JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 26, NO. 15, AUGUST 1, 2008
2449
Impact of Nonlinear Transfer Function and
Imperfect Splitting Ratio of MZM on Optical
Up-Conversion Employing Double Sideband With
Carrier Suppression Modulation
Chun-Ting Lin, Jason (Jyehong) Chen, Sheng-Peng Dai, Peng-Chun Peng, and Sien Chi, Fellow, OSA
Abstract—Generation of optical millimeter-wave (mm-wave)
signal using a Mach–Zehnder modulator (MZM) based on
double-sideband (DSB), single-sideband (SSB), and double-side-
band with carrier suppression (DSBCS) modulation schemes have
been demonstrated for various applications, such as broadband
wireless signals or optical up-conversion for wavelength-di-
vision-multiplexing (WDM) radio-over-fiber (RoF) network,
wideband surveillance, spread spectrum, and software-defined
radio. Among these schemes, DSBCS modulation offers the best
receiver sensitivity, lowest spectral occupancy, the least stringent
requirement of electrical bandwidth, and the smallest receiving
power penalty after long transmission distance. Nonetheless, the
inherent nonlinear E/O (electrical/optical) conversion response
of a MZM is such that the signal quality of the optical mm-wave
suffers. Fabrication tolerances make a balanced 50/50 splitting
ratio of the MZM’s y-splitter particularly difficult to achieve.
As a result, imbalanced MZMs have a finite extinction ratio
(ER) and degrade the optical carrier suppression ratio (OCSR)
using DSBCS modulation. In this paper, the effect of the MZM
nonlinearity and imbalanced y-splitter on optical mm-wave gen-
eration by DSBCS modulation is theoretically and experimentally
investigated. A novel approach with better performance and
greater cost-effectiveness than dual-electrode MZM (DD-MZM)
is presented to realize a DSBCS modulation scheme based on a
single-electrode MZM (SD-MZM).
Index Terms—Microwave photonics, millimeter-wave (mm-
wave) generation, Mach–Zehnder modulator (MZM), MZM
imbalance, MZM nonlinearity, radio-over-fiber (RoF).
I. INTRODUCTION
T
HE pervasiveness of handheld devices has lead to rapid
growth in the demand on broadband wireless commu-
nication. However, insufficient bandwidth and serious propa-
gation loss make traditional coaxial cable unsuitable for the
Manuscript received January 9, 2008; revised May 1, 2008. Current version
published October 10, 2008. This work was supported by the National Sci-
ence Council of R.O.C. under Contract NSC 96-2221-E-155-038-MY2, NSC
96-2752-E-009-004-PAE, and NSC 96-2628-E-009-016.
C.-T. Lin, J. (J.) Chen, and S.-P. Dai, are with the Department of Photonics
and Institute of Electro-Optical Engineering, National Chiao-Tung University,
Hsinchu, Taiwan 300, R.O.C. (e-mail: jinting@ms94.url.com.tw).
P.-C. Peng is with the Department of Applied Materials and Optoelectronic
Engineering, National Chi Nan University, Taiwan 545, R.O.C.
S. Chi is with the Department of Photonics and Institute of Electro-Optical
Engineering, National Chiao-Tung University, Hsinchu, Taiwan 300, R.O.C.,
and also with the Department of Electrical Engineering, Yuan-Ze University,
Chung Li, Taiwan 320, R.O.C.
Digital Object Identifier 10.1109/JLT.2008.927160
transmission of wireless signals in the microwave/millimeter-
wave (mm-wave) range. Therefore, the radio-over-fiber (RoF)
system, which distributes radio-frequency (RF) signals from a
central station (CS) to base stations (BS) over an optical fiber,
is a promising approach because of its almost unlimited band-
width and very low propagation loss [1]–[3].
RoF technology allows the concentration of RF signal
processing and shared mm-wave components at a CS and
makes BS simpler and more cost-effective. The generation and
transmission of optical microwave or mm-wave signals are
crucial to RoF systems. Optical RF signal generation or optical
up-conversion using an external Mach–Zehnder modulator
(MZM) based on double-sideband (DSB), single-sideband
(SSB), and double-sideband with carrier suppression (DSBCS)
modulation schemes have been demonstrated [3]–[7]. The DSB
modulation signal undergoes performance fading problems
because of fiber dispersion, which causes periodic degradation
of the receiver sensitivity varying with the transmission length
of standard single mode fiber (SSMF). The SSB modulation,
which is generated by applying a
phase difference between
the two RF electrodes of the dual-electrode MZM (DD-MZM)
biased at the quadrature point, is developed to overcome the
performance fading. However, since the optical RF signals are
weakly modulated because of the narrow linear region of MZM,
those that undergo DSB and SSB modulations have inferior
sensitivities because the optical modulation depth (OMD)
is limited [4]. Recently, the DSBCS modulation has been
demonstrated in the mm-wave range to have the best receiver
sensitivity and overcome periodic performance fading due to
fiber dispersion. Besides, since optical carrier is suppressed,
a frequency doubling technique can be achieved to reduce the
bandwidth requirement of optical RF transmitter [5].
