## Abstract

We investigate to generate coherent and frequency-lock optical multi-carriers by using cascaded phase modulators and recirculating frequency shifter (RFS) based on an EDFA loop. The phase and amplitude relation of RF signals on two cascaded phase modulators and the impact of EDFA gain are investigated. Experimental results are in good agreement with the theoretical analysis. The performance of 113 coherent and frequency-lock subcarriers with tone-to-noise ratio larger than 26dB and amplitude difference of 5dB obtained after a tilt filter covering totally 22.6nm shows that this scheme is a promising technique for the coming Tb/s optical communication.

©2011 Optical Society of America

## 1. Introduction

Multi-carriers or multi-tone generation has attracted increasing research attentions these days for the promising use in the Tb/s per-channel optical communication [1–5]. A lot of experiments of Tb/s optical communication realized with multi-carriers technique have been reported, including the coherent dense-wavelength-multiplexing (CoDWDM) with polarization-division-multiplexed (PDM) return-to-zero (RZ) QPSK [5–7], optical orthogonal-frequency-division-multiplexing (OOFDM) with different modulation formats [8–11]. There are several methods to generate multi-carriers sources including the optical frequency comb or supercontinuum technique [1,2], the cascaded phase modulator and intensity modulator [5,7,12], single-sideband (SSB) modulator with recirculation frequency shifter (RFS) [3,4,13] and multi-wavelength erbium doped fiber laser(EDFL) [14–17]. Recently, 5.4 Tb/s OFDM PDM-QPSK optical signal has been generated by comb generation or supercontinuum technique [18]. However, due to the limited optical signal noise ratio (OSNR) of the OFDM optical signal generation by supercontinuum technique, the transmission distance is quite limited. Also, 1.2 Tb/s PDM-RZ-QPSK DWDM [7] optical signal is reported by using multi-carriers generated by cascaded modulators. However, only 12 subcarriers (25 GHz spacing) covering ~300GHz bandwidth with flat spectrum amplitude [7] is generated due to the limited amplitude of the RF signals on the phase modulator. Recirculating frequency shifter (RFS) based on the frequency shifting in a SSB modulator has been reported to generate 36 and 50 subcarrier, which shows the potential capability to generate more subcarriers [3,13]. However, the total number of subcarriers is strictly depended on the recirculating times because only one subcarrier generated each time for SSB modulation. Due to the EDFA ASE noise accumulation, the achieved maximum number of subcarriers is less than 50 covering 625GHz spectral range. Also, the SSB modulator based RFS has the significant stability problem due to the nonlinearity, the imbalance of DC bias, and the imbalance of I/Q RF signals of optical I/Q modulator (IQM) [13]. The amount of multi-carriers is also limited less than 26 in the schemes in multi-wavelength EDFL in [14–17].

Recently we demonstrated a novel scheme on the generation and transmission of 11.2 Tb/s by 112 coherent optical subcarriers with the subcarriers spacing of 25GHz using two cascade phase modulators and RFS based on EDFA loop [19]. In this paper we theoretically analyzed and compare the experimental results with the theoretical analysis. We use two phase modulators to generate over 22 subcarriers for one time which works very stable since the phase modulator has no DC bias. The phase and amplitude relation of RF signals on two modulators and the impact of EDFA gain factor are investigated. Experiment results are in good agreement with the theoretical analysis. The performance of 113 coherent subcarriers obtained after tilt filter covering totally 22.6nm with tone-to-noise ratio larger than 26dB shows that this scheme is a promising technique for the coming Tb/s optical communication.

## 2. Principle of multi-carriers generation and theoretical investigation

The schematic configuration of multi-peak generation by RFS based on the frequency shifting in cascaded phase modulators is shown in Fig. 1 . The configuration of the proposed scheme consists of a closed loop, which comprises with two 50:50 polarization maintaining optical couplers, two cascaded phase modulators to generate multi-carriers, an polarization maintaining EDFA amplifier to compensate the loop loss and a tunable polarization maintaining optical phase shifter which is used to adjust the recirculating loop length. Different from the RFS architecture based on SSB modulator, here two optical couplers and cascaded phase modulators are employed, and no band-pass filter is used in the loop which is free run. The subcarriers generated occupy the whole EDFA gain spectrum. The output of the recirculation loop will pass through a wavelength selective switch or waveform shaper to shape the amplitude of each subcarrier and obtain the wanted subcarriers.

