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2360 J. Opt. Soc. Am. B/Vol. 27, No. 11 /November 2010 Gao et al.

Reducing the driving voltage of a phase modulatorwith cascaded four-wave-mixing processes

Ying Gao, Yanqiao Xie, and Sailing He*

Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation,Zhejiang University, Hangzhou 310058, China

*Corresponding author: sailing@zju.edu.cn

Received July 1, 2010; revised August 23, 2010; accepted September 2, 2010;posted September 2, 2010 (Doc. ID 130956); published October 20, 2010

We propose and demonstrate an all-optical phase-shift multiplier through degenerate four-wave mixing (FWM)processes. With the present approach the modulation efficiency of a phase modulator (PM) can be greatly in-creased through cascaded FWM stages. As an experimental example, the equivalent half-wave voltage at1549.3 nm of a commercial LiNbO3 PM is reduced to a quarter by using two cascaded FWM processes. Widelyopened eye-diagrams and error-free demodulation results are obtained at the output of the phase-shiftmultiplier. © 2010 Optical Society of America

OCIS codes: 060.4370, 060.5060, 190.4380.

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. INTRODUCTIONs one of the key elements in an optical communicationystem, optical modulators have received extensive atten-ion. Much progress has been made recently in high speediNbO3 and monolithic silicon modulators [1–4] for highapacity optical networks. Since it is challenging andower-consuming to supply a high driving voltage at highodulation bit-rates, there exists a trade-off between the

ctive modulation length and the modulation speed inodulator designs and fabrications. It is well known that

ll-optical interconnect is the most promising solution forreaking the electrical bottleneck. Besides, a low drivingoltage is also required in the next-generation on-chip op-ical interconnect [5,6]. To achieve a high-speed modula-or using a low driving voltage (with a reasonably shortctive length), the use of resonant-type electrodes [1],hotonic crystal waveguides [2,3], and special traveling-ave electrode design [4] has been investigated to en-ance the phase modulation efficiency (denoted by V�L)

nside the modulator itself. Outside the modulator, it islso desirable to find an effective approach to reduce theriving voltage, which may raise the modulation capabil-ty to a new level.

As a promising nonlinear effect, four-wave mixingFWM) has found many applications in optical signal pro-essing, such as bit-rate tunable differential phase shifteying (DPSK) demodulation, optical multiplexing, andillimeter wave generations [7–9]. Due to its characteris-

ic of format transparency, FWM is suitable for phase in-ormation processing [7,8]. In this paper, we propose tose the degenerate FWM process as an all-optical phase-hift multiplier to reduce the driving voltage outside ahase modulator (PM). The phase-shift generated by amall driving voltage can be easily doubled through oneegenerate FWM process and enhanced further throughascaded operations. Besides, this approach works withinwidely tunable modulation bit-rate range since FWM isbit-rate transparent process. In experiment, the re-

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uired half-wave voltage V� of a commercial PM has beeneduced by 50% and 75%. After doubling the phase-shiftf a �0-� /2� modulated signal, our approach provides a 1.9B improvement in receiver sensitivity, compared to theonventional way to generate a �0-�� modulated DPSKignal with a PM and a radio frequency (RF) amplifier. Af-er doubling the phase-shift of a �0-� /4� modulated signalwice, the obtained �0-�� DPSK signal exhibits a powerenalty of 1.5 dB at 10−9 bit-error-rate (BER). In numeri-al simulation, we further study the potential and theimitations of applying the proposed method up to 160bits/s.

. OPERATING PRINCIPLE ANDUMERICAL SIMULATION

igure 1 illustrates the enhancement of the phase-shifturing degenerate FWM processes. A continuous waveCW) light at �1 is not phase modulated, with a phase-hift of ��1=0. An optical carrier at �2 is modulated by ahase-shift of ��2=���t�, where ���t� represents theriginally modulated time varying phase-shift. After com-ining these two light waves to stimulate a degenerateWM process, a new light wave at �F1=1�2/�2−1/�1� isenerated with a phase-shift of ��F1. According to thehase relationship of the FWM process, the phase-shift ofhis newly generated light is ��F1= �2��2−��1�, i.e.,��. The obtained phase-shift ��F1 is twice as large ashe original phase-shift ��2. After using an optical band-ass filter (BPF) to select the converted light at �F1, it islso combined with the CW light at �1 to stimulate theecond FWM process. As a result of the second FWM, an-ther light wave at �F2 is obtained with a phase-shift of�F2= �2��F1−��1�, i.e., 22��. Therefore, through twoascaded FWM stages, the equivalent electric-field-nduced refractive index changes of some existing materi-ls, such as LiNbO3, silicon waveguide [2–4], and strainedilicon [10], can be easily increased by a factor of 4. Theo-

