Journal of Modern Optics
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Analysis of the dual-parallel Mach–Zehnder
modulator-based equivalent phase modulation
Yang Chen
To cite this article: Yang Chen (2018) Analysis of the dual-parallel Mach–Zehnder modulatorbased equivalent phase modulation, Journal of Modern Optics, 65:18, 2079-2085, DOI:
10.1080/09500340.2018.1496287
To link to this article: https://doi.org/10.1080/09500340.2018.1496287
Published online: 10 Jul 2018.
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JOURNAL OF MODERN OPTICS
2018, VOL. 65, NO. 18, 2079–2085
https://doi.org/10.1080/09500340.2018.1496287
Analysis of the dual-parallel Mach–Zehnder modulator-based equivalent phase
modulation
Yang Chen
a,b
a School of Information Science and Technology, East China Normal University, Shanghai, People’s Republic of China; b Engineering Center of
SHMEC for Space Information and GNSS, East China Normal University, Shanghai, People’s Republic of China
ABSTRACT
ARTICLE HISTORY
In a dual polarization quadrature phase shift keyed (DP-QPSK) modulator, it is desired that one dualparallel Mach–Zehnder (MZ) modulator in it is operated as a phase modulator (PM) to achieve some
functions in conjunction with the other dual-parallel MZ modulator. Equivalent phase modulation is
realized by controlling the bias points of a dual-parallel MZ modulator. If the parameters are accurately set, it functions as a true PM. However, the amplitude imbalance and the different arrival time
of the two RF signals applied to the dual-parallel MZ modulator, and the deviations of the three bias
points in the dual-parallel MZ modulator influence the performance of the equivalent phase modulator (e-PM). In this paper, we study the influences of these non-ideal factors on the performance of the
e-PM. The results show important guidelines for significance for the further use of the dual-parallel
MZ modulator-based equivalent phase modulation in a DP-QPSK modulator.
Received 17 January 2018
Accepted 31 May 2018
1. Introduction
Microwave photonics is an interdisciplinary area of optics
and electronics, which can realize some functions that are
complex or even impossible to be directly implemented
in the radio-frequency (RF) domain (1–3). To connect
the optical world and the electronic world in microwave
photonic systems, the optical modulator is the key device.
Many different kinds of optical modulators (4–8), such as
phase modulator (PM), intensity modulator (IM), polarization modulator (PolM), etc., have been proposed to
fulfil different kinds of applications. In order to implement even more complicated functions, optical modulators with more complicated structures are fabricated.
For example, two IMs and a PM are integrated together
to form a dual-parallel Mach–Zehnder modulator (DPMZM), which is also called IQ modulator because it can
realize optical IQ modulation under special bias points
(9). There is another kind of optical modulator called
dual polarization binary phase shift keyed (DP-BPSK)
modulator, which consists of two IMs and a 90° polarization rotator. The DP-BPSK modulator is designed for DPBPSK modulation format in 40 Gbps optical transmission networks, but it also has numerous applications in
microwave photonics (10,11). A more complicated optical modulator is the dual polarization quadrature phase
shift keyed (DP-QPSK) modulator, which is designed for
CONTACT Yang Chen
ychen@ce.ecnu.edu.cn
© 2018 Informa UK Limited, trading as Taylor & Francis Group
KEYWORDS
Dual-parallel Mach–Zehnder
modulator; equivalent phase
modulation; non-ideal
factors; optical modulation
DP-QPSK modulation format in 100 Gbps optical transmission networks, mainly consisting of two DP-MZMs
and a 90° polarization rotator. Because of its high integration and a large number of controllable parameters,
the DP-QPSK modulator also finds many applications in
microwave photonics (12,13).
