## Abstract

This paper focuses on the studies on the polarization- modulator-based single-side-band modulator (PSSBM) as well as its implementation in generation of frequency-locked multicarrier. The principle and properties of PSSBM have been analyzed in detail with theoretical and simulation results. Then, the PSSBM-based frequency-locked multicarrier generator (PSMCG) with recirculating frequency shifting loop has also been demonstrated via simulation. The results have a good agreement with the theoretical analysis. According to the results, multiple frequency-locked carriers with high quality can be achieved based on the proposed PSMCG. The generated carriers have the potential applications in different scenarios such as optical transmission, microwave photonics and so on.

© 2014 Optical Society of America

## 1. Introduction

Optical frequency comb is broadly applied to optical arbitrary waveform generation [1], precise optical metrology [2], high accuracy optical sensor [3], ultrafast optical signal processing [4], photonic microwave signal processing [5], high data rate optical fiber transmission [6–9], and so on. In those applications except optical transmission, optical combs must have the equal frequency spacing and fixed phase-relation between the comb lines. Hence, optical comb generators in optical transmission can be referred as frequency-locked multicarrier generator (MCG) [10]. To achieve the high-speed large capacity optical transmission for the increasing demand of data traffic, there are some technologies such as coherent wavelength-division-multiplexing (CoWDM) [11], and especially coherent optical orthogonal-frequency-division- multiplexing (CO-OFDM) or direct-detect (DD) OFDM superchannels with different modulation formats [12–16] investigated widely in recent years.

In those superchannels, MCG is a key component. There are many methods to implement the MCG, such as typical overdrive single and cascaded Mach-Zenhder modulators (MZMs) and/or phase modulators (abbr., PM-MZM-based) [17,18], mode-locked lasers (MFL) [19], supercontinuum [20], cascaded polarization modulators (CPolM) [21], CW-seeded Shock-Wave Mixer (CSWM) [22] and the recirculating frequency shifter (RFS)-based MCG [6–8,12,13, 23–32]. Among those methods, the PM-MZM-based method can generate high tone-to-noise- ratio (TNR) carriers with the required high-power electrical amplifiers which decide the number of generated carriers. As for the MFL, it can generate multiple carriers but the stable operation should be guaranteed and the frequency spacing is difficult to tune in a wide range. The weak-point of the supercontinuum is the poor wavelength tunability. Although the CPolM can achieve high-flatness output carriers, the TNR is low and carrier number should be improved if more carriers are required. Although there are amazing 1000 combs demonstrated based on the CSWM, the precise dispersion control and in-line regeneration should be applied. The advantages of the RFS-based MCG, having been studied extensively, are of easing control of carrier number and frequency spacing, low radio frequency (RF) drive power, and high stability. There are two basic configurations of RFS-based MCG, one is single-side-band (SSB) modulator-based MCG (SMCG) [6,7, 12,13,23–28], the other is multi-side-band (MSB) modulator-based (MMCG) [8, 29,30]. Although the MMCG can achieve hundreds of optical carriers, the output stability is poor compared with the SMCG configuration. However, the quality of output carriers, such as the number and TNR of carriers, should be further improved by applying the SMCG configuration. One can use the configuration of multiseed-SMCG [13,27] and dual- [25,26] or multi-loop [28] SMCG to achieve the generation of hundreds of output carriers. Meanwhile, one can also use the improved configuration of SMCG [32] based on the suppressed-third-crosstalk scheme [33] to obtain higher TNR. However, the SMCG implemented by the conventional SSB modulator (CSSBM) based on the integrated LiNbO3 dual-parallel MZM or IQ modulator, has the requirement of three DC bias controls to make the modulator operate at the right point. Thus, the auto bias control is necessary [34] due to the property of the modulator, sensitive to the changes of environmental conditions [35].

