# Electrooptic Modulators with Controlled Frequency Responses by Using Nonperiodically Polarization-Reversed Structure

Authors: Ha Viet Pham; Hiroshi Murata; Yasuyuki Okamura
Journal: Advances in OptoElectronics
 (2008)

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## Abstract

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


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## Body

## 1. Introduction

High-speed traveling-wave electrooptic modulators are very important devices because of their applications
in many optoelectronic  fields, such as telecommunication, optical signal
processing, and optical measurement. With the increasing demand for broadband
communication, many studies on the high-speed electrooptic modulators have been
carried out for optical fiber communication system [1]. In addition, the precise
control of the frequency responses of high-speed electrooptic modulators has been
required for the new generation optical fiber communication systems [2–4]. In a standard
traveling-wave electrooptic modulator, the frequency response of the modulation
index is restricted by two effects: the velocity mismatching between the
lightwave and modulation microwave and the loss of modulation microwave in the
traveling-wave electrodes.The polarization
reversal technology of ferroelectric optical crystals, such as LiNbO3 and LiTaO3, is attractive for realizing high-performance electrooptic
modulators. We have developed traveling-wave electrooptic modulators utilizing
the periodically polarization-reversed structure for quasi-velocity-matching
(QVM) between the lightwave propagating in the optical waveguide and the
modulation microwave traveling along the electrodes. This technique is attractive
because it compensates for the velocity mismatch in the high frequency ranges without
the requirement of specific and fine structures of the optical waveguide and
the electrodes for velocity matching. Several advanced electrooptic modulators
using periodically polarization-reversed structure have been proposed and
demonstrated, such as a QVM electrooptic phase modulator [5], an electrooptic
single-sideband (SSB) modulator [6], and an optical frequency shifter [7]. The
bandwidth of the modulation frequency response in these electrooptic modulators
with the simple periodically polarization-reversed structure is inversely
proportional to its electrode length and becomes relatively narrow for a
long-electrode device.We have
proposed a design to realize the traveling-wave electrooptic modulators
utilizing nonperiodically polarization-reversed structures [8]. Using the
proposed design, it is possible to obtain electrooptic modulators with the
arbitrary frequency responses of the magnitude of the modulation index over a
specified frequency range. The flat broadband electrooptic modulator with the
compensation for the degradation by both velocity mismatch and the microwave
loss is obtained. However, the control of not only the magnitude but also the
phase of the modulation index is very important in order to design the
electrooptic modulators for advanced modulation formats.In this paper, we extend
our design method to control frequency responses of both the magnitude and the phase
of modulation index in electrooptic modulators with nonperiodically
polarization-reversed structures utilizing new flatness parameters. This new approach
is applicable to the electrooptic modulators for advanced modulation formats, such
as duobinary modulation or broadband single-sideband modulation. This paper is
organized as follows. In Section2, the basic structure of the electrooptic
phase modulator using the   nonperiodic polarization reversal and the frequency responses
of modulation index are presented. In Section 3,
the calculation method to control the frequency responses of both the magnitude
and the phase of  the modulation index is described. Several calculation results
are shown in Section 4. In Section 5, the designs of the duobinary modulator
and broadband single-sideband
modulator with nonperiodically polarization-reversed structure
are discussed.