If parallel DP-MZM and PM are used together to
achieve some special functions, we generally need to
employ two discrete modulators and two optical couplers, which will make the system very complicated and
unstable. To integrate the structure of parallel DP-MZM
and PM together to simplify the system structure and
improve the system stability, it is highly desired that
one DP-MZM integrated into the DP-QPSK modulator is operated as an equivalent phase modulator (ePM), which is paralleled with the other DP-MZM in
the DP-QPSK modulator to form the structure of parallel DP-MZM and PM. For example, in (14), we propose
an optoelectronic oscillator using a DP-QPSK modulator, where one DP-MZM in the DP-QPSK modulator is
biased as an e-PM to form a frequency-tenable optoelectronic oscillator, and the other DP-MZM in the DP-QPSK
modulator is used as a frequency multiplier to realize
high-frequency microwave signal generation from the
oscillation signal. The e-PM is the key device to guarantee both large frequency tunability and high frequency
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Y. CHEN
multiplication factor using a single modulator. In (15), we
propose a 360° tenable photonic microwave phase shifter
based on a single DP-QPSK modulator, where equivalent
phase modulation is also the key point to realize the phase
shift without using optical filters or additional optical
modulators.
Equivalent phase modulation plays an important role
in DP-QPSK modulator-based photonic signal generation and processing methods, which can realize some
functions that are difficult or complicated to be realized in discrete component microwave photonic systems.
Actually, equivalent phase modulation is a phase modulation that realized by a DP-MZM. If microwave photonic
systems are realized using integrated photonics (1), the ePM in discrete component microwave photonic systems
can be simply replaced by a PM. However, integrated
photonics has only begun to be extensively studied in
recent years, so there is still a long way from being widely
used. Most of the microwave photonic systems in applications today are based on discrete component microwave
photonics, so it is still valuable to study the equivalent
phase modulation to guide the use of it in microwave
photonic systems. In this paper, the equivalent phase
modulation using a DP-MZM is comprehensively investigated and analysed. The influences of the non-ideal
factors in the e-PM on the performance of the equivalent phase modulation are studied. The key contribution
of the work is that these analyses provide a quantitative
guidance for the use of equivalent phase modulation in
the future applications.
2. Principle
Figure 1 shows the principle of equivalent phase modulation realized by a DP-MZM. The input RF signal can be
an arbitrary electrical signal within the modulation bandwidth of the DP-MZM, which is split into two paths and
then applied to the two electrodes of the two sub-MZMs
in the DP-MZM, respectively, with equal amplitudes and
arrival time. The bias points of the two sub-MZMs and
the main-MZM in the DP-MZM are controlled by a DC
power supply, where the two sub-MZMs are biased at
the minimum transmission point (MITP) and maximum
transmission point (MATP), respectively, and the mainMZM is biased at the quadrature transmission point
(QTP).
Assuming the input optical signal of the DP-MZM is
E0 exp(jωc t), and the RF signals applied to the two subMZMs are both a(t), where E0 and ωc are the amplitude
and angular frequency of the optical signal, respectively,
the optical signal at the output of the DP-MZM can be
expressed as
1
π(2a(t))
Eout (t) = E0 exp(jωc t) cos
2
2Vπ
π π(2a(t) − Vπ )
+ cos
exp j
2Vπ
2
1
π a(t)
π a(t)
= E0 exp(jωc t) cos
+ j sin
2
Vπ
Vπ
1
π a(t)
= E0 exp jωc t + j
,
(1)
2
Vπ
where Vπ is the half-wave voltage of the DP-MZM. As
can be seen from Equation (1), the input RF signal a(t) is
phase modulated onto the optical carrier. The equation
above is derived through rigorous mathematics, so the
equivalent phase modulation in an e-PM is exactly the
same as that in a PM.
Under ideal conditions, the bias points of the DPMZM are completely accurate, the amplitudes of the two
RF signals applied to the two sub-MZMs are identical,
and the arrival time of the two RF signals is also identical.
However, in practical implementations, these conditions
are difficult to be 100% satisfied due to the accuracy of
the devices in the system and the impact of the environmental changes, so the accuracy of the equivalent phase
modulation will be affected, thus leading to a distortion
of the phase modulation and an emergence of an intensity modulation along with the phase modulation. In the
following part, a detailed analysis is made taking these
non-ideal factors into consideration.
