## Abstract

Optical Nyquist pulse generation based on a time lens with subsequent optical filtering is proposed. A nearly chirp-free 10-GHz 8.1-ps Nyquist pulse generator is experimentally demonstrated. By inserting group velocity dispersion (GVD) between cascaded phase and amplitude modulators, 11 tones ultraflat optical frequency comb (OFC) of 10-GHz frequency spacing within 0.9 dB power variation is obtained. The quasi-rectangular shape spectrum is then filtered out with a tunable rectangular-shaped optical band-pass filter (OBPF) and the quasi-linear chirp is compensated by a segment of standard single mode fiber (SSMF). By changing the wavelength of the continuous wave (CW) light, nearly chirp-free Nyquist pulses over C band are obtained. Furthermore, simultaneous dual-wavelength pulse generation is also demonstrated.

© 2015 Optical Society of America

## 1. Introduction

With the rapid development of new services, such as video sharing, cloud computing, internet of Things, etc., existing optical fiber communication systems are faced with enormous challenges. Optical time division multiplexing (OTDM) is an important method of overcoming the electronic speed bottleneck and achieving a serial ~Tbit/s channel capacity [1,2]. As a matter of fact, the transmission cost per bit can be substantially reduced as the single-channel bit rate quadruples. A single-channel bit rate of 10 Tbit/s based on 1.28 Tbaud symbol rate using 16-ary quadrature amplitude modulation (16-QAM) and polarization multiplexing has been demonstrated [3]. To further increase the data capacity, a combination of wavelength division multiplexing (WDM) and OTDM may be the key to optimizing the transmission capacity and cost. However, the Gaussian or sech-shaped optical pulse which is traditionally used in OTDM system spreads over a large bandwidth and results in a relatively low spectral efficiency [4,5].

Recently, a novel OTDM system using time-interleaved optical Nyquist pulses is proposed and demonstrated. OTDM method based on such pulses is called Nyquist optical time-division multiplexing (N-OTDM) [6]. The optical Nyquist pulse has a sinc-like temporal waveform and a rectangular or raised-cosine spectral profile, which is capable of improving spectral efficiency, enhancing the tolerance to inter-symbol interference (ISI), nonlinear impairments, chromatic dispersion and polarization mode dispersion [7,8]. By virtue of these properties, a single-channel bit rate of 2.56 Tbit/s based on 1.28 Tbaud symbol rate using differential phase shift keying (DPSK) and polarization multiplexing has been reported [9]. Pass-drop operations of 4 × 172 Gb/s Nyquist OTDM-WDM are also demonstrated [10].

Unlike the multi-carrier system of Nyquist wavelength division multiplexing (N-WDM) or coherent wavelength division multiplexing (CoWDM) which modulate each carrier individually with a symbol rate equal to the carrier spacing [11], N-OTDM modulates a group of coherent carriers simultaneously to generate a modulated ultrashort Nyquist pulse train. Multiple of such ultrashort pulse trains can be multiplexed in the time domain to obtain an ultra-high-speed “superchannel”. High repetition rate, low duty cycle, ultrashort optical Nyquist pulse generator is the key element for the studies of N-OTDM. Since the ultrashort nature of such Nyquist pulses, it occupies very large bandwidth. Nyquist pulse generation schemes used in N-WDM, such as using electrical Nyquist filtering [12], could not provide such a large bandwidth, so optical methods should be exploited. Supercontinuum generation in high nonlinearity fiber (HNLF) is an effective method to generate broadband optical frequency comb [13]. An optical Nyquist pulse with rectangular-shaped spectrum and linear phase distribution on the frequency domain can be obtained by using a spatial light modulator after the supercontinuum [14]. However, such pulse shaping approach introduces severe optical signal-to-noise ratio (OSNR) degradation and the spatial light modulator should be precisely programmed in a large spectral span line-by-line for both amplitude and phase control. Cascaded Mach-Zehnder modulators (MZMs) are proposed to generate high-quality and low-cost Nyquist pulse [15,16]. However, these methods require synchronization of different frequencies or frequency multipliers which increases the system complexity. Only limited and specific number (3 for the MZM and 5 for the DPMZM) of frequency lines can be generated in these schemes with single stage. Although more lines (9 for MZM and 25 for DPMZM) can be obtained by cascading two stages, the pulse repetition rate should also be reduced accordingly. Optical frequency comb (OFC) generation based on phase-only modulation is a promising method to broaden bandwidth [17]. The phase-only modulation driving by a quadratic signal can be regarded as an ideal single time lens, which causes a linear time-varying instantaneous frequency [18].