In this paper, aim to achieve SSB frequency shifting so as to implement high quality multicarrier generation with recirculating frequency shifting loop, we propose a polarization-modulator-based SSB modulator (PSSBM) with only one DC bias control required. The detailed theoretical analysis and simulation results show that the proposed configurations can be used to achieve the desired frequency shift and generation of multiple frequency-locked multicarriers.

## 2. Theoretical analysis

The schematic of PSSBM is shown in Fig. 1.It consists of a power splitter/combiner, two polarization modulators (PolMs), a phase
modulator (PM), two polarization controllers (PC), a polarizer (Pol), an RF signal and a DC
bias. The input RF signal *f*(t) with its frequency of
*f*_{m} is split into two equal parts with π/2 phase shift and
then drives respective PolMs. As illustrated in Fig. 1,
when the frequency of input seed laser *E*_{in}(*t*) is
*f*_{0}, the novel PSSBM can achieve a desired frequency-spacing
SSB-shift with frequency up-shift (*f*_{0} +
*f*_{m}) or down-shift (*f*_{0} −
*f*_{m}) of seed laser by applying the DC bias control and tuning the
two PCs. In general, the input linearly polarized seed laser from a tunable laser (TLS) can be
represented as *E*_{in}(*t*) =
*E*_{0}exp(*jω*_{0}*t*).
The light-wave with its state of polarization (SOP) is aligned at an angle of
*α*_{1} tuned by PC1 relative to one principal axis of the PolM
and then projected to the two orthogonal directions. At the output of each PolM, the two
modulated light waves are combined with a power combiner and then sent to the polarizer via PC2.
The principal axis of the polarizer is aligned at *α*_{2} relative
to the *x* axis of the PolMs by PC2. The two angles
*α*_{1} and *α*_{2} can be tuned by
the PCs before the PolMs and Pol. We also represent the input RF signals used to drive PolM1 and
PolM2 as *f*_{1}(t) =
*V*_{pp}cos(*ω*_{m}t) and
*f*_{2}(t) =
*V*_{pp}sin(*ω*_{m}t) respectively.
*V*_{PP} is the amplitude of the RF drive signals. Based on the
modulation property of polarization modulator shown in [36], the outputs of the two PolMs can be expressed as follows

*c*

_{1}and

*c*

_{2}represent the portion of input seed laser projected to the two orthogonal directions of PolMs. To obtain the transfer function of PSSBM, we adopt the transfer- matrix-based method, i.e., using

*H*

_{in},

*H*

_{PolM},

*H*

_{PM},

*H*

_{PC}and

*H*

_{DPol}to represent the SOP of input linearly polarized signal and functions of PolMs, PM, PC and polarizer, as shown in Eq. (2),

*V*

_{π}is the half-wave voltage of PolM and

*δ*= (

_{m}*πV*)/(

_{pp}*V*) denotes for the phase modulation depth. The parameters

_{π}*θ*and

*ϕ*are the rotation angle and static phase difference induced by the PC2 between the

*x*- and

*y*-polarization components respectively and can be tuned by the PC2 before the Pol. Note that the obvious difference is the PC model used here is a fully-tunable wave-plate as used in [37] when compared with our previous work [26]. Then, the normalized transfer function of PSSBM can be expressed mathematically as follows

*C*

_{1/2}is the amplitude variation coefficient induced by the PCs and Pol. Obviously, to achieve the desired SSB frequency shift, the required condition deduced from Eq. (3) should be satisfied as follows

*θ*=

*k*π,

*ϕ*= 2

*k*π (

*k*is an integer), then cos

*α*

_{1}cos

*α*

_{2}= −sin

*α*

_{1}sin

*α*

_{2}; or case2,

*θ*= (

*k*π + π/2),

*ϕ*= 2

*k*π (

*k*is an integer), then cos

*α*

_{1}sin

*α*

_{2}= sin

*α*

_{1}cos

*α*

_{2}. Namely,

*α*

_{1}−

*α*

_{2}should be equal to ± π/2 or 0. In other words, the SOPs of the output and input signals should be orthogonal or identical corresponding to the two cases by carefully adjusting the two PCs manually or electrically depending on the types of them. By the way, the stated condition could be also satisfied even if the input seed has more than one wavelength. We then denote the amplitude variation coefficient in this case as an brief function of