## 2. Traveling-Wave Electrooptic Modulators with Polarization-Reversed Structure

A schematic of the basic
structure of the traveling-wave electrooptic modulator is shown in Figure1. It
consists of a single-mode channel waveguide and simple coplanar traveling-wave
electrodes fabricated on a ferroelectric substrate. A Mach-Zehnder waveguide
for intensity modulation is also applicable. The velocity mismatch between the
group velocity of the lightwave propagating in the optical waveguide and the
phase velocity of a modulation microwave traveling along the electrodes is
compensated for by adopting the periodic polarization reversal scheme [9]. The domain
length L of a standard QVM with the periodic polarization reversal
scheme is determined as follows:
(1)L=12fm(1/vm−1/vg),
where fm is the peak modulation frequency, vm is the phase velocity of
the modulation microwave traveling along the electrodes, and vg is the group velocity of
the lightwave propagating in the waveguide. The parameter vm can
be calculated from the effective dielectric constant of the coplanar traveling-wave
electrodes taking account of its structure. The parameter vg can
be derived from both the material dispersion of the refractive index of the ferroelectric
material substrate and the mode dispersion of the optical waveguide.Figure 1
Basic structure of traveling-wave electrooptic phase modulator with nonperiodically polarization-reversed structure.The nonperiodic polarization reversal scheme is used
to control the frequency response of the electrooptic modulation. Figure2
shows the structure of the nonperiodic polarization reversal. The total active
length for modulation is Lt. It is divided into M sections of successive polarization-reversed and nonreversed region. Each
domain length is Li(i=1,2,…,M).Figure 2
Nonperiodically polarization-reversed structure.The modulation indexΔϕ(f), which is a function of the
modulation microwave frequency f, is
calculated using the following equation:
(2)Δϕ(f)=−∫0y1kΔndy+∫y1y2kΔndy−⋯+(−1)M∫yM−1yMkΔndy,where k is the wave vector of the
lightwave in vacuum and Δn is the refractive index change by the Pockels effect. When the light
polarization is along the z-axis and the modulation electrical field is also
along the z-axis, the refractive index change induced by the electrical
field of the microwave at the position y(0≤y≤Lt) is derived as follows, taking
account of the velocity mismatch between the lightwave and the modulation wave,
(3)Δn(y)=12ne3r33VdΓexp(−αy)×exp[j2πf{t0−(1vm−1vg)y}],where ne is the extraordinary
ray refractive index of the substrate, r33 is the Pockels
coefficient of the substrate. V is the voltage
applied to the electrodes, d is the
gap between the electrodes, Γ is the overlap factor
between the optical field and the electrical field, α is the attenuation
coefficient of the electrical field of the modulation microwave, and t0 is the time when the lightwave arrived at the position y=0.


## 3. Control of Frequency Response

When tuning the length
of each domain, the frequency responses of the modulation index magnitude|Δϕ(f)| and phase arg[Δϕ(f)] change. In order to design a nonperiodic
polarization reversal structure for an arbitrary frequency response of the
modulation index magnitude, we have proposed the modified flatness parameter MF
[8], which expresses the difference between the magnitude of the modulation
index |Δϕ(f)| and the target function TF(f)
in the defined frequency range from f1 to f2(4)MF=(f2−f1)∫f1f2|Δϕ(f)/TF(f)|2df[∫f1f2|Δϕ(f)/TF(f)|df]2−1.
By tuning the length of
each domain, the value of the modified flatness parameter changes. If the
modified flatness parameter becomes zero, the magnitude of the modulation index
and the target function completely coincide in the frequency range.We extended this method
for dealing with both the modulation index magnitude and the phase. We define
two flatness parameters,MFM and MFP,
for the magnitude and the phase of the modulation index by using two target
functions: TFM(f) for the magnitude and TFP(f)
for the phase in the defined frequency range from f1 to f2,
as follows:
(5)MFM=(f2−f1)∫f1f2(|Δϕ(f)|2/|TFM(f)|2)df[∫f1f2(|Δϕ(f)|/|TFM(f)|)df]2−1,MFP=(f2−f1)∫f1f2(|arg[Δϕ(f)]|2/|TFP(f)|2)df{∫f1f2(|arg[Δϕ(f)]|/|TFP(f)|)df}2−1,where MFM is the difference between the magnitude of the modulation index |Δϕ(f)| and TFM(f), and MFP is the difference between the phase of the modulation
index arg[Δϕ(f)] and TFP(f).If the modified flatness parameterMFM becomes zero, the magnitude of the modulation index |Δϕ(f)| and the target function TFM(f)
completely coincide in the defined frequency 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 that defined frequency range. We tried to find the
condition for minimizing the two flatness parameters MFM and MFP at the same 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 in
the periodic case Li=L(i=1,2,…,M). At the
first step of calculation, only the length of the first domain L1 is changed, and the corresponding modulation index value is calculated. By
repeating the calculation with tuning the length L1, the
smallest values of MFM and MFP which are called
the local minimizing values in this calculation step are obtained. After that, only
the next domain length L2 is tuned and the next local minimal
values of MFM and MFP are
obtained. These local minimal values are smaller than the previous ones,
respectively. This calculation step with tuning the domain length is repeated
by changing the domain to be tuned from the first domain to the last domain
successively. When finishing the calculation step with tuning the last domain
length, the domain to be tuned is set to the first domain again and these
calculation steps are repeated. In these repeating calculations, the minimal
values of the two flatness parameters MFM and MFP are obtained when the local minimal values become the same with the values in
the previous calculation step, respectively. As a result, the length of each
domain is optimal and the difference between the frequency responses of modulation
index and the target functions becomes minimum. Therefore, it is possible to control the frequency responses of the magnitude
and the phase of modulation index.


