electrooptic modulators with controlled frequency...

Hindawi Publishing CorporationAdvances in OptoElectronicsVolume 2008, Article ID 948294, 8 pagesdoi:10.1155/2008/948294

Research Article

Electrooptic Modulators with Controlled Frequency Responses byUsing Nonperiodically Polarization-Reversed Structure

Ha Viet Pham, Hiroshi Murata, and Yasuyuki Okamura

Graduate School of Engineering Science, Osaka University, Machikaneyama, Toyonaka, Osaka 560-8531, Japan

Correspondence should be addressed to Ha Viet Pham, [email protected]

Received 20 June 2008; Accepted 2 September 2008

Recommended by Chang-qing Xu

We discuss a new method to design traveling-wave electrooptic modulators with controlled frequency responses usingnonperiodically polarization-reversed structure. Using our method, the frequency responses of both magnitude and phaseof modulation index are controllable. Several electrooptic modulators for advanced modulation formats such as duobinarymodulation and wideband single-sideband modulation are proposed.

Copyright © 2008 Ha Viet Pham et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

High-speed traveling-wave electrooptic modulators are veryimportant devices because of their applications in manyoptoelectronic fields, such as telecommunication, opticalsignal processing, and optical measurement. With theincreasing demand for broadband communication, manystudies on the high-speed electrooptic modulators have beencarried out for optical fiber communication system [1]. Inaddition, the precise control of the frequency responses ofhigh-speed electrooptic modulators has been required forthe new generation optical fiber communication systems [2–4]. In a standard traveling-wave electrooptic modulator, thefrequency response of the modulation index is restricted bytwo effects: the velocity mismatching between the lightwaveand modulation microwave and the loss of modulationmicrowave in the traveling-wave electrodes.

The polarization reversal technology of ferroelectric opti-cal crystals, such as LiNbO3 and LiTaO3, is attractive for real-izing high-performance electrooptic modulators. We havedeveloped traveling-wave electrooptic modulators utilizingthe periodically polarization-reversed structure for quasi-velocity-matching (QVM) between the lightwave propagat-ing in the optical waveguide and the modulation microwavetraveling along the electrodes. This technique is attractivebecause it compensates for the velocity mismatch in the highfrequency ranges without the requirement of specific and fine

structures of the optical waveguide and the electrodes forvelocity matching. Several advanced electrooptic modulatorsusing periodically polarization-reversed structure have beenproposed and demonstrated, such as a QVM electroop-tic phase modulator [5], an electrooptic single-sideband(SSB) modulator [6], and an optical frequency shifter [7].The bandwidth of the modulation frequency response inthese electrooptic modulators with the simple periodicallypolarization-reversed structure is inversely proportional toits electrode length and becomes relatively narrow for a long-electrode device.

We have proposed a design to realize the traveling-wave electrooptic modulators utilizing nonperiodicallypolarization-reversed structures [8]. Using the proposeddesign, it is possible to obtain electrooptic modulators withthe arbitrary frequency responses of the magnitude of themodulation index over a specified frequency range. The flatbroadband electrooptic modulator with the compensationfor the degradation by both velocity mismatch and themicrowave loss is obtained. However, the control of notonly the magnitude but also the phase of the modulationindex is very important in order to design the electroopticmodulators for advanced modulation formats.

In this paper, we extend our design method to con-trol frequency responses of both the magnitude and thephase of modulation index in electrooptic modulators withnonperiodically polarization-reversed structures utilizing

mailto:[email protected]

2 Advances in OptoElectronics

Coplannar traveling-wave electrodes

Opticalwaveguide

Microwave modulation signal Terminator (50Ω)

Light input

vg

z

xy

vm

Polarization-reversed region

z-cut LiTaO3

or z-cut LiNbO3

Phase modulatedlight

Figure 1: Basic structure of traveling-wave electrooptic phase modulator with nonperiodically polarization-reversed structure.

new flatness parameters. This new approach is applicableto the electrooptic modulators for advanced modulationformats, such as duobinary modulation or broadband single-sideband modulation. This paper is organized as follows.In Section 2, the basic structure of the electrooptic phasemodulator using the nonperiodic polarization reversal andthe frequency responses of modulation index are presented.In Section 3, the calculation method to control the frequencyresponses of both the magnitude and the phase of themodulation index is described. Several calculation resultsare shown in Section 4. In Section 5, the designs of theduobinary modulator and broadband single-sideband mod-ulator with nonperiodically polarization-reversed structureare discussed.