In this study, we propose and experimental demonstrate an ultrashort optical Nyquist pulse generator using a time lens followed by spectral slicing, which is based on our earlier simulated results [19]. The pulse generator comprises a time lens, which consists of a phase modulator (PM) and a MZM with a segment of dispersion compensating fiber (DCF) inserted between the two modulators, a tunable quasi-rectangular optical band-pass filter (OBPF) and a segment of standard single mode fiber (SSMF). Compared with the cascaded MZM and cascaded DPMZM techniques, this method provides a much simpler approach to generate optical Nyquist pulse by eliminating the requirements for frequency multipliers. Moreover, a large number of frequency lines can be generated without sacrificing the pulse repetition rate. By adjusting the length of the DCF and SSMF, Nyquist pulse with a quasi-rectangular-shaped 11-tone OFC and a duty cycle of 8.1% is experimentally generated. The corresponding spectral flatness is 0.9 dB when the modulation index of the PM is 2π. The pulse source is wavelength tunable from 1535.2 nm to 1565.2 nm, emitting ~8.1 ps Nyquist pulses with the time bandwidth product (TBP) of ~0.863, which is very close to the transform limited TBP of 0.853 with a roll-off factor of 0.15. Furthermore, multi-channel operation can also be achieved based on the proposed Nyquist pulse generator.

## 2. Principle of the Nyquist pulse generator

The temporal waveform of the Nyquist pulse with a repetition rate of *f _{s}* is defined as [6]

*T*= 1/(

*N f*) is the symbol period;

_{s}*α*(0 ≤

*α*≤ 1) is a roll-off factor;

*N*is the number of multiplexed channels by OTDM. When

*α*= 0, the temporal waveform is an ideal sinc function, which has a rectangular-shaped envelope and linear phase in the spectral domain. The rectangular-shaped spectrum can be achieved by many methods, but it is difficult to meet the phase requirement. We all know that phase modulation driving by a cosinusoidal signal has a cosinusoidal temporal phase distribution which is fitted well to a quadratic curve, but only over a very limited time span. With dispersion based chirp linearization which can efficiently improve the phase property, we propose the optical Nyquist pulse generation method with the configuration shown in Fig. 1. The combination of the PM, the DCF and the MZM, when driving the modulators with sinusoidal radio frequency (RF) signal, is called a time lens [18].

The continuous wave (CW) light is modulated by a cosinusoidal RF signal in the PM. The output of the PM can be expressed as

Where*E*is the electric field of the incident CW;

_{in}*f*is the frequency of the RF signal;

_{m}*θ*is the phase modulation index of the PM, which is defined byWhere

*V*is the amplitude of the RF signal and

_{m}*V*is the half-wave voltage of the PM. By taking the derivative of the phase in Eq. (2), the instantaneous frequency

_{π}*f(t)*can be written asEquation (4) and Fig. 2(a) show that the phase modulation in the PM induces a periodic sinusoidal distribution of the instantaneous frequency.

