close

Вход

Забыли?

вход по аккаунту

?

Microwave phase conjugation using artificial nonlinear microwave surfaces

код для вставкиСкачать
INFORM ATION TO USERS
This manuscript has been reproduced from the microfilm master. TJMI
films the text directly from the original or copy submitted. Thus, some
thesis and dissertation copies are in typewriter face, while others may be
from any type o f computer printer.
The quality of this reproduction is dependent upon the quality of the
copy submitted. Broken or indistinct print, colored or poor quality
illustrations and photographs, print bleedthrough, substandard margins,
and improper alignment can adversely afreet reproduction.
In the unlikely event that the author did not send UMI a complete
manuscript and there are missing pages, these will be noted.
Also, if
unauthorized copyright material had to be removed, a note will indicate
the deletion.
Oversize materials (e.g., maps, drawings, charts) are reproduced by
sectioning the original, beginning at the upper left-hand ccmer and
continuing from left to right in equal sections with small overlaps. Each
original is also photographed in one exposure and is included in reduced
form at the back of the book.
Photographs included in the original manuscript have been reproduced
xerographically in this copy. Higher quality 6” x 9” black and white
photographic prints are available for any photographs or illustrations
appearing in this copy for an additional charge. Contact UMI directly to
order.
UMI
A Bell & Howell Information Company
300 North Zed) Road, Ann Arbor MI 48106-1346 USA
313/761-4700 800/521-0600
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
UNIVERSITY OF CALIFORNIA
Los Angeles
Microwave Phase Conjugation
Using Artificial Nonlinear Microwave Surfaces
A dissertation submitted in partial satisfaction of the
requirements for the degree Doctor of Philosophy
in Physics
by
Yian Chang
1997
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
UMI Number: 9725976
Copyright 1997 by
Chang, Yian
All rights reserved.
UMI Microform 9725976
Copyright 1997, by UMI Company. All rights reserved.
This microform edition is protected against unauthorized
copying under Title 17, United States Code.
UMI
300 North Zeeb Road
Ann Arbor, MI 48103
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
© Copyright by
Yian Chang
1997
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The dissertation of Yian Chang is approved.
Ian McLean
Seth J. Pui
J^ e p h A . Rudnick, Committee Co-chair
Harold R
Committee
University of California, Los Angeles
1997
ii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
DEDICATION
To my parents
iii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table of Contents
DEDICATION
.........................................................................................................
iii
.....................................................................................................
iv
List of Figures
.........................................................................................................
vii
List of Tables
............................................................................................................
xi
.......................................................................................
xii
Table of Contents
ACKNOWLEDGMENTS
VITA
......................................................................................................................
PUBLICATIONS AND PRESENTATIONS
ABSTRACT OF THE DISSERTATION
1. INTRODUCTION
.........................................................
.............................................................
...............................................................................................
1.1 Phase-Conjugate Electromagnetic Waves
.....................................................
1.2 Phase Conjugation Using Degenerate Four-Wave Mixing
1.3 Phase Conjugation Using Three-Wave Mixing
..........................
.........................................
iv
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
xiv
xv
xvii
1
5
9
12
2. MICROWAVE PHASE CONJUGATION
.......................................................
15
.................................................
15
..................................................................................
17
2.1
Difficulties to Extend Optical Techniques
2.2
Artificial Kerr Media
2.3
Artificial Nonlinear MicrowaveSurfaces
...................................................
20
3. MICROWAVE PHASE CONJUGATION USING ELECTRICALLY INJECTED
ARTIFICIAL NONLINEAR SURFACES
3.1
Phase-Conjugate Element
.......................................................
31
.........................................................................
32
3.2 8-Element Electrically Injected Artificial Nonlinear Microwave Array
3.3
38
Microwave Phase Conjugation Demonstration Using Electrically Injected Pump
Signal
4.
....
...........................................................................................................
43
MICROWAVE PHASE CONJUGATION USING OPTICALLY INJECTED
ARTIFICIAL NONLINEAR MICROWAVE SURFACES
4.1
.............................
8-Element Optically Injected Artificial Nonlinear Microwave Array
......
62
62
4.2 Microwave Phase Conjugation Demonstration Using Optically Injected Pump
Signal
4.3
5.
...........................................................................................................
Information Transmission Using Phase Conjugation
................................
79
...........................................................
82
..............................................................................
82
DISCUSSION AND CONCLUSIONS
5.1
Suggested Future Work
69
v
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5.2 Potential Applications
.................................................................................
86
.................................................................................................
87
............................................................................................................
90
5.3 Conclusions
Bibliography
vi
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
List of Figures
1.1. Phase-conjugate retrodirectivity compared to reflection and regular retrodirectivity.
................................................................................................................................
1.2. Phase aberration
3
correction.........................................................................
7
1.3. Degenerate four-wave mixing phase conjugation setup......................................
10
1.4. Degenerate four-wave mixing from a holographic point of view.......................
II
1.5. Three-wave mixing phase conjugation setup.......................................................
13
2.1. Four different types of artificial Kerr media........................................................
18
2.2. Grating formation of a suspension of elongated particles by rotationalmechanism.
........................................................................................................................................19
2.3. Microwave phase conjugation using MEMS arrays............................................
21
2.4. The concept of artificial nonlinear microwave surfaces......................................
22
2.5. Microwave phase conjugation using artificial nonlinear microwave surfaces.
23
2.6. Theoretical electric field magnitude distribution using 8 conjugate elements.
27
2.7. Theoretical electric field magnitude distribution using 40 conjugate elements.
28
2.8. Theoretical electric field magnitude distribution using 200 conjugateelements with
small element spacing..........................................................................................
29
3.1. An ideal phase-conjugate element configuration................................................
33
3.2. The real phase-conjugate element configuration................................................
35
3.3. Triple-balanced mixer configuration..................................................................
37
vii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3.4. The 8-element artificial nonlinear microwave surface using electrical injection.
39
3.5. RF distribution and phase-amplitude measurement setup...................................
40
3.6. Traces recorded using a digital sampling oscilloscope for matching all phaseconjugate elements...............................................................................................
42
3.7. Linearity measurement setup...............................................................................
44
3.8. Output power versus input power for an electrically injected phase-conjugate
element.................................................................................................................
45
3.9. The experimental setup used for measuring the electric field magnitude distribution.
..............................................................................................................................
46
3.10. The contour plots of the electric field distribution for a single source, using
electrical injection, with and without distortion..................................................
50
3.11. The surface plot of the electric field distribution for a single source, using electrical
injection, without distortion.................................................................................
51
3.12. The surface plot of the electric field distribution for a single source, using electrical
injection, with distortion......................................................................................
52
3.13. The electric field magnitude of the conjugate beam versus time, using electrical
injection, with and without distortion.................................................................
54
3.14. The contour plots of the electric field distribution for a single source, using
electrical injection, with and without distortion in front of the transmit hom.
55
3.15. The surface plot of the electric field distribution for a single source, using electrical
injection, with distortion in front of the transmit hom........................................
V lll
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
56
3.16. The contour plots of the electric field distribution for two sources, using electrical
injection, with and without distortion..................................................................
58
3.17. The surface plot of the electric field distribution for two sources, using electrical
injection, without distortion.................................................................................
59
3.18. The surface plot of the electric field distribution for two sources, using electrical
injection, with distortion......................................................................................
60
4.1. The 8-element artificial nonlinear microwave surface using optical injection.
63
4.2. The structure of a typical Mach-Zehnder modulator...........................................
65
4.3. The transfer function of a typical Mach-Zehnder modulator..............................
66
4.4. Output power versus input power for an optically injected phase-conjugate element.
68
4.5. The contour plots of the electric field distribution for a single source, using optical
injection, with and without distortion..................................................................
70
4.6. The surface plot of the electric field distribution for a single source, using optical
injection, without distortion.................................................................................
71
4.7. The surface plot of the electric field distribution for a single source, using optical
injection, with distortion......................................................................................
72
4.8. The electric field magnitude of the conjugate beam versus time, using optical
injection, with and without distortion..................................................................
4.9.
73
The electric field magnitude of the conjugate beam versus time, using optical
injection, with and without distortion at different positions...............................
ix
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
75
4.10. The contour plots o f the electric field distribution for two sources, using optical
injection, with and without distortion..................................................................
76
4.11. The surface plot of the electric field distribution for two sources, using optical
injection, without distortion.................................................................................
77
4.12. The surface plot of the electric field distribution for two sources, using optical
injection, with distortion......................................................................................
78
4.13. Detected spectra at different angles with a 10 modulation on the 20.48 GHz pump
signal.....................................................................................................................
80
5.1. An artificial nonlinear microwave surface formed by monolithic one-dimensional
arrays....................................................................................................................
83
5.2. Phase-conjugate element using two-stage mixing...............................................
84
5.3. Free space microwave power amplifier using a phase conjugator......................
88
x
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
List of Tables
2.1. Phase-conjugate wave generation efficiency comparison.
xi
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ACKNOWLEDGMENTS
It is a pleasure for me to acknowledge the people who have given me the help and
encouragement that made this dissertation possible.
First and foremost, I would like to express my deep appreciation to my thesis
advisor Professor Harold R. Fetterman for directing and supporting this work, for
countless valuable discussions and suggestions, and for so much encouragement and
moral support.
I am especially grateful to my co-advisor Professor Joseph A. Rudnick for his
important help and support, and for his encouragement during my years at UCLA. I
would also like to thank Professor Ian McLean and Professor Seth J. Putterman for their
time and efforts in service on my doctoral committee. In addition, I would like to thank
Professor Robert W. Hellwarth of USC for his valuable suggestions.
Special thanks go to Irwin L. Newberg at Hughes Aircraft Company for his
assistance on the necessary microwave components and for his valuable suggestions. I
also highly appreciate Matt Espiau from the Center for High Frequency Electronics at
UCLA for providing well-maintained equipment, valuable discussions, skilled technical
assistance, and his moral support. In addition, I would like to thank Steve K. Panaretos at
Hughes Aircraft Company for his assistance on microwave antenna arrays. Without their
kind help, this work would not be possible.
xii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I would also like to thank current and former members of Professor Fetterman’s
group for all the kind assistance and valuable discussions, and for the friendship we have
shared together. They are Daipayan Bhattacharya, David C. Scott, Heman Erlig, Datong
Chen, Shamino Wang, D. P. Prakash, Dr. Boris Tsap, Dr. Wenshen Wang, and
Mohammed E. Ali. Special thanks go to Daipayan for proofreading this manuscript, for
inspiring discussions, for providing moral support and encouragement, and for being my
roommate in the past three years.
I would like to express my special appreciation to Dr. Howard Schlossberg at Air
Force Office of Scientific Research for his support and encouragement to this study.
Finally and most importantly, I am deeply grateful to my parents, to my sister, to
my uncles and aunts, and to my relatives for their consideration and encouragement.
xui
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
V IT A
1965
Bora, Taipei, Taiwan, Republic of China (R.O.C.)