2. Traveling-Wave Electrooptic Modulators withPolarization-Reversed Structure

A schematic of the basic structure of the traveling-waveelectrooptic modulator is shown in Figure 1. It consistsof a single-mode channel waveguide and simple coplanartraveling-wave electrodes fabricated on a ferroelectric sub-strate. A Mach-Zehnder waveguide for intensity modulationis also applicable. The velocity mismatch between thegroup velocity of the lightwave propagating in the opticalwaveguide and the phase velocity of a modulation microwavetraveling along the electrodes is compensated for by adoptingthe periodic polarization reversal scheme [9]. The domainlength L of a standard QVM with the periodic polarizationreversal scheme is determined as follows:

L = 12 fm

(1/vm − 1/vg

) , (1)

where fm is the peak modulation frequency, vm is the phasevelocity of the modulation microwave traveling along theelectrodes, and vg is the group velocity of the lightwavepropagating in the waveguide. The parameter vm can becalculated from the effective dielectric constant of thecoplanar traveling-wave electrodes taking account of itsstructure. The parameter vg can be derived from both thematerial dispersion of the refractive index of the ferroelectricmaterial substrate and the mode dispersion of the opticalwaveguide.

The nonperiodic polarization reversal scheme is usedto control the frequency response of the electrooptic mod-ulation. Figure 2 shows the structure of the nonperiodicpolarization reversal. The total active length for modulationis Lt. It is divided into M sections of successive polarization-reversed and nonreversed region. Each domain length isLi (i = 1, 2, . . . ,M).

The modulation index Δφ( f ), which is a function of themodulation microwave frequency f , is calculated using thefollowing equation:

Δφ( f ) = −∫ y1

0kΔn dy +

∫ y2

y1

kΔn dy

− · · · + (−1)M∫ yM

yM−1

kΔn dy,

(2)

where k is the wave vector of the lightwave in vacuum andΔn is the refractive index change by the Pockels effect. Whenthe light polarization is along the z-axis and the modulationelectrical field is also along the z-axis, the refractive indexchange induced by the electrical field of the microwave atthe position y (0 ≤ y ≤ Lt) is derived as follows, takingaccount of the velocity mismatch between the lightwave andthe modulation wave,

Δn(y) = 12n3e r33

V

dΓ exp(−αy)

× exp[j2π f

{t0 −

(1vm− 1

vg

)y}]

,(3)

where ne is the extraordinary ray refractive index of thesubstrate, r33 is the Pockels coefficient of the substrate. V isthe voltage applied to the electrodes, d is the gap between theelectrodes, Γ is the overlap factor between the optical fieldand the electrical field, α is the attenuation coefficient of theelectrical field of the modulation microwave, and t0 is thetime when the lightwave arrived at the position y = 0.

3. Control of Frequency Response

When tuning the length of each domain, the frequencyresponses of the modulation index magnitude |Δφ( f )| andphase arg[Δφ( f )] change. In order to design a nonperiodicpolarization reversal structure for an arbitrary frequency

Advances in OptoElectronics 3

Opticalwaveguide

Lt

L1 L2 · · · LM

Polarization-reversedregion 0 y1 y2 · · · yM−1 yM

y

Figure 2: Nonperiodically polarization-reversed structure.

response of the modulation index magnitude, we haveproposed the modified flatness parameter MF [8], whichexpresses the difference between the magnitude of themodulation index |Δφ( f )| and the target function TF( f ) inthe defined frequency range from f1 to f2

MF =( f2 − f1)

∫ f2f1

∣∣Δφ( f )/TF( f )

∣∣2df

[∫ f2f1

∣∣Δφ( f )/TF( f )

∣∣df

]2 − 1. (4)

By tuning the length of each domain, the value of themodified flatness parameter changes. If the modified flatnessparameter becomes zero, the magnitude of the modulationindex and the target function completely coincide in thefrequency range.

