2
^
^ (z,0 = 3 _1{2(z,cy-£yo)}
(27.27)
Pi
dp
dco
(27.28)
P2 =
d2p
dco1
(27.29)
+oo
+OJ
(27.30)
J j |F ( x ,y ) |2J x ^ y J j] F ( x ,y ) |2c&c/y
The pulse propagates at the group velocity, vg, given by:
1
Pi
Define the "local time" variable, T, as:
122
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(27.31)
The resulting pulse propagation equation is then:
=
az
A T ) _a
+ A
2
8T 2
c
2
2
(£>.33)
1
2 2
Aar
123
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BIBLIOGRAPHY
124
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BIBLIOGRAPHY
[1] Y. Gao and I. Wolff, "A New Miniature Magnetic Field Probe for Measuring ThreeDimensional Fields in Planar High-Frequency Circuits," IEEE Transactions on
Microwave Theory and Techniques, vol. 44, pp. 911-918, June 1996.
[2] Y. Gao and I. Wolff, “Miniature electric near-field probes for measuring 3-D fields in
planar microwave circuits,” IEEE Transactions on Microwave Theory and
Techniques, vol. 46, pp. 907-913, July 1998.
[3] T. P. Budka and G. M. Rebeiz, “A microwave circuit electric field imager,” in 1995
IEEEM TT-SInt. Microwave Symp. Dig., vol. 3, pp. 1139-1142, May 1995.
[4] U. Mueller, C. Boehm, J. Sprengepiel, C. Roths, E. Kubalek, A. Beyer, “Geometrical
and Voltage Resolution of Electrical Sampling Scanning Force Microscopy," in
1994 IEEE MTT-S Int. Microwave Symp. Dig., vol. 2, pp. 1005-1008, May 1994.
[5] C. Bohm, C. Roths, and E. Kubalek, “Contactless electric characterization of MMIC’s
by device internal electrical sampling scanning-force-microscopy,” in 1994 IEEE
MTT-S Int. Microwave Symp. Dig., vol. 3, pp. 1605-1608, May 1994.
[6] G. Chiu, J. Halbout, P. May, "High-speed electron beam testing," Journal of Vacuum
Science and Technology B, vol. 6, pp. 1814-1819, November/December 1988.
[7] J. A. Valdmanis, G. Mourou, and C. W. Gabel, “Picosecond electro-optic sampling
system”, Applied Physics Letters, vol. 41, pp. 211-212, August 1982.
[8] M. Shinagawa and T. Nagatsuma, “Electro-optic sampling using an external GaAs
probe tip,” Electronics Letters, vol. 26, pp. 1341-1343, Aug. 1990.
[9] M. R. Freeman, R. R. Ruf, and R. J. Gambino, “Picosecond Pulsed Magnetic Fields
for Studies of Ultrafast Magnetic Phenomena”, IEEE Transactions on Magnetics,
vol. 27, pp. 4840-4842, Nov. 1991.
[10] W. Batty, A. J. Panks, R. G. Johnson and C. M. Snowden, "Electro-thermal
modeling and measurement for spatial power combining at millimeter wavelengths,"
IEEE Transactions on Microwave Theory and Techniques, vol. MTT-47, pp. 25742585, Dec. 1999.
125
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[11] H. M. Gutierrez, C. E. Christoffersen, and M. B. Steer, "An integrated environment
for the simulation of electrical, thermal and electromagnetic interactions in highperformance integrated circuits,” in IEEE 8th Topical Meeting on Electrical
Performance o f Electronic Packaging, pp. 217-20, Oct. 1999.
[12] R. G. Johnson, C. M. Snowden and R. D. Pollard, "A physics-based electro-thermal
model for microwave and millimeter wave HEMTs,” in 1997 IEEE MTT-S Int.
Microwave Symp. Dig., vol. 3, pp. 1485-1488, June 1997.
[13] N. S. Cheng, P. Jia, D. B. Rensch and R. A. York, “A 120-W X-band spatially
combined solid-state amplifier,” IEEE Transactions on Microwave Theory and
Techniques, vol. MTT-47, pp. 2557-2561, Dec. 1999.
[14] J. Hubert, L. Mirth, S. Ortiz and A. Mortazawi, "A 4 Watt Ka-band quasi-optical
amplifier,” in 1999 IEEE MTT-S Int. Microwave Symp. Dig., vol. 2, pp. 551-554,
June 1999.
[15] J. Rizk, E. Chaiban, G. M. Rebeiz, “Steady State Thermal Analysis and High-Power
Reliability Considerations of RF MEMS Capacitive Switches,” in IEEE MTT-S Int.
Microwave Symp. Dig., vol. 1, June 2002, pp. 239-242.
