close

Вход

Забыли?

вход по аккаунту

?

Ring resonator based electro -optic polymer modulators for microwave photonics applications

код для вставкиСкачать
RING RESONATOR BASED ELECTRO-OPTIC POLYMER MODULATORS
FOR MICROWAVE PHOTONICS APPLICATIONS
by
Hidehisa Tazawa
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
December 2005
Copyright 2005
Hidehisa Tazawa
UMI Number: 3219859
UMI Microform 3219859
Copyright 2006 by ProQuest Information and Learning Company.
All rights reserved. This microform edition is protected against
unauthorized copying under Title 17, United States Code.
ProQuest Information and Learning Company
300 North Zeeb Road
P.O. Box 1346
Ann Arbor, MI 48106-1346
ii
Acknowledgements
I would like to take this opportunity to thank all those who have made it
possible for me to undertake and complete my study at USC.
First, I would like to thank my advisor, Professor William H. Steier. He was
always supportive and gave appropriate advice throughout my study. His guidance
and patience enabled me to conduct independent research.
It was a great honor for me to study photonics at USC. Many wonderful classes
and seminars allowed me to acquire the state of the art knowledge in this field. I
would like to specially thank Professor P. Daniel Dapkus and Professor John O’Brien,
who also served on my dissertation committee. I would also like to acknowledge
Professor Eun Sok Kim and Professor William P. Webber for serving on my
qualifying exam committee.
All members of the research group were instrumental in my work. I would like
to thank Dr. Payam Rabiei, Ying-Hao Kuo, Reem Song, Dr. Hyun-Chae Song, Dr.
Atilla Szep, Dr. Seh-Won Ahn, Bipin Bhola, Greeshma Gupta, Andrew Yick, Dr.
Min-Suk Kwon, and Toshiyuki Komikado for teaching device fabrication and
characterization, giving advice and suggestion, and helping to do my experiments.
Students from Professor Dapkus’s group, Professor O’Brien’s group, and Professor
Kim’s group also helped me to do experiments especially in the clean room. I would
like to acknowledge those friendly and kind fellows.
iii
I would like to thank Dr. Cheng Zhang at Pacific Wave Industries, Inc., Dr.
Jingdong Luo, Professor Alex K.-Y. Jen, and Professor Larry R. Dalton at University
of Washington for supplying the electro-optic polymers. Ilya Dunayevskiy in
Professor Harold R. Fetterman’s group at UCLA also contributed to my work by
solving RF related problems.
I am grateful to Ms. Betty Madrid for her administrative support.
I would like to express my gratitude to my family, my parents and sister, for
their encouragement and support.
Finally, I thank my son, Kohki, for being a source of joy and my wife, Atsuko,
for being a partner, a supporter, a friend, an adviser, and much more.
iv
Table of Contents
Acknowledgements
ii
List of Tables
vi
List of Figures
vii
Abstract
xi
Chapter 1: Introduction
1.1 Background and Motivation
1.2 Dissertation Outline
1.3 References
1
1
4
5
Chapter 2: Ring Resonator Based Electro-Optic Modulators
2.1 Introduction
2.2 Ring Resonator Basics
2.3 Electro-Optic Ring Modulators
2.4 Bandwidth of Ring Modulators
2.5 Traveling-Wave Ring Modulators
2.6 References
8
8
10
15
19
22
27
Chapter 3: Demonstration of Electro-Optic Polymer Traveling-Wave
Ring Modulators
3.1 Introduction
3.2 Device Design and Fabrication
3.3 Basic Characteristics of Devices
3.4 High Frequency Measurements and Results
3.5 References
31
31
32
39
42
48
Chapter 4: Linearity of Ring Modulators
4.1 Introduction
4.2 Distortion in Modulators
4.3 Distortion in Ring Modulators
4.4 Double Parallel Ring Modulator
4.5 Experiments and Results
4.6 References
49
49
50
54
56
59
63
v
Chapter 5: Bandwidth of Linearized Ring Resonator Assisted
Mach-Zehnder Modulator
5.1 Introduction
5.2 Ring Resonator Assisted MZ Modulator
5.3 Frequency Properties of RAMZs
5.4 References
65
65
66
69
73
Chapter 6: Conclusions
6.1 Summary
6.2 Future Work
6.3 References
75
75
77
79
Bibliography
80
vi
List of Tables
Table 2.1: Numerical example values of an EO polymer device
18
Table 4.1: Link Parameters
53
Table 4.2: Comparison of the intermodulation-free dynamic ranges for
different modulator types
58
vii
List of Figures
Figure 2.1:
The generic geometry of ring resonator (one bus waveguide).
11
Figure 2.2:
The intensity transfer function and phase shift of a ring
resonator (α = 0.9,τ = 0.95 and 0.85).
12
Figure 2.3:
The generic geometry of ring resonator (two bus waveguides).
14
Figure 2.4:
The transmission spectrum of ring resonator with two bus
waveguides at through and drop ports (α = 0.9,τ1 = 0.85 and τ2
= 0.944).
15
Figure 2.5:
Conceptual drawing of the modulation by a ring modulator.
17
Figure 2.6:
The small signal frequency responses in dBe of the modulated
output from a ring modulator with a lumped electrode
optically biased to the maximum slope with a finesse of 10.
The responses are normalized by low modulation frequency
response.
21
Figure 2.7:
Traveling-wave ring modulator.
23
Figure 2.8:
Modulation frequency responses of velocity-matched
traveling-wave ring modulators with the finesse of 10 and 30.
The responses are normalized by the response by a MZ
modulator with same electrode length.
24
Effect of velocity mismatch (∆n = 0.2, no microwave loss) in
modulation frequency response of the ring modulator with the
FSR of 30 GHz (L = 6.25 mm) and F = 10 compared to the
equivalent broadband MZ modulator (L = 4.04×6.25 mm).
The responses are normalized by the low frequency response.
26
Effect of microwave loss (a = 0.7 dB/cm·GHz1/2, ∆n = 0) in
modulation frequency response of the ring modulator with the
FSR of 30 GHz (L = 6.25 mm) and F = 10 compared to the
equivalent broadband MZ modulator (L = 4.04×6.25 mm).
The responses are normalized by the low frequency response.
26
Figure 2.9:
Figure 2.10:
viii
Figure 3.1:
Calculated mode profiles (a) the fundamental mode of the
waveguide, (b) the even mode of the coupling region, and (c)
the odd mode of the coupling region.
33
Figure 3.2:
The lateral dimensions of the racetrack ring resonator.
35
Figure 3.3:
The chemical structure of AJL8 and APC.
35
Figure 3.4:
Fabrication steps of an EO polymer ring modulator.
37
Figure 3.5:
The top view optical microscope image and schematic cross
section of the fabricated modulator.
38
Optical microscope image of the straight coupling region of
the racetrack ring resonator.
39
Figure 3.7:
Schematic setup for measuring transmission spectrum.
40
Figure 3.8:
The transmission spectrum of the TM mode of the ring
modulator.
40
Figure 3.9:
Schematic setup for measuring EO tuning sensitivity.
41
Figure 3.10:
The modulated TM light from the ring modulator (Vpp = 20V).
41
Figure 3.11:
Optical microscope image of the traveling-wave electrode
with 50 Ω microstrip and two pads.
42
Figure 3.12:
The detailed dimensions of the feeding pad.
43
Figure 3.13:
Schematic drawing of the microstrip termination.
44
Figure 3.14:
S11 (reflection) of the traveling-wave electrode.
44
Figure 3.15:
Optical spectra of the modulated light at 22 GHz, 28 GHz, and
34 GH.
45
The modulation frequency dependence of optical sideband
powers.
46
The bias dependence of 28 GHz modulation spectra.
47
Figure 3.6:
Figure 3.16:
Figure 3.17:
ix
Figure 4.1:
A typical spectrum of the second and third order two-tone IM
products.
51
Figure 4.2:
The model optical link.
53
Figure 4.3:
The signal power and IM power of a MZ modulator as a
function of the input signal power.
54
The signal power and IM power of a ring modulator as a
function of the input signal power.
56
Figure 4.5:
Dual parallel ring modulator.
57
Figure 4.6:
The signal power and IM power of a dual parallel ring
modulator as a function of the input signal power.
58
Figure 4.7:
The transmission spectrum of TM mode of the ring modulator.
60
Figure 4.8:
Schematic setup for measuring modulator distortions.
60
Figure 4.9:
The output fundamental, second harmonic, and third harmonic
signal powers as a function of a bias point. The input RF
power is 6.4 dBm
61
The output fundamental, second harmonic, and third harmonic
signal powers plotted against the input RF power at the bias of
2.2 GHz from the optical resonance. The solid lines are
theoretical calculations based on the experimental link
parameters and the theoretical transfer function
62
(a) The schematic drawing of a ring resonator assisted MZ
modulator, and (b) its low frequency linearized intensity
transfer function compared with a standard MZ modulator.
The voltage is normalized by Vπ.
67
The output signal power and intermodulation power of both a
standard MZ modulator and a ring resonator assisted MZ
(RAMZ) modulator as a function of the input signal power.
The RAMZ calculation is for low modulation frequencies. The
intermodulation power of RAMZ varies as the fifth power of
the input instead of the third in MZ.
69
Figure 4.4:
Figure 4.10:
Figure 5.1:
Figure 5.2:
x
Figure 5.3:
Figure 5.4:
The intermodulation powers of a ring resonator assisted MZ
(RAMZ) modulator with different modulation frequencies,
10-5, 10-3, 10-2, and 10-1 times the FSR of the ring resonator.
71
The modulation frequency dependence of the dynamic range
of a ring resonator assisted RZ (RAMZ) modulator. The
frequency is normalized by the FSR of a ring resonator.
71
xi
Abstract
This dissertation presents the study of ring resonator based electro-optic
polymer optical modulators for microwave photonics applications. Particularly, the
work focuses on two important requirements for external modulators in analog
optical links: high sensitivity at a high frequency and the linearity of a modulator.
The first portion of this work addresses the analysis of ring modulators in terms
of the modulation sensitivity and the modulation bandwidth. The general expression
to analyze the modulation frequency response of a ring modulator is derived and
applied to traveling-wave ring modulators. The modulators show high modulation
efficiency at frequencies around all multiples of the free spectral range, and have
better tolerance for the optical/microwave velocity mismatch and microwave loss of
the electrode than traveling-wave Mach-Zehnder modulators.
Second, the band operation in an electro-optic polymer ring modulator with a
traveling-wave electrode is experimentally demonstrated. The Q of the ring resonator
is 45,000 at 1.31 µm, and the electro-optic tuning sensitivity is 1 GHz/V. The
modulator shows efficient modulation in a 7 GHz band centered at 28 GHz. This
modulation enhancement is due to optical resonance. The device design, fabrication,
and characterization are described in detail.
Finally, the linearity of a ring modulator is theoretically analyzed and
experimentally studied. It is shown that ring modulators have the potential to obtain
xii
a high intermodulation-free dynamic range in sub-octave bandpass optical links,
because they have a bias point at which the third derivative of the transfer function is
zero; eliminating third-order distortion. The scheme to expand the dynamic range
using dual parallel ring modulator is proposed. The experimental result of an
electro-optic polymer ring modulator clearly shows a suppression of third-order
distortion at a certain bias point, verifying the theory. A linearized ring resonator
assisted Mach–Zehnder electro-optic modulator is also analyzed. It is shown that the
linearization bandwidth of the modulator is limited by the resonant nature of a ring
resonator.
1
Chapter 1
Introduction
1.1 Background and Motivation
Microwave photonics is an emerging technology that may be described as the
unification of microwave and photonic techniques for opening up novel information
and communication applications [1]–[6]. Examples are fiber deliveries of
microwaves and millimeter-waves, namely analog optical links, for microcell mobile
systems, radio local area networks, phased array antennas, and various measurement
systems. RF signal processing in optical domain is also promising research area in
microwave photonics. The main motivation to apply lightwave technology to
microwave systems is due to the extremely lower loss and lower dispersion
characteristics of single-mode optical fibers than those of coaxial cables. Recent
rapid development of photonic elements and devices has allowed us to use fiber
optics in microwaves and millimeter-waves. Another important feature of analog
2
optic links is higher isolation between controlling and controlled signals, enabling
systems to be impervious to inductions and noises.
To impose a microwave or a millimeter-wave signal on an optical carrier,
optical modulation technologies are essential. The direct modulation of a
semiconductor laser diode is an easy and powerful choice. However, the modulation
bandwidth is limited in typically several GHz. On the other hand, in the external
modulation technology, the laser operates at a constant optical power and the desired
intensity modulation of the optical carrier is introduced typically via a LiNbO3
Mach-Zehnder modulator. External modulation offers advantages over direct laser
diode modulation in terms of bandwidth and linearity range. Traveling-wave LiNbO3
Mach-Zehnder modulator [7], [8] is a very broadband device, and now 40 GHz
modulators are commercially available. In analog optical links, however, the
broadband operation is not always required; the high modulation sensitivity only
around RF carrier frequencies is required. Recently, resonant modulators have
attracted attention for band-pass operation applications [9]–[11]. The enhancement of
the modulation sensitivity by either a resonant electrode or an optical resonance
reduces the driving power at the expense of a reduced operation bandwidth around
the resonance frequency.
While external optical modulators can be realized in a number of different
materials, the work presented here focuses upon Electro-optic (EO) polymers. EO
polymers have been under development for more than two decades [12]–[15]. The
3
recent progresses have made device quality material available and driven recent
progress in device applications [16], [17]. EO polymers are amorphous organic
materials composed of an electro-optically active, namely highly optically nonlinear,
chromophore, and a polymer matrix. The EO coefficients of polymers are now
comparable to LiNbO3, which is the dominant inorganic crystalline EO material in
today’s technology. Larger coefficients will be achievable by future material
engineering [18]. The small dispersion in dielectric constants between infrared and
millimeter-wave frequencies [19] makes velocity matching between RF and optical
waves easier, enabling high speed or wide bandwidth modulators [20], [21].
Mach-Zehnder EO polymer modulators have been demonstrated with a Vπ of 1.8 V
at 1.55 µm and > 20 GHz bandwidth [22]. Modulators with Vπ < 1 V [23], [24] and
devices that operate at over 100 GHz [25] have also been reported. Other advantages
of EO polymers include their potential ability to integrate easily with other materials
[26] and their potential for low cost. In integrated optics applications, a wide range
of indices of polymers also offers an advantage over LiNbO3, because it is very
difficult to fabricate high index contrast waveguides in a LiNbO3 wafer.
The motivation of this research is to develop novel EO polymer modulators for
future information and communication technologies. The features of EO polymers
make them a good candidate for realizing waveguide resonant modulators for
microwave and millimeter-wave analog optical links. Particularly, this research
studies ring resonator based EO polymer modulators.
4
1.2 Dissertation Outline
In Chapter 2, the theory of ring resonator based EO modulators is described.
After reviewing the basic transmission characteristics of ring resonators, the concept
of a ring modulator is explained and the sensitivity of a modulator is defined. In the
analysis of modulation bandwidth, the general expression to analyze the modulation
frequency response of a ring modulator is derived. Then, a traveling-wave ring
modulator is proposed and analyzed.
Based on the analysis in Chapter 2, Chapter 3 presents the experimental
demonstration of FSR modulation, or band operation, in an EO polymer ring
modulator with a traveling-wave electrode. The device design, fabrication, and
characterization are also explained in detail.
In Chapter 4, the linearity of a ring modulator is theoretically analyzed and
experimentally studied. It is shown that ring modulators have the potential to obtain
a high intermodulation-free dynamic range, which is the key parameter of analog
optical links. The experimental results are compared with the theory.
Chapter 5 discusses the modulation frequency properties of a linearized ring
resonator assisted Mach-Zehnder modulator, which is recently proposed as a new
linearization scheme of external modulators. Using general analytical expressions
established in Chapter 2, the limitation of the linearity at high modulation
frequencies is explored.
5
In Chapter 6, a brief summary of the research work is provided. The future work
is also suggested.
1.3 References
[1] W. S. C. Chang, RF Photonic Technology in Optical Fiber Links, Cambridge
University Press, 2002.
[2] H. Al-Raweshidy, and S. Komaki, Radio over fiber technologies for mobile
communications networks, MA, Artech House, 2002.
[3] A. Vilcot, B. Cabon, and J. Chazelas, Microwave photonics: from components
to applications and systems, Kluwer Academic, 2003.
[4] C. H. Cox, Analog Optical Links, Cambridge University Press, 2004.
[5] M. Izutsu, "Microwave photonics: new direction between microwave and
photonic technologies," Transactions of the Institute of Electronics, Information
and Communication Engineers C-I J81C-I, pp. 47-54, 1998.
[6] E. I. Ackerman and C. H. Cox, "RF fiber-optic link performance," IEEE
Microwave Magazine, vol. 2, pp. 50-58, 2001.
[7] K. Noguchi, O. Mitomi, and H. Miyazawa, "Millimeter-Wave Ti:LiNbO3
Optical Modulators," Journal of Lightwave Technology, vol. 16, no. 4, pp.
615–619, 1998.
[8] M. M. Howerton, R. P. Moeller, A. S. Greenblatt, and R. Krahenbuhl, “Fully
packaged, broad-band LiNbO3 modulator with low drivevoltage,” IEEE
Photonics Technology Letters, vol. 12, no. 7, pp. 792–794, 2000.
[9] C. Lim, A. Nirmalathas, D. Novak, and R.Waterhouse, “Optimization of
baseband modulation scheme for millimeter-wave fiber-radio systems,”
Electronics Letters, vol. 36, pp. 442–443, 2000.
[10] T. Kawanishi, S. Oikawa, K. Higuma, Y. Matsuo, and M. Izutsu, “LiNbO3
resonant-type optical modulator with double-stub structure,” Electronics Letters,
vol. 37, no. 20, pp. 1244–1246, 2001.
6
[11] D. A. Cohen, M. Hossein-Zadeh, and A. F. J. Levi, "Microphotonic modulator
for microwave receiver," Electronics Letters, vol. 37, pp. 300-1, 2001.
[12] S. R. Marder, B. Kippelen, A. K.-Y. Jen, and N. Peyghambarian, "Design and
synthesis of chromophores and polymers for electro-optic and photorefractive
applications," Nature, vol. 388, pp. 845-851, 1997.
[13] L. R. Dalton, "Nonlinear Optics – Applications: Electro-Optics EO,"
Encyclopedia of Modern Optics, pp.121 –129, 2003.
[14] L. R. Dalton, B. H. Robinson, A. K. Jen, W. H. Steier, R. Nielsen, "Systematic
development of high bandwidth, low drive voltage organic electro-optic devices
and their applications," Optical Materials, vol. 21, pp.19 –28, 2003.
[15] L. R. Dalton, "Organic electro-optic materials," Pure and Applied Chemistry,
vol. 76, Iss. 7-8, pp.1421 –1433, 2004.
[16] W. H. Steier, A. Chen, S.-S. Lee, S. Garner, H. Zhang, V. Chuyanov, L. R.
Dalton, F. Wang, A. S. Ren, C. Zhang, G. Todorova, A. Harper, H. R.
Fetterman, D. Chen, A. Udupa, D. Bhattacharya, and B. Tsap, “Polymer
electro-optic devices for integrated optics,” Chemical Physics 245, pp.487-506
1999.
[17] M.-C. Oh, H. Zhang, C. Zhang, H. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep,
W. H. Steier, H. R. Fetterman, and L. R. Dalton, "Recent advances in
electrooptic polymer modulators incorporating highly nonlinear chromophore,"
IEEE Journal of Selected Topics in Quantum Electronics, vol. 7, pp. 826-835,
2001.
[18] J. Luo, M. Haller, M. Ma, S. Liu, T. D. Kim, Y. Tian, S. H. Jang, B. Chen, L. R.
Dalton, A. K. Jen, "Nanoscale architectural controland macromolecular
engineering of nonlinear optical dendrimers and polymers for electro-optics,"
Journal of Physical Chemistry B, vol. 108, Iss. 25, pp. 8523 –8530, 2004.
[19] M. Lee, O. Mitrofanov, H. E. Katz, and C. Erben, "Millimeter-wave dielectric
properties of electro-optic polymer materials," Applied Physics Letters 81, pp.
1474-6, 2002.
[20] C. C. Teng, "Traveling-wave polymeric optical intensity modulator with more
than 40 GHz of 3-dB electrical bandwidth," Applied Physics Letters 60, pp.
1538-40, 1992.
7
[21] M. Lee, H. E. Katz, C. Erben, D. M. Gill, P. Gopalan, J. D. Heber, and D. J.
McGee, "Broadband modulation of light by using an electro-optic polymer,"
Science 298, pp. 1401-3, 2002.
[22] H. Zhang, M.-C. Oh, A. Szep, W. H. Steier, C. Zhang, L. R. Dalton, H. Erlig, Y.
Chang, D. H. Chang, and H. R. Fetterman, "Push-pull electro-optic polymer
modulators with low half-wave voltage and low loss at both 1310 and 1550
nm," Applied Physics Letters 78, pp. 3136-8, 2001.
[23] Y. Shi, Cheng Zhang, Hua Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson,
and W. H. Steier, "Low (sub-1-volt) halfwave voltage polymeric electro-optic
modulators achieved by controlling chromophore shape," Science 288, pp.
119-22, 2000.
[24] Y. Shi, W.. Lin, D. J. Olson, J. H. Bechtel, H. Zhang, W. H. Steier, C. Zhang,
and L. R. Dalton, "Electro-optic polymer modulators with 0.8 V half-wave
voltage," Applied Physics Letters 77, pp. 1-3, 2000.
[25] D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and
Y. Shi, "Demonstration of 110 GHz electro-optic polymer modulators," Applied
Physics Letters 70, pp. 3335–7, 1997.
[26] S. Kalluri, M. Ziari, A. Chen, V. Chuyanov, W. H. Steier, D. Chen, B. Jalali, H.
Fetterman, and L. R. Dalton, "Monolithic integration of waveguide polymer
electrooptic modulators on VLSI circuitry," IEEE Photonics Technology Letters,
vol. 8, pp. 644-646, 1996.
8
Chapter 2
Ring Resonator Based Electro-Optic
Modulators
2.1 Introduction
Integrated optical ring resonators first proposed by Marcatili [1] have attracted
great interest in the last decade because of their various functionalities and the
progress of fabrication technologies. They can be used for laser cavities [2], filters
[3], add/drop multiplexers/demultiplexers [4], sensors [5], and modulators [6]–[11].
They have many potential applications in optical communication systems, and will
be used as building blocks for future VLSI photonics [12]. The progress so far has
worked itself up into books [13], [14]. Recently electro-optically active ring or disk
resonators have been demonstrated vigorously for switching of light by electro-optic
(EO) polymers [6], semiconductors [7]–[11], and nonlinear inorganic crystals
[15]–[18], because they are compact and require low driving power. High Q optical
resonances result in increased modulation efficiency but the RF bandwidth is limited
9
by the resonator line-width [19]. The modulators can be operated at this bandwidth
either at baseband or at an RF frequency equal to a multiple of the free spectral range
(FSR) of the resonator. The 10-100s µm polymer and semiconductor devices in
baseband operation have been proposed to be wavelength sensitive switches or
modulators in digital WDM systems [6]–[11]. On the other hand, the LiNbO3 disk
modulators that utilize whispering-gallery modes in a disk resonator have been
demonstrated in FSR frequency band-pass operation [15]–[18]. The functionalities of
disk resonators are basically equivalent to ring resonators, but in order to obtain the
FSR of microwave or millimeter-wave regions, the sizes of a demonstrated LiNbO3
disks, radii of few millimeters, were larger than polymer and semiconductor
integrated ring resonators. The prism coupling method was used to couple the input
and output light to a disk resonator. These high Q disk modulators are efficient
devices for systems requiring narrow RF bandwidth but operation at high carrier
frequencies. The potential application could be analog optic applications such as
photonic RF receivers for future wireless systems in a millimeter wavelength
domain.
This chapter presents the theory of ring resonator based EO modulators. After
introducing the basic transmission characteristics of ring resonators, the concept of a
ring modulator is explained and the sensitivity of a modulator is defined. The issue
of modulation bandwidth is addressed and the general expression to analyze the
modulation frequency response of a ring modulator is derived. Finally,
10
traveling-wave ring modulators are proposed and analyzed using derived analytical
expressions.
2.2 Ring Resonator Basics
In this section, the basic transmission characteristics of ring resonators are
briefly described for the following discussions. The analysis follows closely
reference [20] and [21]. The detailed analysis is also found in a review paper [22].
The generic geometry of a ring resonator coupled to a bus waveguide is illustrated in
Figure 2.1. Under the condition that a single mode of the resonator is excited and that
the coupling is lossless, the interaction can be described by means of two real
amplitude coupling constants κ and τ and a unitary scattering matrix
 a2   τ
  = 
 b2   − iκ
− iκ  a1 
 ,
τ  b1 
τ 2 + κ 2 = 1.
(2.1)
θ = βL ,
(2.2)
The transmission around the ring is given by
b1 = αe − iθ b2 ,
α =e
−
ρL
2
,
where β, ρ, and L are propagation constant, attenuation coefficient, and perimeter of
a ring, respectively. Thus α and θ represent the loss factor and phase shift after one
round trip. From (2.1) and (2.2), one obtains
τ − α e − iθ
a2 =
a1 .
1 − ταe −iθ
(2.3)
11
a1
a2
κ, τ
b1
b2
Figure 2.1: The generic geometry of ring resonator (one bus waveguide).
Same result can be given by the summation of multiple round trips [23].
a 2 = τa1 − κ 2αe − iθ a1 − κ 2τ (αe − iθ ) 2 a1 − L
∞