We extended this method for dealing with both themodulation index magnitude and the phase. We define twoflatness parameters, MFM and MFP , for the magnitude andthe phase of the modulation index by using two targetfunctions: TFM( f ) for the magnitude and TFP( f ) for thephase in the defined frequency range from f1 to f2, as follows:

MFM =( f2 − f1)

∫ f2f1

(∣∣Δφ( f )∣∣2/∣∣TFM( f )

∣∣2)

df[∫ f2

f1

(∣∣Δφ( f )∣∣/∣∣TFM( f )

∣∣)df

]2 − 1,

MFP =( f2 − f1)

∫ f2f1

(∣∣ arg[Δφ( f )]∣∣2/∣∣TFP( f )

∣∣2)

df{∫ f2

f1

(∣∣ arg[Δφ( f )]∣∣/∣∣TFP( f )

∣∣)df

}2 − 1,

(5)

where MFM is the difference between the magnitude ofthe modulation index |Δφ( f )| and TFM( f ), and MFP isthe difference between the phase of the modulation indexarg[Δφ( f )] and TFP( f ).

If the modified flatness parameter MFM becomes zero,the magnitude of the modulation index |Δφ( f )| and thetarget function TFM( f ) completely coincide in the definedfrequency range. And if the modified flatness parameter MFP

becomes zero, the phase of the modulation index arg[Δφ( f )]and the target function TFP( f ) completely coincide in thatdefined frequency range. We tried to find the condition forminimizing the two flatness parameters MFM and MFP at thesame time by tuning the domain lengths Li (i = 1, 2, . . . ,M)successively and repeatedly. In this calculation, the initial

value for each domain length is set as the same value inthe periodic case Li = L (i = 1, 2, . . . ,M). At the firststep of calculation, only the length of the first domain L1

is changed, and the corresponding modulation index valueis calculated. By repeating the calculation with tuning thelength L1, the smallest values of MFM and MFP which arecalled the local minimizing values in this calculation stepare obtained. After that, only the next domain length L2

is tuned and the next local minimal values of MFM andMFP are obtained. These local minimal values are smallerthan the previous ones, respectively. This calculation stepwith tuning the domain length is repeated by changing thedomain to be tuned from the first domain to the last domainsuccessively. When finishing the calculation step with tuningthe last domain length, the domain to be tuned is set to thefirst domain again and these calculation steps are repeated.In these repeating calculations, the minimal values of thetwo flatness parameters MFM and MFP are obtained whenthe local minimal values become the same with the valuesin the previous calculation step, respectively. As a result, thelength of each domain is optimal and the difference betweenthe frequency responses of modulation index and the targetfunctions becomes minimum. Therefore, it is possible tocontrol the frequency responses of the magnitude and thephase of modulation index.

4. Calculation Results

We tried to calculate the frequency response using ourmethod shown in the previous section. In these calculations,the attenuation coefficient α was set as negligible forsimplicity. It is also possible to calculate and design thefrequency response of the modulation index taking intoaccount the attenuation coefficient [8].

Figure 3 shows examples of calculated frequencyresponses of the magnitude and the phase of the modulationindex in the traveling-wave electrooptic modulators withnonperiodic polarization reversals for the flat, parabolicmagnitude responses and linear phase responses. Thenumber of domains was set as M = 6 and the frequencyrange was set from f1 = 0.7 fm to f2 = 1.3 fm. The targetfunction for the flat magnitude response was defined asTFM1( f ) = c1 (c1 is constant, and its value is proportional tothe applied modulation voltage to the electrodes), and the


1.61.310.70.4

Normalized modulation frequency f / fm

PeriodicTFM2( f )

(2)

TFM1( f )

(1)

Mag

nit

ude

ofE

Om

odu

lati

on|Δφ|(

a.u

.)