1984-1988
B.S. in Physics, National Tsing Hua University
1988-1990
Research Assistant, National Tsing Hua University
xiv
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
PUBLICATIONS AND PRESENTATIONS
Y. Chang, B. Tsap, H. R. Fetterman, D. A. Cohen, A. F. J. Levi, and I. L. Newberg,
“Optically controlled serially fed phased-array transmitter,” IEEE Microwave and Guided
Wave Letters, vol. 7, no. 3, pp. 69-71, 1997.
Y. Chang, H. R. Fetterman, D. A. Cohen, A. F. J. Levi, and I. L. Newberg, “Opticallycontrolled serially-fed phased array system,” Technical Digest, IEEE Lasers and ElectroOptics Society 1996 Annual Meeting Conference Proceedings, vol. 2, pp. 54-55, Nov. 1821, 1996.
Y. Chang, D. C. Scott, and H. R. Fetterman, “Microwave phase conjugation using arrays
of nonlinear optically pumped devices,” Technical Digest, SBMO/IEEE MTT-S
International Microwave and Optoelectronics Conference Proceedings, vol. 2, pp. 909913, July 24-27, 1995.
Y. Chang, D. C. Scott, and H. R. Fetterman, “Microwave phase conjugation using
antenna coupled nonlinear optically pumped surfaces,” Technical Digest, IEEE MTT-S
International Microwave Symposium, vol. 3, pp. 1303-1306, May 16-20, 1995.
xv
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
D. A. Cohen, Y. Chang, A. F. J. Levi, H. R. Fetterman, and I. L. Newberg, “Optically
controlled serially fed phased array sensor,” IEEE Photonics Technology Letters, vol. 8,
no. 12, pp. 1683-1685, 1996.
L. Eldada, R. Scarmozzino, R. M. Osgood, Jr., D. C. Scott, Y. Chang, and H. R.
Fetterman, “Laser-fabricated delay lines in GaAs for optically steered phased-array
radar," Journal o f Lightwave Technology, vol. 13, no. 10, pp. 2034-2040, 1995.
H. R. Fetterman, Y. Chang, D. C. Scott, S. R. Forrest, F. M. Espiau, M. Wu, D. V. Plant,
J. R. Kelly, A. Mather, W. H. Steier, R. M. Osgood, Jr., H. A. Haus, and G. J. Simonis,
“Optically controlled phased array radar receiver using SLM switched real time delays,”
IEEE Microwave and Guided Wave Letters, vol. 5, no. 11, pp. 414-416, 1995.
xvi
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ABSTRACT OF THE DISSERTATION
Microwave Phase Conjugation
Using Artificial Nonlinear Microwave Surfaces
by
Yian Chang
Doctor of Philosophy in Physics
University of California, Los Angeles, 1997
Professor Joseph A. Rudnick, Co-chair
Professor Harold R. Fetterman, Co-chair
A new technique is developed and demonstrated to simulate nonlinear materials in the
microwave and millimeter wave regime. Such materials are required to extend nonlinear
optical techniques into longer wavelength areas.
Using an array of antenna coupled
mixers as an artificial nonlinear surface, we have demonstrated two-dimensional free
space microwave phase conjugation at 10 GHz. The basic concept is to replace the weak
nonlinearity of electron distribution in a crystal with the strong nonlinear V-I response of
a P-N junction. This demonstration uses a three-wave mixing method with the effective
nonlinear susceptibility x(2) provided by an artificial nonlinear surface. The pump signal
xvii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
at 2 a) (20 GHz) can be injected to the mixing elements electrically or optically. Electrical
injection was first used to prove the concept of artificial nonlinear surfaces. However,
due to the loss and size of microwave components, electrical injection is not practical for
an array of artificial nonlinear surfaces, as would be needed in a three-dimensional free
space phase conjugation setup. Therefore optical injection was implemented to carry the
2 eo microwave pump signal in phase to all mixing elements.
In both cases, two-
dimensional free space phase conjugation was observed by directly measuring the electric
field amplitude and phase distribution. The electric field wavefronts exhibited retro­
directivity and auto-correction characteristics o f phase conjugation. This demonstration
surface also shows a power gain of 10 dB, which is desired for potential communication
applications.
xviii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1. INTRODUCTION
The scientific and engineering communities have been interested in constructing
wavefronts of electromagnetic waves for many years.
There has been a significant
amount of theoretical and experimental work on this subject. The development of such
techniques in the microwave and millimeter wave (MMW) regime has been concentrated
in phased array antennas. [1] The idea behind these phased arrays is fairly simple: by
controlling the amplitudes and phases of smaller antenna elements, a “lens” can be
constructed dynamically to generate or to focus any wavefronts. In the past decade,
researchers have been trying to realize systems with broadband capabilities. The most
promising concept calls for true time delays (TTDs) of the MMW signals.
For a
broadband array, the wavefront shape and direction should be independent of the
frequency.
This requires the propagation time of the signal to an array element be
independent of the frequency.
Traditional phase shifter arrays generate frequency
independent phase delays directly, therefore the equivalent time delays depend on the
frequency. This limits the bandwidth to a very narrow region. In a TTD system, MMW
signals are processed in the time domain directly to avoid any frequency dependency in
the generated time delays. Therefore TTD systems can provide broadband operations.
Unfortunately because of the loss and size constraints of MMW components, such TTD
systems are difficult to build. However, fiber optic systems have been introduced as a
mean of overcoming these obstacles. Optically controlled phased arrays [2, 3, 4] use
1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
lightweight and low loss fiber optics to generate time-delayed signals. These systems use
laser light modulated at MMW frequencies, which are subsequently processed with
optical components. The delayed MMW signals are then extracted from the optical
carrier and used for radiation or signal processing.
The goal of this study is to
demonstrate a special type of optically controlled phased array that can be treated as a
new artificial medium for generating MMW phase conjugation (MPC) and other
nonlinear optics analogies. These phased arrays will be referred to as artificial nonlinear
microwave surfaces (ANMSs) throughout this dissertation.
Since its first demonstration, optical phase conjugation (OPC) has been studied
intensively.
Most of this interest can be traced to potential applications in imaging
processing and in dynamic compensation for distortion.
This technique utilizes the
nonlinear susceptibility of a medium to reverse the phase factor of an incoming wave.
The phase-conjugate wave propagates backward and has the same wavefronts as that of
the incoming wave. [5, 6, 7] Fig. 1.1 shows this feature in comparison with regular
reflection and retrodirectivity. This unique property of phase-conjugate waves is useful
in applications requiring automatic pointing and tracking [8], phase aberration corrections
[9], phase-conjugate resonators [10, 11, 12], and many other devices. To date, most of
the phase conjugation development has been concentrated in the optical (visible and IR)
regime. Efforts to extend this technique to MMW have encountered severe difficulties
due to the small nonlinearity of crystals and the low power density at these wavelengths.
In the search for alternative materials suitable for the use in MMW nonlinear optics,
2
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Phase
Conjugator
i b
Phase Conjugation
Mirror
Reflection
Corner
Reflector
Regular Retrodirectivity
Fig. 1.1.
Phase-conjugate retrodirectivity compared to reflection and regular
retrodirectivity.
3
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
artificial media were found to have much larger nonlinearities than that of crystals.
Using shaped microparticle suspensions, microwave phase conjugation has been
demonstrated in a waveguide environment using a degenerate four-wave mixing
(DFWM) technique. [13]
In this study, two-dimensional free space MPC has been
demonstrated using an ANMS.
In the following sections, the basic concept of phase conjugation and two
traditional phase-conjugate generation techniques of nonlinear optics are reviewed and
discussed.
In chapter 2, we concentrate on microwave and millimeter wave phase
conjugation. The difficulties of phase-conjugate generation in this regime are analyzed
first, followed by two techniques using artificial Kerr media to extend existing nonlinear
optical approaches.
We then present the concept and theory of our technique in
generating microwave phase-conjugate waves.
Chapter 3 contains the experimental setups and results of a two-dimensional
microwave phase conjugation demonstration using an artificial nonlinear microwave
surface with electrically injected pump signals. Retrodirectivity and automatic phase
correction characteristics of phase conjugation are proven using direct electric field
distribution measurements.
In chapter 4, we present the experimental setups and results of optically controlled
microwave phase conjugation.
As in chapter 3, the same detection techniques have
successfully verified phase conjugation properties.
The capability of transmitting
4
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
information using a phase-conjugate wave is then demonstrated by modulating the pump
signal and detecting the transmitted data near the source.
In chapter 5, we discuss possible extensions and potential applications of
nonlinear artificial microwave surfaces. After that discussion, we summarize this study
and present our conclusions.
1.1 Phase-Conjugate Electromagnetic Waves
Let’s consider an electromagnetic wave propagating along the positive z direction. Its
electric field can be written as:
E = A(r)e'l<uf' fc'?,(r)1 + c.c.
(1.1)
where co is the frequency and k is the wave number of the monochromatic optical wave.
The amplitude A and the phase <pare real functions of position r. Normally A is a slow
varying function of z compared with e'[" 'fc' ?’(r)l, therefore the wave propagation can be
understood in terms of the motion of wavefronts, which are three-dimensional surfaces
defined by:
kz + <p(r) = constant
(1.2)
The phase-conjugate wave of equation 1.1 is defined as:
E c = A(r)e'[" +fc+¥’(r)I + c.c.
By comparing
(1.3)
equation1.1 and equation 1.3, we find the two waves have the same
wavefronts at any pointin space, but they travel in oppositedirections.
Wealso notice
5
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
that the conjugate wave can be obtained by a time reversal t - * - t transformation, or by
taking the complex conjugate only on the spatial part of the electric field.
To appreciate the property of phase conjugation, let’s consider a plane wave
propagating through a distorting medium such as clouds in atmosphere. Because o f the
nonuniform distribution o f refractive index n(r), the incident wavefronts are no longer
planar after passing through the distorting medium, as shown in Fig. 1.2. From definition
equation 1.3, we have seen that the conjugate wave has the same wavefronts as those of
the incident wave. To prove that the conjugate wave satisfies Maxwell’s equations and
therefore can propagate backward as a time reversed incident wave through space and the
distortion, we consider the wave equation:
V, E
d E
c 2 dt2
he
where fj. isthe permeability o f
the medium is s and P
jvz .
the
4n n o BE _ Ann d Psl
c 2 dt
c2 dt2
( {4)
medium and <ris its conductivity.Thepermittivity of
is the induced nonlinear polarization in the medium. In deriving
equation 1.4, we have assumed the fractional changes of e and fi are small within one
wavelength. Now let’s define complex amplitude:
a(r) = A(r)e~'p(r)
(1.5)
then, electric field can be written as:
E = a (r)e'(ay"fc) + c.c.
Ec =a*(r )e,{a,+kz)+c.c.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
( 1.6)
Phase
Conjugator
Distorting
Medium ^
Fig. 1.2. Distorted wavefronts will be auto-corrected after phase conjugation and passing
through the same distorting medium the second time.
7
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
If we consider the waves are propagating in a medium that has negligible loss and
nonlinear effects, as in most of the interested cases, the wave equation 1.4 can be written
as:
V2a + ^ - n 2 - k 2 a - 2 i k — = 0
c
dz
using the slowly varying envelope approximation d%a, «
dz2
(1.7)
da.
k ,—
J dz
Now taking a
mathematical complex conjugate of equation 1.7, we obtain:
G> n 2 -,k2
V2a ’ + —p
c
a ' + 2/*— = 0
dz
( 1-8)
Equation 1.8 is the wave equation for an electromagnetic wave traveling in the negative z
direction with the following form:
E'c = a'(r)e'(" +fc) + c.c.