## 4. Calculation Results

We tried to calculate the frequency response
using our method shown in the previous section. In these calculations, the
attenuation coefficientα was set as negligible for simplicity. It is
also possible to calculate and design the frequency response of the modulation
index taking into account the attenuation coefficient [8].Figure3 shows examples of calculated
frequency responses of the magnitude and the phase of the modulation index in
the traveling-wave electrooptic modulators with nonperiodic polarization
reversals for the flat, parabolic magnitude responses and linear phase
responses. The number of domains was set as M=6 and the frequency range was set from f1=0.7fm to f2=1.3fm. The target function for the flat magnitude response was defined as TFM1(f)=c1 (c1 is constant, and its value is proportional to the applied modulation
voltage to the electrodes), and the target function for the linear phase
response was defined as TFP1(f)=a1[(f/fm)−1] (a1 is constant, and it is set as 6.5 rad in calculation). With these
conditions, the calculation for minimizing the flatness parameters was carried
out. The obtained frequency responses of the magnitude and the phase are shown
by the curves (1) in Figures 3(a) and 3(b), respectively.Frequency dependence of modulation index in traveling-wave electrooptic modulators for flat, parabolic magnitude responses with linear phase responses. (a) Magnitude responses, (b) phase responses.
(a)(b)The target function for the parabolic
magnitude response was also defined asTFM2(f)=c2[(f/fm)2−1]+c1 (with c2/c1 is set as 0.6) and
the target function for the linear phase response was defined as TFP2(f)=a2[(f/fm)−1]
(with a2 is set as 10 rad). The calculation was also carried out. The obtained frequency
responses of the magnitude and the phase are also shown as the curves (2) in Figures 3(a) and 3(b), respectively. For comparison, the frequency responses
of the magnitude and the phase in traveling-wave electrooptic modulator with the
periodic polarization reversal are also shown in the figures.The obtained frequency responses almost coincide with
the target functions in the designed frequency ranges. Table1 shows the values
of the obtained domain lengths normalized by the length L. The length L is the domain length in the periodic polarization reversal for QVM at the peak
modulation frequency fm. For example, if we set the peak
modulation frequency as fm=15GHz and the lightwave
wavelength as λ = 1.55 μm, then the corresponding length of L becomes L=4.33mm
for a LiTaO3 guided-wave modulator (microwave phase velocity vm=6.47×107m/s and lightwave group
velocity vg=1.29×108m/s).Table 1
(1) Obtained normalized domain lengths for the flat magnitude response and the linear phase response, and (2) the parabolic magnitude response and the linear phase response.
L1/LL2/LL3/LL4/LL5/LL6/L(1)0.030.220.410.401.070.77(2)0.220.410.580.580.770.96We confirmed the
validity of the proposed method. It is possible to obtain the traveling-wave
electrooptic modulators with the required frequency responses of both the
magnitude and the phase of the modulation index by using our new approach.