(a)

1.61.310.70.4


PeriodicTFP2( f )

(2)

TFP1( f )

(1)

−2π

−π

0

π

2π

Ph

ase

ofE

Om

odu

lati

onar

g(Δ

φ)

(rad

)

(b)

Figure 3: Frequency dependence of modulation index in traveling-wave electrooptic modulators for flat, parabolic magnitude responseswith linear phase responses. (a) Magnitude responses, (b) phase responses.

Table 1: (1) Obtained normalized domain lengths for the flatmagnitude response and the linear phase response, and (2) theparabolic magnitude response and the linear phase response.

L1/L L2/L L3/L L4/L L5/L L6/L

(1) 0.03 0.22 0.41 0.40 1.07 0.77

(2) 0.22 0.41 0.58 0.58 0.77 0.96

target function for the linear phase response was defined asTFP1( f ) = a1[( f / fm) − 1] (a1 is constant, and it is set as6.5 rad in calculation). With these conditions, the calculationfor minimizing the flatness parameters was carried out. Theobtained frequency responses of the magnitude and thephase are shown by the curves (1) in Figures 3(a) and 3(b),respectively.

The target function for the parabolic magnitude responsewas also defined as TFM2( f ) = c2[( f / fm)2 − 1] + c1 (withc2/c1 is set as 0.6) and the target function for the linearphase response was defined as TFP2( f ) = a2[( f / fm) − 1](with a2 is set as 10 rad). The calculation was also carriedout. The obtained frequency responses of the magnitudeand the phase are also shown as the curves (2) in Figures3(a) and 3(b), respectively. For comparison, the frequencyresponses of the magnitude and the phase in traveling-wave electrooptic modulator with the periodic polarizationreversal are also shown in the figures.

The obtained frequency responses almost coincide withthe target functions in the designed frequency ranges. Table 1shows the values of the obtained domain lengths normalizedby the length L. The length L is the domain length inthe periodic polarization reversal for QVM at the peakmodulation frequency fm. For example, if we set the peakmodulation frequency as fm = 15 GHz and the lightwavewavelength as λ = 1.55 μm, then the corresponding lengthof L becomes L = 4.33 mm for a LiTaO3 guided-wave

modulator (microwave phase velocity vm = 6.47 × 107 m/sand lightwave group velocity vg = 1.29× 108 m/s).

We confirmed the validity of the proposed method.It is possible to obtain the traveling-wave electroopticmodulators with the required frequency responses of boththe magnitude and the phase of the modulation index byusing our new approach.

5. Applications

Recently, there are many reports related to the advancedmodulation formats such as duobinary, SSB, QPSK modu-lation to increase the capacity of the data transmission forthe new generation optical fiber communication systems.Using the control technique of the frequency responses in theelectrooptic modulators with the nonperiodic polarizationreversal, it is possible to design the new electrooptic mod-ulators for the advanced modulation formats.

5.1. Electrooptic Intensity Modulator forDuobinary Modulation

The optical duobinary modulation format offers a largercapacity of data transmission and a large tolerance for fiberchromatic dispersion in optical fiber communication system[3, 10]. Several experimental studies on the generation of theoptical duobinary modulation signals have been reported.In these reports, the electrical/optical filters are requiredto limit the spectrum bandwidth of the generated signals.By using the nonperiodically polarization-reversed structure,it is possible to obtain the electrooptic modulators withspecifically tuned filter-like modulation frequency responseswith any passband (low-pass, high-pass, band-pass, Gaussianlike, etc.). It can be used for the generation of the duobinarymodulation signals without the external electric/optic filters.