= τ − κ 2 ∑τ n −1 (αe −iθ ) n  a1
n =1


− iθ
τ − αe
=
a1
1 − ταe −iθ
(2.4)
This expression is useful in analyzing the properties of EO modulation later. The
transmission of a ring resonator is
a
T (θ ) = 2
a1
2
= 1−
(1 − α )(1 − τ )
2
2
(1 − ατ )2 + 4ατ sin 2 (θ 2)
.
(2.5)
Optical resonances occur where θ = 2mπ , where m is some integer. When the
internal losses in ring, α, are equal to the coupling losses, τ, the transmitted power
vanishes. This condition is called critical coupling. For α < τ, the resonator is said to
be undercoupled and for α > τ the resonator is said to be overcoupled. The
12
1
Intensity
0.85 (over)
0.95 (under)
0.5
0
2mπ
2(m+1)π
Phase θ
3π
0.85 (over)
Phase Sift
2π
π
0
0.95 (under)
−π
2mπ
Phase θ
2(m+1)π
Figure 2.2: The intensity transfer function and phase shift of a
ring resonator (α = 0.9,τ = 0.95 and 0.85).
critically coupled ring resonator can be used as a notch filter. In case of low loss
(α ≅ 1) and over-coupling (α > τ ), the relatively flat intensity response and the rapid
phase change at resonances can be used as a phase filter or all-pass filter. Figure 2.2
shows the optical intensity transfer function T(θ) and the phase shift of slightly over
and under coupled ring resonators.
13
The full phase width at half maximum (FWHM), ∆θ, and the finesse of a
transfer function are obtained from (2.5)
∆θ = 4 sin −1 (
1 − ατ
2 + 2α 2τ 2
)≈
2(1 − ατ )
ατ
2π π ατ
≈
F=
∆θ 1 − ατ
.
(2.6)
The separation of each resonance peaks that is called the free spectral range, FSR, is
given by
FSR =
c
ng L
,
ng =
∂β
∂n
= n−λ
,
∂k
∂λ
(2.7)
where ng is the group index and c is the speed of light. Translating to wavelength,
one gets
FSRλ =
λ2
ng L
.
(2.8)
Using the relation that F = FSR / ∆f , the full frequency and wavelength width at
half maximum (FWHM) are
∆f =
λ2
c
, ∆λ =
.
Fn g L
Fn g L
(2.9)
The quality factor Q of a resonator is given by
Q=
Fn g L
f
λ
=
=
.
λ
∆f ∆λ
To derive the expression of intrinsic or unloaded Q0, setting τ = 1 and α ≈ 1 ,
(2.10)
14
Q0 ≈
πn g L
2πn g
≈
.
(1 − α )λ
ρλ
(2.11)
Thus, Q0 is dominated only by attenuation coefficient, namely loss per unit length.
The intrinsic finesse is also obtained as
F0 ≈
2π
.
ρL
(2.12)
Thus, F0 is dominated by loss per round trip. When the resonator is coupled to two
bus waveguides as illustrated in Figure 2.3, the outputs are similarly derived as
athrough =
τ 1 − ατ 2 e −iθ
ainput
1 − ατ 1τ 2 e −iθ
−
a drop
iθ
− α κ 1κ 2 e 2
=
ainput
1 − ατ 1τ 2 e −iθ
.
(2.13)
The condition for critical coupling is modified to τ1 = ατ2. As shown in Figure 2.4,
this situation can be used as channel add/drop filters. Note that this configuration is
totally equivalent to Fabry-Perot resonators.
ain
κ1, τ1
athrough
κ2, τ2
adrop
aadd
Figure 2.3: The generic geometry of ring resonator (two bus waveguides).
15
Intensity at Through
1
0.5
0
2mπ
2(m+1)π
Phase θ
Intensity at Drop
1
0.5
0
2mπ
2(m+1)π
Phase θ
Figure 2.4: The transmission spectrum of ring resonator with two bus
waveguides at through and drop ports (α = 0.9,τ1 = 0.85 and τ2 = 0.944).
2.3 Electro-Optic Ring Modulators
A ring resonator made of EO material is considered. When a voltage V0 is
applied to a ring, the phase shift θ is expressed by [24]
16
πno 3 rΓV0
,
θ = θ 0 + ∆β L , ∆β =
λg
(2.14)
where θ0 is the bias phase, L is the perimeter of the ring, no is the effective index of
the ring waveguide, λ is the free space optical wavelength, r is the EO coefficient, g
is the electrode gap, and Γ is the electrical-optical overlap integral. The output
intensity is given by (2.5). If the frequency of the incident light is adjusted to around
resonances or the ring resonator is properly voltage-biased, the output intensity will
be strongly modulated with a small modulating voltage. This situation is illustrated
in Figure 2.5. The high modulation depth results from the sharp slope of the
transmission spectrum. Higher Q of a ring resonator provides higher sensitivity. Ring
modulators are categorized in optical resonant modulators, and the basic mechanism
of modulation is similar to Fabry-Perot modulators [24]–[28].
The EO tuning efficiency of resonant frequencies is given by
3
2
cn rΓ
df
df dn
f n o rΓ
=
=−
=− o
.
dV dn dV
no 2 g
2λg
(2.15)
For example, when no = 1.6, r = 50 pm/V, Γ = 1, λ = 1.31 µm, and g = 10 µm, the
EO tuning sensitivity is 1.47 GHz/V. Hence the voltage needed for tuning the
FWHM of a resonance, V∆f, is
V∆f =
∆f
.
df
dV
(2.16)
It is obvious that smaller ∆f, namely higher Q, gives smaller V∆f. Therefore, the
Intensity
17
Voltage
Figure 2.5: Conceptual drawing of the modulation by a ring modulator.
sensitivity of ring modulators is basically dominated not by the diameter of the
resonator but by its Q as discussed in [6]. This feature of ring modulators is
important for future VLSI photonics, because micro-modulators can provide high
modulation sensitivity in principle. V∆f corresponds roughly to the on-off voltage,
and is a useful measure for digital applications. Another definition of the modulator
sensitivity is based on the slope of the transfer function with respect to voltage and is
useful for analog optical link applications. By comparing dT dV
max
of a ring
modulator with that of a Mach-Zehnder (MZ) modulator, the sensitivity of a ring
modulator, an equivalent Vπeq, can be defined as [19]
18
Vπ
eq
π  dT