## 5. Applications

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


### 5.1. Electrooptic Intensity Modulator for Duobinary Modulation

The
optical duobinary modulation format offers a larger capacity of data
transmission and a large tolerance for fiber chromatic dispersion in optical
fiber communication system [3, 10]. Several experimental studies on the
generation of the optical duobinary modulation signals have been reported. In
these reports, the electrical/optical filters are required to limit the spectrum
bandwidth of the generated signals. By using the nonperiodically polarization-reversed
structure, it is possible to obtain the electrooptic modulators with
specifically tuned filter-like modulation frequency responses with any passband
(low-pass, high-pass, band-pass, Gaussian like, etc.). It can be used for the
generation of the duobinary modulation signals without the external
electric/optic filters.Figure4 shows the structure of the electrooptic intensity modulator for duobinary
modulation using nonperiodic polarization reversal. It consists of the Mach-Zehnder
waveguide, coplanar traveling-wave electrodes, and nonperiodically
polarization-reversed structures. The lengths of each domain are the same in
the two arms of the Mach-Zehnder waveguide, however, the polarity is opposite in
the two arms. Therefore, by applying the electrical fields with the same
direction, the push-pull intensity modulation with the same modulation index
magnitude for the duobinary operation is obtained with a single modulation
signal.Basic structure of duobinary modulator with nonperiodic polarization reversal. (a) Whole view, (b) cross-section view, (c) polarization-reversed patterns.
(a)(b)(c)Using the
proposed method for the frequency response control, we tried to obtain a Gaussian
filter-like frequency response in the electrooptic modulation with a cutoff
frequencyfc for generating the optical duobinary modulation
signals. The target function for the Gaussian filter-like magnitude response
was defined as TFMG(f)=Δϕ0exp[−g(f/fm)2]
(with g is set as 2) and the target function for the linear phase
response was defined as TFPG(f)=a(f/fm)
(with a is set as 5.5 rad). The number of domains was set as M=8 and
the frequency range was set as the baseband from f1=0 to f2=fm.
The obtained results are shown in Figure 5. The targets functions are shown
as the dashed lines. The obtained frequency responses of the magnitude and the
phase of electrooptic modulation are shown as the solid lines. Table 2 shows
the obtained domain lengths normalized by the periodic case length L. By using the Gaussian filter-like magnitude and
the linear phase responses in electrooptic modulation, it is possible to
generate the duobinary modulation signals by simple digital electrical driving
signal without any filter.Table 2
Obtained normalized domain lengths for the Gaussian-like magnitude response and the linear phase response.
L1/LL2/LL3/LL4/LL5/LL6/LL7/LL8/L0.1020.3590.2811.9990.1000.1010.1590.111Figure 5
Frequency dependence of modulation index in traveling-wave electrooptic modulator for the Gaussian-like filter magnitude response and the linear phase response.We also applied the calculated polarization
reversal pattern into the two arms of the Mach-Zehnder waveguide in the proposed
duobinary modulator and calculated its performance. For the design of a 10 Gbps
duobinary modulator, the cutoff frequencyfc was set as 5 GHz and the lightwave wavelength as λ=1.55μm. Then, the total electrode length Lt became Lt=24mm for a LiTaO3-based
device.We also checked the effect caused by the
attenuation of the modulation microwave in the electrodes. We assumed a typical
attenuation coefficient of the modulation microwave (α=0.25dB/cm/GHz0.5) in coplanar
electrodes. As a result, the frequency response of the 10 Gbps duobinary
modulator with the microwave attenuation became almost the same with the
calculated one with the negligible attenuation coefficient in the frequency
range from 0 to 10 GHz. Therefore,
an ∼10Gbps duobinary modulator is expected using our new approach.


### 5.2. Broadband Single-Sideband Modulator

By using optical single-sideband
modulation formats, it is possible to reduce the optical power in the signal transmission.
This is attractive in long-haul optical fiber communication systems with higher
density wavelength multiplexing [4]. We proposed and demonstrated the SSB modulators using the periodic polarization
reversal [6].
By using our new approach, the SSB modulator with
the flat and wider operational frequency range can be designed.Figure6 shows the structure of this electrooptic modulator using nonperiodic polarization reversal. It
consists of the Mach-Zehnder waveguide, coplanar traveling-wave electrodes, and
two nonperiodically polarization-reversed patterns set in the two arms of the Mach-Zehnder
waveguide. In order to have the SSB modulation characteristics, it is required
that the magnitudes of the modulation index are the same in the two arms of the
Mach-Zehnder waveguide and the phases of the modulation index in the two arms
are different as π/2 in the designed frequency range. For realizing
these two modulation characteristics, we applied the control method of the
frequency responses.Basic structure of SSB modulator with nonperiodic polarization reversal. (a) Whole view, (b) cross-section view, (c) polarization-reversed patterns.
(a)(b)(c)Figure7 shows the calculated frequency responses for the SSB modulator with
nonperiodic polarization reversal for the 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=4rad, b is a common phase offset value). In this
example, the number of domains was set as M=6 and the frequency range was set as f1=0.7fm and f2=1.3fm. The calculated frequency
responses of the magnitude and the phase of modulation index are shown by
curves (A) and (B) in Figure 7. The obtained frequency responses of the modulation
index magnitudes are flat and almost the same. The obtained frequency responses
of the modulation index phase are linear and have a phase difference of about π/2 in the designed frequency range. Table 3 shows the obtained domain
lengths normalized by the periodic case length L.Table 3
Obtained normalized domain lengths for the designed SSB modulator.
L1/LL2/LL3/LL4/LL5/LL6/L(A)0.651.310.580.510.480.28(B)0.190.961.420.450.510.24Frequency dependence of modulation index in designed SSB modulator for flat magnitude responses and linear phase responses withπ/2 difference. (a) Magnitude responses, (b) phase responses.
(a)(b)We applied the calculated polarization reversal patterns (A) and (B) into
the two arms of the Mach-Zehnder waveguide in the SSB modulator and calculated
the performance of the SSB modulation. The obtained   frequency dependence of the
upper sideband (USB) and the lower sideband (LSB) is shown in Figure8,
where we assumed the optical delay of λ/4 in the two arms of the Mach-Zehnder
waveguide by supplying an appropriate DC bias  voltage to the electrodes. It is
shown that the USB is generated around the designed frequency range, while the
LSB is almost suppressed. The sideband suppression is expected over 20 dB
around the designed frequency range. The characteristics of the USB and the LSB
can be switched by changing the DC bias voltage. Therefore, the broadband SSB
modulation characteristics are expected with our new approach.Figure 8
Frequency responses of USB and LSB components of designed SSB modulator.