The CW lightwave generated from one narrow linewidth laser is connected with one optical coupler as the seed source for frequency shifting in cascaded phase modulators. Here, the CW input optical seed source is represented as${E}_{c}={E}_{o}\mathrm{exp}(j2\pi {f}_{c}t)$. The output from one port of the optical coupler is modulated by two cascaded phase modulators. Each phase modulator is driven by a RF clock signal with a fixed frequency of${f}_{s}$. To obtain more subcarriers, two booster electrical amplifiers (EA) are used.

#### 2.1 Analysis of two cascade phase modulators

The phase modulators used here are identical and the output optical signal can be expressed as

where ${V}_{d}$ is the drive signal and the ${V}_{\pi}$ is the half-wave voltage of the phase modulator. Considering the input optical signal of phase modulator is${E}_{c}$and the RF drive signal represented as${f}_{s}(t)=R{V}_{\pi}\mathrm{sin}(2\pi {f}_{s}t)$, the output optical signal is given by*n*,

*R*is the modulation index representing the rate of RF signal amplitude to the half-wave voltage ${V}_{\pi}$and in this Eq. (3) we have ${J}_{-n}(\pi R)={(-1)}^{n}{J}_{n}(\pi R)$. From Eq. (3), we can see that the output optical signal after the phase modulator generates several subcarriers with the frequency of${f}_{c}+n{f}_{s}$, where$n=\pm 1,\pm 2,\mathrm{...}$. The amplitude of

*n*th harmonics optical subcarrier ${J}_{n}(\pi R)\mathrm{exp}[j2\pi ({f}_{c}+n{f}_{s})t]$ is determined by the first kind Bessel function${J}_{n}(\pi R)$.

In General, increasing the modulation index *R* increases the power transferred to the higher order subcarriers, and increases the number of higher order subcarriers. Also, the flatness of generated subcarriers varies with *R*. In this way, the maximum number of subcarriers is depended on the modulation index *R*. Assuming the total number of subcarriers generated is 2*m + 1*, Eq. (3) can be expressed as follows

^{th}high order subcarriers are counted.

By increasing the power level of RF drive signal, we can increase the modulation index to obtain more subcarriers. However, due to the output power limit of electrical amplifier, the amplitude of RF driven signal is limited in practice operation. In order to obtain more subcarriers, we cascade another phase modulator also driven by a high-level RF signal.

We use ${f}_{1}(t)={R}_{1}{V}_{\pi}\mathrm{sin}(2\pi {f}_{s}t)$ and ${f}_{2}(t)={R}_{2}{V}_{\pi}\mathrm{sin}(2\pi {f}_{s}t+\Delta \varphi )$to represent the two drive RF signals, here$\Delta \varphi $ is the phase deviation of the two RF signals. The CW seed optical source is firstly modulated by the cascaded phase modulation and the output of the second phase modulator can be expressed as follows

*R*and the phase deviation on the number of generated subcarriers when${R}_{1}={R}_{2}=R$. As shown in Fig. 2(b), the worst case is when phase deviation$\Delta \varphi $ is around

*π*. In this case, the subcarriers amount decreases sharply. It can be explained well with Eq. (6). The number of generated subcarriers mentioned in Fig. 2 and Fig. 3 indicates the amount of subcarriers between the two high order harmonic subcarriers which are 3dB power decline to the maximum power. Assuming the modulation index of two cascaded phase modulator is the same

*R*, the combined modulation index is expressed aswhich is a cosine function of $\Delta \varphi /2$. Equation (7) shows that maximized combined RF drive signal modulation index can be obtained when there is no phase deviation between two RF signals and$\Delta \varphi =0,\pm 2\pi \mathrm{...}$, as$\mathrm{cos}(\Delta \varphi /2)=\pm 1$. The worst case happens when the phase of two RF drive signal is opposite and$\Delta \varphi =\pm \pi ,\pm 3\pi ,\mathrm{...}$, as$\mathrm{cos}(\Delta \varphi /2)=0$.