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Gao et al. Vol. 27, No. 11 /November 2010 /J. Opt. Soc. Am. B 2361

etically, the phase-shift of the light wave generated aftercascaded stages of FWM is ��FN=2N��.As the FWM effect is an ultrafast nonlinear process, it

as a potential to be operated beyond 600 Gbits/s [11].he fundamental bandwidth of the proposed scheme isot limited by FWM itself. Nonetheless, optical powermplifiers and extra light sources are necessary fortimulating FWM-based phase-shift multiplications,hich may add extra amplitude and phase noise to thehase-shift multiplication results. To reveal the potentialnd the limitations of the proposed scheme, numericaltudies are performed using highly nonlinear fibersHNLFs) as the nonlinear elements. The fiber model heres based on the standard split-step Fourier algorithm. Theimulations have been carried out by using of a 27-1,seudorandom binary sequence (PRBS) modulated non-eturn-to-zero DPSK signal, while the modulation bit-ratearies from 10 to 160 Gbits/s. Within each FWM stage,he output power and noise figure of the erbium-doped fi-er amplifier (EDFA) are set to 21 dBm and 6 dB, respec-ively. The linewidth of the optical source is set to0 kHz. The length, nonlinear coefficient, dispersion, andispersion slope at 1550 nm of the HNLF are 500 m,1 W−1 km−1, �0.025 ps/(nm·km), and.016 ps/ �nm2·km�, respectively. As for optical filtering,everal second-order Gaussian BPFs are adopted whileetting their bandwidths to four times of the operationit-rate. Theoretically, the �0-�� modulated DPSK signalan be generated after multiplying the phase-shift of a0-� /2N� modulated DPSK signal by N FWM stages. Fornstance, the phase shift of a �0-� /4� modulated DPSKignal at 10 Gbits/s is multiplied by two FWM stages. Theimulated constellation diagrams of the original andhase-shift multiplied DPSK signals are plotted step bytep in Fig. 2(a). As expected, the original �0-� /4� phasehift is successfully multiplied to the �0-�� phase shifthrough two FWM stages.

In order to get a rough estimation on the performancef a phase-shift multiplication, the demodulated resultsre evaluated by Q factors. Each Q factor is estimatedrom 2048 different bits, while the bit number is chosens a compromise of the computation accuracy and com-lexity. Figure 2(b) depicts the Q2 parameter in a loga-ithmic scale �20 log Q� after a phase-shift multiplierith N cascaded FWM stages at different bit-rates. The

tage number N=0 here represents a perfect �0-�� phaseodulation that is provided by driving the PM in the ab-

Fig. 1. (Color online) Schematic ill

ence of any RF amplification. Numerical results showhat less FWM stages are permitted for phase-shift mul-iplication at higher modulation bit-rates. A larger modu-ation bit-rate requires larger bandwidths of the utilizedPFs, which may introduce more amplified spontaneousmission (ASE) noise after each optical amplifier. For gen-rating a high quality phase-shift multiplication result,ess EDFAs and FWM stages can be adopted within thecheme. As shown in Fig. 2(b), opened demodulation eye-iagrams can be obtained when Q2 of the demodulated re-ult is larger than 18 dB. In this condition, the cascadedumber N at 160 Gbits/s varies from 1 to 3. Each stageill reduce the driving voltage by 50%, and thus the driv-

ng voltage of a 160 Gbits/s DPSK system can be reducedy 87.5% in maximum. Besides, if the requirement of Q2

s enhanced to be larger than 25 dB, widely opened de-odulation eye-diagrams at 160 Gbits/s can be obtained

fter one or two FWM stages. The driving voltage at 160

on of the cascaded FWM processes.

ig. 2. (Color online) (a) Estimated constellation diagrams ofhe original and generated DPSK signals during two stages ofWM-based phase-shift multiplication at 10 Gbits/s. (b) Q2 pa-ameters of the demodulated DPSK signals after N stages ofWM-based phase-shift multiplications at different bit-rates.