= 
2  dV max 
−1
π  dT dθ
= 
2  dθ dV


max 
−1
(2.17)
Since the Vπ of a single-arm driven MZ modulator is expressed by
Vπ
MZ
 dθ
= π 
 dV
−1

 ,

(2.18)
the enhancement of the modulation sensitivity by optical resonance is the factor of
2 × dT dθ if the device parameters are same. For example, the condition of a
finesse of 10 and critical coupling provides α = τ = 0.8524 and dT dθ
max
= 2.02 at
θ0 = 0.059π. A MZ modulator must have an electrode length of 4.04 × L to obtain the
same modulation sensitivity as the ring modulator with a finesse of 10. Of course,
higher finesse gives higher enhancement. Table 2.1 summarizes the numerical
example values and sensitivities of an EO polymer device.
Table 2.1: Numerical example values of an EO polymer device
Index of polymer no
EO coefficient r
Overlap integral Γ
Wavelength of light λ
Electrode gap g
Tuning sensitivity df/dV
VπΜΖL
VπeqL (Finesse 10)
1.6
50 pm/V
1
1.31 µm
10 µm
1.47 GHz/V
6.4 Vcm
1.58 Vcm
19
2.4 Bandwidth of Ring Modulators
The bandwidth of a ring modulator is limited by several physical constraints.
The modulation bandwidth of semiconductor ring or disk modulators using free
carrier injection mechanism is usually limited to a few GHz [9], [11]. The use of
depletion width transition improved it to be 8 GHz [10], but the limitation is still due
to the material response. The Pockels effect in nonlinear inorganic crystals and EO
polymers is a very fast process, enabling the material limitation to be negligible.
When the electrode of a modulator is a lumped element, usually there are two types
of bandwidth limitations: the capacitance limited bandwidth and the transit-time
limited bandwidth [24]. When the capacitance between electrodes, C, is parallel to
termination load R, the bandwidth is given by BWcap ≈ 1 / πRC . When the transit
time for light to pass through the electrode region, t = nL / c , is comparable to the
modulation period 1/fm, the optical phase no more follows the time-varying refractive
index adiabatically. This bandwidth is arbitrarily but conventionally given by
BWtransit ≈ c / 2nL . Another limitation of the bandwidth in optical resonator based
modulators is the optical resonator line width, the FWHM of optical resonance, thus
BWopt ≈ ∆f around the frequencies of n × FSR , where n is an integer. This is a
trade-off for an increase in sensitivity by optical resonance structures. In EO polymer
microring modulators, BWopt < BWtransit = FSR/2 < BWcap, since the capacitance C is
20
small. Therefore, the modulation bandwidth of lumped element microring
modulators is BWopt and operated in baseband (0 ~ BWopt).
The general expression to analyze modulation properties of ring modulators is
derived in the following. When a modulation RF signal V0sinωmt is applied to an EO
ring, the output amplitude Eout(t), using the multiple round trips approach (2.4), is
given by [23]
∞


Eout (t ) = τ − κ 2 ∑τ n−1α n exp[− i (nθ + δ n sin(ω m t − nφ ))] Ein (t )
n =1


(2.19)
where φ = ωm/FSR. It is assumed that the group index and effective index of a
waveguide are same. The dispersions of propagation constants, coupling coefficients,
and loss are neglected. The modulation index δn depends on the electrode structure.
In case of a lumped electrode, it is given by [24]


δ n sin (ω m t − nφ ) = ∫ ∆β sin ω m  t +
nL
no
c


z  − nφ  dz


 
sin (nφ 2 ) 
n 
sin  ω m t − φ 
= ∆β L
φ 2
2 

0
.
(2.20)
Now the optical power of the transmitted signal can be given by substituting (2.20)
into (2.19) and calculating the first component of the Fourier expansion of the output
intensity
I ωm =
2 T
2
E out (t ) e iωmt dt
∫
T 0
(2.21)
where T = 2π/ωm. Note that the electrical signal power in a photo detector is
21
proportional to the square of the optical signal power. Figure 2.6 shows the
small-signal frequency responses in dBe of the modulated output from lumped ring
modulators, optically biased to the maximum slope with a finesse of 10. The
responses are normalized by low modulation frequency response. The modulating
frequency is normalized by the FSR. The modulation is clearly limited by optical
resonator bandwidth. The 3 dBe bandwidth BWopt is 0.0845. Notice that this
bandwidth is somewhat larger than the half of the resonator line-width (0.05 for
Response (dB in electrical)
F=10).
0
-5
-10
-15
-20
0
0.1
0.2
0.3
0.4
Modulation Frequency (FSR)
0.5
Figure 2.6: The small-signal frequency responses in dBe of the
modulated output from a ring modulator with a lumped electrode,
optically biased to the maximum slope with a finesse of 10. The
responses are normalized by low modulation frequency response.
22
2.5 Traveling-Wave Ring Modulators
At baseband, an electrode, which fully covers the ring resonator, can be
considered a lumped electrode. However, for operation at a multiple of the FSR, the
circumference of the electrode is a multiple of the RF wavelength and the electrode
must be considered as a traveling-wave structure, or a RF resonant frequency of the
resonant electrode must coincide with a FSR modulation frequency as demonstrated
in [15]–[18]. In [29], the electrode was a traveling-wave RF resonator whose
resonant frequency equaled the FSR of the disc resonator. In this section, the
performance of a ring modulator with a traveling-wave electrode is analyzed, and is
compared to that of a MZ modulator. The effects of an optical/microwave velocity
mismatch and the loss of the microwave transmission line on the performance
comparison are included.
The traveling-wave ring modulator is illustrated in Figure 2.7. A microstrip line
electrode that is impedance-matched to the driving cable and termination covers an
EO ring resonator. Assuming no microwave loss, one considers the drive signal
 n 
V ( z , t ) = V0 sin ω m  t − m z 
c 

(2.22)
where nm is the microwave effective index. The voltage seen at position z along the
ring resonator waveguide by photons that enter the z = 0 at t = t is given by [30]
 ∆n 
V ( z , t ) = V 0 sin ω m  t −
z
c 

(2.23)
23
z
0
microwave in
Figure 2.7: Traveling-wave ring modulator
where no is the optical index and ∆n = nm − no . The modulation index δn is given by

∆n 

z  − nφ  dz
c 
k =0
 

sin (ψ / 2) sin (nφ 2) 
ψ n +1 
= ∆βL
φ
sin  ω m t − −
(ψ / 2) sin (φ 2) 
2
2 
n −1

δ n sin (ω m t − nφ ) = ∑ ∫ ∆β sin ω m  (t + kt r ) −
L
0
(2.24)
where t r = n o L c is the optical round trip time and ψ = ω m ∆nL c is the velocity
matching factor. The optical power of the transmitted signal can be given by
substituting (2.24) into (2.19), and then using (2.21).
The small-signal frequency responses in dBe of the modulated output from
velocity-matched (∆n = 0) ring modulators, optically biased to the maximum slope,
with a finesse of 10 and 30 are shown in Figure 2.8. The responses are normalized by
the small-signal response of a MZ modulator biased at quadrature with same
electrode length. The modulating frequency is normalized by the FSR. The
24
Response (dB in electrical)
25
F=30
20
15
F=10
10
5
0
-5
0
0.5
1
1.5
2
2.5
3
Modulation Frequency (FSR)
Figure 2.8: Modulation frequency responses of velocity-matched
traveling-wave ring modulators with the finesse of 10 and 30. The
responses are normalized by the response by a MZ modulator with same
electrode length.
velocity-matched traveling-wave ring modulators provide high modulation efficiency
at frequencies around all multiples of FSR. The 3 dBe bandwidth for F = 10 is 0.174
and for F = 30 is 0.0516. Notice that this bandwidth is somewhat larger than the
resonator line-width (0.1 for F = 10 and 0.033 for F = 30).
In addition to the velocity mismatch, another bandwidth limitation in
traveling-wave modulators is the loss of the microwave transmission line. For a
given electrode dimension, the high frequency microwave loss is determined by the
skin depth and one expects a loss in dB/cm of a = a0 f1/2, where a0 depends on
electrode conductivity and geometry. Assuming no velocity mismatch, the effect of
loss on the modulation index δn is [30]
25
n −1
δ n sin (ω m t − nφ ) = ∑ ∫ ∆βe −α z sin[ω m (t + kt r ) − nφ ]dz
k =0
L
m
0
1 − e −α m L sin (nφ 2) 
n +1 
= ∆β L
sin  ω m t −
φ
α m L sin (φ 2)
2 