3. Analysis of non-ideal factors
3.1. Amplitude imbalance
Figure 1. Principle of equivalent phase modulation using a DPMZM. DP-MZM, dual-parallel Mach–Zehnder modulator; MITP,
minimum transmission point; MATP, maximum transmission
point; QTP, quadrature transmission point.
As discussed above, the amplitudes of the two RF signals
applied to the two sub-MZMs in the DP-MZM should
be identical to guarantee an exact phase modulation. To
analyse the influence of the amplitude imbalance, two
amplitude imbalance coefficients η and κ are introduced,
which represent the relative amplitudes of the two RF signals. In the ideal case, η = κ = 1 establishes, whereas in
an unideal case, η=1, κ=1 or κ=η=1 establishes. Under
JOURNAL OF MODERN OPTICS
this condition, the optical signal at the output of the
DP-MZM can be expressed as
1
π(2κa(t))
Eout_amp (t) = E0 exp(jωc t) cos
2
2Vπ
π π(2ηa(t) − Vπ )
+ cos
exp j
2Vπ
2
1
= E0 exp(jωc t)[cos κx(t) + j sin ηx(t)]
2
1
= E0 exp(jωc t)A(t) exp(j(t)),
(2)
2
where x(t) = πa(t)/Vπ , A(t) represents the amplitude
modulation term, and (t) represents the phase modulation term. If κ = η = 1 establishes, Equation (2) can
be simplified as Equation (1). As shown in Equation (2),
the amplitude imbalance of the RF signals introduces
an amplitude modulation term, as well as distorting the
phase modulation term compared with Equation (1). To
simplify the analysis, two specific cases are selected in the
study: κ = 1, η changes; η = 1, κ changes.
Figure 2(a) shows the simulated amplitude modulation term versus the amplitude of the applied RF signal
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with different amplitude imbalance coefficient η when
κ = 1. As shown in Figure 2(a), when η = 1, a straight
line is observed, which means the relative amplitude of
the output signal is always 1, regardless of the amplitude
of the input signal. It is observed that when η deviates
from 1 to greater than 1 or less than 1, the amplitude of
the optical signal varies with the amplitude of the input
RF signal x(t), which means an amplitude modulation is
introduced due to the amplitude imbalance. Figure 2(b)
shows the phase modulation term versus the amplitude of
the applied RF signal with different amplitude imbalance
coefficient η when κ = 1. Figure 2(c) shows the corresponding first-order derivative of the phase modulation
term. When η = 1, a straight line is also observed with a
value of 1, which means the slope of the phase modulation term is always 1, regardless of the amplitude of the
input signal, thus realizing a phase modulation. When η
deviates from 1 to greater than 1 or less than 1, the slope
of the phase modulation terms is no longer a straight line.
When the input signal x(t) is in the range of −1.6 to 1.6,
the slope of the phase modulation term varies in a relatively small range, and when x(t) is even larger, the slope
of the phase modulation term changes much greater.
Figure 2. Simulated (a) amplitude modulation term, (b) phase modulation term, (c) first-order derivative of the phase modulation term,
versus the amplitude of the applied signal with different amplitude imbalance coefficients when κ = 1, η changes; simulated (c) amplitude modulation term, (d) phase modulation term, (e) first-order derivative of the phase modulation term, versus the amplitude of the
applied signal with different amplitude imbalance coefficients when η = 1, κ changes.
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Y. CHEN
Figure 2(d) shows the simulated amplitude modulation term versus the amplitude of the applied RF signal
with different amplitude imbalance coefficients κ when
η = 1. The curve in Figure 2(d) and the corresponding curve with the same deviation in Figure 2(a) have
roughly symmetrical characteristics. Under small signal
modulation condition (x(t) < < 1), the amplitude modulation terms in Figure 2(a,d) are both still very close to 1
and with slopes close to 0, which means small amplitude
imbalance has relatively small influence on the amplitude modulation term under small signal modulation
condition in both cases. Figure 2(e) shows the phase
modulation term versus the amplitude of the applied
RF signal with different amplitude imbalance coefficients
κ when η = 1. Figure 2(f) shows the corresponding
first-order derivative of the phase modulation term. The
curve of the phase modulation term in Figure 2(e) and
that in Figure 2(b) has very different characteristics. In
Figure 2(e), when the system is operating under small
signal modulation condition (x(t) < < 1), the slopes of
the curves are still very close to 1. When the amplitude
of x(t) further increases, the slopes change greatly. In
Figure 2(b), the slopes are away from 1 even if x(t) < < 1.