(1.9)
provided a' = aa* for all positions, where a is an arbitrary constant. Therefore we have
shown that the conjugate wave satisfies Maxwell’s equations. Since equation 1.8 is first
order in z, a' can be determined for all positions if it’s known on some plane z = z0.
Physically, this means that if we generate a conjugate field Ec on some plane, this field
will remain the phase-conjugate of E everywhere and it will propagate backward with
wavefronts which coincide with those of the incident wave. This is one of the key issues
to accomplish phase conjugation using artificial nonlinear microwave surfaces, as it will
be explained in the next chapter.
8
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1.2 Phase Conjugation Using Degenerate Four-Wave Mixing
In the optical regime, there have been many techniques to generate phase-conjugate
waves. One of the most efficient and common methods is DFWM [5, 6, 7, 14]. The
basic configuration of a DFWM experiment is shown in Fig. 1.3. In a lossless isotropic
nonlinear medium, the induced polarization is in the same direction as the electric field,
and can be written as:
P = Z mE + Z (2)E 2 + Z 0)E 2 +■■■
where
zln) is the n^-order susceptibility of the medium.
( 1. 10)
In DFWM phase conjugation
experiments, the useful nonlinear polarization is PNL = ^ (3>£ 3. Of all possible thirdorder terms that arise from £ 3, we are interested only in the terms that satisfy the
frequency and momentum relation:
6). + a , = o>, + co-, = 2co
k, +k4 = k2 +k3
( 1.1 1 )
'
The quantum-mechanical picture of the process involves annihilation of a photon from
each pump wave with the simultaneous creation of a photon for both the incident and the
phase-conjugate wave. From a holographic point of view, the conjugate phase generation
process can be explained by grating formation inside a z 0) medium, as shown in Fig.
1.4. Index gratings are formed by the interference of a pump beam and the incident
beam. The other pump beam is then Bragg scattered to form the phase-conjugate wave.
The total radiated conjugate wave is due to the coherent superposition of both processes.
9
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Pump
E2(o>)
Incident
Nonline ar Me diu m
Ei(co)
Phase-Conjugate
E4(cd)
Pump
E3(co)
Fig. 1.3. Basic configuration of degenerate four-wave mixing phase conjugation setup.
10
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
E2
Pump (Write)
Incident
(Object)
Phase-Conjugate
(Image)
Pump (Read)
Pump (Read)
e4
PhaseConjugate
(Image)
jk
m
Ei
Incident (Object)
nil
Pump (Write)
Fig. 1.4. Degenerate four-wave mixing from a holographic point of view. In the first
case, El and E2 form the grating to Bragg scatter E3 into E4. In the second case, El and
E3 form another grating to Bragg scatter E2 into E4. The final conjugate wave will be a
coherent sum of these two possibilities.
11
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
One way to quantify the efficiency of DFWM is by defining the phase-conjugate
reflectivity R:
" w 5-
(u2)
where A4(0) is the electric field amplitude of the conjugate beam at the output plane of
the nonlinear medium and At0 is the amplitude of the incident beam before it enters the
medium. Under the assumptions of negligible absorption and undepleted equal-intensity
pumps, R can be written as: [15]
R = tan2(— )
4
3 2 ;rV //>
—
cX
K 5 = ----------
where L is the interaction length and
k
is called the four-wave mixing coefficient. From
equation 1.13 we can see that if kL is greater than 1, the conjugate beam will be more
powerful than the incident beam. The difficulties of MPC will be discussed based on this
equation in the next chapter.
1.3 Phase Conjugation Using Three-Wave Mixing
Theoretically, phase conjugation can also be achieved through three-wave mixing
(TWM) in a nonlinear medium. The basic configuration is shown in Fig. 1.5. Instead of
using the third order susceptibility %0) as in DFWM, the second order
is utilized.
12
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Pump E2(2a)
Incident E^o)
Nonlinear M ed iu m
< 4 .............................
Phase-Conjugate
E3(co)
Mirror
Fig. 1.5. Conceptual configuration of three-wave mixing phase conjugation setup.
13
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
In this technique, the incident beam and the pump beam create a polarization wave in the
%(2) medium:
(1.14)
This polarization wave will excite an electromagnetic wave E, with the conjugate phase
of the incident wave. However if we apply the frequency and momentum relation:
0)i = C02 - 6 ) j = 2 o ) - a ) = 6 )
(1.15)
k, =k2 -k , =2k- k =k
Equation 1.15 shows that this excited wave E, travels along with the incident beam
although it carries the conjugate phase. Therefore the propagation direction of E, has to
be reversed in order to form the conjugate beam £ 3. This can be accomplished with a
regular mirror, as shown in the setup. Yet, since there is no simple way to separate the
excited beam from the incident beam for reflection correction, the above mentioned
TWM technique has difficulties to be realized. However, if the %(2) medium has large
enough nonlinearity so that only a thin layer of such medium is needed, the momentum
relation can be relaxed and TWM can be realized. Since ANMSs satisfy this criterion,
TWM is used for microwave phase conjugation in this study.
The details will be
explained in the following chapters.
14
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2. MICROWAVE PHASE CONJUGATION
2.1 Difficulties to Extend Optical Techniques
Based on the great success of optical phase conjugation, the most straight forward
thought to accomplish microwave phase conjugation is simply to extend the well
developed OPC techniques to microwave and millimeter wave regime.
However, a
closer look at the efficiency of phase-conjugate wave generation will show this extension
is not a trivial problem. Let’s use DFWM as an example. From equation 1.13, the fourwave mixing coefficient
k
is directly proportional to both %0) and the pump intensity
I P, and inversely proportional to the free space wavelength X . At visible and infrared
wavelengths, pump sources can readily achieve power levels of tens to hundreds of
MW/cm2 . In MMW regime, typical laboratory signal sources are usually limited to
under \K W /c m 2 because the beam cannot be focused down to spot sizes smaller than X
due to diffraction limits. This five orders of magnitude reduction of I p in conjunction
with four orders o f magnitude increase of X will lower
k
by nine orders of magnitude.
These considerations, summarized in Table 2.1, suggest that OPC techniques cannot be
extended to MMW wavelengths unless novel materials with nonlinear susceptibilities on
the order of 10' 3 to 10"4 cm-s2/ g can be found.
15
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Parameter
Visible
Microwave
/I
0.5 ion
3 cm
h
108 Wjcm2
103 W/cm2
Z (3)
10"'° cm -s2/ g
10'10 cm -s2/ g
K
21 cm~l
3.5x lO '9 cm'1
L
1 mm
30 cm
kL
2.1
l.lxlO'7
R
161 (Gain)
7.5xlO-15 (Negligible)
Table 2.1. Phase-conjugate wave generation efficiency comparison between visible and
microwave frequencies.
16
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2.2 Artificial Kerr Media
In search for alternative materials suitable for the use in MMW extension of OPC
techniques, much larger nonlinearity can be found in artificial Kerr media [16] than that
in traditional nonlinear crystals. In general, the rather large nonlinear susceptibility of
these artificial materials originates from the motion of macroscopic objects in fluid
suspensions. Four types of suspended particle behavior: translation [16], rotation [17,
18], compression [19], and deformation [20] are shown in Fig. 2.1. Under the influence
of the pump beams and the probe beam in a DFWM experiment, these suspensions form
holographic gratings that consist of periodic spatial distribution. Fig. 2.2 shows a grating
of suspended particles formed through rotational mechanism.
Although these artificial Kerr media have demonstrated j(3 )
as high as
10"4 cm - s2/ g [21], they bear some intrinsic problems. Due to the required movements
of macroscopic particles in viscous fluid, these media suffer from the slow response time.
For the translation type particles, it can take as long as a few days for the grating to form
in the fluid. The other three types are faster, but it can still take tens of seconds to form
the grating. This precludes the use of these artificial Kerr media involving any applicable
frequency changes. Another disadvantage of these media is that motion and vibration can
easily disturb the gratings formed in fluid.
Another different class of artificial Kerr media has been proposed. It involves the
use o f micro-electromechanical systems (MEMS) as the source of z ° ]. [22] Instead of
having particles suspended in fluid, rotating rods can be manufactured on a silicon wafer
17
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Translation
Low
Field
Rotation
/
Compression Deformation
•
High
Field
Fig. 2.1. Four different types of artificial Kerr media.
18
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(0
o
a.
■H
Light Intensity
c
o
Position
Fig. 2.2. Two-dimensional view of the grating formation of a suspension of elongated
particles by rotational mechanism as a function of light intensity.
19
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
through photolithography techniques.
Structures with metal coated dielectric beams
supported by polyimide torsional springs, as shown in Fig. 2.3, have demonstrated
grating formation suitable for DFWM in MMW regime [23]. In these artificial media the
torque needed to rotate the springs has to be small in order to exhibit large nonlinearity.
However this requirement makes the springs so fragile that slight airflow or vibration
may damage the structures. This problem has not yet been solved.
2.3 Artificial Nonlinear Microwave Surfaces
Because of all the above mentioned difficulties in achieving microwave phase
conjugation with traditional DFWM technique, this study approaches the problem from a
very different perspective. Instead of using the third order mixing as in DFWM, the
second order mixing is used in a three-wave mixing configuration. To avoid the phase
matching problem mentioned in 1.3, we need a medium with very high nonlinearity so
that only a “sheet” of such material will be used. To satisfy this requirement, we turn to
the nonlinear V-I characteristic of diodes. Microwave circuits that combine antennas and
microwave mixers, as shown in Fig. 2.4, can effectively replace the nonlinear dipoles of a
medium.
The idea is to “sample” the incident wave at different positions of the
wavefront and then generate phase-conjugate currents using microwave mixers. These
currents will then excite a phase-conjugate field at each sampling point. The combined
field of all elements will be the phase-conjugate wave of the incident beam.
This
sampling concept is shown in Fig. 2.5. It was proposed in the 60’s, but due to the lack of
20
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
aa
aa
aaa
i
■>
»
.
!i
Rexolite Frame
Metal Covered
Dielectric Beams
\
Polyimide String
Polyimide Supporting Frame
Fig. 2.3.
Two-dimensional arrays of rotating MEMS elements stacked into three-
dimensional structure.
21
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Nonlinear Dipoles
Nonlinear Medium
Microwave Mixing Elements
Artificial Nonlinear Microwave Surface
Fig. 2.4. Nonlinear dipoles in a nonlinear medium can be simulated by microwave
mixing elements. Because of its high nonlinearity, only a “sheet” of such medium is
required for generating phase-conjugate waves.
22
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
V
V
Fig. 2.5.
First, the incident wavefront is sampled at different positions. Then each
element generates a phase-conjugate current using microwave circuitry. This current will
excite a phase-conjugate field at the sampling point. The superposition of these fields
becomes the phase-conjugate wave.