(2.25)
where αm = a/8.7 converts from power loss in dB/cm to an exponential amplitude
loss coefficient.
To evaluate the effect of velocity mismatch and microwave loss in
traveling-wave ring modulators, the small-signal frequency responses of the output
with a MZ modulator with equal low frequency Vπ is compared. As a numerical
example, the parameters in Table 2.1 are used. Assuming a FSR of 30 GHz, a finesse
of 10, and critical coupling, the perimeter of the ring resonator is set to be 6.25 mm
and the Vπeq is 2.53 V. The electrode length of the equivalent MZ modulator is related
to be 2.53 cm.
Figure 2.9 shows the effect of velocity mismatch in the modulation frequency
response of the ring modulator and the equivalent MZ modulator for ∆n = 0.2. The
mismatch in LiNbO3 is much larger (∆n ~ 2) but can be reduced by design, while the
mismatch is negligible in EO polymer modulators. ∆n = 0.2 was chosen as a
compromise which clearly shows the effect. Figure 2.10 shows the effect of
microwave loss in the modulation frequency response of the ring modulator and the
MZ modulator with equal low frequency Vπ. The microwave power loss coefficient
of the microstrip line is 0.7 dB/cm·GHz1/2 which is typical for modulators [31]. No
26
Response (dB in electrical)
0
Ring
-5
-10
-15
MZ
-20
0
15
30
45
60
75
90
Modulation Frequency (GHz)
Response (dB in electrical)
Figure 2.9: Effect of velocity mismatch (∆n = 0.2, no microwave loss) in modulation
frequency response of the ring modulator with the FSR of 30 GHz (L = 6.25 mm)
and F = 10 compared to the equivalent broadband MZ modulator (L = 4.04×6.25
mm). The responses are normalized by the low frequency response.
0
Ring
-5
MZ
-10
-15
-20
0
15
30
45
60
Modulation Frequency (GHz)
75
90
Figure 2.10: Effect of microwave loss (a = 0.7 dB/cm·GHz1/2, ∆n = 0) in modulation
frequency response of the ring modulator with the FSR of 30 GHz (L = 6.25 mm)
and F = 10 compared to the equivalent broadband MZ modulator (L = 4.04×6.25
mm). The responses are normalized by the low frequency response.
27
velocity mismatch is assumed. In both cases, the ring modulator shows higher
modulation efficiency at frequencies around multiples of FSR than the equivalent
MZ modulator because of the shorter electrode length.
In summary, ring resonator based traveling-wave modulators have been
analyzed. The modulators show high modulation efficiency at frequencies around all
multiples of the FSR, and have better tolerance for the velocity mismatch and
microwave loss of the electrode than traveling-wave Mach-Zehnder modulators, thus
making them useful in microwave photonics applications. An example other than
communication applications is metrology systems [32]. Efficient generation of
modulation sidebands improves the precision of measurements. A ring modulator is
mathematically identical to a Fabry-Perot modulator as in [19]. In the traveling-wave
Fabry-Perot modulator [33], however, the microwave can interact only with one
direction of propagated light. In traveling-wave ring modulators, the microwave can
interact with light in the full length of a round trip due to unidirectional propagation.
Hence, they have a great potential not only for modulators but also for other
applications such as comb generation and pulse generation previously demonstrated
by Fabry-Perot modulators [33], [34].
2.6 References
[1] E. A. J. Marcatili, “Bends in optical dielectric waveguides” The Bell System
Technical Journal, 48, pp. 2103-2132, 1969.
28
[2] S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan,"
Whispering-gallery mode microdisk lasers," Applied Physics Letters, vol. 60, no.
3, pp 289-291,1992.
[3] B. E. Little, S. T. Chu, H. A. Haus, J. Foresi and J.-P. Laine, “Microring
Resonator Channel Dropping Filters,” Journal of Lightwave Technology, vol.
15, pp. 998-1005, June 1997.
[4] B. E. Little, S. T. Chu, W. Pan, Y. Kokubun, “An eight-channel add-drop filter
using vertically coupled microring resonators over a cross grid,” IEEE
Photonics Technology Letters, vol. 11, pp. 691-693, 1999.
[5] R. W. Boyd, and J. E. Heebner, “Sensitive disk resonator photonic biosensor,”
Applied Optics, 40, 31, pp. 5742-5747, 2001.
[6] P. Rabiei, W. H. Steier, C. Zhang, L. R. Dalton, “Polymer Micro-ring Filters
and Modulators,” Journal of Lightwave Technology, vol. 20, pp. 1968-75, 2002.
[7] K. D. Djordjev, S. J. Choi, S. J. Choi, and P. D. Dapkus, “Active semiconductor
microdisk device,” Journal of Lightwave Technology, vol. 20, no. 1, pp.
105-113, Jan. 2002.
[8] D. Rafizadeh, J. P. Zhang, S. C. Hagness, A. Taflove, K. A. Stair, S.T. Ho, and
R. C. Tiberio, “Waveguide-coupled AlGaAs/GaAs microcavity ring and disk
resonators with high finesse and 21.6-nm free spectral range,” Optics Letters,
vol. 22, no. 16, pp. 1244–1226, 1997.
[9] T. Sadagopan, S. J. Choi, S. J. Choi, K. D. Djordjev, and P. D. Dapkus,
“Carrier-Induced Refractive Index Changes in InP-Based Circular
Microresonators for Low-Voltage High-Speed Modulation," IEEE Photonics
Technology Letters, vol.17, no. 2, pp. 414–416, Feb. 2005.
[10] T. Sadagopan, S. J. Choi, S. J. Choi, P. D. Dapkus, and A. E. Bond, “Optical
Modulators Based on Depletion Width Translation in Semiconductor Microdisk
Resonators," IEEE Photonics Technology Letters, vol.17, no. 3, pp. 567–569,
Mar. 2005.
[11] Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon
electro-optic modulator,” Nature, vol. 435, pp. 325–327, May 2005.
29
[12] S. T. Chu, B. E. Little, W. Pan, T. Kaneko, S. Sato, and Y. Kokubun,
“Microring resonator arrays for VLSI photonics,” IEEE Photonics Technology
Letters, vol. 12, pp. 323-325, 2000.
[13] K. Vahala, Optical microcavities, World Scientific, 2004.
[14] F. Michelotti, A. Driessen, and M. Bertolotti, Microresonators as building
blocks for VLSI photonics, American Institute of Physics, 2004.
[15] D. A. Cohen and A. F. J. Levi, “Microphotonic components for a mm-wave
receiver,” Solid-State Electronics, vol. 45, pp. 495-505, 2001.
[16] D. A. Cohen, M. Hossein-Zadeh and A. F. J. Levi, “High-Q microphotonic
electro-optic modulator,” Solid-State Electronics, vol. 45, pp. 1577-1589, 2001.
[17] V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko and L. Maleki, “Sub-Micro
Watt Photonic Microwave Receiver,” IEEE Photonics Technology Letters, vol.
14, pp. 1602-1604, Nov. 2002.
[18] V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko and L. Maleki,
“Whispering-gallery-mode electro-optic modulator and photonic microwave
receiver,” Journal of the Optical Society of America B, vol. 20, pp. 333-342,
Feb. 2003.
[19] I.-L. Gheorma and R. M. Osgood, Jr., “Fundamental Limitations of Optical
Resonator Based on High-Speed EO Modulators,” IEEE Photonics Technology
Letters, vol. 14, pp. 795-797, June 2002.
[20] A. Yariv, “Universal relations for coupling of optical power between
microresonators and dielectric waveguides,” Electronics Letters, vol. 36, pp.
321-322, Feb. 2000.
[21] K. Okamoto, Fundamentals of Optical Waveguides, Academic Press, 2000.
[22] O. Schwelb, "Transmission, group delay, and dispersion in single-ring optical
resonators and add/drop filters-a tutorial overview," Journal of Lightwave
Technology, vol. 22, pp. 1380-1394, 2004.
[23] K.-P. Ho and J. M. Kahn, “Optical Frequency Comb Generator Using Phase
Modulation in Amplified Circulating Loop,” IEEE Photonics Technology
Letters, vol. 5, pp. 721-725, June 1993.
30
[24] A. Yariv and P. Yeh, Optical Waves in Crystals, John Wiley & Sons, 1984.
[25] E. I. Gordon and J. D. Rigden, “The Fabry-Perot Electrooptic Modulator,” The
Bell System Technical Journal, pp. 155-179, Jan. 1963.
[26] T. Kobayashi, T. Sueta, Y. Cho and Y. Matsuo, “High-repetition-rate optical
pulse generator using a Fabry-Perot electro-optic modulator,” Applied Physics
Letters, vol. 21, pp. 341-343, Oct. 1972.
[27] M. Kourogi, K. Nakagawa and M. Ohtsu, “Wide-Span Optical Frequency Comb
Generator for Accurate Optical Frequency Difference Measurement,” IEEE
Journal of Quantum Electronics, vol. 29, pp. 2693-2701, Oct. 1993.
[28] A. J. C. Vieira, P. R. Herczfeld, V. M. Contarino and G. Mizell, “Bulk
Fabry-Perot Intensity Modulator for LIDAR Systems,” IEEE Photonics
Technology Letters, vol. 8, pp. 782-784, June 1996.
[29] M. Hossein-Zadeh and A.F.J. Levi, “A new electrode design for microdisk
electro-optic RF modulator,” CLEO’03, pp. 863–865, June 2003.
[30] R. C. Alferness, “Waveguide Electooptic Modulators,” IEEE Transactions on
Microwave Theory and Techniques, vol. MTT-30, pp. 1121–1137, Aug. 1982.
[31] M. C. Oh, H. Zhang, C. Zhang, H. Erlig, C. Yian, B. Tsap, D. Chang, A. Szep,
W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent Advances in
Electrooptic Polymer Modulators Incorporating Highly Nonlinear
Chromophore,” IEEE Journal of Selected Topics in Quantum Electronics, vol. 7,
pp. 826–835, Sept./Oct. 2001.
[32] O. P. Lay, S. Dubovitsky, R. D. Peters, J. P. Burger, S.-W. Ahn, W. H. Steier, H.
R. Fetterman and Y. Chang, “MSTAR: a submicrometer absolute metrology
system,” Optics Letters, vol. 28, pp. 890-892, June 2003.
[33] T. Saitoh, S. Mattori, S. Kinugawa, K. Miyagi, A. Taniguchi, M. Kourogi, and
M. Ohtsu, “Modulation Characteristic of Waveguide-Type Optical Frequency
Comb Generator,” Journal of Lightwave Technology, vol. 16, pp. 824–832,
May 1998.
[34] M. Kato, K. Fujiura and T. Kurihara, “Generation of super-stable 40 GHz
pulses from Fabry-Perot resonator integration with electro-optic phase
modulator,” Electronics Letters, vol. 40, pp. 299 -301, March 2004.
31
Chapter 3
Demonstration of Electro-Optic Polymer
Traveling-Wave Ring Modulators
3.1 Introduction
The analysis in Chapter 2 shows the potential of an electro-optic (EO) polymer
ring modulator with a traveling-wave electrode for FSR modulation. This chapter
presents the experimental demonstration of FSR modulation, or band operation, in an
EO polymer ring modulator. The device designs of optical waveguides and RF
microstrip lines, device fabrications, and device characterizations in both low speed
and high speed are also described. The features of the modulator are as follows: (i)
modest Q optical resonance and modulation at the FSR result in efficient modulation
in a 7 GHz band centered at 28 GHz, (ii) the modulator is a waveguide device,
whereas previous LiNbO3 disk resonator based modulators used prism coupling to
input and output light, and (iii) the use of a traveling-electrode rather than a
capacitive electrode shows efficient modulation around the FSR frequency.
32
3.2 Device Design and Fabrication
To realize FSR modulation in EO polymer ring modulators, the initial target
modulation frequency was set to 30 GHz, because of the limitation of measurement
systems. Since the diameter of a ring resonator is in the millimeter range to obtain
the FSR of 30 GHz, the device design is different from previously demonstrated EO
polymer ring resonators [1]. The waveguide structure is rib-shaped instead of a
channel waveguide, because a rib-waveguide is enough to support the mode in a
bend of radius of 1 mm without bending loss. The racetrack shape ring resonator
with a straight coupling region is used to increase coupling interaction between a
ring resonator and a bus waveguide. The lateral coupling scheme can be used instead
of vertical coupling, because the straight coupling region allows 2 µm gap, which
can be fabricated by standard lithography, to obtain enough coupling power from a
bus waveguide to a resonator. All waveguide mode simulations and designs are done
by commercial mode solver Olympios® (C2V). Figure 3.1 (a) shows the calculated
the TM fundamental mode profile. The rib-shaped waveguide structure with 2 µm
width, 1 µm high rib, and 1 µm high slab is considered. The indices of the core and
the background are set to 1.61 and 1.5, respectively. The waveguide structure gives
the single mode. The effective index of the TM mode is 1.5784 at the wavelength of
1.31 µm. The group index (2.7) is estimated to be 1.622 at 1.31 µm. To estimate the
coupling strength at the straight coupling region, the even and odd modes in the
33
(a)
(b)
(c)
Figure 3.1: Calculated mode profiles (a) the fundamental mode of the waveguide, (b)
the even mode of the coupling region, and (c) the odd mode of the coupling region.
34
coupling region are calculated. The 2 µm separation between waveguides is
considered. The calculated even and odd modes are shown in Figure 3.1 (b) and (c).
Since the mode coupling coefficient Κ is given by [2]
Κ=
π
(neven − nodd ) ,
λ
(3.1)
Κ is given to be 2.926×10-3 µm-1 at 1.31 µm. The amplitude coupling constants κ and
τ (2.1) are given by [2]
κ = sin (ΚLeff ) , τ = cos(ΚLeff ) ,
(3.2)
where Leff is the effective coupling length. For example, the effective coupling length
of 200 µm gives κ = 0.552 and τ = 0.834. Note that the effective coupling length is
longer than the straight coupling length because of the contribution from transition
regions between the curved region and the straight region. For reference, if the
waveguide loss of 4 dB/cm is assumed, a ring resonator with 2 mm diameter gives
the round trip loss factor α of 0.749. The critical coupling (α = τ) is the best
condition for amplitude modulators. Figure 3.2 illustrates lateral dimensions of the
ring resonators. The straight coupling region lengths of 100 µm, 150 µm, 200 µm,
and 250 µm were considered to obtain near critical coupling condition.
The ring modulator was made from EO polymer AJL8/APC [3]. Highly
nonlinear AJL8 chromophore is doped into amorphous polycarbonate (APC, Aldrich)
host matrix. The weight ratio of AJL8 to APC is 1 to 3. A solution of 7 vol.% in
1,1,2-trichloroethane was used for this experiment. The chemical structures of AJL8
35
1 mm
100 - 250 µm
Waveguide Width: 2 µm
Coupling Gap: 2 µm
Figure 3.2: The lateral dimensions of the racetrack ring resonator.
AJL8
APC
Figure 3.3: The chemical structures of AJL8 and APC.
36
chromophore and APC are shown in Figure 3.3. The single layer films of AJL8/APC
showed a high EO coefficient r33 of 94 pm/V at 1.3 µm [3].
The fabrication steps are shown in Figure 3.4. First, the 200 nm thick bottom Au
electrode is deposited on a 10 nm thick Cr coated silicon substrate and then the
electrode is patterned. The 5 µm thick UV15LV (Master Bond Co.) lower cladding is
spin coated and cured by UV light for 30 sec and the sample is baked for 2 hrs at
160 °C. The waveguide pattern in a photo mask is transferred on UV15 lower
cladding layer by standard lithography. MICROPOSIT® S1800® series photo resist
(Shipley) is used to obtain 2 µm line/space structures. UV15 layer is etched using
RIE in oxygen to form ribs of waveguides [4]. The etched rib depths are from 0.9 –
1.2 µm. Next, a 1 µm thick AJL8/APC layer is coated and baked for 1 hr at 120 °C.
The surface of the core layer is almost flat. Then, the 4 µm thick UFC170A (Uray
Co.) upper cladding is spin coated and cured by UV light for 10 sec and the sample is
baked for 1 hr at 120 °C. The sample is corona-poled to align AJL8 chromophore at
145 °C for 10 min. The poling voltage is set to 11 kV and the distance between the
tip of the electrode and the sample is 2 cm. Then, the top Au electrode is formed by
vacuum evaporation and electroplating with 2 µm thickness and 17 µm width. The
top Au electrode is microstrip line for which the characteristic impedance is designed
to be 50 Ω. Finally, the device is cut by a Ni dicing blade for fiber coupling.
37
Patterned Cr/Au
Si
Spin Cladding
UV15
Lithography
RIE
Spin Core
AJL8/APC
Spin Cladding
UFC170
Corona Poling
Cr/Au deposition
Lithography
Au Plating
Au
Figure 3.4: Fabrication steps of an EO polymer ring modulator.
38
The top view optical microscope image and the schematic cross section of the
fabricated modulator are shown in Figure 3.5. Both the ring and the bus waveguide
are rib-shaped with 2 µm width, 1 µm high rib, and 1 µm high slab. The gap between
the top and bottom electrodes is 10 µm. The refractive indices of UV15LV,
AJL8/APC, and UFC170A are 1.505, 1.61, and 1.50, respectively, which are
measured by an ellipsometer. Figure 3.6 is the microscope image of the straight
coupling region. The 150 µm straight coupling region of the ring resonator is
laterally coupled to a bus waveguide with the gap being 2 µm.
r = 1 mm
Light In
Light Out
RF Out
RF In
Au
AJL8/APC
UFC170
4 µm
1 µm
UV15
2µm 2µm 2µm
2µm
5 µm
Si
Au
Figure 3.5: The top view optical microscope image and schematic
cross section of the fabricated modulator.
39
Figure 3.6: Optical microscope image of the straight coupling region
of the racetrack ring resonator.
3.3 Basic Characteristics of Devices
The basic characteristics of the modulator are measured. The light source is a
tunable laser (New Focus 6200) at the wavelength of 1.31 µm. The input and output
light are butt-coupled through the small core fibers (UHNA3). The fiber-to-fiber
insertion loss is –10 ~ –12 dB. The transmission spectrum is measured by the
frequency modulation of the laser source. The schematic setup for measuring the
transmission spectrum is shown in Figure 3.7. Figure 3.8 shows the transmission
spectrum of the TM mode of the ring modulator. The polarization of input light is
selected by a polarization controller. The full width at half maximum (FWHM) and
the FSR of the device are 5.1 GHz and 28 GHz, respectively. Thus the experimental
or loaded Q is 4.5×104 and the finesse is 5.5. From the extinction ratio of -14 dB, the
intrinsic Q and the waveguide loss are estimated to be 7.1×104 and 4.8 dB/cm,
respectively. Since the material loss of AJL8/APC is approximately 2 dB/cm, the
40
Function
Generator
Oscillo
scope
Ring
Resonator
Tunable
Laser
Detector
Figure 3.7: Schematic setup for measuring transmission spectrum.
Normalized Intensity (dB)
0
-3
-6
-9
-12
-15
-10
0
10
20
30
40
Frequency Detuning from Resonance (GHz)
Figure 3.8: The transmission spectrum of the TM mode of the ring modulator.
excess 2.8 dB/cm is the scattering loss from the sidewall roughness due to
fabrication. The parameters in the theoretical transfer function (2.5) is given to be α
= 0.696 and τ = 0.783.
The EO tuning sensitivity is measured by applying a 100 Hz triangle voltage to
the electrode. The laser wavelength is fixed. The schematic setup for measuring the
41
EO tuning sensitivity is shown in Figure 3.9. Figure 3.10 shows the modulated TM
light from the ring modulator. The applied peak-to-peak voltage is 20 V. The EO
tuning sensitivity is 1 GHz/V, which corresponds to an effective EO coefficient r =
33 pm/V of the core layer. The FWHM voltage V∆f (2.15) is 5.1 V. The equivalent
Vπeq (2.16) is estimated to be 7 V.
Function
Generator
Oscillo
scope
Ring
Modulator
Tunable
Laser
Detector
Figure 3.9: Schematic setup for measuring EO tuning sensitivity.
Figure 3.10: The modulated TM light from the ring modulator (Vpp = 20 V).
42
3.4 High Frequency Measurements and Results
The 50 Ω microstrip line electrode consists of the microstrip section, feeding
pad, and termination pad, as shown in Figure 3.11. The purpose of the feeding and
termination pad is to give better transition between a RF probe and the microstrip.
The detailed dimensions of the feeding pad are shown in Figure 3.12. Since the
width of the microstrip is 17 µm, a contact pad must be incorporated to allow a RF
probe to touch it. To maintain the 50 Ω input impedance, the ground plane must be
cut out underneath the pad. The contact pad and the cutout ground plane form a
quasi-CPW transmission line. At the other end of the line, a RF terminator is required
to minimize the reflection. A 50 Ω chip resistor (State of the Arts S0202AF) is put on
Figure 3.11: Optical microscope image of the traveling-wave electrode
with 50 Ω microstrip and two pads.
43
the side of the pad, and then the contact on the resistor is connected to the
termination pad on the device by Au ribbon. The ground plane is also bonded to
common ground by Au ribbons. The situation is illustrated in Figure 3.13. Figure
3.14 shows the S-parameter, S11, of this traveling-wave electrode from 1 to 40 GHz,
which is measured by HP RF network analyzer. The signals are launched onto the
feeding pad by a coplanar probe (Cascade ACP40). Since the S-parameter, S11, is less
than –10 dB from 0 to 30 GHz, the impedance matching is good.
50Ω Microstrip (17 µm)
394 µm
Top View
500 µm
517 µm
250 µm
Ground
Contact Pad
Cross Section
Substrate
Polymer
Figure 3.12: The detailed dimensions of the feeding pad.
44
Bottom Electrode
Microstrip
Device
Au Ribbon
Ground
Contact
Chip Resistor
Figure 3.13: Schematic drawing of the microstrip termination.
0
S11 (dB)
-10
-20
-30
0
10
20
30
40
Frequency (GHz)
Figure 3.14: S11 (reflection) of the traveling-wave electrode.
45
The response to high frequency modulation is measured by the modulation
sideband power in the optical spectrum analyzer (Ando AQ6317B). This method is
consistent with previous experiments on broadband modulators [5]–[7]. Sinusoidal
modulation signals up to 40 GHz are generated by a signal generator (Agilent
8244A). The microwave power is 10 dBm at each frequency. Optical spectra of the
modulated light at 22 GHz (0.125 nm), 28 GHz (0.16 nm), and 34 GHz (0.194 nm)
are shown in Figure 3.15. The input light was tuned at a resonance of the ring
modulator, because it is easy to repeat the same bias point in each modulation
frequency. Observed sidebands are due to phase modulation. The data shows that the
sideband power peaks at the modulation frequency of 28 GHz, which is the FSR of
-25
22 GHz
28 GHz
-30
Optical Power (dBm)
34 GHz
-35
-40
-45
-50
-55
-60
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Wavelength Shift (nm)
Figure 3.15: Optical spectra of the modulated light at 22 GHz, 28 GHz, and 34 GHz
46
Sideband Power (dBm)
-30
-35
-40
-45
-50
0
10
20
30
40
Modulation Frequency (GHz)
Figure 3.16: The modulation frequency dependence of optical sideband powers.
the ring modulator. Figure 3.16 shows the modulation frequency dependence of
optical sideband powers. The side band power shows the minimum at the modulation
frequency of 14 GHz, which is off-resonance for the resonator, and the maximum at
28 GHz. The 3 dBe bandwidth of the detected signal power is the same as the 3 dB
bandwidth of the sideband power. From Figure 3.16, the signal 3 dBe bandwidth is
~7 GHz. This modulator would find application in analog optical links with the
sub-carrier frequency of around 28 GHz. The bias dependence of 28 GHz
modulation spectra is shown in Figure 3.17. When the input light is tuned at a
resonance, the carrier shows 15 dB suppression by optical resonance and the 28 GHz
47
-10
+0.014nm
Resonance
Optical Power (dBm)
-20
-0.014nm
-30
-40
-50
-60
1309.4
1309.5
1309.6
1309.7
1309.8
1309.9
1310
Wavelength (nm)
Figure 3.17: The bias dependence of 28 GHz modulation spectra.
modulation sidebands are observed. When the input light is tuned at near a half
transmission point, ±2.5 GHz (±0.014 nm) from a resonance, the carrier suppression
is approximately 3 dB and the 28 GHz modulation sidebands are also observed. By
considering the modulation scheme of a ring modulator described in Figure 2.5, the
modulation spectrum when the carrier is biased at 2.5 GHz from a resonance gives
the amplitude modulation signal. The modulation frequency dependence of the
amplitude modulation sideband power (±2.5 GHz from a resonance) is similar to that
of phase modulation (at a resonance) in Figure 3.16.
48
3.5 References
[1] P. Rabiei, W. H. Steier, C. Zhang, L. R. Dalton, “Polymer Micro-ring Filters
and Modulators,” Journal of Lightwave Technology, vol. 20, pp. 1968–75,
2002.
[2] K. Okamoto, Fundamentals of Optical Waveguides, Academic Press, 2000.
[3] J. Luo, S. Liu, M. Haller, J.-W. Kang, T.-D. Kim, S.-H. Jang, B. Chen, N.
Tucker, H. Li, H.-Z. Tang, L. R. Dalton, Y. Liao, B. H. Robinson, and A. K.-Y.
Jen, “Recent progress in developing highly efficient and thermally stable
nonlinear optical polymers for electro-optics,” Proceedings of the SPIE - The
International Society for Optical Engineering 5351, no. 1, pp.36–43, 2004.
[4] S. Kim, H. Zhang, D.H. Chang, C. Zhang, C. Wang, W.H. Steier, and H.R.
Fetterman, “Electrooptic polymer modulators with an inverted-rib waveguide
structure,” IEEE Photonics Technology Letters, vol. 15, pp. 218–220, Feb.
2003.
[5] D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and
Y. Shi, "Demonstration of 110 GHz electro-optic polymer modulators" Applied
Physics Letters, vol. 70, 3335–7, 1997.
[6] K. Noguchi, O. Mitomi, and H. Miyazawa, "Millimeter-Wave Ti:LiNbO3
Optical Modulators," Journal of Lightwave Technology, vol. 16, no. 4, pp.
615-619, 1998.
[7] M. Lee, H. E. Katz, C. Erben, D. M. Gill, P. Gopalan, J. D. Heber and D. J.
McGee, “Broadband Modulation of Light by Using an Electro-Optic Polymer,”
Science, vol. 298, pp. 1401–1403, Nov. 2002.
49
Chapter 4
Linearity of Ring Modulators
4.1 Introduction
In addition to the high modulation sensitivity at a RF carrier frequency, there is
another requirement for external Electro-optic (EO) modulators in analog optical
links: high linearity [1], [2]. The nonlinear transfer function of external modulators
results in generating harmonics and intermodulation (IM) products, limiting the
dynamic range (DR) of the link. A ring modulator has the potential for giving high
DR, since the Lorentzian-like transfer function of a ring modulator has a bias point at
which the third derivative is zero. In this chapter, the DR of ring modulators is
theoretically evaluated by the method by Bridges [3]. It is shown that ring
modulators provide the high IM-free DR, thus is useful in sub-octave bandpass
analog links. The scheme to expand DR using dual ring modulators is also
investigated. Finally, the linearity of ring modulators is experimentally studied to
confirm the theory.
50
4.2 Distortion in Modulators
In this section, the nonlinear distortion in modulators, the analytical method for
evaluating distortion in modulators, and the distortion in a Mach-Zehnder (MZ)
modulator are explained. The transfer function of any modulator can be modeled as a
Taylor series in terms of the input signal voltage
T (V ) = a 0 + a1V + a 2V 2 + a3V 3 + L .
(4.1)
Consider a two-tone input voltage, consisting of two closely spaced frequencies, ω1
and ω2
V = V0 (cos ω1t + cos ω 2 t )
(4.2)
From (4.1) the output is
T = a 0 + a1V0 cos ω1t + a1V0 cos ω 2 t +
1
2
a 2V0 (1 + cos 2ω1t )
2
1
2
2
2
a 2V0 (1 + cos 2ω 2 t ) + a 2V0 cos(ω1 − ω 2 )t + a 2V0 cos(ω1 + ω 2 )t
2
1
1