*α*

_{1}and

*α*

_{2}as |

*C*

_{avc}(

*α*)| = |sin(2

*α*)|/2. By applying this guiding result and setting

*V*

_{DC}(

*t*) = ±

*V*

_{π}/2 (‘ + ’ and ‘−’ represent the desired SSB frequency up- and down-shift respectively), the final transfer function of PSSBM can be expressed as follows

*J*

_{2}

_{k-}_{1}(

*δ*) are the odd-order Bessel functions of the first kind. Ignoring all the high order harmonics beyond the third order, then the normalized transfer function of PSSBM obtained from Eq. (6) has the same expression as in [24]where

_{m}*b*= −

*J*

_{3}/

*J*

_{1}, stands for the third-order crosstalk coefficient depended on the modulator drive voltage

*V*

_{pp}, which can affect the output property of PSSBM. In order to decrease the crosstalk, we must apply proper

*V*

_{pp}to make |

*b*|<<1. In addition, we should also take the optimal value of |

*C*

_{avc}(

*α*,

*V*

_{pp})| to maximize the conversion efficiency of desired frequency SSB shifted signal.

Figure 2 shows the amplitude variation coefficient
corresponding to the converted power of desired SSB signal as a function of angle
*α* and drive voltage *V*_{pp}. There are three features that can be found from these figures: (1) Given a fixed
*V*_{pp}, the amplitude variation coefficient of desired signal shows a
periodic change with the variation of angle *α*. The extremum will appear
at *α* = kπ/4 corresponding to the two cases. (2) Given a fixed
angle *α*, the amplitude variation coefficient of desired signal shows a
symmetric change with the variation of *V*_{pp} where the extremum
appears nearby *V*_{pp} = 0.6*V*_{π}. (3)
The amplitude variation coefficient shows a contrary variation of the two cases. Hence, the
maximum conversion efficiency of PSSBM can be obtained by tuning *α* =
π/4 and *V*_{pp} = 0.6*V*_{π}.

## 3. Modeling results

#### 3.1 Modeling results of PSSBM

To validate our proposed PSSBM scheme, we do the simulation through VPI software [38]. Figure 3 shows
the output spectra of the PSSBM with frequency up- and down-shifted respectively with different
SOPs under case1 (*θ* = 0, *ϕ* = 0) and case2
(*θ* = π/2, *ϕ* = 0). The global parameters we used here are, *f*_{m} = 12.5GHz and
*V*_{pp} = 0.27 *V*_{π} of RF signal,
*λ*_{0} = 1552.52 nm and *P*_{in} = 0 dBm
for the input seed laser, and *V*_{DC} =
−*V*_{π}/2. In these figures,
*F*_{n} = *f*_{0} +
*nf*_{m} (*n* is an integer) represents the generated
components of PSSBM (under the condition, the frequency down-shifted signal is the desired SSB
signal *F*_{−1}). The *α*_{1} and
*α*_{2} equal 0 and −π/2 in Fig. 3(a), and 0 and −π/3 in Fig. 3(b) respectively. Obviously, the desired SSB frequency shift can be achieved as
shown in Fig. 3(a) when the condition shown in Eq. (4) is satisfied. However, if the condition does
not meet the requirement of the SSB frequency shift, the output will contain other unwanted
crosstalk components as shown in Fig. 3(b), such as
0th-order *F*_{0} and 2nd-order *F*
_{± 2}. Figures 3(i) and 3(ii) display the SOPs of the input (red point) and output
(blue point) signals. We can see that the simulation results are in agreement with the above
theoretical analysis where the SOPs of the input and output signals should be kept orthogonal.
For case2 (*θ* = π/2, *ϕ* = 0), the same
feature has been shown in Figs. 3(c) and 3(d). To achieve desired SSB frequency shift, the SOPs of the
input and output signals should be kept identical as shown in Figs. 3(iii) and 3(iv). If not, the other
unwanted components *F*_{0}, *F*
_{± 2} and *F*
_{± 4} are existed.