A DCF is used as a dispersive medium after the PM to stretch the sinusoidal distribution chirp. The medium also can be a fiber Bragg grating (FBG) or a SSMF. The propagation of the optical pulse in the fiber can be described by the nonlinear Schrödinger equation

*E*is the slowly varying pulse envelop;

*β*

_{2}and

*β*

_{3}are the dispersion parameter;

*γ*is the nonlinear parameter;

*α*is the loss of the DCF. The symmetrized split-step Fourier method [20] is subsequently used to solve the pulse-propagation in the fiber and the complex amplitude of the pulse at the output of the DCF is expressed as

*E*

_{out}_{2}. As shown in Fig. 2(b), the up-chirp region is stretched and the linearity is improved due to the group velocity dispersion (GVD) in DCF. In the simulation, the nonlinear effect is ignored.

The following MZM, which is biased at the half-maximum transmission point, acts as a flat-top pulse carver. A cosinusoidal electrical wave from an RF source is split into two signals to drive the PM and MZM. The electrical phase shifter is used to adjust the relative phase of the two signals so that the up-chirp part passes through the MZM while the down-chirp part is suppressed. The output of the MZM can be expressed as

*V*is the half-wave voltage of the MZM;

_{πMZM}*V*is the DC bias voltage;

_{bias}*φ*is the phase difference between the RF signals applied to PM and MZM. Figure 2(c) shows that the phase is quasi-quadratic and the corresponding chirp is quasi-linear in the central region of the pulse.

It is noted that how much phase modulation and accumulated dispersion in DCF are applied to the time lens is crucial to the flatness of the spectrum at the output of the MZM. Figures 3(a) and 3(b) show the flatness and the number of comb lines as functions of the phase modulation index (PMI) and the amount of dispersion. As shown in Fig. 3(c), the number of frequency tones under certain power variation can be significantly improved by increasing the PMI. We also can see that there is a compromise between the flatness and the number of comb lines with a certain PMI. In the following simulation, we assume that the modulation index of the PM is 2π which can be practically achieved. With −20 ps/nm dispersion, the power variation of 11 tones is reduced from 3.87 dB (without the DCF) to 0.88 dB (with DCF), which is shown in Figs. 4(a) and 4(b). The out-of-band-suppression ratio of the generated spectrum is only 2.51 dB. Figure 4(c) shows that a flatness of less than 0.25 dB can also be achieved as the accumulated dispersion is −25 ps/nm, but the number of comb lines decreases to 9.

The quasi-linear chirp is compensated by a piece of SMF subsequently to achieve quasi-linear phase. After the dispersion compensation, the corresponding temporal waveform of the 11 tones OFC within 0.88 dB power variation is similar to a sinc function, which is shown in the inset of Fig. 5(a). However, the zoomed-in diagram shows that the oscillating tail of generated pulse has a significant mismatch with sinc function. We attributed the mismatch to the poor out-of-band-suppression ratio. The side lobes are then suppressed by optical filtering and the spectrum with a quasi-rectangular shape is obtained. A 5-order super-Gaussian OBPF is used in the simulation. It has a 3-dB bandwidth of 0.75 nm and an edge roll-off of 285 dB/nm (from −3 dB to −40 dB). As shown in Fig. 5(b), the temporal waveform of the pulse after spectral slicing and dispersion compensation is well fitted to a Nyquist pulse with a full width at half maximum (FWHM) of 8.1 ps and a roll-off factor *α* of 0.15. The two curves are also highly consistent in zero crossings with a minor amplitude deviation. The local peak values and zero crossings of the temporal oscillating tail are dependent on *α*, which is obtained by the method of least-squares curve-fitting for the generated pulse. A roll-off factor of 0.01 can be obtained when a 9-order super-Gaussian OBPF with an edge roll-off of 529 dB/nm (from −3 dB to −40 dB) is used. Such a small or even smaller roll-off factor can be achieved with commercial flat-top OBPF, such as Yenista XTA-50, which has an edge roll-off of 800 dB/nm. By cascading multiple OBPFs, further reduction on the roll-off factors can be achieved.