23
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
modern semiconductor and optical technologies, researchers did not have a practical way
to realize the concept. [24, 25] To understand how the conjugate signal can be generated
at each element using microwave circuitry, let’s consider the incident wave shown in
equation 1.1. At the/*1element, the electric field is:
E = A(ry)e,(‘“"’’/) + c.c.
(2.1)
<P, = k - r , + P (r,)
(2.2)
where
The signal picked up by the antenna and then sent to the mixer can be written as:
Fj l ocA(rJ)e'(01" Vl)+c.c.
(2.3)
The 2(0 pump signal has to be delivered to all elements at the sameamplitude and phase;
otherwise the mixed output will contain a term other than V]X that depends on j. If this
happens, the sum of the excited field at each element will be distorted and will not form
the conjugate beam. Consider the 2co pump signal delivered to the mixer is:
Vj2 = Ce110* + c.c.
(2.4)
For a diode, the ideal current-voltage relation can be written as:
I = I , ( e " " kT- l )
(2.5)
where Is is the reverse saturation current. At room temperature with small input signal:
2 Z -+ l< s L )'
kT
2 kT
( 2 .6 )
When we apply V = VjX + Vj2 to the diode, the second term of equation 2.6 is nonlinear
and will give us a current component:
24
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I c oze2"*
= e'{M+*‘)
(2.7)
This current component has the conjugate phase + <p} instead of the input phase - (p} .
Therefore when it is delivered to the antenna, it will excite the conjugate field at ry.
Eq fry) * A(ry
1+ C £ .
X
When the sampling spacing is less than —, the combined field E r
2
(2.8)
) forms
i
the phase-conjugate wave on the sampling surface. In the previous chapter we have
proven that if phase-conjugate field is generated on a plane, it will propagate backward
and be conjugate to the incident beam everywhere.
In the above discussion we ignored all other current components in equation 2.6.
With a single diode as the mixing device, these components will exist in the output
current and will destroy the formation of the phase-conjugate wave. However, by using
multiple diodes in a triple-balanced mixer configuration, these unwanted components can
be cancelled. The details will be discussed in the next chapter.
Another important point we need to address is the effect of finite number of
elements. To demonstrate this effect, the phase-conjugate wave of a dipole source has
been calculated for three arrays having different number of elements. The first array is
formed by 8 elements, the second one by 40 elements, and the third one by 200 elements.
For the 8- and 40-element arrays, the spacing between elements is 0.467A. The 200element array has a spacing of 0.093/1, which is one-fifth of that of the 40-element array.
Therefore the 40-element array has five times the aperture size of the 8-element one, with
the same sampling density. And the 200-element array has the same aperture size as the
25
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
40-element one but with five times the sampling density. The antenna elements are
assumed to have dipole radiation patterns: [26]
E(r) oc
2/
Lw
2
1
c o s tfr +
{krY
[ kr
J
’
/
1
sin
(kr)2 (kr)3
(2.9)
where 6 is the angle between the dipole axis and the position vector r .
The source is located at (57.9,15.6) for all three cases.
Fig. 2.6 shows the
conjugate electric field magnitude distribution for the 8-element array at a given time. It
clearly exhibits retrodirectivity but does not show the conjugate beam focusing back to
the source.
This is caused by the diffraction effect of a small aperture size.
conjugate electric field “snapshot” of the 40-element array is shown in Fig2.7.
The
It
demonstrates fairly well wavefront reconstruction as both retrodirectivity and focusing
can be clearly seen. The conjugate field distribution of the 200-element array, shown in
Fig. 2.8, displays little improvement over the 40-element one. Therefore a sampling
spacing slightly less than — is acceptable for most cases. If the spacing is greater than
X
—, grating sidelobes can develop and therefore destroy the conjugate wavefront patterns.
From these comparisons, we have seen the main factor determining the resolution
2
is not the sampling density, as long as it is greater than —, but the aperture size. If we
X
require the phase conjugator to have a high resolving power, equally spaced arrays with
X
< — spacing, like the examples, will not be practical as the number of elements will be
astronomical. For example, a resolving power of 10"5 to 10~'t rad would require 4x 108
26
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
8-Element Array
Fig. 2.6. The “snapshot” of the conjugate electric field magnitude generated by an 8element array. The element spacing is 0.4672. and a dipole source is located at (57.9,
15.6), as marked by the arrow.
Only retrodirectivity is observable because of the
diffraction effect.
27
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
40-Element Array
Fig. 2.7. The “snapshot” of the conjugate electric field magnitude generated by a 40element array. The element spacing is 0.4672 and a dipole source is located at (57.9,
15.6), as marked by the arrow.
Both retrodirectivity and focusing can be observed
clearly.
28
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
200-Element Array
Fig. 2.8. The “snapshot” of the conjugate electric field magnitude generated by a 200element array. The element spacing is 0.093Z and a dipole source is located at (57.9,
15.6), as marked by the arrow. Although the sampling density is increased by five times,
compared to that of the 40-element array, no significant improvement in the conjugate
field.
29
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
to 4 x l0 10 elements. Using randomly distributed elements over the aperture to prevent
the development of grating lobes can solve this problem [27].
30
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3.
MICROWAVE PHASE CONJUGATION USING
ELECTRICALLY INJECTED ARTIFICIAL NONLINEAR
SURFACES
The concepts of microwave phase conjugation using artificial nonlinear surfaces have
been discussed in the previous chapters. To prove the feasibility of this approach, we
build an array of 8 phase-conjugate elements to demonstrate the generation of phaseconjugate waves.
The equipment and devices available to us limit the number of
elements used in the demonstration. Although an 8-element surface will not be able to
focus a diverging incident beam back to its source due to diffraction limitations, as
mentioned in the previous chapter, it can exhibit retrodirectivity and phase auto­
correction when distortion medium exists in the beam path.
These two key
characteristics of phase conjugation are strong evidences of the feasibility of this
technique.
It has been mentioned earlier that optical injection of the pump signal 2co is the
crucial technique for constructing a full size artificial nonlinear microwave surface
because of the large loss, size, and weight of microwave components. However, for an 8element demonstration surface, it is feasible and more straightforward to build using
electrical (direct microwave) injection of the pump signal. Therefore we will discuss the
construction and measurements of an electrically injected surface first in this chapter. Its
optically injected counterpart will be considered in the next chapter.
31
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3.1 Phase-Conjugate Element
As mentioned in the previous chapter, each element on an artificial nonlinear microwave
surface will generate the conjugate field at that sampling point. Fig. 3.1 shows an ideal
elementary configuration. The sampled signal goes through a circulator into a low noise
amplifier. This amplifier provides the compensation to the conversion loss of the mixing
process in the next step. It can also provide a gain so that the conjugate signal is more
intense than the input one. After mixing with the 2a) pump signal in a mixer, the signal
carries the conjugate phase and it is sent to the sampling antenna through the circulator.
In this configuration, the antenna has to be very efficient.
The reason is that any
reflection of the conjugate signal from the antenna will go through the circulator as it
were the sampled incident signal. This would affect the phase of the output signal and
thus destroy the conjugate-phase generation. If the reflection is large enough, the circuit
will even start oscillating by itself. To study this more closely, let’s assume the return
loss of the antenna is R, the gain of the amplifier is G and the conversion loss of the
mixer is C. R, G, and C are complex output to input voltage ratios to include the phase
change at each stage.
The circulator and the mixer are assumed to be perfect, no
unwanted signal leakage between their ports. In order to generate the phase-conjugate
wave, we require the reflected conjugate signal be much smaller than the sampled signal.
This requirement can be written as:
G C R « 1
And when G •C • R = 1, the system starts to oscillate.
32
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(3.1)
Antenna
RF
Circulator
Mixer
Low Noise
Amplifier
LO
2ca
Fig. 3.1. An ideal phase-conjugate element: a single antenna samples the incident wave
and excites the conjugate wave at the same position. A circulator directs the incoming
and outgoing signals to and from two different ports. An amplifier is added to the
element to provide gain.
33
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Commercial mixers normally have a conversion loss around 10 dB, which
corresponds to |c| = 0.32. With a specially designed narrow band antenna array, a 30 dB
return loss can be achieved. This corresponds to |/?| = 0.032. Equation 3.1 gives us
|C/|« 1 0 0 . If we choose |G| = 10, the phase-conjugate signal will be a hundred times
more powerful. Unfortunately, the antenna array available to us has a return loss about 7
dB at the desired 10.24 GHz, which corresponds to |i?| = 0.45. This high reflection is a
side effect of the wide band design of the antenna. Applying equation 3.1, we obtain
|<7|« 7. Basically this means there can be no gain in this phase-conjugate element.
Therefore somehow we need to reduce the antenna reflection.
Since we plan to demonstrate two-dimensional free space phase conjugation using
a one-dimensional artificial nonlinear microwave array.
Instead of designing new
antennas, we have chosen to separate the transmit and the receive antennas. This means
the sampling of the incident field and the excitation of the conjugate field happen at the
same (x, y) coordinates but slightly different z coordinate. This small shift in the z
direction will only disturb the electric field distribution on the z = 0 plane to a negligible
level.
The modified elementary configuration used in this study is shown in Fig. 3.2.
The amplitude adjustment and phase adjustment have been added to the configuration to
compensate any differences between the phase-conjugate elements.
adjustment is achieved by inserting different attenuators.
Amplitude
Changing the length of a
variable delay line accomplishes the phase adjustment. The low noise amplifier used in
34
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
w
Transmit
Antenna
Phase
Adjustment
w
J\
—
Mixer
Receive
Antenna
Fig. 3.2.
Amplitude
Adjustment
B andpass
Filter
Low Noise
Amplifier
The configuration of a phase-conjugate element used in this study.
The
transmit and the receive antennas are separated. A bandpass filter, a phase adjustment,
and an amplitude adjustment are added to the circuit.
35
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the setup provides 30 dB of power gain with 1 - 1 8 GHz bandwidth. This wideband
amplifier is used not because the experiment needs the bandwidth but because of the
availability of amplifiers to us. Because of this wide gain bandwidth, a bandpass filter is
used to limit only the desired frequency enters the mixing element. This will lower the
noise of the system and prevent two-frequency oscillations.
possible to have two signals with frequencies
Without the filter, it is
and o)2 oscillating in the element if
to, + o)2 = 2co is satisfied and the coupling between the transmit and the receive antennas
are large enough at cox and co2. The passband of the filter used is centered at the desired
signal frequency 10.24 GHz, with a 3 dB bandwidth of 50 MHz. This filter can be
removed if the amplifier has a narrower bandwidth around 1 - 2 GHz.
The mixer is the key component of a phase-conjugate element. It provides the
nonlinearity for generating the phase-conjugate wave.
In this study, MY50C triple-
balanced mixers from Watkins-Johnson are used. As mentioned in the previous chapter,
using a single diode as the mixing element will result in unwanted current components.
These unwanted components can be minimized by using multiple diodes configured as a
triple-balanced mixer shown in Fig. 3.3. [28]
As an example, the linear current
component at the IF port from the LO port through diode D1 will be cancelled by that
through D4. And the component at the IF port from the RF port through D1 will be
cancelled by that through D6. With this help, the leakage from the input (RF) to the
output port (IF) o f the mixer is about 20 dB lower. The conversion loss of these mixers
at 10.24 GHz input and output signals with 20.48 GHz LO (pump) signal is around 10
36
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
h-O
RF
Fig. 3.3.