[16] W. Thiel, K. Tomquist, R. Reano, L. P. B. Katehi, “A Study of Thermal Effects in
RF-MEM-Switches using a Time Domain Approach,” in IEEE MTT-S Int.
Microwave Symp. Dig., vol. 1, June 2002, pp. 235-238.
[17] J. A. Valdmanis and S. S. Pei, "A non-contact picosecond prober for integrated
circuit testing," in Picosecond Electronics and Optoelectronics, New York:
Springer-Verlag, 1987.
[18] J.A. Valdmanis, "Electro-optic measurement techniques for picosecond materials,
devices, and integrated circuits," in Semiconductors and Semimetals, vol. 28. New
York: Academic, 1990.
[19] B. H. Kolner, and D. M. Bloom, “Electrooptic Sampling in GaAs Integrated
Circuits”, IEEE Journal o f Quantum Electronics, vol. QE-22, pp. 79-93, January
1986.
[20] K. J. Weingarten, M. J. W. Rodwell, D. M. Bloom, “Picosecond Optical Sampling of
GaAs Integrated Circuits”, IEEE Journal o f Quantum Electronics, vol. QE-24, pp.
198-220, February 1988.
[21] Y. V. Gulyaev, Y. L. Kopylov, V. B. Kravchencko, V. V. Kucha, V. V. Kutsaenko,
V. T. Potapov, R. V. Shpilevskii, "Fiber optical electric field sensor,", Sov. Phys.
Tech. Phys, vol. 29, pp. 1064-1065, September 1984.
126
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[22] V. K. Gorchakov, V. V. Kutsaenko, V. T. Potapov, "Fiber optical sensor for an rf
electric field,", Sov. Phys. Tech. Phys, vol. 36, pp. 347-349, March 1991.
[23] S. Wakana, T. Ohara, M. Abe, E. Yamazaki, M. Kishi, and M. Tsuchiya, “Fiberedge electrooptic/magnetooptic probe for spectral-domain analysis of
electromagnetic field,” IEEE Transactions on Microwave Theory and Techniques,
vol. MTT-48, pp. 2611-2616, Dec. 2000.
[24] K. Yang, L. P. B. Katehi, and J. F. Whitaker, “Electric-field mapping system using
an optical-fiber-based electro-optic probe,” IEEE Microwave and Wireless
Components Letters, vol. 11, pp. 164-166, Apr. 2001.
[25] K. E. Meyer, G. A. Mourou, "Two-dimensional E-field mapping with subpicosecond
resolution," in Picosecond Electronics and Optoelectronics, New York: SpringerVerlag, pp. 54-57, 1985.
[26] J. F. Whitaker, J. A. Valdmanis, T. A Jackson, K. B. Bhasin, R. Romanofsky, G. A.
Mourou, "External electro-optic probing of millimeter-wave integrated circuits," in
1989 IEEE MTT-S Int. Microwave Symp. Dig., vol. 1, pp. 221-224, June 1989.
[27] T. Nagatsuma, T. Shibata, E. Sano, A. Iwata, "Subpicosecond sampling using a
noncontact electro-optic probe," Journal o f Applied Physics, vol. 66, pp. 4001-4009,
November 1989.
[28] K. Kamogawa, I. Toyoda, K. Nishikawa, T. Tokumitsu, "Characterization of a
Monolithic Slot Antenna Using an Electro-Optic Sampling Technique," IEEE
Microwave and Guided Wave Letters, vol. 4, pp. 414-416, December 1994.
[29] G. David, D. Jagerr, R. Tempel, I. Wolff, "Analysis of microwave propagation
effects using two-dimensional electrooptic field mapping techniques," Opt.
Quantum Electron., vol. 28, pp. 919-932, 1996.
[30] K. Yang, G. David, S. V. Robertson, J. F. Whitaker, L. P. B. Katehi, "Electro-optic
mapping of near-field distributions in integrated microwave circuits," IEEE
Transactions on Microwave Theory and Techniques, vol. 46, pp. 2338-2343,
December 1998.
[31] K. Yang, G. David, J. G. Yook, I. Papapolymerou, L. P. B. Katehi, J. F. Whitaker,
“Electro-optic mapping and finite-element modeling of the near-field pattern of a
microstrip patch antenna,” IEEE Transactions on Microwave Theory and
Techniques, vol. 48, pp. 288-294, Feb 2000.
[32] M. N. Deeter, A. H. Rose, G. W. Day, "Fast, sensitive, magnetic field sensors based
on the Faraday effect in YIG," Journal of Lightwave Technology, vol. 8, pp. 18381842, December 1990.