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2362 J. Opt. Soc. Am. B/Vol. 27, No. 11 /November 2010 Gao et al.

bits/s can be reduced by 75% in this more restrict con-ition. For 80 Gbits/s modulation bit-rate, the bandwidthsf the utilized BPFs are narrower than those at 160bits/s, such that less ASE noise is induced by eachDFA. When the obtained Q2 of the demodulated DPSKignal is around 25 dB after phase-shift multiplication at0 Gbits/s, three FWM stages can be performed, wherehe driving voltage can be reduced by 87.5%.

. EXPERIMENTAL SETUPhe experimental setup of our proposed optical phase-hift multiplier is shown in Fig. 3. First, the phase-shift of�0-� /2� phase modulated DPSK signal is doubled to the

hase-shift of a �0-�� modulated DPSK signal in a sectionf the HNLF. A CW light is generated from a distributedeedback laser at 1548.5 nm. An optical carrier is gener-ted from a tunable laser at 1549.3 nm, and then passeshrough a PM to generate a �0-� /2� modulated DPSK sig-al. The PM is directly driven by a 215-1, 10 Gbits/s,RBS electrical signal from a programmable pattern gen-rator (PPG). The peak-to-peak voltage of the electricallyriving signal is set to 2.5 V in the PPG to generate the0-� /2� phase modulation. In this process, no RF ampli-er is required and adopted. After boosting the phaseodulated light to around 20 dBm by an EDFA, it is com-

ined with part of the CW light, with a power of 5.6 dBm,o stimulate the FWM process in a section of the 500 mNLF. The nonlinear coefficient, dispersion and disper-

ion slope at 1550 nm of the HNLF are 11 W−1 km−1,0.025 ps/(nm·km), and 0.016 ps/ �nm2·km�, respec-

ively. As a result of this FWM, a �5.8 dBm light wave at550.1 nm is generated.In order to evaluate the exponential enhancement con-

ept of using cascaded FWM stages in a phase-shift mul-iplier, a semiconductor optical amplifier (SOA) is addeds the second FWM medium. Under this circumstance,he original peak-to-peak voltage of the electrical PMriving signal is set to 1.2 V so that a �0-� /4� modulatedPSK signal is generated at 1549.3 nm. After selecting

he light wave generated by the first FWM with a BPF at550.1 nm, it is amplified to about 5 dBm by the secondDFA. Then, the amplified light and another part of theW light, with a power of �2 dBm, are combined and in-

ig. 3. (Color online) Experimental setup of the phase-shiftultiplier. The �0-�� modulated DPSK signals are obtained

hrough three methods: (1) driving PM with a large voltage, (2)ultiplying the phase-shift of a �0-� /2� modulated DPSK signal

y one phase-shift multiplier, (3) multiplying the phase-shift of a0-� /4� modulated DPSK signal by two cascaded phase-shiftultipliers.

ected into the SOA to stimulate the second degenerateWM process. Similarly, a new light wave at 1551.7 nm isenerated and selected by a BPF. The measured opticalower of this light wave at 1551.7 nm is �14 dBm. As aeference, the �0-�� modulated DPSK signal is directlyenerated through a PM after using a RF amplifier to am-lify the peak-to-peak electrical driving voltage to 5 V.In our experiment, the polarizations of all the related

ight waves are set in the same direction in order to ob-ain the largest FWM efficiency. The HNLF and SOA arehosen as the first and second FWM media according tohe equipment availability in our laboratory. Both outputsf the HNLF and the SOA are directed to an optical spec-rum analyzer for spectral analysis. The phase-shift mul-iplied light waves are then selected with a 0.8 nm opticalPF, amplified with the third EDFA, filtered with anotherPF, demodulated with a 100 ps delay interferometer,nd evaluated by the BER measurement.

. RESULTS AND DISCUSSIONigure 4 shows the optical spectra measured after a tun-ble attenuator. The optical spectra obtained after therst and second FWM processes are plotted by the dashednd solid lines, respectively. In Fig. 4, the power axis onlyresents a relative power relationship in each FWM pro-ess, while measuring these two spectra. The resultshow that the FWM processes have been successfully per-ormed both in the HNLF and in the SOA.