Therefore, amplitude imbalance in Figure 2(b) has a
larger influence on the phase modulation term than that
in Figure 2(e) under small signal modulation condition.
Although the slopes in Figure 2(c) changes a lot under
small signal modulation condition, they have the same
level of change when x(t) is in the range from −1.6 to 1.6.
The slopes in Figure 2(f) have relatively larger changes
when x(t) is in the same range. However, when x(t) is
further increased, the curves in Figure 2(e) have smaller
slopes than those in Figure 2(b).
For the amplitude imbalance of the two RF signals
applied to the DP-MZM, even 10% amplitude imbalance,
which corresponds to no more than 1 dB power difference, will lead to about 15% amplitude fluctuation when
x(t) is in the range of –π to π. For the phase modulation, the theoretical curve is a straight line with a slope of
1. 10% amplitude imbalance will distort the slope of the
curve with a maximum value of about 1.3 when x(t) is
in the range of –π to π. In order to avoid the influence
of the amplitude imbalance of the RF signal applied to
the DP-MZM, the power of the two RF signals should be
carefully controlled.
3.2. Different arrival time
Equivalent phase modulation requires the two RF signals
applied to the two sub-MZMs to have the same arrival
time. It is a very impressive feature because no delay lines
or RF phase shifters are needed to introduce a phase
difference or time delay between the two signals, which
makes the system frequency independent. However, the
two RF signals applied to the DP-MZM may have different arrival time because they are transmitted and applied
to the DP-MZM from different paths. To simplify the
analysis of the influence of the arrival time on the equivalent phase modulation, the applied RF signal is assumed
to be a sinusoidal wave (a(t) = Vcosωs t, V and ωs are the
amplitude and angular frequency of the RF signal), so the
optical signal from the e-PM under this condition can be
expressed as
1
π(2V cos ωs t)
Eout_delay (t) = E0 exp(jωc t) cos
2
2Vπ
⎤
⎛
⎞
π(2V cos ωs
⎥
⎜ (t − τ ) − Vπ ) ⎟
⎟ exp j π ⎥
+ cos ⎜
⎝
⎠
2Vπ
2 ⎦
⎡
⎞
⎛
1
⎟
⎢ ⎜
= E0 exp(jωc t) ⎣cos ⎝χ cos ωs t ⎠
2
x(t)
⎛
⎞⎤
⎜
⎟⎥
+j sin ⎝χ cos ωs (t − τ )⎠⎦
x(t−τ )
1
= E0 exp(jωc t)A(t) exp(j(t)),
2
(3)
where x(t) = χ cosωs t, χ = πV/Vπ is the modulation
index, τ is the time delay between the two RF signals, A(t)
represents the amplitude modulation term and (t) represents the phase modulation term. Here, the variations
of A(t) and (t) with the time delay τ and modulation
index χ are studied. The influence of the time delay is
studied in terms of phase delay ωs τ in the analysis.
Figure 3(a) shows the simulated amplitude modulation term versus ωs t under different phase delays ωs τ and
different modulation indices χ . From the overall observation of the figure, a smaller modulation index in the
range from 0.5 to 1.5 corresponds to a smaller amplitude modulation under the same phase delays ωs τ , which
means smaller modulation index has better tolerance on
the phase delay ωs τ . Figure 3(b) shows a specific case of
Figure 3(a) when χ = 1. The solid line in Figure 3(b)
shows the ideal case with no phase delay. With different ωs t, the output signal has the same amplitude. When
the phase delay changes from 0 to −4π/12 or 4π /12,
the amplitude term is no longer a constant. It is also
noticed that the curves of the amplitude modulation term
are symmetric about ωs t = 0 when the phase delays are
deviating from 0 in the positive direction and in the negative direction. Figure 3(c) shows the simulated phase
modulation term versus ωs t under different phase delays
JOURNAL OF MODERN OPTICS
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Figure 3. Simulated (a,b) amplitude modulation term, (c,d) phase modulation term, versus ωs t under different phase delays ωs τ and
different modulation indices χ . (b) is a specific case of (a) when χ = 1, and (d) is a specific case of (c) when χ = 1.