## 5.1. Electrooptic Intensity Modulator for Duobinary Modulation

The
optical duobinary modulation format offers a larger capacity of data
transmission and a large tolerance for fiber chromatic dispersion in optical
fiber communication system [3, 10]. Several experimental studies on the
generation of the optical duobinary modulation signals have been reported. In
these reports, the electrical/optical filters are required to limit the spectrum
bandwidth of the generated signals. By using the nonperiodically polarization-reversed
structure, it is possible to obtain the electrooptic modulators with
specifically tuned filter-like modulation frequency responses with any passband
(low-pass, high-pass, band-pass, Gaussian like, etc.). It can be used for the
generation of the duobinary modulation signals without the external
electric/optic filters.Figure4 shows the structure of the electrooptic intensity modulator for duobinary
modulation using nonperiodic polarization reversal. It consists of the Mach-Zehnder
waveguide, coplanar traveling-wave electrodes, and nonperiodically
polarization-reversed structures. The lengths of each domain are the same in
the two arms of the Mach-Zehnder waveguide, however, the polarity is opposite in
the two arms. Therefore, by applying the electrical fields with the same
direction, the push-pull intensity modulation with the same modulation index
magnitude for the duobinary operation is obtained with a single modulation
signal.Basic structure of duobinary modulator with nonperiodic polarization reversal. (a) Whole view, (b) cross-section view, (c) polarization-reversed patterns.
(a)(b)(c)Using the
proposed method for the frequency response control, we tried to obtain a Gaussian
filter-like frequency response in the electrooptic modulation with a cutoff
frequencyfc for generating the optical duobinary modulation
signals. The target function for the Gaussian filter-like magnitude response
was defined as TFMG(f)=Δϕ0exp[−g(f/fm)2]
(with g is set as 2) and the target function for the linear phase
response was defined as TFPG(f)=a(f/fm)
(with a is set as 5.5 rad). The number of domains was set as M=8 and
the frequency range was set as the baseband from f1=0 to f2=fm.
The obtained results are shown in Figure 5. The targets functions are shown
as the dashed lines. The obtained frequency responses of the magnitude and the
phase of electrooptic modulation are shown as the solid lines. Table 2 shows
the obtained domain lengths normalized by the periodic case length L. By using the Gaussian filter-like magnitude and
the linear phase responses in electrooptic modulation, it is possible to
generate the duobinary modulation signals by simple digital electrical driving
signal without any filter.Table 2
Obtained normalized domain lengths for the Gaussian-like magnitude response and the linear phase response.
L1/LL2/LL3/LL4/LL5/LL6/LL7/LL8/L0.1020.3590.2811.9990.1000.1010.1590.111Figure 5
Frequency dependence of modulation index in traveling-wave electrooptic modulator for the Gaussian-like filter magnitude response and the linear phase response.We also applied the calculated polarization
reversal pattern into the two arms of the Mach-Zehnder waveguide in the proposed
duobinary modulator and calculated its performance. For the design of a 10 Gbps
duobinary modulator, the cutoff frequencyfc was set as 5 GHz and the lightwave wavelength as λ=1.55μm. Then, the total electrode length Lt became Lt=24mm for a LiTaO3-based
device.We also checked the effect caused by the
attenuation of the modulation microwave in the electrodes. We assumed a typical
attenuation coefficient of the modulation microwave (α=0.25dB/cm/GHz0.5) in coplanar
electrodes. As a result, the frequency response of the 10 Gbps duobinary
modulator with the microwave attenuation became almost the same with the
calculated one with the negligible attenuation coefficient in the frequency
range from 0 to 10 GHz. Therefore,
an ∼10Gbps duobinary modulator is expected using our new approach.