3 3
3 3
+ a 3V0  cos ω1t + cos 3ω1t  + a3V0  cos ω 2 t + cos 3ω 2 t 
4
4
4

4

+
(4.3)
3
3

3 3
+ a 3V0  cos ω 2 t + cos(2ω1 − ω 2 )t + cos(2ω1 + ω 2 )t 
4
4
2

3
3

3 3
+ a 3V0  cos ω1t + cos(2ω 2 − ω1 )t + cos(2ω 2 + ω1 )t  + L
4
4
2

Figure 4.1 shows a typical spectrum of the second and third order two-tone IM
products. If ω1 and ω2 are close, all distortion products except for 2ω1 – ω2 and 2ω2 –
ω1 are far from ω1 and ω2, and can easily be filtered from the output component.
51
ω1 ω2
0
ω2−ω1
2ω1−ω2
2ω2−ω1
ω2+ω1
2ω1
2ω1+ω2 2ω2+ω1
2ω2
3ω1
3ω2
ω
Figure 4.1: A typical spectrum of the second and third order two-tone IM products.
Therefore, the IM products, 2ω1 – ω2 and 2ω2 – ω1, will usually limit the DR of the
links.
The transfer function of a MZ modulator is given by [1]
TMZ (V ) =

 V
1
+ φ 
1 + cos π
2

 Vπ
(4.4)
where Vπ is the half-wave voltage and φ is the bias. This can be expanded around a
quadrature bias point φ = π/2, which is a standard operating point,
1 1 π
1π
TMZ (V ) ≈ +
V − 
2 2 Vπ
12  Vπ
3
 3
1 π

 V +
240
 Vπ

5
 5
 V − L

(4.5)
There are no even order terms, generating no even order distortions in MZ
modulators. However, the odd order terms, especially the third order term, causes
generating the IM products.
To evaluate and compare the linearity of modulators, Bridges [3] used
numerically calculated DR values by assuming link parameters. This method is very
convenient to analyze the arbitrary shape transfer function of modulators. Here the
52
method will be followed to evaluate the linearity of ring modulators in the next
section. Table 4.1 shows the link parameters. The model optical link is schematically
shown in Figure 4.2. If the input power Pin is applied to the modulator, the voltage
applied to the modulator is given by
V (t , Pin ) = 2 RM Pin (sin (2πat ) + sin (2πbt ))
(4.6)
The two-tone signal at frequencies a and b is assumed. The fundamental signal
power PSIG at the detector is given by
R
PSIG (Pin ) = D
2
2 T


 PL Loη ⋅ T ∫0 T (V (t , Pin )) exp(− i 2πat )dt 
2
(4.7)
where T = 1/(b–a). This integral is easily calculated by commercial software, such as
MathCAD®. Similarly, the second harmonic signal power P2H and the third-order IM
signal power PIM are given by
P2 H (Pin ) =
R
PIM (Pin ) = D
2
RD
2
2 T