However, independent of the modulation scheme employed,
MZM modulation is associated with an inherently nonlinear
E/O conversion response. Hence, the MZM nonlinear distortion
negatively affects the performance of the mm-wave signal.
Besides, fabrication tolerances make a balanced 50/50 splitting
ratio of the MZM’s Y-splitter particularly difficult to achieve.
Therefore, imbalanced MZMs have a finite extinction ratio
(ER) and the mm-wave signals based on DSBCS modulation
have finite optical carrier suppression ratio (OCSR), degrading
the quality of mm-wave signals. Although numerous studies of
the nonlinear distortion of mm-wave signals generated using
the DSB and SSB modulation approaches have been recently
0733-8724/$25.00 © 2008 IEEE
2450 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 26, NO. 15, AUGUST 1, 2008
Fig. 1. The principle diagram of the optical mm-wave generation using bal-
anced MZM based on DSBCS modulation.
conducted [8]–[11], to the author’s best knowledge, no infor-
mation is available on the combined effects of MZM nonlinear
distortion and imbalance on mm-wave generation or optical
up-conversion by the DSBCS modulation scheme. This investi-
gation theoretically and experimentally analyzes the impacts of
both MZM nonlinearity and imbalance on the mm-wave signal
performance. Optimal conditions for optical mm-wave genera-
tion using imbalanced MZM based on DSBCS modulation are
discussed. In conventional DSBCS modulation scheme, a full
swing (2V
, typically 10–14 V) electrical RF driving signal is
necessary to ensure high OCSR. The limited driving capability
of the electrical amplifier requires a push-pull DD-MZM to be
used to weaken the demanding driving voltage requirement.
This limitation increases the system complexity and cost be-
cause extra and more expensive components are needed. This
work presents a novel method that uses a single-electrode MZM
(SD-MZM) to generate the mm-wave signal with performance
improvement based on DSBCS modulation scheme. Both theo-
retical and experimental results show that the proposed system
is compact, cost-effective, and performs better.
II. T
HEORETICAL ANALYSIS OF MILLIMETER-WAV E
GENERATION BY DSBCS MODULATION
A. Generation of mm-Wave Signal Using Balanced MZM
Fig. 1 displays the principle of the optical mm-wave gener-
ation by the DSBCS modulation scheme. The power splitting
ratio of two arms of a balanced MZM is 0.5. The electrical field
at the output of the MZM is given by
(1)
where
and denote the amplitude and angular frequency of
the input optical carrier, respectively,
is the applied driving
voltage, and
is the optical carrier phase difference that
is induced by
between the two arms of the MZM. The loss
of MZM is neglected.
consisting of an electrical sinusoidal
signal and a dc biased voltage can be written as
(2)
where
is the dc biased voltage, and and are the
amplitude and the angular frequency of the electrical driving
signal, respectively. The optical carrier phase difference in-
duced by
is given by
(3)
Fig. 2. Illustration of the optical spectrum at the output of the balanced MZM.
Fig. 3. Illustration of the electrical spectrum of the mm-wave signal using bal-
anced MZM after square-law PD detection.
where is the half-wave voltage of the MZM. Therefore, the
output electrical field can be rewritten as
(4)
where is a constant phase shift that is
induced by the dc biased voltage, and
is the
phase modulation index. Expanding (4) using Bessel functions,
as detailed in Appendix I, yields Fig. 2, which illustrates the
optical spectrum of the mm-wave signals obtained by DSBCS
modulation with the MZM biased at the null point. All of
the even-order optical sidebands are eliminated, so only the
odd-order optical sidebands remain in the spectrum. Square-law
photo-diode (PD) detection yields the corresponding electrical
spectrum of the generated mm-wave signals which are shown
in Fig. 3. No original driving signal
and the odd terms
of its harmonics distortions
exist. A
strong anticipated double-frequency signal
and the odd
terms of the harmonic distortions
are
observed.