Triple-balanced mixer configuration: unwanted current components are
cancelled through the use of two double-balanced bridges.
37
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
dB. Therefore the unwanted 10.24 GHz input leakage is 10 dB smaller than the desired
phase-conjugate output signal. This can be further reduced by using two-stage mixing,
which will be discussed in the last chapter.
3.2 8-Element Electrically Injected Artificial Nonlinear Microwave
Array
After discussed individual phase-conjugate element, we now concentrate on the
8
-
element array used in this study to demonstrate microwave phase conjugation. In the first
demonstration, the
2
a pump signal is delivered to each phase-conjugate element
electrically. Fig 3.4 shows this configuration. The 10.24 GHz (of) signal is frequency
doubled to 20.48 GHz using a frequency doubling amplifier made by Acurrel. This 2o)
signal is then further amplified using a Hughes travelling wave amplifier to 25 dBm. The
signal then undergoes a l-to-2 power splitting followed by two l-to-4 power splittings to
form
8
20.48 GHz pump signals at 5.5 dBm for the 8 phase-conjugate elements.
Because discrete components are used, these eight phase-conjugate elements are
not exactly the same in terms of output amplitude and phase. This is why we need to
have the amplitude adjustment and the phase adjustment in each element. All these
elements have to be adjusted after the 2o) pump signals have been connected. To be able
to adjust both phase and amplitude, we have to find a way to measure them at 10.24 GHz
accurately. Fig. 3.5 shows the measuring setup. The “a) signal output” is connected to
38
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
To Transmit Antenna *1
From Racshra Antanna #1
To Transmit Antanna #2
From Racaiva Antanna *2
Power
Splitter
To Transmit Antanna (3
From Racaiva Antanna #3
To Transmit Antenna M
From Racaiva Antanna M
Power
Splitter
To Transmit Antenna #5
From Racaiva Antenna 15
To Transmit Antenna M
From Racaiva Antanna M
Power
Splitter
To Transmit Antanna #7
From Racaiva Antanna *7
To Tranamit Antenna W
From Racaiva Antenna 18
cd Signal
from
Synthesizer
Frequency Doubler
Fig. 3.4. The 8 -element artificial nonlinear microwave surface using electrical injection
for the 2 co pump signal.
39
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Digital Sampling
Oscilloscope
Fig. 3.5. RF distribution and phase-amplitude measurement setup.
40
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the input port o f a phase-conjugate element and the output from that element is sent back
to the
“ <0
signal input”. Part of the 10.24 GHz signal from the synthesizer is used to
trigger the digital sampling oscilloscope. Another portion of the signal is sent to the
channel 2 of the oscilloscope as a reference signal.
The conjugate signal from the
undertesting element is amplified and sent to the channel 1 of the oscilloscope. The
waveforms of these two 10.24 GHz sinusoidal signals are recorded by a computer. Fig.
3.6 is an example of the recordings.
Discrete Fourier transforms are then applied to the two traces to obtain their
complex amplitudes at the first harmonic frequency 10.24 GHz. All other components of
Fourier transformations are discarded as noises. The real amplitudes and phases of the
two signals are then calculated. By subtracting the channel 1 phase from the channel 2
phase, the relative phase of the conjugate signal can be measured accurately.
To
understand this, assume there is a Atp jittering in the synthesizer. This Atp will reflect
on the measured channel 1 phase. The jitter of the 2at pump signal will be 2Acp because
of the frequency doubling process.
Because the conjugate wave is formed through
difference frequency generation, its jitter will be 2Atp-Atp = Atp. Therefore this Atp
jitter can be removed by subtracting channel 1 phase from channel 2 phase. The accuracy
of this phase measurement is better than 1 ps in time domain. Also, by dividing the
channel 2 amplitude with the channel
1
amplitude, the relative amplitude of the conjugate
signal can be measured accurately.
Using this measurement setup, the amplitudes of all phase-conjugate elements are
first matched, with different attenuators, to within ± 2% . The phases are then matched to
41
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
200
100
1
9
0
-100
-200
-300
-400
0
20
40
60
80
100
120
140
160
180
200
Time (ps)
Fig. 3.6. This is a typical pair of traces recorded using the digital sampling oscilloscope
for adjusting the phase and amplitude of each phase-conjugate element. The CHI signal
is the conjugate output from an element and the CH2 signal is the reference.
components have been added to the two signals for a better viewing result.
42
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
DC
within ± 0.2 ps (0.2 %) by adjusting the variable delay line of each element. These
adjustments are accomplished at an input power level about -50 dBm. To ensure the
elements will still be matched at other input power levels, linearity tests are performed
using the setup shown in Fig. 3.7.
In this linearity test, a power meter is used to measure the output power of
conjugate elements against different input power.
A computer controlled variable
attenuator is used to change the input power of the undertesting phase-conjugate element.
First, the input power at each attenuator setting is measured with the power meter and
recorded by the computer.
Then the output power o f the undertesting element is
measured at each attenuator setting and recorded. Fig. 3.8 is an example of the results. It
shows excellent linearity with an 18 dB of power gain.
All the
8
phase-conjugate
elements have similar results. Therefore these elements are matched well across a wide
input power range and can now be used to demonstrate microwave phase conjugation.
3.3 Microwave Phase Conjugation Demonstration Using Electrically
Injected Pump Signal
To demonstrate microwave phase conjugation using the
8
-element artificial nonlinear
microwave surface, we prepare an electric field mapping setup in an anechoic chamber.
This setup is shown in Fig. 3.9.
As mentioned earlier, the transmit and the receive antennas of the conjugator are
separated in the z direction (height) by 1.4 cm. This small spacing will only perturb the
43
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
a Signal from
Computer Controlled
Variable Attenuator
2oo Pump
Signal
Synthesizer
Fig. 3.7. This experimental setup is used to measure the linearity of the phase-conjugate
elements with respect to the input power.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-25
-30
eg -35
-45
-50
-70
-65
-60
-55
-50
-45
-40
Input Power (dBm)
Fig. 3.8. The output power of a phase-conjugate element versus the input power. It
demonstrates excellent linearity with an 18 dB of power gain. All
8
elements have
similar results.
45
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Transmit
Horn #1
Transmit
Phase Conjugate
Antenna Array Element Array
*
Receive
Hom
Transmit
Hom #2
Receive
Antenna Array
Amplitude
and Phase
Measurement
Fig. 3.9.
This setup is used to map out two-dimensional electric field magnitude
distribution. The receive horn is at a lower height than the transmit horns to prevent
blocking of the incident beams. It can be moved to different positions (p, <p) to measure
the electric field strength.
46
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
electric field distribution on the z = 0 plane to a negligible level. Although two transmit
horns are shown in the figure, some experiments are conducted with only one hom
connected to the synthesized source. The transmit horns are slightly higher than and
tilted toward the conjugator. Both transmit horns are 60 cm from the conjugator. This
distance is chosen because of the sizes of the chamber and the conjugator. The receive
hom is slightly lower than and tilted toward the conjugator.
The height difference
between the receive hom and the transmit homs is needed to avoid the incident beams
being blocked by the receive hom.
The receive hom is mounted on a translation stage for radial movement.
Its
distance to the conjugator (p) can be varied from 25 cm to 55 cm. The translation stage
itself is mounted on a stepping motor stage for angular control. This rotation stage can
cover angles (<j)) between -30° to +30° with a resolution of 0.1°. Its motion is controlled
by a computer. The signal detected by the receive hom is proportional to the electric
field at that point and is sent to the “ m signal input” port of the phase-amplitude
measuring setup, which has been mentioned earlier and shown in Fig. 3.5. The “co
signal output” port of the measuring setup provides the 10.24 GHz signals for the
transmit homs.
To measure the electric field distribution of the conjugate beam within a chosen
area, the computer first asks the receive hom to be manually placed at a certain distance
from the conjugator. It then controls the rotation stage to step through the desired angles.
At each angular step, the phase and amplitude of the electric field will be measured from
the sampling oscilloscope and recorded as a function of {p,<f>). After each angular
47
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
scanning, the computer will request the next distance p and then the angular scanning
process starts over again. This continues until the entire chosen area has been covered.
Using this technique, the conjugate electric field is measured in a polar coordinate
system as a function of p and <f>. However, it is more convenient to process Ec (x,y)
than Ec (p,<f>). Therefore a computer program has been written to convert Ec {p,<f>) to
Ec (x ,y ) . This program first finds the four measured surrounding points: Ei( p <,0<),
E2(P<’0>)>
and E ^ p ^ f c )for a given (x,y).
Where p << p < p >,
tj)< <(f> <<f>>, p = yjx2 + y 2 , and <f) - tan ' 1 —. It then uses the following equations to
x
interpolate the desired electric field Ec (x, y) = Ac (x, y )e‘q>c(x'y) + c.c. :
+I z A . . £ ^ Ay
1
Ac=
V
P>~P
0>~0< P>~P<
$>-$< P>~P<
, (/)>-(f) p ~ p < A |
p ~p< {
V
■o-
A
1
i
V
1
11
A
V
1
<P\ + ,
, P>~P _
P>~P<
$>-<!>< P>~P<
(32)
V
.
1
V
V
1
-<s£
*0
V
Q.
<f)>~(f)
A
J
1
1
CPc ~ t
V
1
A
„ _ .-
„ ,
< P~P< _
------1----------V
*
Pi 0>~<
f>< P>~P<
For all of the following measurements, electric field is measured at 1 ° intervals
from <f>= -30° to 0 = 30°, and 0.5 cm intervals from p = 45 cm to p = 55 cm. This
£ c (p ,^ ) matrix is then converted to an Ec (x,y) matrix with 0.25 cm intervals from
x = 39 cm to x = 55 cm, and 0.5 cm intervals from y = -27.5 cm to y = 27.5 cm. The
obtained conjugate electric field Ec (x, y) is then plotted in two different formats:
48
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
contour and surface. Contour plots have better phase resolution while surface plots show
more amplitude information.
In the first set of measurement, only the transmit hom #1 is used as the single
source. It is placed at <f>= -15°. This angle is chosen for convenience, it can be varied
between -30° to + 30°. The conjugate electric field distribution is shown in Fig. 3.10 and
3.11, labeled as “without distortion”. In the contour plot Fig. 3.10, gray scale is used to
represent the magnitude of electric field. The black dot next to the plot is the source
location. The tick mark labels are in centimeters. The wavefronts of the conjugate wave
can be seen clearly and are travelling from left to right. Although the focusing effect can
not be observed because of the diffraction limits, the retrodirectivity is certainly
demonstrated. In the surface plot Fig. 3.11, electric field magnitude is represented by the
height at a given point. The white dot on the zero field plane marks the source position.
The smaller bumps in this figure are caused by the amplified incident signals leaking
through the mixers and small reflections in the chamber. Their amplitude is about onethird to one-fourth of that of the conjugate beam. This means the leakage power is about
-10 dB of the conjugate power, as mentioned earlier in section 3.1. Because the leakage
signal has a phase similar to a reflected signal, we will refer it as reflection for simplicity
when explaining the results.