#### 3.2 Modeling results of PSMCG

As analyzed above, the PSSBM can be achieved. In this section, we mainly give the configuration and simulation results of the proposed PSSBM-based frequency-locked multicarrier generator (PSMCG) with recirculating frequency loop as shown in Fig. 4. The principle of PSMCG is the same as the typical SMCG with recirculating frequency loop [24]. The seed light from the TLS is fed into the PSSBM via a polarization-maintained optical coupler (PMOC). After the desired SSB frequency shifted by the PSSBM, the generated signals are amplified by the optical amplifier (OA) and then filtered by the optical bandpass filter (OBF) and finally coupled into the PSSBM again to form a recirculating frequency loop so as to generate the desired multiple frequency-locked carriers. PC1 and PC2 are used to adjust the SOPs of seed light and signals in the loop to maximize the output power. The generated carriers can be observed by the optical spectrum analyzer (OSA). If the high-flatness of output signals is required, the waveshaping devices, such as wavelength-selective-switch (WSS) shown in the dash-box in Fig. 4, can be used to further improve the output quality. By changing the bias control voltage of PSSBM, the frequency up- or down- converted carriers can be obtained.

The output spectra of PSMCG have been also simulated through the VPI software. Figure 5 shows the output spectra of PSMCG with 50 and 80
carriers corresponding to the bandwidth of 5nm and 8nm respectively. Here, the drive voltage *V*_{pp} = 0.27
*V*_{π}, and the optical bandpass filter used in simulation is
an ideal rectangle model with proper bandwidth which covers the desired 50- and 80-carrier
frequency ranges. The assumed stopband attenuation is 40dB which is a common parameter and can
be realized by the commercial products. The optical amplifier we used is an EDFA with black-box
model which is operated at saturation mode with 23 dBm output power and 4 dB noise figure (NF).
By sweeping the PC in the loop, the final 50- and 80-carrier outputs with an acceptable
flatness have been obtained by the PSMCG as shown in Figs.
5(a) and 5(b) respectively. The insets show the
SOPs of the output signals. Although the generated power of TNR is just 20 dB for 80-carrier
output, there is no doubt that the proposed PSSBM can be used to achieve the generation of
high-quality frequency-locked multicariers under further improved configuration. However, to
implement the proposed scheme in practice, the polarization extinction ratio, which is the most
critical property of the polarization modulator, is desired to be as high as possible.
Meanwhile, some practical factors should be considered to improve the TNR of the generated
carriers, including the SOPs of the input and output signals, the crosstalk of the undesired
sideband components, the DC bias control, the gain and noise figure of the optical amplifier
and the qualities of the optical bandpass filter etc.

## 4. Conclusions

In conclusion, we have theoretically studied the proposed polarization-modulator-based SSB modulator as well as the frequency-locked multicarrier generator by utilizing it with recirculating frequency shifting loop, including the theoretical analysis and simulation of basic principle and output properties. Compared with the conventional integrated LiNbO3-based SSBM, the proposed PSSBM will only require two phase modulators and one DC bias control and also can be fabricated with integrated structure. Meanwhile, the typical operation frequency range of PolM is larger than 40 GHz which means the output carriers with large tunable frequency spacing can be achieved. According to the theoretical analysis and simulation results, the proposed PSSBM would find some potential applications in various scenarios.

## Acknowledgments

This work is supported by the National Basic Research Programme of China (973) Project (No. 2012CB315603), the Open Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), National Natural Science Foundation of China (NSFC) under Grant No. 61307092, the Planned Science and Technology Project of Guangzhou (Grant No. 2012J5100028), the Fundamental Research Funds for the Central Universities and the Program for New Century Excellent Talents in University (NCET-12-0679) in China.

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**38. ** VPIsystemsTM, “VPltransmissionMakerTM”.