ωs τ and different modulation indices χ . Theoretically,
the phase term of the output optical signal varies sinusoidally with ωs t. When a phase delay ωs τ is introduced,
the curves are no longer a standard sinusoidal wave. It
can be observed from Figure 3(c) that the distortion of
the curve is more serious with a larger modulation index
under the same phase delays ωs τ . As a result, smaller
modulation index also has better tolerance on the phase
delay ωs τ . Figure 3(d) shows a specific case of Figure 3(c)
when χ = 1. The solid line in Figure 3(d) shows the ideal
case with no phase delay, which is a standard sinusoidal
wave. It is noticed that the curves of the phase modulation
term are also symmetric about ωs t = 0 when the phase
delays are deviating from 0 in the positive direction and
in the negative direction.
For the different arrival time of the two RF signals applied to the DP-MZM, it should be noticed that
the influence of the non-ideal arrival time on the performance of the equivalent phase modulation is much
related to the frequency of the RF signal, which means
the arrival time of the two RF signals should be controlled
more precisely when the frequency of the applied signals
is higher. For example, to obtain the same performance,
the arrival time difference of 10-GHz RF signals needs
to be controlled 10 times more precisely than that of
1-GHz RF signals. Therefore, the system should be controlled more precisely when higher operating frequency
is used.
3.3. Bias points deviation
The DP-MZM based e-PM has three bias points to be
controlled: two bias points of the two sub-MZMs and a
bias point of the main-MZM. If the bias points of the
DP-MZM are controlled precisely, the equivalent phase
modulation from the DP-MZM is an exact phase modulation. However, the bias points of the e-PM are hard to be
controlled and maintained as the desired values in longterm operation, which will influence the performance of
the phase modulation from the DP-MZM. In the analysis, the bias point deviation of the DP-MZM is studied
using the bias voltage deviation. The bias voltage deviations of the sub-MZMs biased at the MATP and the MITP
are assumed to be V 1 and V 2 , respectively, whereas
the bias voltage deviation of the main-MZM biased at the
QTP is assumed to be V 3 . The optical signal from the
DP-MZM can be expressed as
1
π(2a(t) + V 1 )
Eout_bias (t) = E0 exp(jωc t) cos
2
2Vπ
π(2a(t) − Vπ − V 2 )
+ cos
2Vπ
πV 3
π
× exp j + j
2
Vπ
1
= E0 exp(jωc t)[cos(x(t) + 1 )
2
+ j sin(x(t) − 2 ) exp(j 3 )]
1
= E0 exp(jωc t){[cos(x(t) +
2
− sin(x(t) − 2 ) sin 3 ]
+ j sin(x(t) −
2 ) cos
1)
3}
1
= E0 exp(jωc t)A(t) exp(j(t)),
2
(4)
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Y. CHEN
Figure 4. Simulated (a) amplitude modulation term, (b) phase modulation term, (c) first-order derivative of the phase modulation term,
versus the amplitude of the applied signal with different bias voltage deviation 1 ; simulated (d) amplitude modulation term, (e) phase
modulation term, (f) first-order derivative of the phase modulation term, versus the amplitude of the applied signal with different
bias voltage deviation 2 ; simulated (g) amplitude modulation term, (h) phase modulation term, (i) first-order derivative of the phase
modulation term, versus the amplitude of the applied signal with different bias voltage deviation 3 .
where x(t) = π a(t)/Vπ , i = πV i /2Vπ (i = 1, 2),
3 = πV 3 /Vπ , A(t) represents the amplitude modulation term, and (t) represents the phase modulation
term. In order to simplify the analysis, influences of the
three bias voltages are considered separately. The simulation results are shown in Figure 4.