The TBP is then calculated, which is defined as [6]

Where Δ*τ*is the FWHM pulsewidth and Δ

*ν*is the FWHM spectral width. It can be seen that the TBP is a function of

*α*. The corresponding TBP of the generated pulse is 0.86 as

*α*is 0.15, which is very close to the transform limited TBP of 0.853. The phase property of the generated pulse is also investigated. According to the definition, the chirp-free Nyquist pulse has a strict linear phase in the spectral domain. As shown in Fig. 6, the phase of the 11 tones in our scheme is well fitted to a linear curve, which also indicates that the generated pulse is nearly a chirp-free Nyquist pulse.

To test if the generated Nyquist pulse can be used in N-OTDM system, we perform numerical simulation of time-domain multiplexing with such pulse. The generated Nyquist pulse is subsequently encoded using DPSK modulation with a 10-Gb/s pseudo-random binary sequence (PRBS) signal, spilt, delayed and multiplexed into 110-Gb/s N-OTDM signal by a fiber-based time-division multiplexer. The eye diagram of the multiplexed DPSK signal is shown in Fig. 7. It can be seen that there is no ISI at any symbol interval. The characteristics of the multiplexed eye diagram is consistent with the reported result of ref [6], demonstrating that the Nyquist pulse can be used for N-OTDM system.

The robustness in regarding to the central wavelength of optical pulse is further studied to demonstrate the feasibility of multicolor operation. Because pulses at different wavelengths propagate at different speeds in DCF, they cannot overlap with each other when arriving at the MZM switching window, as shown in Fig. 8(a). As the wavelength of input CW light is adjusted, the phase delay between the PM and MZM should be changed accordingly. By adjusting the RF phase shifter between the PM and MZM, the central region of the pulse at a specific wavelength can be aligned with the time switching window of MZM and Nyquist pulse can be generated. When two CW lights with arbitrary wavelength interval are injected into the time lens simultaneously, it is unlikely that Nyquist pulses can be achieved on both wavelengths due to the walk-off between different wavelengths after transmission in the DCF. However, it is possible to generate Nyquist pulses on different wavelengths simultaneously when the wavelength interval of two wavelengths satisfies certain condition. The time-delay between two wavelengths at the input of MZM can be expressed as

*L*is the length of the DCF,

*λ*

_{1}and

*λ*

_{2}are the central wavelength of pulses, Δ

*λ*is the wavelength difference, and

*c*is the speed of light in vacuum. To make the both pulses coincide with the center of the time switching window, Δ

*τ*should be an integral multiple of the clock periodWhere

*M*is an integer number and

*T*is the clock period. The Δ

*λ*can be written as

*λ*should be an integral multiple of 4.8 nm. To demonstrate the theoretical analysis, Δ

*λ*is further obtained in simulation by changing the central wavelength from 1546.96 nm to 1559.2 nm with a fixed RF phase delay between the PM and MZM. Figure 8(b) shows the power variation between comb lines as a function of the wavelength of the input CW light. Significant power variation also can be observed as the central regions of the pulses at other wavelengths are mismatched with the center of the time switching window. The local minimum power variation of spectrum at the output of MZM is 0.88 dB as the central wavelength is located at 1548.2 nm, 1553.2 nm and 1558.02 nm, respectively. When these wavelengths are launched into the time lens at the same time, high-quality Nyquist pulses can be generated simultaneously. The wavelength interval is 5 nm and 4.82 nm in the simulation. Compared with the theoretical value, the minor difference can be explained by that

*β*

_{2}is regarded as a constant in analysis, which is a variable with

*β*

_{3}in simulation. According to the above analysis, the scheme can be applied for simultaneous multicolor operation. It should be noted the wavelength differences of 5 nm and 4.82 nm are relative values, the absolute value of wavelengths can be changed by changing the RF phase delay between the PM and MZM. When several different sets of such time lens configuration are used, it is possible to cover a continuous region of optical spectrum seamlessly.