Assuming the modulation index is limited (in experiments less than 2.2), to obtain more than 20 subcarriers, the modulation index of RF driven signals should more than 1.5 and the phase deviation should be less than 0.45*π*(−0.45*π* to 0.45*π*) as shown in Fig. 3(a). The more detailed variation of calculated power mean square deviation (MSD) representing flatness for generated subcarriers with the modulation index R and phase deviation $\Delta \varphi $ is shown in Fig. 3(b). The phase deviation between the two RF driven signals is sensitive to affect the performance of generated subcarriers. More subcarriers with good flatness can be generated for some cases of modulation index *R* which is blue zone in Fig. 3 (b). When *R* is around 2.1 and phase deviation is around 0.15*π*, more than 22 subcarriers can be obtained and the tolerance for phase deviation can be more than 0.1*π*.

#### 2.2 The principle of EDFA loop for RFS

Considering the EDFA loop with the RFS configuration, the output of cascade phase modulators is split into two branches by OC2, one coupled out and the other recirculating back into a EDFA amplify to compensate the losses in the closed loop. This scheme induces power transferring to subcarriers in the loop. The principle for multi-carriers generation is shown in Fig. 4 .

The output expressed in Eq. (5) is defined as output 1 which contains${N}_{1}$ subcarriers and can be expanded by Eq. (4) as

As shown in Eq. (9), the gain of EDFA should be large enough to compensate the insertion losses and modulation loss for ${N}_{1}/2$ order subcarrier to run following round trips to generate more subcarriers.

Assuming the losses in the closed loop are compensated, the normalized outputs after each round trip can be expressed as

Our scheme is different with multi-wavelength EDFL reported in [14–17] which generally consist of a kind of comb or period filter and a kind of frequency shifter or phase modulators. The principle of sharing gain among generated multi-carriers is similar. However, there are several differences between our scheme and multi-wavelength EDFL:

- • There is no comb or period filter in the EDFA loop in our scheme. In [14–17], comb or period filter is the basic element for wavelength selection which is necessary for multi-carriers generation. However, it is free run in our scheme and there is no filter in the loop. The wavelength is not selected by any period filter.
- • In [14–17], the phase modulator or frequency shifter used is driven by kHz sinusoidal signal which is necessary for sharing the uniform gain among selected wavelength to suppress the homogenous line bordering. However, the cascaded phase modulators in our scheme are driven by 25 GHz RF signals for power transferring and a generation of multi-carriers with subcarriers spacing of 25 GHz.

## 3. Experimental results

The multi-carriers generation experiment is carried out as shown in Fig. 1. The output power for the ECL at 1557.42nm is 14.5dBm and the linewidth of the ECL is less than 100 kHz. Here the RF clock frequency is 25 GHz and the RF peak to peak voltage after the booster electrical amplifier is 17V, and the half-wave voltage of the phase modulator is 4V. In this way, the amplitude of the drive RF signal is 8.5V which is about 2.1 to the half-wave voltage of the cascaded phase modulators in order to generate more subcarriers with good flatness and large phase tolerance to the phase deviation. The output of the recirculation loop will pass through a tilt filter to shape the amplitude of each subcarrier. In this experiment, all optical components except the tilt filter are polarization maintaining. There is no any DC bias controller in the phase modulators, so the excellent stability can be obtained. The two phase modulators have the identical performance. The insertion loss of each phase modulator is 4 dB. The two polarization maintaining optical couplers (PM-OC) are also identical with the insertion loss of 3.1dB and coupling ratio of 50:50. The optical time delay has an insertion loss of 1.8 dB, which is used for synchronization in the recirculation loop. The total insertion loss is 16dB including the insertion of two phase modulator, two OC and one optical time delay in our experiment.

After PM1, sub-carriers can be generated as shown in Fig. 5 (a) . Due to the power limit of the RF dive signal, only about 10 subcarriers are generated. The optical spectrum after PM2 is shown in Fig. 5(b). We can see that by using cascaded phase modulators driven by high amplitude RF signal, we can generate over 22 optical subcarriers. The output of PM2 is connected with another optical coupler (OC2).

The phase relationship of the electrical signals on PM1 and PM2 should be carefully adjusted to generate more peaks according to the analysis in section 2.1. Figure 6
shows the results of optical spectrum after PM2 when we adjust the phase shifter to change the phase deviation between the two RF drive signals. We can see that the number of generated decreases with the increased phase deviation. Figure 6 (a) is measured when the phase deviation is around zero where nearly 22 subcarriers can be obtained. When we increase the phase deviation, we obtain 20, 6, 0 subcarriers respectively in Fig. 6(b), 6(c) and 6(d). Figure 6 (d) is measured when the phase deviation is about *π* where the two RF drive signals are opposite in phase and no subcarriers are generated in 3 dB. It is worth noting that the flatness of generated subcarriers also changes with the phase deviation. The results are in good agreement with the analysis in section 2.1 with Fig. 2 and Fig. 3.