In order to observe the phase information processing ofhe optical phase-shift multiplier, the generated DPSKignals with different methods are amplified to around 0Bm and then demodulated for eye-diagram measure-ent. In this measurement, the eye-diagrams are re-

orded at the constructive demodulation port. If a �0-��odulation occurs, phase transition between adjacent

its will result in a demodulated optical power of zero.therwise, the bottom line of the recorded eye-diagramill be above the zero baseline. The obtained eye-iagrams are shown in Fig. 5. As a reference, the result of�0-�� modulated DPSK signal through a PM and a RF

mplifier is plotted in Fig. 5(a). The result of a one-stageWM-based phase-shift multiplication from an originally

0-� /2� modulated DPSK signal is plotted in Fig. 5(b).he demodulated eye-diagram in Fig. 5(b) is widelypened. One can see that the time width of the eye-iagram in Fig. 5(b) is larger than that in Fig. 5(a). Com-

ig. 4. (Color online) Measured optical spectra (--) after the firstnd (–) after the second FWM processes.

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ared to a RF amplifier, the FWM-based phase-shift mul-iplier provides instantaneous response speed, whichnables the shorter rising/falling time in Fig. 5(b). Be-ides, the noise in Fig. 5(b) is also less than that in Fig.(a), which indicates that less noise is introduced fromne FWM process than that of a RF amplifier. Resultshow that the one-stage FWM-based phase-shift multi-lier can amplify the original phase-shift with less perfor-ance degradation than that of a RF amplifier.For two cascaded stages of FWMs, the obtained results

f the first and second stages from an originally �0-� /4�odulated DPSK signal are shown in Figs. 5(c) and 5(d),

espectively. As predicted, a �0-� /2� modulated DPSK sig-al is obtained after the first phase-shift multiplier, and a0-�� modulated DPSK signal is obtained after the secondhase-shift multiplier. Comparing to the PM-generatedPSK signal in Fig. 5(a), one sees that some noise ap-ears in the demodulated DPSK signal in Fig. 5(d). It isoted that the second FWM medium is a SOA, which gen-rates ASE noise itself. This ASE noise can be finallydded on the demodulation result of the generated DPSKignal [12].

The corresponding BER curves of the three �0-�� modu-ated DPSK signals are measured and plotted in Fig. 6.he square marks represent the back-to-back DPSK sig-al, which is generated through a PM with the help of aF amplifier. The triangle and circle marks represent the

0-�� modulated DPSK signals generated with one andwo FWM processes, respectively. At a BER of 10−9, a 1.9B improvement in receiver sensitivity has been observedn the demodulated result from the one stage FWM-

ig. 5. (Color online) Demodulated DPSK eye-diagrams of (a)ack-to-back �0-�� modulated DPSK signal after a PM and a RFmplifier; (b) �0-�� modulated DPSK signal after one FWM pro-ess; (c) �0-� /2� modulated DPSK signal after one FWM process;d) �0-�� modulated DPSK signal after two cascaded FWMrocesses.

ig. 6. (Color online) Measured BER curves of �0-�� modulatedPSK signals generated by different methods.

enerated DPSK signal. In accordance with the eye-iagrams shown in Fig. 5, the phase-shift multiplier inptical domain performs better than a RF amplifier inlectrical domain if only one fiber-based FWM stage is uti-ized. After two cascaded FWMs, the resulted �0-�� modu-ated DPSK signal has a power penalty of 1.5 dB. Theata degradation here ascribes to the imperfect noiseharacteristics of the SOA and larger number of utilizedDFAs. This performance can be partially improved bysing another HNLF to replace the SOA or using a BPFith a narrower bandwidth after the SOA.

. CONCLUSIONn conclusion, an optical phase-shift multiplier has beenroposed to reduce the driving voltage of a PM. The ap-licability of the concept at higher data rates (up to 160bits/s) has been indicated by simulation studies. In ourxperiment, the driving voltage of a commercial PM haslso been successfully reduced to a quarter with two cas-aded degenerate FWM processes. It provides an attrac-ive method to effectively enhance the phase modulationfficiency without modifying the material or structure ofhe modulator.

CKNOWLEDGMENTShe authors thank Yongbo Tang and Shiming Gao forelpful discussions. This work was supported by the Na-ional Natural Science Foundation of China (NSFC)Grant Nos. 60688401 and 60708006).

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