B. Generation of mm-Wave Signal Using Imbalanced MZM
Fig. 4 shows the MZM with an imbalanced power splitting
ratio of the Y-splitter. The electrical field at the output of the
MZM can be written as
(5)
where
and are the power splitting ratios of the first and
second Y-splitters in MZM, respectively;
and are the op-
tical carrier phase shifts induced by the applied driving voltages
LIN et al.: IMPACT OF NONLINEAR TRANSFER FUNCTION AND IMPERFECT SPLITTING RATIO 2451
Fig. 4. The principle diagram of the optical mm-wave generation using imbal-
anced MZM based on DSBCS modulation.
in the upper and lower arms of the MZM, respectively. The ER
of the imbalanced MZM can be expressed as
(6)
Notably, the MZM ER is infinite as
or
. If not, the MZM ER will have a finite value. Without
loss of generality, the assumption that
, enables (6) to be rewritten as
(7)
Accordingly, the modulation of the MZM with imbalanced
power splitting ratios can be regarded as the sum of a bal-
anced MZM modulation plus a modulation by an extra phase
modulator (PM) modulation which are represented by the
first and second terms of (7), respectively. Evidently, for a
balanced MZM with
or , no phase
modulation term exists. However, fabrication tolerances make
both conditions difficult to achieve. Thus, the inherent PM
modulation that is caused by the imbalanced splitting ratios
of the MZM cannot be avoided. Expanding (7), as detailed
in Appendix II, yields the optical spectrum of the mm-wave
signal using DSBCS modulation that is displayed in Fig. 5. A
comparison with Fig. 3 indicates that the main effects of the un-
desired PM modulation, caused by imbalanced MZMs, are the
generation of the superfluous optical carrier
and even-order
sidebands (
. Additionally, the even-
and odd-order terms are mutually orthogonal. Fig. 6(a) and (b)
present back-to-back (BTB) and following fiber transmission
electrical spectra of the generated mm-wave signals. Notably,
only the even-order BTB mm-wave signals are observed as
shown in Fig. 6(a). However, after transmission over a disper-
sive fiber, the even- and odd-order terms are no longer mutually
orthogonal because of fiber dispersion. Therefore, following
square-law PD detection, the cross-terms generate the undesired
odd-order signals
and also produce
unwanted signals fall inside the target
mm-wave band.
C. Optical Carrier and Distortion Suppression Analysis
An RoF lightwave system primarily consists of transmitters,
a fiber link, and receivers. One of the key issues that govern
Fig. 5. Illustration of the optical spectrum at the output of the imbalanced
MZM.
Fig. 6. Illustration of the electrical spectrum of generated mm-wave signals
using imbalanced MZM after square-law PD detection. (a) BTB mm-wave sig-
nals. (b) Mm-wave signals after transmission over dispersion fiber.
the performance of the RoF system is the linearity of E/O con-
version especially for external MZM modulation. The inherent
nonlinearity of MZM makes the undesired optical sidebands of
the mm-wave signals
employing DSBCS
modulation scheme unavoidable, as shown in Figs. 2 and 5.
These unwanted optical sidebands can degrade the performance
of the desired electrical mm-wave signals. For mm-wave signal
generation using balanced MZMs, the amplitudes of the optical
sidebands are only proportional to the Bessel functions of the
corresponding orders. However, for mm-wave signal genera-
tions using imbalanced MZMs, the amplitudes of optical side-
bands are related to not only the Bessel functions of the cor-
responding orders but also the weighting factors consisting of
and which are defined in Appendix II. As modulation
index (MI
is the peak-to-peak voltage of the
MZM driving signal) for driving MZM increases from zero to
one, the zeroth-order Bessel function and the Bessel function of
2452 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 26, NO. 15, AUGUST 1, 2008
Fig. 7.
E
and
E
varied with
r
.
Fig. 8. MZM ER varied with
r
.
order of more than one will decrease and increase, respectively.
Fig. 7 plots
and as a function of , with set at 0.5.
As
moves away from the ideal condition, decreasing from
0.5 to zero, as expected, the pure amplitude modulation term
declines and the phase modulation term increases.
The ER of MZM is determined by the combined effect of
and . Fig. 8 plots the ER versus , for a commercially avail-
able MZM, the typical value of ER is 25 dB, which corresponds
to
.
For the mm-wave signal produced by DSBCS modulation,
the two first-order sidebands are the desired optical signals, and
the suppression ratio of the other undesired distortion sideband
caused by the MZM nonlinearity and the imbalance is the key
parameter in the RoF system. The commercial software, VPI
WDM-TransmissionMaker 5.0, is used to simulate numerically
the suppression ratio. Fig. 9 shows the optical carrier and distor-
tion suppression ratio (OCDSR,
) as a function of MI for the
driving the MZM with an ER of 25 dB. The
is defined as
(8)
where
and are the optical powers of the first-order side-
band
and the th-order sideband
, respectively. Notably, is the OCSR. As MI falls from one
to zero, the distortion suppression ratios
are
improved, but the OCSR
decreases. When the MZM ER
Fig. 9. OCDSR versus the MI for driving MZM. The MZM ER is 25 dB. A:
Theoretical analysis, N: Numerical stimulation.