Duobinary signal

Light input

vv0

“1” “0” “−1” · · · Coplanar electrodes

50Ω

Duobinary output


2 fc

vv0

(a)

SiO2 buffer layer Electrodes

Optical waveguide Polarization-reversedregion

(b)

Optical waveguideL1 L2 L3 L4 L5 L6 L7 L8


(c)

Figure 4: Basic structure of duobinary modulator with nonperiodic polarization reversal. (a) Whole view, (b) cross-section view, (c)polarization-reversed patterns.

Figure 4 shows the structure of the electrooptic intensitymodulator for duobinary modulation using nonperiodicpolarization reversal. It consists of the Mach-Zehnder waveg-uide, coplanar traveling-wave electrodes, and nonperiodi-cally polarization-reversed structures. The lengths of eachdomain are the same in the two arms of the Mach-Zehnderwaveguide, however, the polarity is opposite in the two arms.Therefore, by applying the electrical fields with the samedirection, the push-pull intensity modulation with the samemodulation index magnitude for the duobinary operation isobtained with a single modulation signal.

Using the proposed method for the frequency responsecontrol, we tried to obtain a Gaussian filter-like fre-quency response in the electrooptic modulation with acutoff frequency fc for generating the optical duobinarymodulation signals. The target function for the Gaussianfilter-like magnitude response was defined as TFMG( f ) =Δφ0 exp[−g( f / fm)2] (with g is set as 2) and the targetfunction for the linear phase response was defined asTFPG( f ) = a( f / fm) (with a is set as 5.5 rad). The numberof domains was set as M = 8 and the frequency range was setas the baseband from f1 = 0 to f2 = fm. The obtained resultsare shown in Figure 5. The targets functions are shown as

2 fcfc0

Normalized modulation frequency

3 dB bandwidth TFPG( f )

TFMG( f )

0

Δφ0

Mag

nit

ude

ofE

Om

odu

lati

on|Δφ|(

a.u

.)

0

π

2π

3π

Ph

ase

ofE

Om

odu

lati

onar

g(Δ

φ)

(rad

)

Figure 5: Frequency dependence of modulation index in traveling-wave electrooptic modulator for the Gaussian-like filter magnituderesponse and the linear phase response.

the dashed lines. The obtained frequency responses of themagnitude and the phase of electrooptic modulation areshown as the solid lines. Table 2 shows the obtained domain


Microwavemodulation signal

Coplanarelectrodes

Light input

v0v

50Ω

LSB

SSB output

Vb


USB

v0v

(a)

SiO2 buffer layer Electrodes

Optical waveguide Polarization-reversedregion

(b)

Optical waveguideLA1 LA2 LA3 LA4 LA5 LA6

Polarization-reversedregion LB1 LB2 LB3 LB4 LB5 LB6

(c)

Figure 6: Basic structure of SSB modulator with nonperiodic polarization reversal. (a) Whole view, (b) cross-section view, (c) polarization-reversed patterns.

1.61.310.70.4


TFM( f )

(A)

(B)

Mag

nit

ude

ofE

Om

odu

lati

on|Δφ|(

a.u

.)

(a)

1.61.310.70.4


0

π

2π

3π

Ph

ase

ofE

Om

odu

lati

onar

g(Δ

φ)

(rad

)

TFPA( f )

(A)

(B)

TFPB( f )π/2

(b)

Figure 7: Frequency dependence of modulation index in designed SSB modulator for flat magnitude responses and linear phase responseswith π/2 difference. (a) Magnitude responses, (b) phase responses.


Table 2: Obtained normalized domain lengths for the Gaussian-like magnitude response and the linear phase response.

L1/L L2/L L3/L L4/L L5/L L6/L L7/L L8/L

0.102 0.359 0.281 1.999 0.100 0.101 0.159 0.111

lengths normalized by the periodic case length L. By using theGaussian filter-like magnitude and the linear phase responsesin electrooptic modulation, it is possible to generate theduobinary modulation signals by simple digital electricaldriving signal without any filter.