P
L
η
T (V (t , Pin )) exp(− i 2π 2at )dt 
⋅
L
o
∫

0
T

2
2 T


 PL Loη ⋅ T ∫0 T (V (t , Pin )) exp(− i 2π (2a − b )t )dt 
(4.8)
2
(4.9)
The noise output power N in detector load is given by
2
N = GkT + RIN ⋅ I DC RD + 2eI DC RD + kT
(4.10)
where IDC is the average photocurrent and G is the small signal gain of the link. The
first term is the thermal noise from the modulator; the second is the relative intensity
noise of the laser; the third is the shot noise; the fourth is the thermal noise from the
53
Table 4.1: Link Parameters [3]
Laser Power
PL
0.1 W
Laser Noise
RIN
-165 dB/Hz
Total Optical Loss
Lo
-10 dB
Modulator sensitivity
Vπ, V∆f
10 V
Modulator Impedance
RM
50 Ω
Detector Responsivity
η
0.7 A/W
Detector Lord
RD
50 Ω
Noise Bandwidth
BW
1 Hz
Max Current
PL Lo η
7 mA
Pin
Laser
Modulator
PSIG, PIM
Fiber
Detector
Figure 4.2: The model optical link.
detector. Since G is usually less than unity, thermal noises are negligible in the
typical link parameters. In case of a MZ modulator, the parameters in Table 4.1 give
IDC = 3.5 mA. The noise power N becomes –161.2 dBm/Hz. Now the DR can be
calculated. The IM-free DR is defined as the ratio of the signal to IM power, when
the IM power equals the noise power. Figure 4.3 shows the signal power and IM
power of a MZ modulator as a function of the input signal power. The IM power
54
shows the third-order dependence. The link gain is –25.2 dB, the DR is 109.9 dB,
and the noise figure, N – GkT, is 38.0 dB, as in [3].
0
Output Power (dBm)
-40
-80
Signal
DR
IM
-120
-160
-200
-160
Noise Floor
-120
-80
-40
0
40
Input Power (dBm)
Figure 4.3: The signal power and IM power of a MZ modulator as a
function of the input signal power.
4.3 Distortion in Ring Modulators
Many of analog optical link applications require high IM-free DR, but have
bandwidths less than an octave; so second-order distortion is not a problem [4], [5].
As seen in the previous section, a MZ modulator is operated at the quadrature bias
point at which the second derivative of the transfer function is zero; eliminating
second-order distortion but with a remaining third-order distortion. On the other
55
hand, a directional coupler modulator and an electro-absorption modulator have a
bias point at which the third derivative of the transfer function is zero, providing high
IM-free DR for sub-octave systems [3], [6]. The transfer function of a ring modulator
has a bias point at which the third derivative is zero and a second bias point at which
the second derivative is zero. The ring modulator could therefore be used at the first
bias point in a sub-octave system to obtain high IM-free DR.
The response of any resonator can be modeled by a Lorentzian function [7]. The
analytical transfer function (2.5) of a ring resonator converges to a Lorentzian
function as the finesse increases. Therefore, the transfer function of a ring modulator
can be modeled as
TRing (V ) =
V2
V 2 + (V∆f 2 )
2
(4.11)
where V∆f is the FWHM voltage (2.15). The third derivative of the transfer function
is zero at V = V∆f /2. The Taylor expansion around V = V∆f /2 becomes
TRing (V ) ≈
1
11
1
2
4
V−
V2 +
V4 −
V 5 +L
+
2
4
5
2 5V∆f
V∆f
V∆f
V∆f
(4.12)
The bias at V = V∆f /2 gives the half transmission and no third-order distortion. The
IM power will be produced by the fifth-order distortion, which is the lowest odd
order distortion. Figure 4.4 shows the signal power, the second harmonic power and
the IM power of a ring modulator as a function of the input signal power. The link
parameters in Table 4.1 are used. The IM power shows the fifth-order dependence,
56
because of no third-order distortion. The link gain is –29.1 dB, the IM-free DR is
125.5 dB, and the noise figure is 41.9 dB. The similar results have also been obtained
by the study in a Fabry-Perot intensity modulator [8]. This higher IM-free DR and
the high modulation sensitivity at a high RF frequency of ring modulators will be
suitable for sub-octave bandpass analog optical links.
Output Power (dBm)
0
-40
-80
DR
Signal
IM
-120
2H
-160
Noise Floor
-200
-160
-120
-80
-40
0
40
Input Power (dBm)
Figure 4.4: The signal power and IM power of a ring modulator as a
function of the input signal power.
4.4 Double Parallel Ring Modulator
The dual parallel scheme is widely used to remove undesired distortion in a MZ
modulator [9]–[13]. This scheme is applied to a ring resonator, as illustrated in
57
V1
Detector
P1
P2
-V2
Figure 4.5: Dual parallel ring modulator.
Figure 4.5. The applied RF signals are same, but at different levels and 180° out of
phase. The two optical outputs are combined either coherently or incoherently. The
RF and optical power splitting ratios are chosen so that the fifth-order distortion is
canceled. When ring modulators are biased at V = V∆f /2, the splitting ratios, V1 : V2
= 1 : 1.9, P1 : P2 = 1.95 : 1 provide the highest IM-free DR. Figure 4.6 shows the
output signal, second harmonic and IM powers of dual parallel ring modulators. The
link parameters in Table 4.1 are used. In fact, the splitting ratio of P1 : P2 = 24.6 : 1
improves somewhat the IM-fee DR. The IM power shows the ninth-order
dependence because the seventh derivative of a Lorentzian transfer function is zero
at V = V∆f /2. The link gain is –39.4 dB, the IM-free DR is 136.1 dB, and the noise
figure is 52.2 dB. This scheme provides the highest order correction of distortion
using two modulators. Table 4.2 compares the IM-free DRs for different modulator
types.
58
0
Output Power (dBm)
-40
-80
IM
Signal
DR
-120
2H
-160
Noise Floor
-200
-160
-120
-80
-40
0
40
Input Power (dBm)
Figure 4.6. The signal power and IM power of dual parallel ring modulators
as a function of the input signal power
Table 4.2: Comparison of the intermodulation-free dynamic
ranges for different modulator types
Modulator Type
Dynamic Range
Mach-Zehnder
109.9 dB [3]
Dual Mach-Zehnder
129.7 dB [3]
Directional Coupler
135.4 dB [3]
Ring
125.5 dB
Dual Ring
136.1 dB
59
4.5 Experiments and Results
To confirm the theoretical transfer function (2.5) and (4.11), the linearity of a
ring modulator is experimentally studied. The device used in this experiment is the
same design and fabrication described in Chapter 3. Figure 4.7 shows the
transmission spectrum of TM mode of a ring modulator at the laser wavelength of
1.31 µm. The full width at half maximum (FWHM) bandwidth and the FSR of the
device are 4.5 GHz and 30 GHz, respectively, thus the experimental or loaded Q of
5.1×104 and the finesse of 6.7. From the extinction ratio of –7 dB, the intrinsic Q and
the waveguide loss are estimated to be 7.1×104 and 4.5 dB/cm, respectively. The EO
tuning sensitivity is 1 GHz/V which corresponds to an effective EO coefficient r = 33
pm/V of the core layer. From the data in Figure 4.7, the parameters in the theoretical
transfer function (2.5) is given to be α = 0.715 and τ = 0.878.
Figure 4.8 shows the schematic setup for measuring modulator distortions. The
tunable laser (New Focus 6200) at 1.31 µm with 0.8 mW output is frequency
scanned to measure the bias point dependence of the distortion. The fiber-to-fiber
optical insertion loss of the modulator was -11 dB. The detector (New Focus 2011)
responsivity is 0.8 A/W. The lock-in amplifier (SR830) feeds 30 kHz sinusoidal
signal to the ring modulator, and detected the fundamental, the second harmonic, and
the third harmonic of the photo detector output. The data is collected by the
oscilloscope (HP54522A). Whereas only IM is an issue in sub-octave optical links,
60
1.2
Intensity (a.u)
1
0.8
0.6
0.4
0.2
0
-5
0
5
10
15
20
25
30
35
Frequency (GHz)
Figure 4.7: The transmission spectrum of TM mode of the ring modulator.
Oscillo
scope
Function
generator
Lock-In
Amplifier
Ring
Modulator
Tunable
Laser
Detector
Figure 4.8: Schematic setup for measuring modulator distortions.
the third harmonic is measured as an indication of third-order distortion, because
both the third harmonic and the third-order IM result from third-order distortion of
the transfer function and relate linearly.
61
Figure 4.9 shows the output fundamental, second harmonic, and third harmonic
signal powers as a function of a bias point. The input RF power is 6.4 dBm. The
suppression of the third harmonic is clearly observed at 2.2 GHz from the optical
resonance and the second harmonic at 1.2 GHz. The second and third derivatives of
the theoretical transfer function (1) are zero at 1.3 GHz (T = 0.4) and 2.2 GHz (T =
0.59), respectively. This theoretical prediction is in close agreement with the
measurements. Figure 4.10 shows the output fundamental, second harmonic, and
third harmonic signal powers plotted against the input RF power. The data is
collected at the third-order distortion suppression bias point (2.2 GHz from the
resonance). The solid lines in Figure 4.10 are theoretical calculations based on the
Output RF Power (dBm)
-40
ω
-60
-80
2ω
-100
3ω
-120
-140
0
1
2
3
4
5
Frequency Detuning from Resonance (GHz)
Figure 4.9: The output fundamental, second harmonic, and third harmonic
signal powers as a function of a bias point. The input RF power is 6.4 dBm.
62
Output RF Power (dBm)
-40
-60
-80
ω
-100
-120
2ω
-140
3ω
-160
-40
-30
-20
-10
0
10
20
Input RF Power (dBm)
Figure 4.10: The output fundamental, second harmonic, and third harmonic signal
powers plotted against the input RF power at the bias of 2.2 GHz from the
resonance. The solid lines are theoretical calculations based on the experimental
link parameters and the theoretical transfer function.
experimental link parameters and the theoretical transfer function (2.5). The
simulations are done by the method described in this chapter. The calculated results
fit reasonably to the experimental plots. The theoretical transfer function (2.5) can be
used to predict the performance of ring modulators.
To compare the IM-free DR of a ring modulator to a MZ modulator, the typical
link parameters in Table 4.1 are used. The theoretical transfer function (2.5) biased at
which the third derivative is zero provides a link gain of –24.1 dB, IM-free DR of
123.0 dBHz4/5, broadband DR of 82.6 dBHz1/2, and a noise figure of 37.8 dB. If the
63
ring modulator is critically coupled (α = τ = 0.715), the IM-free DR is improved to
be 127.7 dBHz4/5. The theoretical transfer function (2.5) somewhat deviates from the
Lorentzian transfer function (4.11). However, the experimental results clearly verify
the suppression of third-order distortion, and the theoretical transfer function (2.5)
also provides high IM-free DR. The argument developed in this chapter using the
Lorentzian transfer function (4.11) is still applicable.
4.6 References
[1] W. S. C. Chang, RF Photonic Technology in Optical Fiber Links, Cambridge
University Press, 2002.
[2] C. H. Cox, Analog Optical Links, Cambridge University Press, 2004.
[3] W. B. Bridges and J. H. Schaffner, “Distortion in linearized electrooptic
modulators,” IEEE Transactions on Microwave Theory and Techniques, vol. 43,
pp. 2184–2197, Sept. 1995.
[4] G. E. Betts, “Linearized modulator for suboctave-bandpass optical analog
links,” ” IEEE Transactions on Microwave Theory and Techniques, vol. 42, pp.
2642–2649, Dec. 1994.
[5] G. E. Betts and F. J. O’Donnell, “Microwave analog optical links using
suboctave linearized modulators,” IEEE Photonics Technology Letters, vol. 8,
pp. 1273–1275, Sept. 1996.
[6] R. B. Welstand, C.K. Sun, S.A. Pappert, Y.Z. Liu, J.M. Chen, J.T. Zhu, A.L.
Kellner, P.K.L. Yu, “Enhanced linear dynamic range property of Franz-Keldysh
effect waveguide modulator,” IEEE Photonics Technology Letters, vol. 7, pp.
751-753, 1995.
[7] H. A. Haus, Waves and Fields in Optoelectronics, Prentice-Hall, 1984.
64
[8] A. J. C. Vieira, P. R. Herczfeld, and V. M. Contarino, “Linearity study of a
Fabry-Perot intensity modulator,” Journal of the Franklin Institute, vol. 335B,
no. 1, pp. 109–115, 1998.
[9] L. M. Johnson and H. V. Roussell, “Reduction of intermodulation distortion in
interferometric optical modulators,” Optics Letters, vol. 13, no. 10, pp. 928–930,
1988.
[10] S. K. Korotky and R. M. Ridder, “Dual parallel modulation schemes for
low-distortion analog optical transmission,” IEEE Journal of Selected Areas of
Communication, vol. 8, pp. 1377–1381, Sept. 1990.
[11] A. Djupsjobacka, “A linearization concept for integrated-optic modulators,”
IEEE Photonics Technology Letters, vol. 9, pp. 869–879, Aug. 1992.
[12] J. L. Brooks, G. S. Maurer, and R. A. Becker, “Implementation and evaluation
of a dual parallel linearization system for AM-SCM video transmission,”
Journal of Lightwave Technology, vol. 11, pp. 34–41, Jan. 1993.
[13] E. Ackerman, “Broadband linearization of a Mach-Zehnder electro-optic
modulator,” IEEE Transactions on Microwave Theory and Techniques, vol. 47,
pp. 2271-2279, Dec. 1999.
65
Chapter 5
Bandwidth of Linearized Ring Resonator
Assisted Mach-Zehnder Modulator
5.1 Introduction
To increase the dynamic range (DR) of the analog optical links, several
approaches to linearization have been proposed, including predistortion, dual parallel
Mach-Zehnder (MZ) schemes, dual cascaded MZ schemes, and directional coupler
based modulators [1] - [3]. Xie et al. [4] have recently proposed that a Ring
Resonator Assisted MZ (RAMZ) modulator could provide linear responses. Yang et
al. [5] have analyzed the influence of ring resonator waveguide loss in a RAMZ. The
phase response of a ring resonator can be tuned by changing the coupling coefficient
between the ring resonator and the bus waveguide. At a certain coupling strength, the
transfer function of a RAMZ becomes linear, namely no third-order harmonic term
exists at a quadrature point of the transfer function. The advantage of this scheme is
that there are no complicated electric or optical controls, once the appropriate
66
coupling coefficient is determined by fabrication. The use of a Gires-Tournois
interferometer [6] instead of a ring resonator is the same concept as a RAMZ. In
these publications, however, the bandwidth of the linearization was not considered;
only the signal bandwidth limit due to the electrode configuration was considered.
In this chapter, the modulation frequency properties of a RAMZ due to the
resonant nature of a ring resonator are investigated by following [7]. It will be shown
that the linear response of a RAMZ deteriorates as the modulation frequency
increases.
5.2 Ring Resonator Assisted MZ Modulator
Figure 5.1 (a) shows the schematic drawing of a RAMZ modulator. An RF