Fig. 10. OMI-OCDSR and the corresponding maximum OCDSR versus MZM
ER.
equals 25 dB and MI exceeds 0.79, the third-order optical side-
band
is key to determining the degradation of OCDSR.
However, for MI
is less than , and the OCSR,
rather than OCDSR, dominates the system performance. There-
fore, the optimal MI for maximum OCDSR (OMI-OCDSR) ex-
ists at the intersection of
and and is determined by the
MZM ER. Fig. 10 plots the OMI-OCDSR and the corresponding
maximum OCDSR versus the MZM ER. When the MZM ER is
less than 17 dB,
is always less than . Thus, the OCSR
controls the system performance and the OMI-OCDSR is one.
For a commercially available MZM with a typical ER of 25
dB, the OMI-OCDSR is about 0.79 and the corresponding max-
imum OCDSR is 23 dB.
D. Generated Electrical mm-Wave Signal Analysis
Fig. 6(b) presents the generated electrical spectra following
square-law PD detection. The desired electrical signal origi-
nates from the beating between two optical sidebands with a
frequency difference that is twice the frequency of the electrical
driving signal, and the beating of the two first-order optical side-
bands dominates the power intensity of the desired electrical
signal. Notably,
and m, which originate in MZM
imbalance and MI for driving MZM, respectively, determine the
power intensity of the desired and undesired electrical signal,
LIN et al.: IMPACT OF NONLINEAR TRANSFER FUNCTION AND IMPERFECT SPLITTING RATIO 2453
Fig. 11.
I
versus MI and MZM ER after PD detectin.
Fig. 12. OMI-
I
versus MZM ER. The solid circle indicates the
OMI-
I
, and the error-bar of the OMI-
I
corresponds to 1-dB toler-
ance of the maximum
I
.
as shown in Appendix II. For optical mm-wave signal genera-
tion or optical up-conversion for RoF links, since the undesired
electrical signals can be easily removed by an electrical filter,
the normalized power intensity of the desired electrical signal
is the key parameter as the MZM ER and MI vary.
Fig. 11 plots the
versus MI and MZM ER after PD
detection. The power of the optical mm-wave signals before PD
detection is normalized to be 0 dBm. As MI increases from zero
to one, the
increases first and then declines. Notably, the
maximum
decreases as the MZM ER decreases. Further-
more, the optimal MI for the maximum
(OMI- ) in-
creases as the MZM ER falls from 35 to 10 dB, as shown in
Fig. 12. For a commercial MZM with a typical ER of 25 dB, the
OMI-
is for a maximum with a tolerance
of 1 dB.
Since fiber chromatic dispersion induces different phase vari-
ations of the optical sidebands,
varies with the trans-
mission length of the SSMF. Fig. 13(a) plots the power inten-
sity fluctuation of the electrical 40-GHz mm-wave signal that
Fig. 13. (a) Power fluctuation of the 40-GHz mm-wave signal transmitted over
50-km SSMF. (b) Periodic fading power variation versus the MZM ER fol-
lowing 50-km transmission of SSMF.
is transmitted over 50-km SSMF. The MZM ER is 25 dB and
the power of the optical mm-wave signal is normalized to be
0 dBm before PD detection. The periodic fading power varia-
tion, which is associated with undesired optical sidebands, is
less than 0.5 dB. Fig. 13(b) plots the periodic fading power
variation versus the MZM ER following 50-km transmission of
SSMF. As the MZM ER falls, the periodic fading power varia-
tion increases. When the MZM ER is 10 dB, the periodic fading
power variation reaches 3.3 dB and the receiver sensitivity of
the mm-wave signal is clearly degraded. When the MZM ER
exceeds 20 dB, the periodic fading power variation is less than
1 dB and is negligible.
E. Comparison of Different Optimal MIs
In summary, the MZM nonlinearity and imbalance were theo-
retically demonstrated to strongly influence the performance of
the optical mm-wave signals based on the DSBCS modulation
scheme. Table I presents the different optimal MIs for the max-
imum OCDSR and desired electrical signal
for different
applications. The optimal MI that maximizes OCDSR can be
used to generate a tunable optical mm-wave signal for a wide-
band surveillance, spread spectrum or software-defined radio
[12], [13]. For those systems, the undesired electrical signal