We also applied the calculated polarization reversalpattern into the two arms of the Mach-Zehnder waveguidein the proposed duobinary modulator and calculated its per-formance. For the design of a 10 Gbps duobinary modulator,the cutoff frequency fc was set as 5 GHz and the lightwavewavelength as λ = 1.55 μm. Then, the total electrode lengthLt became Lt = 24 mm for a LiTaO3-based device.

We also checked the effect caused by the attenuation ofthe modulation microwave in the electrodes. We assumed atypical attenuation coefficient of the modulation microwave(α = 0.25 dB/cm/GHz0.5) in coplanar electrodes. As a result,the frequency response of the 10 Gbps duobinary modulatorwith the microwave attenuation became almost the samewith the calculated one with the negligible attenuation coeffi-cient in the frequency range from 0 to 10 GHz. Therefore, an∼10 Gbps duobinary modulator is expected using our newapproach.

5.2. Broadband Single-Sideband Modulator

By using optical single-sideband modulation formats, itis possible to reduce the optical power in the signaltransmission. This is attractive in long-haul optical fibercommunication systems with higher density wavelengthmultiplexing [4]. We proposed and demonstrated the SSBmodulators using the periodic polarization reversal [6]. Byusing our new approach, the SSB modulator with the flat andwider operational frequency range can be designed.

Figure 6 shows the structure of this electrooptic mod-ulator using nonperiodic polarization reversal. It consistsof the Mach-Zehnder waveguide, coplanar traveling-waveelectrodes, and two nonperiodically polarization-reversedpatterns set in the two arms of the Mach-Zehnder waveguide.In order to have the SSB modulation characteristics, it isrequired that the magnitudes of the modulation index arethe same in the two arms of the Mach-Zehnder waveguideand the phases of the modulation index in the two arms aredifferent as π/2 in the designed frequency range. For realizingthese two modulation characteristics, we applied the controlmethod of the frequency responses.

Figure 7 shows the calculated frequency responses for theSSB modulator with nonperiodic polarization reversal forthe same target function TFMA( f ) = TFMB( f ) = TFM( f ) =c (constant) and linear target functions TFPA( f ) = a( f / fm)+b and TFPB( f ) = a( f / fm) + b − π/2 (with a = 4 rad,b is a common phase offset value). In this example, thenumber of domains was set as M = 6 and the frequency

21.510.50


−30

−20

−10

0

Ou

tpu

tin

ten

sity

(dB

)

USB

LSB

Figure 8: Frequency responses of USB and LSB components ofdesigned SSB modulator.

Table 3: Obtained normalized domain lengths for the designed SSBmodulator.

L1/L L2/L L3/L L4/L L5/L L6/L

(A) 0.65 1.31 0.58 0.51 0.48 0.28

(B) 0.19 0.96 1.42 0.45 0.51 0.24

range was set as f1 = 0.7 fm and f2 = 1.3 fm. Thecalculated frequency responses of the magnitude and thephase of modulation index are shown by curves (A) and(B) in Figure 7. The obtained frequency responses of themodulation index magnitudes are flat and almost the same.The obtained frequency responses of the modulation indexphase are linear and have a phase difference of about π/2in the designed frequency range. Table 3 shows the obtaineddomain lengths normalized by the periodic case length L.

We applied the calculated polarization reversal patterns(A) and (B) into the two arms of the Mach-Zehnder waveg-uide in the SSB modulator and calculated the performanceof the SSB modulation. The obtained frequency dependenceof the upper sideband (USB) and the lower sideband (LSB)is shown in Figure 8, where we assumed the optical delayof λ/4 in the two arms of the Mach-Zehnder waveguide bysupplying an appropriate DC bias voltage to the electrodes.It is shown that the USB is generated around the designedfrequency range, while the LSB is almost suppressed. Thesideband suppression is expected over 20 dB around thedesigned frequency range. The characteristics of the USB andthe LSB can be switched by changing the DC bias voltage.Therefore, the broadband SSB modulation characteristics areexpected with our new approach.