modulation signal is applied to the electro-optic ring resonator. The intensity transfer
function of a RAMZ is
1 1
1 − iφ
T (θ ) =
a (θ ) e −i arg( a (θ )) +
e
2 2
2
τ − α e − iθ
a (θ ) =
1 − ατe −iθ
2
(5.1)
(5.2)
where a (θ ) and φ are the amplitude transfer function of the ring resonator and the
DC phase bias between two arms, respectively. θ, τ, and α represent the roundtrip
phase shift, the amplitude transmission constant between the ring and the waveguide,
and the round trip loss factor, respectively. An applied voltage changes the round trip
67
(a)
Modulation Signal
DC Bias
Intensity
1
0.5
RAMZ
(b)
0
0
MZ
0.5
1
Voltage (Vπ)
1.5
2
Figure 5.1: (a) The schematic drawing of a ring resonator assisted MZ
(RAMZ) modulator, and (b) its low frequency linearized intensity transfer
function compared with a standard MZ modulator. The voltage is
normalized by Vπ.
phase shift θ by the electro-optic effect. For the lossless ring resonator (α = 1), and
the case when τ = 2 − 3 and φ = π/2, the transfer function of a RAMZ is
linearized around θ = π, i.e. off-resonance for a ring resonator. Although a lossless
ring is assumed in the following discussion, this assumption does not affect the
68
conclusion. Figure 5.1 (b) shows the low frequency linearized intensity transfer
function of a RAMZ compared with a standard MZ modulator. The half wave
voltage Vπ of a RAMZ is defined as θ = π (V Vπ ) , where V is the voltage of the
modulation signal. While this Vπ does not move the modulator from maximum to
minimum transmission, as does the Vπ of a MZ, this is useful measure of the
modulator sensitivity.
To evaluate the linearity of a RAMZ, the intermodulation-free DR is calculated.
The DR is defined as the ratio of the signal to intermodulation (IM) power, when the
IM power equals the noise power. As an example, we assume the photonic link
parameters as follows. The laser power is 10 mW with laser noise (RIN) of –160
dB/Hz. The optical loss of the link is –3 dB. The modulator and detector impedances
are 50 Ω. The detector sensitivity is 0.8 A/W. The Vπ of modulators is 10 V. These
link parameters give a noise power dominated by both the relative intensity noise and
shot noise to be – 162.8 dBm. The thermal noise is negligible. Figure 5.2 shows the
signal power and IM power of both a RAMZ, at low modulation frequencies, and a
standard MZ as a function of the input signal power. The link gain and the DR of the
standard MZ are –30 dB and 107.9 dBHz2/3, respectively. The DR of the RAMZ is
expanded to 125.5 dBHz4/5, because there is no third-order distortion. The IM results
from the fifth-order distortion. This value is almost comparable to that of other
linearization schemes [2], [3]. The link gain of RAMZ is –34.8 dB. If the loss in the
ring is considered, both the gain and the DR decrease. If one assumes different link
69
parameters, the numbers will change but will not affect the basic comparison
between the MZ and the RAMZ.
0
Output (dBm)
-40
RAMZ
126 dB
-80
Signal
-120
MZ
108 dB
Intermod
-160
-200
-160
Noise Floor
-120
-80
-40
Input Power (dBm)
0
40
Figure 5.2: The output signal power and intermodulation power of
both a standard MZ modulator and a ring resonator assisted MZ
(RAMZ) modulator as a function of the input signal power. The
RAMZ calculation is for low modulation frequencies. The
intermodulation power of RAMZ varies as the fifth power of the input
instead of the third in MZ.
5.3 Frequency Properties of RAMZ
In order to study the modulation frequency properties of a RAMZ, the general
expression established in Chapter 2 is used. By substituting (2.19) and (2.20) instead
of (5.2) into (5.1) and using the Bessel-function identities, the output RF signal
70
power of a RAMZ is
∞
Psig ∝ (1 − τ )∑τ
2
n −1
e
−in (π +
ψ
2
2
)
n =1
J 0 (δ n ) J 1 (δ n )
(5.3)
Similarly, the IM power is
∞
PIM ∝ (1 − τ )∑τ
2
n =1
n −1
ψ
e
−in (π +
2
2
)
J 1 (δ n ) J 2 (δ n )
(5.4)
It is assumed that the ring is lossless (α = 1), and the input light is adjusted to be at
the off-resonance (θ 0= π). It is also assumed that the input signal consists of two
closely spaced frequencies ω1 and ω2 with equal amplitudes. Therefore, the IM
frequency 2ω1 - ω2 is close to the frequency of the signal. The generated IM
sideband is considered to experience the same phase shift π + ψ/2 in a round trip of
the ring as the signal sidebands.
Figure 5.3 shows the IM power of a RAMZ at different modulation frequencies
as a function of the input signal power. The modulation frequencies are normalized
by the FSR. The IM power exhibits fifth power dependence on the input power at
low modulation frequency. However, the third-order behavior of the IM power is
evident as the modulation frequency increases. The modulation frequency
dependence of IM-free DR is shown in Figure 5.4. The DR of the standard MZ is
ideally independent of the modulation frequency. The DR of the RAMZ falls off
71
0
Intermod Power (dBm)
-40
MZ
Slop 3
-80
RAMZ
Slop 5
-120
-160
Noise Floor
-1
-2
10
-200
-30
10
-20
-3
10
-5
10
-10
0
10
Input Power (dBm)
30
20
Figure 5.3: The intermodulation powers of a ring resonator assisted MZ
(RAMZ) modulator with different modulation frequencies, 10-5, 10-3, 10-2,
and 10-1 times the FSR of the ring resonator.
Dynamic Range (dB)
130
120
RAMZ
110
MZ
100
0
0.05
0.1
0.15
0.2
Modulation Frequency (FSR)
0.25
0.3
Figure 5.4: The modulation frequency dependence of the dynamic range of
a ring resonator assisted MZ (RAMZ) modulator. The frequency is
normalized by the FSR of a ring resonator.
72
significantly as the frequency increases. As a result, the RAMZ offers improved DR
over the standard MZ at modulation frequencies up to 15% of the FSR.
As a numerical example, the parameters of the electrooptic polymer ring
resonators are chosen as in [8]. The refractive index of the electrooptic polymer is
1.6 with an electrooptic coefficient r33 of 47 pm/V at the wavelength of 1.31 µm [9].
The gap between electrodes is 10 µm. To obtain Vπ = 10 V, the perimeter of ring
resonator must be 6.6 mm, providing a FSR of 28 GHz. Thus, the linearization
bandwidth is estimated to be 4.2 GHz. The figure of merit, the ratio of linearized
bandwidth/voltage, is 0.42 GHz/Vπ. This bandwidth limitation resulting from the
optical resonance of the ring resonator is more severe than either the RC limitation or
the transit-time limitation in a lumped electrode. A small ring with a larger FSR gives
a larger linearization bandwidth and a larger Vπ, thus decreasing the link gain. The
use of a signal pre-amplifier to compensate for the larger Vπ is not always possible
because of the amplifier bandwidth limitation and nonlinear distortion. The two-ring
RAMZ working in a push-pull operation [4] will also suffer from this bandwidth
limitation.
In summary, the IM-free DR and the linearization bandwidth of RAMZ
modulators by considering the modulation response of a ring resonator have been
analyzed. The DR of the RAMZ falls off significantly as the modulation frequency
increases and is superior to the standard MZ only up to modulation frequencies of
~15% of the FSR. The linearized bandwidth is therefore inversely related to the
73
diameter of the ring resonator, as is Vπ. There is therefore a trade-off between
linearized bandwidth and Vπ.
5.4 References
[1] W. S. C. Chang, RF Photonic Technology in Optical Fiber Links, Cambridge
University Press, 2002, ch. 4.
[2] C. H. Cox, Analog Optical Links, Cambridge University Press, 2004, ch. 6.
[3] W. B. Bridges and J. H. Schaffner, “Distortion in linearized electrooptic
modulators,” IEEE Transactions on Microwave Theory and Techniques, vol. 43,
pp.2184 - 197, Sept. 1995.
[4] X. Xie, J. Khurgin, J. Kang and F.-S. Chow, “Linearized Mach-Zehnder intensity
modulator,” ," IEEE Photonics Technology Letters, vol. 15, pp. 531-533, Apr.
2003.
[5] J. Yang, F. Wang, X. Jiang, H. Qu, M. Wang, and Y. Wang, "Influence of loss on
linearity of microring-assisted Mach-Zehnder modulator," Optics Express, 12, 18,
pp.4178-4188, 2004.
[6] N. Reingand, I. Shpantzer, Ya. Achiam, A. Kaplan, A. Greenblatt, G. Harston,
and P.S. Cho, "Novel design for the broadband linearized optical intensity
modulator," Military Communications Conference, 2003. MILCOM 2003. IEEE,
vol. 2, p.p. 1208 -1212, Oct. 2003.
[7] H. Tazawa and W. H. Steier, "Bandwidth of Linearized Ring Resonator Assisted
Mach–Zehnder Modulator," IEEE Photonics Technology Letters, vol. 17, no. 9,
pp. 1851–1853, Sep. 2005.
[8] P. Rabiei, W. H. Steier, C. Zhang, and L. R. Dalton, “Polymer micro-ring filters
and modulators,” Journal of Lightwave Technology, vol. 20, pp. 1968-75, Nov.
2002.
74
[9] H. Zhang, M-C Oh, A. Szep, W. H. Steier, C. Zhang, L. R. Dalton, H. Erlig, Y.
Chang, D. H. Chang, and H. R. Fetterman, “Push Pull Electro-optic Polymer
Modulators with Low Half-Wave Voltage and Low Loss at both 1310 nm and
1550 nm,” Applied Physics Letters, vol. 78, pp. 3116 –8, May 14, 2001.
75
Chapter 6
Conclusions
6.1 Summary
The previous chapters address the study of ring resonator based electro-optic
polymer optical modulators for microwave photonics applications. Particularly, the
work focuses on two important requirements for external modulators in analog
optical links: high modulation sensitivity at a high frequency and the linearity of a
modulator.
In Chapter 2, the analysis of ring modulators in terms of the modulation
sensitivity and the modulation bandwidth is described. The general expression to
analyze the modulation frequency response of a ring modulator is derived and
applied to traveling-wave ring modulators. The modulators show high modulation
efficiency at frequencies around all multiples of the FSR, and have better tolerance
for the optical/microwave velocity mismatch and microwave loss of the electrode
than traveling-wave Mach-Zehnder modulators. The modulators would find
76
applications in metrology systems, comb generations, and pulse generations, as well
as communication areas.
In Chapter 3, the band operation around the FSR frequency in an electro-optic
polymer ring modulator with a traveling-wave electrode is experimentally
demonstrated. The Q of the ring resonator is 45,000 at 1.31 µm, the extinction ration
at resonance is –14 dB, and the electro-optic tuning sensitivity is 1 GHz/V. The
equivalent half-wave voltage at a low frequency is estimated to be 7 V. The
modulator shows efficient modulation in a 7 GHz band centered at 28 GHz. This
modulation enhancement is due to optical resonance. The device design, fabrication,
and characterization are described in detail.
The theme in Chapter 4 and Chapter 5 is linearization of external modulators.
First, the linearity of a ring modulator is theoretically analyzed. It is shown that ring
modulators have the potential to obtain a high intermodulation-free dynamic range in
sub-octave bandpass optical links, because they have a bias point at which the third
derivative of the transfer function is zero; eliminating third-order distortion. Then,
the scheme to expand the dynamic range using dual parallel ring modulator is
proposed and analyzed. The scheme provides the highest order correction of
distortion using two modulators. Next, the experimental result of an electro-optic
polymer ring modulator clearly shows a suppression of third-order distortion at a
certain bias point, verifying the theory. Finally, a linearized ring resonator assisted
Mach–Zehnder electro-optic modulator, which is recently proposed as a new
77
linearization scheme of external modulators, is also analyzed using the method
established in Chapter 2. It is shown that the linearization bandwidth of the
modulator is limited by the resonant nature of a ring resonator.
6.2 Future Work
It would be necessary to challenge the following approaches to improve the
performance of electro-optic polymer ring modulators.
Higher Q resonator: Currently, the resonator Q is limited by both material loss
and fabrication induced scattering loss. The possible ideas include (i) changing host
material from APC to lower loss polymer, (ii) developing a new lower loss
electro-optic polymer, and (iii) making waveguides without dry etching. The
waveguide scattering loss is mainly due to the roughness by RIE etching. One
possibility to decrease the scattering loss is the use of a photo-bleaching induced
waveguide [1]. The refractive index of an electro-optic polymer can be changed by
UV irradiation, and the maximum change reaches 0.05, which is enough to make a
ring resonator with 1 mm bending radius. The mechanism is due to photochemical
decomposition of chromophore. The devices fabricated by photo-bleaching have
shown low insertion loss [1]. Ultra high Q resonator is not always required because
of RF bandwidth limitation, but the improvement, for example, from ∆f = 5 GHz to 3
78
GHz is desired. The approaches from both materials and fabrications would be
realistic challenges.
RF resonator: If the resonant electrode is properly designed to get reasonable
RF Q and the RF resonant frequency coincides with one of the multiples of the FSR
of an optical resonator, the efficient modulation is given as demonstrated by LiNbO3
disk modulators [2], [3]. Although there are several electrode designs and RF related
problems to be solved, the use of RF resonator would be also a feasible approach.
However, the enhancement by either high optical Q or RF resonance sacrifices
the bandwidth as emphasized through this work. It should be noticed that only
material evolution and innovative device design, for example narrower electrode gap,
essentially improve the device performances.
Although the electro-optic polymer waveguide technologies still have concerns
such as stability and material loss, it is easy to obtain relatively large index contrast
electro-optic waveguides, as mention in Chapter 1. This feature allows us to use
electro-optic polymers to verify ideas of new devices. In specific applications such as
very high frequency modulators and optical circuits on electronic chips, the
advantage of electro-optic polymer devices is already undoubted. In addition, time
and efforts by chemists and engineers will solve all concerns.
79
6.3 References
[1] S. Kim, K. Geary, H. R. Fetterman, C. Zhang, C. Wang, and W. H. Steier,
“Photo-bleaching induced electro-optic polymer modulators with dual driving
electrodes operating at 1.55 µm wavelength,” Electronics Letters, vol. 39, pp.
1321 - 1322, Sept. 2003.
[2] D. A. Cohen, M. Hossein-Zadeh and A. F. J. Levi, “High-Q microphotonic