Figure 4(a,d,g) shows the simulated amplitude modulation terms versus the amplitude of the applied RF signal
with different bias voltage deviations. The curves in the
three figures have essentially similar variations except
some differences near the intersections with A(t) = 1.
Figure 4(b,e,h) shows the simulated phase modulation
terms versus the amplitude of the applied signal with
different bias voltage deviations, whereas Figure 4(c,f,i)
shows the corresponding first-order derivatives of the
phase modulation term. It is observed that the deviations of V 1 and V 3 have similar influences compared with the deviation of V 2 when the amplitude of
the applied RF signal is small. If the e-PM is operating
under small signal modulation condition (x(t) < < 1),
the curves representing the deviations of V 1 and V 3
have slopes nearer to 1 than that representing the deviation of V 2 . As a result, V 2 has a larger influence on the
phase modulation of an e-PM than V 1 and V 3 under
small signal modulation condition. When the amplitude
of the applied RF signal increases, V 1 , V 2 and V 3
have similar influences because the curves have the same
amplitudes and similar trends.
For the bias points deviation, it is noticed that the bias
points deviations of the three biases have similar curves.
When the input RF signals have the same amplitudes, the
influences on the performance of the equivalent phase
modulation are within the same range. If the bias deviation is 0.2, the amplitude fluctuation is about 10%, and the
influence of the slope of the phase modulation is about
20%. To solve the problem introduced by bias deviation
in a DP-MZM based e-PM, the bias control is very important. Using the commercially available bias control circuit
to stabilize the bias points of the DP-MZM will greatly
decrease the influences from bias deviation.
In theory, if all the factors are as ideal as we assumed
in Equation (1), the equivalent phase modulation using
an e-PM is an accurate phase modulation. Taking some
non-ideal factors that may appear in the real-world systems into account in Section 3.1 to 3.3, we know that these
different kinds of non-ideal factors introduce an amplitude modulation besides the desired phase modulation
and also distort the phase modulation to a certain degree.
JOURNAL OF MODERN OPTICS
In most cases, it is observed that the undesired amplitude
modulation is relatively smaller, and the distortion of the
desired phase modulation is smaller when the amplitude
of the input signal is small, which means the system has
better tolerance on non-ideal factors when the amplitude
of the input signal is smaller. With the increase of the
amplitude of the input signal, both the amplitude modulation and the distortion of the phase modulation will
be increased.
4. Conclusion
In conclusion, the DP-MZM-based equivalent phase
modulation is comprehensively studied in this paper. The
principle of the DP-MZM-based equivalent phase modulation is demonstrated, and the influences of three kinds
of non-ideal factors, including amplitude imbalance and
different arrival time of RF signals, and bias points deviations, are theoretically investigated and numerically simulated. The study in this paper quantifies the impact of
different non-ideal factors of an e-PM, which can be used
in subsequent systems employing equivalent phase modulation. Although the equivalent phase modulation is
proposed based on a DP-MZM, directly using a discrete
DP-MZM to achieve equivalent phase modulation is not
a good idea because a PM can realize the same function
with a simpler structure. Equivalent phase modulation is
most likely to find applications in a DP-QPSK modulator, where one DP-MZM in the DP-QPSK modulator can
be operated as an e-PM in conjunction with the other
DP-MZM to realize some functions that are difficult or
even impossible to be realized without phase modulation.
Compared with the same structure using two discrete
modulators and two optical couplers, the integrated parallel DP-MZM and e-PM in a DP-QPSK modulator can
simplify the system structure and improve the system
stability.
Disclosure statement
No potential conflict of interest was reported by the author.
Funding
This work was supported by the National Natural Science
Foundation of China (NSFC) [grant number 61601297], the
Open Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts
and Telecommunications), P. R. China and the Fundamental
Research Funds for the Central Universities.
2085
ORCID
Yang Chen
http://orcid.org/0000-0003-3400-1661
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