6. Conclusion

We proposed the novel design of the traveling-wave elec-trooptic modulators using nonperiodically polarization-reversed structures to control frequency responses of boththe magnitude and the phase of the modulation index. It is


possible to design advanced electrooptic modulators such asduobinary modulators or broadband SSB modulators. Thisapproach is also applicable to design other devices such asbroadband optical frequency-shift-keying (FSK) modulator,and broadband optical frequency shifter (OFS).

Acknowledgments

This work was supported in part by Grants-in-Aid forScientific Research from the Ministry of Education, Culture,Sports, Science, and Technology of Japan. This research wasalso partially support by a grant from the Global COEProgram, “Center for Electronic Devices Innovation,” fromthe Ministry of Education, Culture, Sports, Science, andTechnology of Japan.

References

[1] E. L. Wooten, K. M. Kissa, A. Yi-Yan, et al., “A review of lithiumniobate modulators for fiber-optic communications systems,”IEEE Journal of Selected Topics in Quantum Electronics, vol. 6,no. 1, pp. 69–82, 2000.

[2] T. Kawanishi, T. Sakamoto, and M. Izutsu, “High-speedcontrol of lightwave amplitude, phase, and frequency by use ofelectrooptic effect,” IEEE Journal of Selected Topics in QuantumElectronics, vol. 13, no. 1, pp. 79–91, 2007.

[3] K. Yonenaga and S. Kuwano, “Dispersion-tolerant opticaltransmission system using duobinary transmitter and binaryreceiver,” Journal of Lightwave Technology, vol. 15, no. 8, pp.1530–1537, 1997.

[4] S. Shimotsu, S. Oikawa, T. Saitou, et al., “Single side-bandmodulation performance of a LiNbO3 integrated modulatorconsisting of four-phase modulator waveguides,” IEEE Pho-tonics Technology Letters, vol. 13, no. 4, pp. 364–366, 2001.

[5] H. Murata, K. Kinoshita, G. Miyaji, A. Morimoto, andT. Kobayashi, “Quasi-velocity-matched LiTaO3 guided-waveoptical phase modulator for integrated ultrashort optical pulsegenerators,” Electronics Letters, vol. 36, no. 17, pp. 1459–1460,2000.

[6] H. Murata, K. Kaneda, and Y. Okamura, “38 GHz opticalsingle-sideband modulation by using guided-wave electroop-tic modulators with periodic polarization-reversal,” in Pro-ceedings of Conference on Lasers and Electro-Optics (CLEO ’04),vol. 2, p. 3, San Francisco, Calif, USA, May 2004.

[7] H. Murata, T. Iwamoto, and Y. Okamura, “Novel electroopticoptical frequency shifters by use of 3-branch waveguide inter-ferometer and polarization-reversal structures,” in Proceedingsof the 9th Optoelectronics and Communications Conference(OECC ’04), pp. 564–565, New York, NY, USA, July 2004.

[8] H. V. Pham, H. Murata, and Y. Okamura, “Travelling-waveelectrooptic modulators with arbitrary frequency responseutilising non-periodic polarisation reversal,” Electronics Let-ters, vol. 43, no. 24, pp. 1379–1381, 2007.

[9] H. Murata, A. Morimoto, T. Kobayashi, and S. Yamamoto,“Optical pulse generation by electrooptic-modulation methodand its application to integrated ultrashort pulse generators,”IEEE Journal of Selected Topics in Quantum Electronics, vol. 6,no. 6, pp. 1325–1331, 2000.

[10] D. M. Gill, A. H. Gnauck, X. Liu, et al., “42.7-Gb/s cost-effective duobinary optical transmitter using a commercial 10-Gb/s mach-zehnder modulator with optical filtering,” IEEEPhotonics Technology Letters, vol. 17, no. 4, pp. 917–919, 2005.

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