electro-optic modulator,” Solid-State Electronics, vol. 45, pp. 1577-1589, 2001.
[3] V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko and L. Maleki, “Sub-Micro
Watt Photonic Microwave Receiver,” IEEE Photonics Technology Letters, vol.
14, pp. 1602-1604, Nov. 2002
80
Bibliography
E. Ackerman, “Broadband linearization of a Mach-Zehnder electro-optic modulator,”
IEEE Transactions on Microwave Theory and Techniques, vol. 47, pp. 2271–2279,
Dec. 1999.
E. I. Ackerman and C. H. Cox, "RF fiber-optic link performance," IEEE Microwave
Magazine, vol. 2, pp. 50–58, 2001.
R. C. Alferness, “Waveguide Electooptic Modulators,” IEEE Transactions on
Microwave Theory and Techniques, vol. MTT-30, pp. 1121–1137, Aug. 1982
H. Al-Raweshidy, and S. Komaki, Radio over fiber technologies for mobile
communications networks, MA, Artech House, 2002.
G. E. Betts, “Linearized modulator for suboctave-bandpass optical analog links,” ”
IEEE Transactions on Microwave Theory and Techniques, vol. 42, pp. 2642–2649,
Dec. 1994.
G. E. Betts and F. J. O’Donnell, “Microwave analog optical links using suboctave
linearized modulators,” IEEE Photonics Technology Letters, vol. 8, pp. 1273–1275,
Sept. 1996.
R. W. Boyd, and J. E. Heebner, “Sensitive disk resonator photonic biosensor,”
Applied Optics, 40, 31, pp. 5742-5747, 2001
W. B. Bridges and J. H. Schaffner, “Distortion in linearized electrooptic modulators,”
IEEE Transactions on Microwave Theory and Techniques, vol. 43, pp. 2184–2197,
Sept. 1995.
81
J. L. Brooks, G. S. Maurer, and R. A. Becker, “Implementation and evaluation of a
dual parallel linearization system for AM-SCM video transmission,” Journal of
Lightwave Technology, vol. 11, pp. 34–41, Jan. 1993.
W. S. C. Chang, RF Photonic Technology in Optical Fiber Links, Cambridge
University Press, 2002.
D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi,
"Demonstration of 110 GHz electro-optic polymer modulators," Applied Physics
Letters 70, pp. 3335–7, 1997.
S. T. Chu, B. E. Little, W. Pan, T. Kaneko, S. Sato, and Y. Kokubun, “Microring
resonator arrays for VLSI photonics,” IEEE Photonics Technology Letters, vol. 12,
pp. 323–325, 2000.
D. A. Cohen, M. Hossein-Zadeh, and A. F. J. Levi, "Microphotonic modulator for
microwave receiver," Electronics Letters, vol. 37, pp. 300–1, 2001.
D. A. Cohen and A. F. J. Levi, “Microphotonic components for a mm-wave
receiver,” Solid-State Electronics, vol. 45, pp. 495–505, 2001.
D. A. Cohen, M. Hossein-Zadeh and A. F. J. Levi, “High-Q microphotonic
electro-optic modulator,” Solid-State Electronics, vol. 45, pp. 1577–1589, 2001.
C. H. Cox, Analog Optical Links, Cambridge University Press, 2004.
L. R. Dalton, "Nonlinear Optics – Applications: Electro-Optics EO," Encyclopedia of
Modern Optics, pp.121 –129, 2003.
L. R. Dalton, B. H. Robinson, A. K. Jen, W. H. Steier, R. Nielsen, "Systematic
development of high bandwidth, low drive voltage organic electro-optic devices and
their applications," Optical Materials, vol. 21, pp.19 –28, 2003.
L. R. Dalton, "Organic electro-optic materials," Pure and Applied Chemistry, vol. 76,
Iss 7-8, pp.1421 –1433, 2004.
K. D. Djordjev, S. J. Choi, S. J. Choi, and P. D. Dapkus, “Active semiconductor
microdisk device,” Journal of Lightwave Technology, vol. 20, no. 1, pp. 105–113,
Jan. 2002.
82
A. Djupsjobacka, “A linearization concept for integrated-optic modulators,” IEEE
Photonics Technology Letters, vol. 9, pp. 869–879, Aug. 1992.
I.-L. Gheorma and R. M. Osgood, Jr., “Fundamental Limitations of Optical
Resonator Based on High-Speed EO Modulators,” IEEE Photonics Technology
Letters, vol. 14, pp. 795–797, June 2002.
E. I. Gordon and J. D. Rigden, “The Fabry-Perot Electrooptic Modulator,” The Bell
System Technical Journal, pp. 155–179, Jan. 1963.
H. A. Haus, Waves and Fields in Optoelectronics, Prentice-Hall, 1984.
K.-P. Ho and J. M. Kahn, “Optical Frequency Comb Generator Using Phase
Modulation in Amplified Circulating Loop,” IEEE Photonics Technology Letters, vol.
5, pp. 721–725, June 1993.
M. Hossein-Zadeh and A. F. J. Levi, “A new electrode design for microdisk
electro-optic RF modulator,” CLEO’03, pp. 863–865, June 2003.
M. M. Howerton, R. P. Moeller, A. S. Greenblatt, and R. Krahenbuhl, “Fully
packaged, broad-band LiNbO3 modulator with low drivevoltage,” IEEE Photonics
Technology Letters, vol. 12, no. 7, pp. 792–794, 2000.
V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko and L. Maleki, “Sub-Micro Watt
Photonic Microwave Receiver,” IEEE Photonics Technology Letters, vol. 14, pp.
1602–1604, Nov. 2002.
V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko and L. Maleki,
“Whispering-gallery-mode electro-optic modulator and photonic microwave
receiver,” Journal of the Optical Society of America B, vol. 20, pp. 333–342, Feb.
2003.
M. Izutsu, "Microwave photonics: new direction between microwave and photonic
technologies," Transactions of the Institute of Electronics, Information and
Communication Engineers C-I J81C-I, pp. 47–54, 1998.
L. M. Johnson and H. V. Roussell, “Reduction of intermodulation distortion in
interferometric optical modulators,” Optics Letters, vol. 13, no. 10, pp. 928–930,
1988.
83
M. Kato, K. Fujiura and T. Kurihara, “Generation of super-stable 40 GHz pulses
from Fabry-Perot resonator integration with electro-optic phase modulator,”
Electronics Letters, vol. 40, pp. 299–301, March 2004.
S. Kalluri, M. Ziari, A. Chen, V. Chuyanov, W. H. Steier, D. Chen, B. Jalali, H.
Fetterman, and L. R. Dalton, "Monolithic integration of waveguide polymer
electrooptic modulators on VLSI circuitry," IEEE Photonics Technology Letters, vol.
8, pp. 644–646, 1996.
T. Kawanishi, S. Oikawa, K. Higuma, Y. Matsuo, and M. Izutsu, “LiNbO3
resonant-type optical modulator with double-stub structure,” Electronics Letters, vol.
37, no. 20, pp. 1244–1246, 2001.
S. Kim, H. Zhang, D.H. Chang, C. Zhang, C. Wang, W.H. Steier, and H.R. Fetterman,
“Electrooptic polymer modulators with an inverted-rib waveguide structure,” IEEE
Photonics Technology Letters, vol. 15, pp. 218–220, Feb. 2003.
S. Kim, K. Geary, H. R. Fetterman, C. Zhang, C. Wang, and W. H. Steier,
“Photo-bleaching induced electro-optic polymer modulators with dual driving
electrodes operating at 1.55 mm wavelength,” Electronics Letters, vol. 39, pp. 1321 1322, Sept. 2003
T. Kobayashi, T. Sueta, Y. Cho and Y. Matsuo, “High-repetition-rate optical pulse
generator using a Fabry-Perot electro-optic modulator,” Applied Physics Letters, vol.
21, pp. 341–343, Oct. 1972.
S. K. Korotky and R. M. Ridder, “Dual parallel modulation schemes for
low-distortion analog optical transmission,” IEEE Journal of Selected Areas of
Communication, vol. 8, pp. 1377–1381, Sept. 1990.
M. Kourogi, K. Nakagawa and M. Ohtsu, “Wide-Span Optical Frequency Comb
Generator for Accurate Optical Frequency Difference Measurement,” IEEE Journal
of Quantum Electronics, vol. 29, pp. 2693–2701, Oct. 1993.
O. P. Lay, S. Dubovitsky, R. D. Peters, J. P. Burger, S.-W. Ahn, W. H. Steier, H. R.
Fetterman and Y. Chang, “MSTAR: a submicrometer absolute metrology system,”
Optics Letters, vol. 28, pp. 890–892, June 2003.
M. Lee, O. Mitrofanov, H. E. Katz, and C. Erben, "Millimeter-wave dielectric
properties of electro-optic polymer materials," Applied Physics Letters 81, pp.
1474–6, 2002.
84
M. Lee, H. E. Katz, C. Erben, D. M. Gill, P. Gopalan, J. D. Heber, and D. J. McGee,
"Broadband modulation of light by using an electro-optic polymer," Science 298, pp.
1401–3, 2002.
C. Lim, A. Nirmalathas, D. Novak, and R.Waterhouse, “Optimization of baseband
modulation scheme for millimeter-wave fiber-radio systems,” Electronics Letters,
vol. 36, pp. 442–443, 2000.
B. E. Little, S. T. Chu, H. A. Haus, J. Foresi and J.-P. Laine, “Microring Resonator
Channel Dropping Filters,” Journal of Lightwave Technology, vol. 15, pp. 998–1005,
June 1997.
B. E. Little, S. T. Chu, W. Pan, Y. Kokubun, “An eight-channel add-drop filter using
vertically coupled microring resonators over a cross grid,” IEEE Photonics
Technology Letters, vol. 11, pp. 691–693, 1999.
J. Luo, S. Liu, M. Haller, J.-W. Kang, T.-D. Kim, S.-H. Jang, B. Chen, N. Tucker, H.
Li, H.-Z. Tang, L. R. Dalton, Y. Liao, B. H. Robinson, and A. K.-Y. Jen, “Recent
progress in developing highly efficient and thermally stable nonlinear optical
polymers for electro-optics,” Proceedings of the SPIE - The International Society for
Optical Engineering 5351, no. 1, pp.36–43, 2004.
J. Luo, M. Haller, M. Ma, S. Liu, T. D. Kim, Y. Tian, S. H. Jang, B. Chen, L. R.
Dalton, A. K. Jen, "Nanoscale architectural controland macromolecular engineering
of nonlinear optical dendrimers and polymers for electro-optics," Journal of Physical
Chemistry B, vol. 108, Iss. 25, pp. 8523–8530, 2004.
E. A. J. Marcatili, “Bends in optical dielectric waveguides” The Bell System
Technical Journal, 48, pp. 2103–2132, 1969.
S. R. Marder, B. Kippelen, A. K.-Y. Jen, and N. Peyghambarian, "Design and
synthesis of chromophores and polymers for electro-optic and photorefractive
applications," Nature, vol. 388, pp. 845–851, 1997.
S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan,"
Whispering-gallery mode microdisk lasers," Applied Physics Letters, vol. 60, no. 3,
pp 289–291,1992.
F. Michelotti, A. Driessen, and M. Bertolotti, Microresonators as building blocks for
VLSI photonics, American Institute of Physics, 2004.
85
K. Noguchi, O. Mitomi, and H. Miyazawa, "Millimeter-Wave Ti:LiNbO3 Optical
Modulators," Journal of Lightwave Technology, vol. 16, no. 4, pp. 615–619, 1998.
K. Okamoto, Fundamentals of Optical Waveguides, Academic Press, 2000
M. C. Oh, H. Zhang, C. Zhang, H. Erlig, C. Yian, B. Tsap, D. Chang, A. Szep, W. H.
Steier, H. R. Fetterman, and L. R. Dalton, “Recent Advances in Electrooptic Polymer
Modulators Incorporating Highly Nonlinear Chromophore,” IEEE Journal of
Selected Topics in Quantum Electronics, vol. 7, pp. 826–835, Sept./Oct. 2001.
P. Rabiei, W. H. Steier, C. Zhang, L. R. Dalton, “Polymer Micro-ring Filters and
Modulators,” Journal of Lightwave Technology, vol. 20, pp. 1968–75, 2002.
D. Rafizadeh, J. P. Zhang, S. C. Hagness, A. Taflove, K. A. Stair, S.T. Ho, and R. C.
Tiberio, “Waveguide-coupled AlGaAs/GaAs microcavity ring and disk resonators
with high finesse and 21.6-nm free spectral range,” Optics Letters, vol. 22, no. 16, pp.
1244–1226, 1997.
N. Reingand, I. Shpantzer, Ya. Achiam, A. Kaplan, A. Greenblatt, G. Harston, and P.
S. Cho, "Novel design for the broadband linearized optical intensity modulator,"
IEEE Military Communications Conference, 2003. MILCOM 2003, vol. 2, p.p. 1208
-1212, Oct. 2003.
T. Sadagopan, S. J. Choi, S. J. Choi, K. D. Djordjev, and P. D. Dapkus,
“Carrier-Induced Refractive Index Changes in InP-Based Circular Microresonators
for Low-Voltage High-Speed Modulation," IEEE Photonics Technology Letters,
vol.17, no. 2, pp. 414–416, Feb. 2005.
T. Sadagopan, S. J. Choi, S. J. Choi, P. D. Dapkus, and A. E. Bond, “Optical
Modulators Based on Depletion Width Translation in Semiconductor Microdisk
Resonators," IEEE Photonics Technology Letters, vol.17, no. 3, pp. 567–569, Mar.
2005.
T. Saitoh, S. Mattori, S. Kinugawa, K. Miyagi, A. Taniguchi, M. Kourogi, and M.
Ohtsu, “Modulation Characteristic of Waveguide-Type Optical Frequency Comb
Generator,” Journal of Lightwave Technology, vol. 16, pp. 824–832, May 1998.
O. Schwelb, "Transmission, group delay, and dispersion in single-ring optical
resonators and add/drop filters-a tutorial overview," Journal of Lightwave
Technology, vol. 22, pp. 1380–1394, 2004.
86
Y. Shi, Cheng Zhang, Hua Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, and
W. H. Steier, "Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators
achieved by controlling chromophore shape," Science 288, pp. 119–22, 2000.
Y. Shi, W.. Lin, D. J. Olson, J. H. Bechtel, H. Zhang, W. H. Steier, C. Zhang, and L.
R. Dalton, "Electro-optic polymer modulators with 0.8 V half-wave voltage,"
Applied Physics Letters 77, pp. 1–3, 2000.
W. H. Steier, A. Chen, S.-S. Lee, S. Garner, H. Zhang, V. Chuyanov, L. R. Dalton, F.
Wang, A. S. Ren, C. Zhang, G. Todorova, A. Harper, H. R. Fetterman, D. Chen, A.
Udupa, D. Bhattacharya, and B. Tsap, “Polymer electro-optic devices for integrated
optics,” Chemical Physics 245, pp.487–506 1999.
H. Tazawa and W. H. Steier, "Bandwidth of Linearized Ring Resonator Assisted
Mach–Zehnder Modulator," IEEE Photonics Technology Letters, vol. 17, no. 9, pp.
1851–1853, Sep. 2005.
C. C. Teng, "Traveling-wave polymeric optical intensity modulator with more than
40 GHz of 3-dB electrical bandwidth," Applied Physics Letters 60, pp. 1538–40,
1992.
K. Vahala, Optical microcavities, World Scientific, 2004.
A. J. C. Vieira, P. R. Herczfeld, V. M. Contarino and G. Mizell, “Bulk Fabry-Perot
Intensity Modulator for LIDAR Systems,” IEEE Photonics Technology Letters, vol.
8, pp. 782–784, June 1996.
A. J. C. Vieira, P. R. Herczfeld, and V. M. Contarino, “Linearity study of a
Fabry-Perot intensity modulator,” Journal of the Franklin Institute, vol. 335B, no. 1,
pp. 109–115, 1998.
A. Vilcot, B. Cabon, and J. Chazelas, Microwave photonics: from components to
applications and systems, Kluwer Academic, 2003.
R. B. Welstand, C.K. Sun, S.A. Pappert, Y.Z. Liu, J.M. Chen, J.T. Zhu, A.L. Kellner,
P.K.L. Yu, “Enhanced linear dynamic range property of Franz-Keldysh effect
waveguide modulator,” IEEE Photonics Technology Letters, vol. 7, pp. 751–753,
1995.
X. Xie, J. Khurgin, J. Kang and F.-S. Chow, “Linearized Mach-Zehnder intensity
modulator,” ," IEEE Photonics Technology Letters, vol. 15, pp. 531-533, Apr. 2003.
87
Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon
electro-optic modulator,” Nature, vol. 435, pp. 325–327, May 2005.
J. Yang, F. Wang, X. Jiang, H. Qu, M. Wang, and Y. Wang, "Influence of loss on
linearity of microring-assisted Mach-Zehnder modulator," Optics Express, 12, 18,
pp.4178-4188, 2004
A. Yariv and P. Yeh, Optical Waves in Crystals, John Wiley & Sons, 1984.
A. Yariv, “Universal relations for coupling of optical power between microresonators
and dielectric waveguides,” Electronics Letters, vol. 36, pp. 321–322, Feb. 2000.
H. Zhang, M.-C. Oh, A. Szep, W. H. Steier, C. Zhang, L. R. Dalton, H. Erlig, Y.
Chang, D. H. Chang, and H. R. Fetterman, "Push-pull electro-optic polymer
modulators with low half-wave voltage and low loss at both 1310 and 1550 nm,"
Applied Physics Letters 78, pp. 3136–8, 2001.
Документ
Категория
Без категории
Просмотров
0
Размер файла
1 551 Кб
Теги
sdewsdweddes
1/--страниц
Пожаловаться на содержимое документа