Our next step is to demonstrate automatic phase correction. This is achieved by
inserting a distorting medium in front of the phase conjugator.
We use a piece of
Plexiglas as the distorting medium. The conjugate electric field is shown in Fig. 3.10 and
3.12, labeled as “with distortion”.
By comparing the two plots in Fig. 3.10, the
49
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Without Distortion
With Distortion
Fig. 3.10. The contour plots of the phase-conjugate electric field of a source at +15° as
marked by the black dots.
They demonstrate retrodirectivity and automatic phase
correction when a distorting medium is inserted in front of the conjugator.
50
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Without Distortion
Fig. 3.11. The surface plot of the phase-conjugate electric field of a source at +15° as
marked by the white dot. It shows retrodirectivity. The smaller bumps are caused by
amplified “reflection” as explained in the text.
51
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
With Distortion
Fig. 3.12. When a distorting medium is inserted in front of the conjugator, the reflected
bumps are destroyed while the phase-conjugate beam remains the same phase and
amplitude.
52
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
wavefronts of the conjugate beam remain the same shape and phase with or without the
distortion, as the theory predicted in chapter 1 . The reflection wavefronts are distorted
when the distorting medium is present. In Fig. 3.12, the reflected bumps are destroyed by
the distortion while the phase-conjugate beam maintains its phase and amplitude. These
results demonstrate the retrodirectivity and automatic phase correction ability of phase
conjugation unquestionably.
In order to reveal the automatic phase correction more quantitatively, the receive
hom is placed in the conjugate beam at 55 cm from the conjugator. The electric field
versus time is recorded and then plotted in Fig. 3.13 with and without the distortion. The
phase difference in time is less than 1 ps for a distorting medium capable of 25 ps one­
way delay.
To further demonstrate the phase-conjugate beam does carry a negative incident
phase, we move the distorting medium to cover the source only. Therefore now only the
incident beam goes through the distortion. The electric field distribution is shown in Fig.
3.14 and 3.15, labeled as “with distortion”. Because of the existence of the distorting
medium, the phase of the incident beam is retarded by A(p. If this signal is reflected, it
will carry the same phase retardation Aq>. However if the incident beam is phaseconjugated by the conjugator, the phase of the conjugate beam wilt be - A q>, which
means its phase is advanced by A(p. This theory is evidently shown in Fig. 3.14 and 3.15
as the conjugate wavefronts move toward the source (advanced phase) while the reflected
wavefronts move toward the conjugator (retarded phase). Also noticeable in Fig. 3.14
and 3.15, the reflection beam is deflected away from the center because of the distortion.
53
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[
Without D istortion
With Distortion |
8 -10
-20
-30
-40
-50
0
20
40
60
80
100
120
140
160
180
200
Time (ps)
Fig. 3.13. The electric field versus time at +15°, 55 cm from the conjugator. It shows
excellent phase auto-correction when a distorting medium is inserted in front of the
conjugator. Note that DC components have been added to the two traces to separate them
for viewing.
54
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Without Distortion
With Distortion
Fig. 3.14. The distorting medium covers the transmit hom only. The conjugate beam
now has advanced wavefronts while the reflected beam is distorted and has retarded
wavefronts.
55
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
With Distortion
Fig. 3.15. When a distorting medium is inserted in front of the transmit hom, the phase
of the conjugate beam is advanced and that of the reflected beam is retarded.
conjugate beam maintains the same path while the reflected beam is deflected.
56
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The
This shows the Plexiglas does act as an effective distorting material and further
consolidates the previous experiments.
After we have demonstrated single source retrodirectivity and automatic phase
correction, our next step is to verify the same properties using two sources. While the
first source is still located at +15°, we add a second one at -2 0 ° . Again this angle is
chosen for convenience and can be changed. The conjugate electric field distribution is
shown in Fig. 3.16 and 3.17, labeled as “without distortion”. Although multiple-source
retrodirectivity can certainly be seen, the two conjugate beams do seem to move toward
negative angles by about 3 degrees. This small angle shift is caused by the interference
between the reflection of one source and the conjugate beam of the other. To prove this
point, the following test is performed. First, the hom at - 20° is disconnected from the
source and the conjugate field of the +15° hom is recorded. Then the hom at +15° is
disconnected and the field of - 20° is measured. In both cases, retrodirectivity is shown
without the angle shift. A computer then adds up the two single source electric fields.
The calculated sum field shows the same angle shift and is almost identical to the
measured two source electric field. Therefore the interference from the reflections are
causing the problem. This can be solved by using two-stage mixing to avoid leakage, it
will be explained in chapter 5.
To demonstrate automatic phase correction, the distorting medium is again
inserted in front of the conjugator. The electric field distribution is shown in Fig. 3.16
and 3.18, labeled as “with distortion”. Once again the phase remains constant with or
without the distortion for both conjugate waves. Also the small angle shift disappears
57
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Without Distortion
With Distortion
Fig. 3.16. The contour plots of the phase-conjugate electric field of two sources at +15°
and -20°.
They demonstrate multiple-source retrodirectivity and automatic phase
correction when a distorting medium is inserted in front of the conjugator.
58
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Without Distortion
Fig. 3.17. The surface plot of the phase-conjugate electric field of two sources at +15°
and -20°. It shows multiple-source retrodirectivity. The smaller bumps near 0° are
caused by reflections.
59
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
With Distortion
Fig. 3.18. When a distorting medium is inserted in front o f the conjugator, the reflected
bumps near 0 ° are destroyed while the phase-conjugate beams maintain their phases and
amplitudes.
60
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
when the distortion is present. This is because the existence o f a distorting medium can
destroy a reflected signal while maintaining a conjugate signal, as shown in previous
experiments. Therefore the distorting medium actually cleans up the output signal for us,
as it can be evidently seen that the smaller bumps near 0° in Fig. 3.17 are removed in Fig.
3.18.
Based on this series of experiments, we have demonstrated the two-dimensional
retrodirectivity and automatic phase correction properties of phase conjugation at 10.24
GHz using an electrically injected artificial nonlinear microwave surface. Although a
complete wavefront reconstruction could not be observed due to diffraction limits, we
have shown theoretically that it can be achieved with a larger array (e.g. 40 elements).
Therefore we have proven the possibility of using this sampling approach to generate
microwave and millimeter wave phase conjugation.
61
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4. MICROWAVE PHASE CONJUGATION USING
OPTICALLY INJECTED ARTIFICIAL NONLINEAR
MICROWAVE SURFACES
In the previous chapter, we have demonstrated two-dimensional microwave phase
conjugation using an electrically injected artificial nonlinear microwave array. However,
as mentioned earlier, electrical injection will not be able to handle a full size twodimensional surface for complete three-dimensional wavefront reconstruction.
The
problems in the electrical injection scheme are due to the high loss, heavy weight, and
large size of microwave and millimeter wave components.
However, using optical
injection, the 2co pump signal can be delivered to all elements with very little loss (~ 0.3
dB/Km) at very high density (e.g. 1 element/mm for millimeter wave arrays). Therefore
in this study we propose and demonstrate the optical injection technique to address these
electrical injection problems.
4.1 8-Element Optically Injected Artificial Nonlinear Microwave Array
The configuration of the 8 -element array using optical injection mechanism is shown in
Fig. 4.1.
The
8
phase-conjugate elements are the same as in the electrical injection
configuration, shown in Fig. 3.2. A Lightwave 122 diode-pumped Nd:YAG laser is used
as the light source. The optical wavelength is at 1319 nm, with a linewidth < 5 KHz/ms.
This wavelength is chosen to minimize the dispersion in optical fiber systems. In our
62
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
To Transmit Antsnru *1
From Racaiva Antanna #1
To Transmit Antanna *2
From Racaiva Antarma #2
Signal
Carried
To Tranamtt Antarma *3
From Racaiva Antanna #3
To Tranamtt Antanna M
From Racaiva Antanna M
Optical
Power
Splitter
To Tranamtt Antanna *5
From Racaiva Antanna K
To Transmit Antenna M
From Racaiva Antanna M
To Transmit Antanna *7
From Racaiva Antanna *7
To Tranamtt Antanna M
From Racaiva Antanna 09
Laser Light
o) Signal from
Synthesizer
DC Bias
Frequency Doubler
Fig. 4.1. The 8 -element artificial nonlinear microwave surface using optical injection for
the 2ct) pump signal.
63
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
demonstration, it is not an important issue because of the relatively short propagation
distances.
However, to be able to extend this technique into large surfaces and/or
millimeter wave frequencies, minimized dispersion will be a crucial factor.
The laser light is directed into a Mach-Zehnder optical modular, manufactured by
United Technologies Photonics, using a polarization preservation fiber. A typical MachZehnder modulator structure is shown in Fig. 4.2.
The light is split into two arms
coherently. An applied electric field on one arm will change the optical phase of that arm
through electro-optical effect. The two arms are then recombined coherently. Therefore
the output optical power depends on the phase difference between the two arms and the
transfer function of the Mach-Zehnder modulator can be written as: [29]
p
1+ a - c o s i x V / ^ + c )
(41)
where P is the output optical power, V is the applied voltage, Vr is the half-wave
voltage, a and c are constants caused by imperfect arms.
A transfer function similar to that of our modulator is shown in Fig. 4.3. The
optimal bias point for linear modulation is marked by an arrow. In our experiments, we
bias the modulator at that point and modulate the light with a 20.48 GHz signal. Because
of photo-refractive and thermal effects, the transfer function and the quadrature point
actually move around. To solve this problem, the DC light intensity is monitored and
maintained at half of its maximum value by a computer controlled bias.
A more interesting way to modulate the light at 2a> is to bias the modulator at its
transfer function minimum and apply a a> signal to the RF electrode.
Due to the
64
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
DC Bias Electrode
Fig. 4.2. A typical Mach-Zehnder interferometric modulator. An applied electric field
changes the optical phase in one arm through electro-optical effect. Output optical power
depends on the phase difference between the two arms when they are recombined.
65
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1.2
0.8
5 0.6
0.4
0.2
0
5
10
15
20
25
30
Applied Voltage (V)
Fig. 4.3. A typical transfer function for a Mach-Zehnder optical modulator. The arrow
marks the quadrature point, which is the optimal bias point for linear modulation.
66
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
nonlinearity of the transfer function at the minimum, the optical power varies at 2co as
desired. The advantage of this technique is that no frequency doubler is required. The
disadvantage is that the modulation efficiency is not as high as the linear region.
Therefore more efficient photodetectors or higher gain amplifiers will be required to
compensate that loss. Using the next generation phototransistors may solve this problem
[30].
This 20.48 GHz modulated light then enters a 1x8 optical power splitter and splits
into 8 equal-intensity equal-phase signals. These optical signals can now be delivered to
the photodetector-attached phase-conjugate elements, which may be far way for a large
surface or close together for high operating frequency.
Before entering each phase-
conjugate element, the 20.48 GHz pump signal is extracted by a PIN diode manufactured
by Fermionics Corp. with an Ino.5 3 Gao.4 7 As active layer. This 20.48 GHz pump signal is
amplified to a power level of 9 dBm then fed to the phase-conjugate element as in the
electrical injection system.