The impact of EDFA gain in the loop on the multi-carriers generation is illustrated in Fig. 7 and Fig. 8 . Figure 7 shows the optical spectrum of the output of OC2 after the RFS loop varies with different EDFA output power (different EDFA gain). We increase the EDFA output power to change the gain in the RFS loop at (a) 11.5dBm, (b) 15.5dBm, (c) 19.5dBm and (d) 21.5dBm respectively. When the EDFA gain is small, higher orders subcarriers beyond 1565nm can’t be compensated perfectly to generate more subcarriers with good tone-to-noise ratio (TONR) and only about 62 subcarriers with TONR larger than 30dB are generated as shown in Fig. 7(a). However, when we increase the EDFA output power to 19.5dBm, more about 100 subcarriers covering about 20nm bandwidth can be obtained with tone-to-noise ratio larger than 30dB in Fig. 7(c). The relation between the measured subcarriers amount and the EDFA output power in shown in Fig. 8. The tone-to-noise ratio is the ratio of the power per tone to the power of noise mainly induced by EDFA amplified spontaneous emission (ASE). The noise bandwidth is 0.02nm, and bandwidth for the tone is also 0.02nm. In order to study the impact of EDFA output power on the obtained subcarriers amount, we count the subcarriers with tone-to-noise ratio larger than 30dB (which is good for practice use). Figure 8 indicates that the amount of generated subcarriers measured increases with the EDFA gain in the loop. The EDFA output power increases from 11.5dBm to 21.5dBm, and the amount of generated subcarriers with 30dB tone-to-noise rate increases from 62 to 106. Results in Fig. 7 and Fig. 8 are in good agreement with the analysis in section 2.2.

Due to the non-flatness of EDFA gain spectrum, subcarriers generated from the output port of OC2 are not so flat. One wavelength selective switch or waveform shaper is optimal for this amplitude equalization. But the generated optical subcarriers cover one part of EDFA C-band and one part of EDFA L-band. There is no available WSS to shape both bands at this time, so we use one tilt filter to shape the subcarriers. Figure 9(a) shows optical spectrum of the stable multi-carriers obtained after tilt filter with the total 113 subcarriers with the tone-to-noise ratio larger than 26dB. The shortest wavelength is 1552.97nm and the longest wavelength is 1575.60nm. The amplitude difference of all subcarriers at this wavelength range is smaller than 5dB. We can see that multi-carriers obtained after tilt filter cover nearly 22.6nm. The detailed optical spectrum of subcarriers with good shape from 1562 nm to1564 nm is illustrated in Fig. 9(b).The resolution of all optical spectra in Fig. 9 is 0.02nm. The model number of this OSA is Yokogawa AQ6370B. It cannot show the correct spectrum, especially when the optical power is small, such as at −40dBm where the spectral width of each subcarrier seems wider. The generated 113 subcarriers with the subcarrier spacing of 0.2 nm (25GHz) covering totally 2.8THz is more than 26dB which shows that this scheme is a promising technique for the coming Tb/s optical communication.

## 4. Conclusion

We theoretically analyze coherent and frequency-lock optical subcarriers generation using RFS based on the frequency shifting in two cascade phase modulators. The phase and amplitude relation of RF signals on two modulators and the impact of EDFA gain factor are investigate. More than 22 subcarriers can be generated after the cascaded phase modulators for one time when phase deviation is around zero. By increasing the EDFA gain, more subcarriers can be generated. In our scheme we successfully generate 113 subcarriers with the subcarrier spacing of 25GHz. The performance of 113 coherent subcarriers obtained after tilt filter covering totally 2.8THz with the tone-to-noise ratio larger than 26dB and amplitude difference of 5dB shows that this scheme is a promising technique for the coming Tb/s optical communication which is demonstrated in our previous report on 11.2-Tbit/s optical PM-QPSK-OFDM signal over 640-km SMF-28.

## Acknowledgments

This work is partially supported by the National High Technology Research and Development Program (973) of China (Grant No. 2010CB328300), National Natural Science Foundation of China (No. 600837004), Chinese Postdoctoral Science Foundation funded project (No. 20090460593) and the Creative Talent Project Foundation for Key Disciplines of Fudan University.

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