127
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[33] J. A. Riordan, F. G. Sun, Z. G. Lu, and X. C. Zhang, “Free-space transient magnetooptic sampling”, Applied Physics Letters, vol. 71, pp. 1452-1454, September 1997.
[34] A. Yariv and P. Yeh, Optical Waves in Crystals, John Wiley & Sons, Inc., New
York, 1984.
[35] K. Kyuma, S. Tai, T. Sawada, and M. Nunoshita, “Fiber-Optic Instrument for
Temperature Measurement”, IEEE Journal of Quantum Electronics, vol. QE-18, pp.
676-679, April 1982.
[36] S. R. Johnson, and T. Tiedje, “Temperature dependence of the Urbach edge in
GaAs”, Journal of Applied Physics, vol. 78, pp. 5609-5613, November 1995.
[37] K. Yang, Application o f Ultrafast Optical Techniques to the Characterization o f
MM-Wave Integrated Circuits and Radiating Structures, Ph.D. thesis, University of
Michigan, Ann Arbor, MI, 2001.
[38] Y. P. Varshni, “Temperature dependence of the energy gap in semiconductors,”
Physica, vol. 34, pp. 149-154, May 1967.
[39] H. C. Casey, D. D. Sell, and K. W. Wecht, “Concentration dependence of the
absorption coefficient for n- and p-type GaAs between 1.3 and 1.6 eV,” Journal o f
Applied Physics, vol. 46, pp. 250-257, Jan. 1975.
[40] R. F. Harrington, Time-Harmonic Electromagnetic Fields, McGraw-Hill, New York,
1961.
[41] Ansoft Maxwell HFSS, Release 6, 1998.
[42] T. Nagatsuma, T. Shibata, E. Sano, and A. Iwata, “Subpicosecond sampling using a
noncontact electro-optic probe”, Journal o f Applied Physics, vol. 66, pp. 4001-4009,
Nov. 1989.
[43] D. Conn, X. Wu, J. Song, and K. Nickerson, “A full wave simulation of disturbances
in picosecond signals by electro-optic probing,” in 1992 IEEE MTT-S Int.
Microwave Symp. Dig., pp. 665-668, June 1992.
[44] X. Wu, D. Conn, J. Song, and K. Nickerson, “Invasiveness of LiTa03 and GaAs
probes in external E -0 sampling”, Journal of Lightwave Technology, vol. 11, pp.
448-454, March 1993.
[45] M. Y. Frankel, J. F. Whitaker, G. A. Mourou, and A. Valdmanis, “Experimental
characterization of external electrooptic probes,” IEEE Microwave and Guided
Wave Letters, vol. 1, pp. 60-62, Mar. 1991.
128
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[46] G. Liang, Y. Liu, and K. Mei, “Full-wave analysis of coplanar waveguide and
slotline using the time-domain finite-difference method,” IEEE Transactions on
Microwave Theory and Techniques, vol. 37, pp. 1949-1957, Dec. 1989.
[47] Hewlett-Packard EEsof Series IV Libra 6.1, 1997.
[48] A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in
dispersive dielectric fibers. II. Normal dispersion,” Applied Physics Letters, vol. 23,
pp. 171-172, Aug. 1973.
[49] T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, and E. W. Van Stryland,
“Optical Limiting in GaAs,” IEEE Journal o f Quantum Electronics, vol. QE-21, pp.
488-494, May 1985.
[50] F. P. Incropera and D. P. De Witt, Fundamentals o f Heat and Mass Transfer, 3rd
ed., Wiley and Sons, 1990.
[51] D. T. F. Marple, “Refractive index of GaAs,” Journal o f Applied Physics, vol. 35,
pp. 1241-42, Apr. 1964.
[52] S. R. Johnson, and T. Tiedje, “Temperature Dependence of the Urbach Edge in
GaAs,” Journal of Applied Physics, vol. 78, pp. 5609-5613, Nov. 1995.
[53] C. R. Pidgeon, B. S. Wherrett, A. M. Johnston, J. Dempsey, and A. Miller, “TwoPhoton Absorption in Zinc-Blende Semiconductors,” Physical Review Letters, vol.
42, pp. 1785-1788, Jun. 1979.
[54] Ansoft, Maxwell 3D Version 9, Pittsburgh, PA, 2002.
[55] A. J. C. Grellier, N. K. Zayer, and C. N. Pannell, “Heat Transfer Modelling in C02
Laser Processing of Optical Fibers,” Optics Communications, vol. 152, pp. 324-328,
Jul. 1998.
[56] S. M. Sze, Physics o f Semiconductor Devices, 2nd Ed., Wiley and Sons, 1981.
[57] C. S. Namba, “Electro-optical effect of zincblende,” Journal of the Optical Society
of America., vol. 51, pp. 76-79, Jan. 1961.