Using the experimental setups and procedures mentioned in section 3.2, the
output amplitudes of these
8
elements are matched to within ± 6% and their phases are
matched to within ± 0.2 ps (0.2%). A sample of the linearity test results is shown in Fig.
4.4. It shows excellent linearity with a 20 dB power gain when the input power level is
above -58 dBm. Below that input level, the phase-conjugate is not as sensitive due to the
noise in the 20.48 GHz pump signal. Using narrower band modulator, photodetectors,
and amplifiers designed for the desired operating frequency should greatly reduce the
noise.
In
the
following
experiments,
the
input
power
level
67
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
will
be
-25
-30
m -35
~ -40
-50
-70
-65
-55
-60
-50
-45
-40
Input Power (dBm)
Fig. 4.4. The output power of a phase-conjugate element versus the input power, using
optically injected 20.48 GHz pump. It demonstrates excellent linearity with a 20 dB of
power gain when the input level is above -58 dBm. Below that input level, the element is
not as sensitive because of the noise in the pump. All 8 elements have similar results.
68
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
around -50 dBm, in the range that these 8 elements are matched well. Therefore we can
use this optically injected 8-element artificial nonlinear microwave array to demonstrate
microwave phase conjugation.
4.2 Microwave Phase Conjugation Demonstration Using Optically
Injected Pump Signal
Using the same measurement setups and procedures as described in chapter 3, we are
able to demonstrate two-dimensional microwave phase conjugation using an optically
injected artificial nonlinear microwave surface. All the tests performed in the electrical
demonstration have been successfully duplicated.
In our first set of experiment, a single hom is placed at +15°. The measured
electric field distribution is shown in Fig. 4.5 and 4.6, labeled as “without distortion”.
These figures demonstrate retrodirectivity. To demonstrate automatic phase correction, a
distorting medium is inserted in front of the conjugator. As shown in Fig. 4.5 and 4.7,
labeled as “with distortion”, the conjugate beam maintains its amplitude and phase while
the reflection is reduced and distorted.
To exhibit this automatic phase correction effect more quantitatively, the receive
hom is moved into the conjugate beam at +15°, 55 cm from the conjugator.
The
measured electric field versus time is shown in Fig. 4.8, with and without the distorting
medium. This clearly demonstrates the phase correction ability to within 1 ps for a ~ 25
ps one-way delay.
69
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
40
45
50
r
55
40
Without Distortion
i
45
i
i
SO
55
With Distortion
Fig. 4.5. The contour plots of the phase-conjugate electric field of a source at +15° as
marked by the black dots.
They demonstrate retrodirectivity and automatic phase
correction when a distorting medium is inserted in front of the conjugator.
70
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Without Distortion
-
0 . 02\
Fig. 4.6. The surface plot of the phase-conjugate electric field of a source at +15c
marked by the white dot. It shows retrodirectivity.
71
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
With Distortion
Fig. 4.7. When a distorting medium is inserted in front of the conjugator, the phaseconjugate beam maintains the same phase and amplitude.
72
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
|
WHhout Distortion
With Distortion 1
3
m
u.
a
O
w
ui
-20
-40
-60
0
20
40
60
100
80
120
140
160
180
200
Time (ps)
Fig. 4.8. The electric field versus time at +15°, 55 cm from the conjugator. It shows
excellent phase auto-correction when a distorting medium is inserted in front of the
conjugator. Note that DC components have been added to the two traces to separate them
for viewing.
73
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
In order to check the sign of the output electric field phase, we perform the
following tests. The receive hom is placed in the conjugate beam at +15°, 45 cm from
the conjugator. The electric field versus time is recorded for three different cases and the
results are shown in Fig. 4.9. The middle curve is for no distortion. When a distorting
medium is inserted to cover the transmit hom only, the phase of the conjugate beam is
advanced. This can be seen from the shift of the top curve to the left. Therefore a
retarded incident wave generates an advanced conjugate wave.
This tells us the
conjugate beam indeed carries a negative phase, relative to the incident beam. When the
same distorting medium is inserted to cover the receive hom only, the phase of the
conjugate beam is retarded as shown with the bottom curve.
This is because the
retardation happens after the conjugation and therefore can not be reversed.
To demonstrate phase conjugation with more complicated wavefronts, we add a
second source at - 20°, 60 cm from the conjugator. Because of the interference between
the two sources, the combined incident wavefronts should be good examples as
complicated wavefronts. The results are shown in Fig. 4.10 and 4.11, labeled as “without
distortion”. They exhibit multiple-source retrodirectivity with both conjugate beams
shifted ~ 3° toward the negative angles. This is caused by the interference between the
reflection of one source and the conjugate beam of the other, as explained in section 3.3.
In order to verify the phase correction ability, a distorting medium is inserted in front of
the conjugator. The conjugate electric field distribution is shown in Fig. 4.10 and 4.12,
labeled as “with distortion”. By comparing the two plots in Fig. 4.10, the automatic
phase correction effect can be confirmed. It can also be noticed that the small angular
74
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
|
Without Distortion
Transmit Distortion
Receive Distortion |
100
3
■
U.
o
o
«
ui
•S
-20
-40
-60
-80
-100
0
20
40
60
80
100
120
140
160
180
200
Time (ps)
Fig. 4.9. The electric field versus time at +15°, 45 cm from the conjugator. When a
distorting medium is inserted in front of the transmitter, the phase is advanced. When the
same distorting medium is moved in front of the receiver, the phase is retarded. Note that
DC components have been added to the two traces to separate them for viewing.
75
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Without Distortion
With Distortion
Fig. 4.10. The contour plots of the phase-conjugate electric field of two sources at +15°
and -20°.
They demonstrate multiple-source retrodirectivity and automatic phase
correction when a distorting medium is inserted in front of the conjugator.
76
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Without Distortion
Fig. 4.11. The surface plot of the phase-conjugate electric field of two sources at +15°
and -20°. It shows multiple-source retrodirectivity. The smaller bumps near 0° are
caused by reflections.
77
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
With Distortion
Fig. 4.12. When a distorting medium is inserted in front o f the conjugator, the reflected
bumps near 0° are destroyed while the phase-conjugate beams maintain their phases and
amplitudes.
78
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
shifts mentioned above are disappeared because the reflections are destroyed by the
distortion. Fig. 4.12 shows clearly that the conjugate beams maintain their amplitudes
and phases while the reflection near 0° disappears.
Based on this series of experiments, we have demonstrated two-dimensional
phase conjugation at 10.24 GHz with diffraction limited results using an optically
injected artificial nonlinear microwave array. By extending this linear array into a twodimensional surface, complete wavefront reconstruction can be realized at microwave
and millimeter wave frequencies.
4.3 Information Transmission Using Phase Conjugation
To exhibit a phase conjugator can transmit information back to sources illuminating it,
we AM modulate the 20.48 GHz pump signal before it is used to modulate the light. The
modulation frequency is at 10 MHz. This frequency is chosen by convenience and can be
varied as long as it is small compared to the phase conjugation frequency. If it becomes
comparable to the phase conjugation frequency, the output signal will not be the
conjugate beam any more. The two sources used in the previous experiments are used to
illuminate the conjugator. The detected spectra at different angles are shown in Fig. 4.13.
The top spectrum is detected in the +15° conjugate beam. It shows the 10.24 GHz
carrier and two AM modulation sidebands at 10.23 GHz and 10.25 GHz. The bottom
spectrum is detected in the - 20° conjugate beam and it shows the same characteristics as
the +15° one. When the receive hom is moved out of the conjugate beams to 0°, the
79
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
!
!-
t
_
1
a■o
----------------.........
............
.........
—-
...
— -
—
i —
. -
-
—
_
— -
—
—
— _
1
1
.1.. ....
...
•-------------------—..----------------------------!
I
OL
............... i ___________ ---------------- A
>
53
<8
*5
x
-
. . . .~
.....-
-----------------J...............................................
------------------------------ .----------
-----------------
10.21
jEEEr-j
A
----- ----^
« 10.22
------------
i,
,,
..
-
- -
■■
:
'
10.23
10-24
10.25
10.26
10.27
Frequency (GHz)
Fig. 4.13. Detected spectra at different angles with a 10 MHz modulation on the 20.48
GHz pump signal. This demonstrates retrodirectivity can also be used to communicate
between a conjugator and sources. The signal between the conjugate beams is about 20
dB smaller than that of a conjugate beam. Note that these spectra have been moved in the
vertical direction for better viewing results.
80
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
carrier and sidebands are about 20 dB lower than those of the conjugate beams. The
signal detected here is mainly due to reflection and diffraction. Using a large artificial
nonlinear microwave surface, this contrast ratio can be further increased because of the
reduction of diffraction effects.
To this point, we have demonstrated a conjugator can communicate with sources
illuminating it without the knowledge of where they are. The information will be carried
by the phase-conjugate signal with retrodirectivity and automatic phase correction. In the
following chapter we will discuss its potential applications.
81
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5. DISCUSSION AND CONCLUSIONS
5.1 Suggested Future Work
So far we have demonstrated two-dimensional microwave phase conjugation in free
space.
In order to extend this effort to complete three-dimensional wavefront
reconstruction, two-dimensional arrays have to be used. In microwave frequencies, the
conjugation array can be constructed using discrete components as we have done in this
study. As we have explained earlier, optical injection can solve the 2m pump signal
distribution problem for a large artificial nonlinear microwave surface. However, in the
millimeter wave regime, monolithic design will be needed in order to satisfy the small
I f ! spacing requirement. Using high-speed photodetectors and mixing devices [31, 32]
in conjunction with polyimide optical waveguides [33], two-dimensional millimeter wave
artificial nonlinear microwave surfaces can be realized. Fig. 5.1 shows this concept.
To address the problem of amplified leakage signals coming out from our phaseconjugate elements, a two-stage mixing technique has been proposed. Its configuration is
shown in Fig. 5.2. To understand how it works, let’s consider the sampled incident signal
has a phase factor of mt + (p. This incident signal will be mixed with a pump signal
having a phase factor of Q t . Where m < Q < 2m and this phase factor Qt is the same
for all elements. After this first stage mixing, there will be four major components
coming out from the mixer: (Q - m)t -<p, (Q + m)t + tp, mt + <p and Q t. The first term
is the signal we want because of its reversed phase - tp. The second term is the sum
82
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Optically Carried 2co Pump Signal
Fig. 5.1. Monolithic one-dimensional arrays forming a two-dimension artificial nonlinear
microwave surface for generating three-dimensional microwave phase conjugation.
83
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Antenna
A
Circulator
Filter
A
B andpass
Filter
Fig. 5.2. Phase-conjugate element using two-stage mixing. Leakages through the mixers
can be filtered out by the bandpass filters.
84
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
frequency and the last two terms are the leakage through the mixer. Because these four
signals are at different frequencies if Q * 2eo, a bandpass filter at Q - a> can be used to
remove the three unwanted components. A second stage mixing is need because the
signal carrying the conjugate phase is not at the incident frequency yet. To convert the
(Q - a>)t- (p signal back to frequency a , it is mixed with a second pump signal
(2<o-Q.)t. Again, this pump signal has to be the same for all elements. As the first
stage, four components will appear on the output port: m - ( p ,
(2 f2 -3 co)t-<p,
(Q - o>)t - <p, and (2a>- Q) t . Using a second bandpass filter at frequency co, only the
conjugate signal oit-cp will be radiated back to form the conjugate beam. Therefore this
two-stage mixing scheme can eliminate the leakage problem caused by mixers.