## 5.2. Broadband Single-Sideband Modulator

By using optical single-sideband
modulation formats, it is possible to reduce the optical power in the signal transmission.
This is attractive in long-haul optical fiber communication systems with higher
density wavelength multiplexing [4]. We proposed and demonstrated the SSB modulators using the periodic polarization
reversal [6].
By using our new approach, the SSB modulator with
the flat and wider operational frequency range can be designed.Figure6 shows the structure of this electrooptic modulator using nonperiodic polarization reversal. It
consists of the Mach-Zehnder waveguide, coplanar traveling-wave electrodes, and
two nonperiodically polarization-reversed patterns set in the two arms of the Mach-Zehnder
waveguide. In order to have the SSB modulation characteristics, it is required
that the magnitudes of the modulation index are the same in the two arms of the
Mach-Zehnder waveguide and the phases of the modulation index in the two arms
are different as π/2 in the designed frequency range. For realizing
these two modulation characteristics, we applied the control method of the
frequency responses.Basic structure of SSB modulator with nonperiodic polarization reversal. (a) Whole view, (b) cross-section view, (c) polarization-reversed patterns.
(a)(b)(c)Figure7 shows the calculated frequency responses for the SSB modulator with
nonperiodic polarization reversal for the 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=4rad, b is a common phase offset value). In this
example, the number of domains was set as M=6 and the frequency range was set as f1=0.7fm and f2=1.3fm. The calculated frequency
responses of the magnitude and the phase of modulation index are shown by
curves (A) and (B) in Figure 7. The obtained frequency responses of the modulation
index magnitudes are flat and almost the same. The obtained frequency responses
of the modulation index phase are linear and have a phase difference of about π/2 in the designed frequency range. Table 3 shows the obtained domain
lengths normalized by the periodic case length L.Table 3
Obtained normalized domain lengths for the designed SSB modulator.
L1/LL2/LL3/LL4/LL5/LL6/L(A)0.651.310.580.510.480.28(B)0.190.961.420.450.510.24Frequency dependence of modulation index in designed SSB modulator for flat magnitude responses and linear phase responses withπ/2 difference. (a) Magnitude responses, (b) phase responses.
(a)(b)We applied the calculated polarization reversal patterns (A) and (B) into
the two arms of the Mach-Zehnder waveguide in the SSB modulator and calculated
the performance of the SSB modulation. The obtained   frequency dependence of the
upper sideband (USB) and the lower sideband (LSB) is shown in Figure8,
where we assumed the optical delay of λ/4 in the two arms of the Mach-Zehnder
waveguide by supplying an appropriate DC bias  voltage to the electrodes. It is
shown that the USB is generated around the designed frequency range, while the
LSB is almost suppressed. The sideband suppression is expected over 20 dB
around the designed frequency range. The characteristics of the USB and the LSB
can be switched by changing the DC bias voltage. Therefore, the broadband SSB
modulation characteristics are expected with our new approach.Figure 8
Frequency responses of USB and LSB components of designed SSB modulator.


## 6. Conclusion

We proposed the novel design of the traveling-wave electrooptic modulators using nonperiodically
polarization-reversed structures to control frequency responses of both the magnitude
and the phase of the modulation index. It is possible to design advanced
electrooptic modulators such as duobinary modulators or broadband SSB
modulators. This approach is also applicable to design other devices such as
broadband optical frequency-shift-keying (FSK) modulator, and broadband optical
frequency shifter (OFS).



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*Source: 948294-2008-10-30.xml*