[58] R. Reano, K. Yang, L. P. B. Katehi, and J. F. Whitaker, “Simultaneous
measurements of electric and thermal fields utilizing an electrooptic semiconductor
probe,” IEEE Transactions on Microwave Theory and Techniques, vol. 49, pp.
2523-2531, Dec. 2001.
[59] K. Yang, L. P. B. Katehi, and J. F. Whitaker, “Electro-optic field mapping system
utilizing external gallium arsenide probes,” Applied Physics Letters, vol. 77, pp.
486-488, July 2000.
129
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[60] L. Duvillaret, S. Rialland, and J. L. Coutaz, “Electro-optic sensors for electric field
measurements. II. Choice of the crystals and complete optimization of their
orientation,” Journal o f the Optical Society o f America B, vol. 19, pp. 2704-2715,
November 2002.
[61] Ansoft HFSS Release 8, Pittsburgh, PA, 2001.
[62] K. R. Carver and J. W. Mink, “Microstrip Antenna Technology,” IEEE Transactions
on Antennas and Propagation, vol. AP-29, pp. 2-24, Jan. 1981.
[63] R. M. Reano, D. Peroulis, J. F. Whitaker, L. P. B. Katehi, “Electro/thermal
Measurements of RF MEMS Capacitive Switches," in 2003 IEEE MTT-S Int.
Microwave Symposium Digest, vol. 3, pp. 1923-1926, June 2003.
[64] W. Thiel, "A Surface Impedance Approach for Modeling Transmission Line Losses
in FDTD", IEEE Microwave and Guided Wave Letters, vol. 10, pp. 89-91, March
2000 .
[65] J. W. Thomas, Numerical Partial Differential Equations, Finite Difference Methods,
New York: Springer, 1995.
[66] A. J. Chapman, Fundamentals o f Heating Transfer, McMillan Publishing, New
York, 1987.
[67] D. M. Pozar, Microwave Engineering, 2nd Ed., John Wiley and Sons, Inc., New
York, 1998.
[68] W. L. Stutzman and G. A. Thiele, Antenna Theory and Design, 2nd Ed., John Wiley
and Sons, Inc., 1998.
[69] W. P. Harokopus, High-Frequency Characterization o f Open Microstrip
Discontinuities, PhD thesis, The University of Michigan, Ann Arbor, MI, 1991.
[70] S. P. Pacheco, C. T. Nguyen, L. P. B. Katehi, “Design of Low Actuation Voltage
RF MEMS Switch,” IEEE MTT-S Int. Microwave Symp. Dig., vol. 1, pp. 165-168,
June 2000.
[71] D. Peroulis, S. P. Pacheco, K. Sarabandi, L. P. B. Katehi, “Electromechanical
Considerations in Developing Low-Voltage RF MEMS Switches” IEEE
Transactions on Microwave Theory and Techniques, vol. 51, pp. 259-270, January
2003.
[72] K. Ando, W. Zaets, and K. Watanabe, “Diluted Magnetic Semiconductor MagnetoOptic Waveguides for Monolithic-Integration with Semiconductor Optic Devices”,
1998 Mat. Res. Soc. Symp. Proc. Vol. 517, pp. 625 - 631, April 1998.
130
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[73] R. M. Reano, J. F. Whitaker, L. P. B. Katehi, “Field-tunable probe for combined
electric and magnetic field measurements,” in 2002 IEEE MTT-S Int. Microwave
Symposium Digest, vol. 3, pp. 1513-1516, June 2002.
[74] R. M. Reano, L. P. B. Katehi, J. F. Whitaker, “Resonant-cavity magnetic field probe
for millimeter-wave frequency domain spatial field mapping,” 2002 Optical Society
o f America Thirteenth International Conference on Ultrafast Phenomena Technical
Digest, vol. 72, pp. 129-130, May 2002.
[75] R. M. Reano, W. Thiel, L. P. B. Katehi, J. F. Whitaker, “Measured and simulated
electric, magnetic, and thermal field distributions of a patch antenna operating at
high power,” 2002 IEEE Antennas and Propagation Society International
Symposium Digest, vol. 1, pp. 886-889, June 2002.
[76] J. S. Hayden III, High-Performance Digital X-Band and Ka-Band Distributed
MEMS Phase Shifters, Ph.D. thesis, University of Michigan, Ann Arbor, MI, 2002.
[77] Spectra-Physics, Tsunami Mode-Locked Ti:sapphire Laser Users Manual, May
1995.
[78] Spectra-Physics, Millenia Users Manual, March 1997.
[79] G. P. Agarwal, Nonlinear Fiber Optics 3rd ed., Academic Press, San Diego, CA
1989.
131
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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