However, there are still other sources can contribute to the output phase error,
namely the leakage of the circulator and the reflection of the antenna. We solved this
problem in our study by separating the sampling and radiating antennas. For a true threedimensional wavefront reconstruction setup, sampling and radiating should occur at the
same point therefore only one antenna is desired. Both the circulator leakage and antenna
reflection can be reduced to below 30 dB if they are specially designed for a certain
narrow band. Also, for pulsed applications, wide band operations can still be realized if
the sampled signal and the conjugate signal can be separated in time.
This can be
achieved by delaying the conjugate signal in a long optical fiber during the sampling
period. During the radiating period, the mixer input is blocked therefore the reflected
conjugate signal will not enter the mixer.
85
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
In our study, we have concentrated on generating phase conjugation using
artificial nonlinear microwave surfaces. This technique can also be extended to other
nonlinear optics analogies. For example, by replacing the 2a pump signal feeding the
mixer in a phase-conjugate element with the sampled co signal, the element can generate
2a> therefore acting as a second-harmonic element. This type of artificial nonlinear
microwave surfaces can perform free space second-harmonic generation. Using different
configurations for the basic elements, these artificial nonlinear microwave surfaces
provide very high effective %{2) or ^ (3), which are not available in any real media.
5.2 Potential Applications
Because of the retrodirectivity and automatic phase correction properties, microwave and
millimeter wave phase conjugation is useful in applications requiring automatic pointing
and tracking and phase aberration corrections. Also, we have demonstrated in section 4.3
that information can be transmitted in the conjugate signals without knowing where the
targets are. Therefore microwave and millimeter phase conjugation can be very useful
for communication systems. For example, if a satellite uses this type of communication
system, it does not need to point its antenna toward a fixed point on the earth. Instead,
ground stations send out guidance signals to the satellite. Through the phase conjugator
on the satellite, information can be retrodirected back to the stations even the satellite is
not facing these stations.
86
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Another interesting application of microwave and millimeter phase conjugation is
that it can be used to amplify signal in free space directly. This is shown in Fig. 5.3. The
output beam has a duplicated beam pattern o f the reference source but a much higher
power because of the gain from the conjugator.
This is a very effective way of
combining the output power o f each array element.
5.3 Conclusions
In this study, we have developed and demonstrated a new technique to simulate nonlinear
materials in the microwave and millimeter wave regime. Our technique uses the strong
nonlinear V-I response of a P-N junction to replace the weak nonlinearity of electron
distribution in a crystal.
Using an array o f antenna coupled mixers as an artificial
nonlinear medium, we have demonstrated two-dimensional free space microwave phase
conjugation at 10.24 GHz. Because of the high nonlinearity of our artificial medium, we
have used a three-wave mixing method instead of the more commonly used degenerate
four-wave mixing found in nonlinear optics experiments. Two different approaches to
inject the required 20.48 GHz pump signals have been tested and discussed.
The evidences of two-dimensional free space phase conjugation have been
obtained by direct measurement of the output electric field magnitude distribution. Using
a distorting medium and two sources, retrodirectivity and automatic phase correction
have been observed directly on the electric field wavefronts. Also, the capability of data
communication using phase conjugation has been demonstrated by transmitting 10 MHz
87
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Beam Splitter
Duplicated
Amplified
Pattern
P hase
Conjugator
Reference Pattern
Fig. 5.3. Free space power amplifier. The output beam has the same beam pattern as the
reference source but a much high power because of the gain from the conjugator.
88
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
modulated signal back to two sources illuminating the conjugator.
Furthermore, the
conjugate signal has shown a 10 dB power gain, which is desired for communication
applications.
We have obtained similar results for both electrical and optical injection
techniques. However, for complete three-dimensional wavefront reconstruction, optical
injection is necessary because it takes advantage of low-loss, lightweight and small sized
optical components. It also provides a way to integrate this artificial nonlinear technique
with a variety of new photonic technologies. In this study, we have constructed an
artificial nonlinear medium suitable for microwave phase conjugation. By changing the
configuration of each element, other types of artificial media can be created to provide
large %a) and ^ (3) on single surfaces at microwave and millimeter wave frequencies.
We foresee many nonlinear optical techniques being extended to the microwave and
millimeter wave regime and also new microwave and millimeter wave applications being
developed using these artificial nonlinear surfaces.
89
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Bibliography
[1]
Eli Brookner, Practical Phased-Array Antenna Systems, Artech House, Boston,
1991.
[2] D. Dolfi, P. Joflre, J. Antoine, J.-P. Huignard, et al., “Photonics for phased array
radars,” Proceedings o f the SPIE - The International Society fo r Optical
Engineering, vol. 2560, pp. 158-165, 1995.
[3] H. R. Fetterman, Y. Chang, D. C. Scott, S. R. Forrest, et al., “Optically controlled
phased array radar receiver using SLM switched real time delays,” IEEE
Microwave And Guided Wave Lett., vol. 5, no. 11, pp. 414-416, 1995.
[4] Y. Chang, B. Tsap, H. R. Fetterman, D. A. Cohen, et al., “Optically controlled
serially fed phased-array transmitter,” IEEE Microwave And Guided Wave Lett.,
vol. 7, no. 3, pp. 69-71, 1997.
[5] A. Yariv, and P. Yeh, Optical Waves in Crystals, Wiley, New York, 1984.
[6] B. Ya. Zel’dovich, N. F. Pilepetsky, and V. V. Shkunov, Principles o f Phase
Conjugation, Springer-Verlag, Berlin; New York, 1985.
[7]
M. Gower, and D. Proch, Eds., Optical Phase Conjugation, Springer-Verlag,
Berlin; New York, 1994.
[8]
Y. I. Kruzhilin, “Self-adjusting laser-target system for laser fusion,” Sov. J. o f
Quantum Electron., vol. 8, no. 3, pp. 359-363, 1978.
90
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[9]
D. M. Pepper, and A. Yariv, “Compensation for phase distortions in nonlinear
media by phase conjugation,” Opt. Lett., vol. 5, no. 2, pp. 59-60, 1980.
[10] J. A. Yeung, D. Fekete, D. M. Pepper, and A. Yariv, “A theoretical and
experimental investigation of the modes of optical resonators with phase-conjugate
mirrors,” IEEE J. o f Quantum Electron., vol. QE-15, no. 10, pp. 1180-1188, 1979.
[11] P. A. Belanger, A. Hardy, and A. E. Siegman, “Resonant modes of optical cavities
with phase conjugate mirrors: higher-order modes,” Appl. Opt., vol. 19, no. 4, pp.
479-480, 1980.
[12] P. A. Belanger, A. Hardy, and A. E. Siegman, “Resonant modes of optical cavities
with phase conjugate mirrors,” Appl. Opt., vol. 19, no. 4, pp. 602-609, 1980.
[13] R. Shih, H. R. Fetterman, W. W. Ho, R. McGraw, et al., “Microwave phase
conjugation in a liquid suspension of elongated microparticles,” Phys. Rev. Lett.,
vol. 65, no. 5, pp. 579-582, 1990.
[14] R. W. Hellwarth, “Generation of time-reversed wave fronts by nonlinear
refraction,” /, o f The Opt. Soc. o f Am., vol. 67, no. I, pp. 1-3, 1977.
[15] Y. R. Shen, The Principles o f Nonlinear Optics, J. Wiley, New York, 1984.
[16] P. W. Smith, A. Ashkin, and W. J. Tomlinson, “Four-wave mixing in an artificial
Kerr medium,” Opt. Lett., vol. 6, no. 6, pp. 284-286, 1981.
[17] S. O. Sari, and D. Rogovin, “Degenerate four-wave mixing from anisotropic
artificial Kerr media,” Opt. Lett., vol. 9, no. 9, pp. 414-416, 1984.
91
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[18] A. J. Palmer, “Nonlinear optics in aerosols,” Opt. Lett., vol. 5, no. 2, pp. 54-55,
1980.
[19] E. R. Cohen, and D. Rogovin, “Frequency shifting in artificial Kerr media
composed of compressible microparticles,” Opt. Lett., vol. 8, no. 7, pp. 362-364,
1983.
[20] G. Mayer, “Kerr effects in two-phase systems with bubbles and drops,” Opt.
Commun., vol. 52, no. 3, pp. 215-220, 1984.
[21] R. Shih, “Microwave phase conjugation in an artificial Kerr medium,” Ph.D.
Dissertation, University of California, Los Angeles, 1991.
[22] B. Tsap, K. S. J. Pister, and H. R. Fetterman, “MEMS orientational optomechanical
media for microwave nonlinear applications,” IEEE Microwave And Guided Wave
Lett., vol. 6, no. 12, pp. 432-434, 1996.
[23] B. Tsap, K. S. J. Pister, and H. R. Fetterman, “Grating formation in orientational
optomechanical media at microwave frequencies,” accepted for publication in Appl.
Phys. Lett., May 1997.
[24] C. C. Cutler, R. Kompfner, and L. C. Tillotson, “A self-steering array repeater,”
Bell Syst. Tech. J., vol. 42, pp. 2013-2032, 1963.
[25] E. L. Gruenberg, H. P. Raabe, and C. T. Tsitsera, “Self-directional microwave
communication system,” IBM J. o f Research And Development, vol. 18, no. 2, pp.
149-163, 1974.
92
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[26] R. K. Wangsness, Electromagnetic Fields, J. Wiley, New York, 1979.
[27] B. D. Steinberg, Principles o f Aperture And Array System Design: Including
Random And Adaptive Arrays, Wiley, New York, 1976.
[28] Watkins-Johnson Company, R F And Microwave Designer’s Handbook, WatkinJohnson, Palo Alto, 1993.
[29] B. E. A. Saleh, and M. C. Teich, Fundamentals o f Photonics, J. Wiley, New York,
1991.
[30] D. P. Prakash, D. C. Scott, H. R. Fetterman, M. Matloubian, et al., “Integration of
polyimide waveguides with traveling wave phototransistors,” accepted for
publication in IEEE Phot. Tech. Lett., July 1997.
[31] D. C. Scott, D. V. Plant, and H. R. Fetterman, “60 GHz sources using optically
driven heterojunction bipolar transistors,” Appl. Phys. Lett., vol. 61, no. 1, pp. 1-3,
1992.
[32] D. Bhattacharya, P. S. Bal, H. R. Fetterman, and D. Streit, “Optical mixing in
epitaxial lift-off pseudomorphic HEMTs,” Phot. Tech. Lett., vol. 7, no. 10, pp.
1171-1173, 1995.
[33] D. P. Prakash, D. V. Plant, H. R. Fetterman, and B. Jalali, “Optically integrated
millimeter wave systems,” Proceedings o f the SPIE - The International Society for
Optical Engineering, vol. 2153, pp. 101-110, 1994.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Документ
Категория
Без категории
Просмотров
0
Размер файла
3 075 Кб
Теги
sdewsdweddes
1/--страниц
Пожаловаться на содержимое документа