## 3. Experimental results and discussion

Corresponding experiments based on the configuration shown in Fig. 1 are performed to demonstrate the proposed method. The CW light is emitted from a tunable laser. The PM and MZM are modulated with a 10-GHz cosinusoidal RF signal. The modulation index of the PM is 2π. The MZM is biased at the half-maximum transmission point and peak-to-peak voltage of RF signal is around the half-wave voltage of the MZM, which is used as a flat-top pulse carver. The two modulators are synchronized by a phase shifter. The inserted DCF with −20 ps/nm between the modulators provides linear GVD, which stretches the PM induced cosinusoidal distribution chirp more fitted to linear curve in time span of 90% period. Then, the ultraflat OFC is filtered by a tunable flat-top quasi-rectangular OBPF (Yenista WSM-160), the bandwidth of the passband is tuned to 0.835 nm. The quasi-linear chirp is compensated by 3.64-km SSMF subsequently to achieve quasi-linear phase. The spectrum is observed by an optical spectrum analyzer (Ando AQ6317) and the pulsewidth is measured by an optical sampling oscilloscope (EXFO PSO-102) with a time resolution better than 1ps.

The proposed optical Nyquist pulse generator is first test with single-channel operation at the central wavelength of 1553.2 nm. Figure 9(a) shows the spectrum of the obtained pulse without optical filtering. Thanks to the linearization of frequency chirp by the time lens, an ultraflat OFC of 11 tones within 0.9 dB power variation is obtained. The oscillating tail of the corresponding pulse shown in Fig. 9(b) is smooth and the required amplitude fluctuation cannot be observed. As the side lobes are sliced by optical filtering, the spectrum with a quasi-rectangular shape is obtained, which is shown in Fig. 9(c). Figure 9(d) shows that the generated optical pulse is well fitted to a sinc function with a FWHM of 8.1 ps after the optical filtering and dispersion compensation, which indicated that the experimental results are highly consistent with the theoretical analysis. It is noted that a much lower duty cycle of Nyquist pulse with more number of frequency tones can be obtained by increasing the modulation index.

In order to verify that the scheme can be applied to generate wavelength-tunable optical Nyquist pulse, the performance of the pulse source with different wavelengths is subsequently studied. The output power of the tunable CW source is all ~8.6 dBm and the central wavelengths are 1535.2 nm, 1541.2 nm, 1547.2 nm, 1553.2 nm, 1559.2 nm, and 1565.2 nm, respectively. The central wavelength of the tunable quasi-rectangular OBPF is correspondingly adjusted and the bandwidth is fixed as 0.835 nm. The phase between the RF signals applied to PM and MZM is also adjusted when the wavelength is changed due to group velocity mismatch in DCF. Figures 10(a)–10(e) show the waveforms of the pulses at different wavelengths. The waveforms are well fitted to a sinc function with a duty cycle of ~8.1%. The TBP of the pulse is shown in Fig. 11 as a function of the central wavelength, which demonstrated that the Nyquist pulses are nearly chirp-free over the C-band.

To demonstrate the feasibility of multicolor operation, simultaneous dual-channel Nyquist pulse generation is further performed. Using the theoretical analysis and simulation as a guideline, the central wavelengths of CW lights are located at 1548.08 nm and 1562.77 nm (about 3Δ*λ* apart), respectively. The lights are then combined with a 3-dB coupler and launched into the time lens. After the spectrum slicing and dispersion compensation, both pulses in the two channels are well fitted to a sinc function with a FWHM of ~8.2 ps, as shown in Figs. 12(a) and 12(b). The corresponding TBP is ~0.874, indicating that the generated pulse is a nearly transform-limited Nyquist-like pulse.

## 4. Conclusion

A flexible method for ultrashort optical Nyquist pulse generation is demonstrated using a time lens with subsequent optical filtering. Nearly transform-limited Nyquist pulse with a FWHM of 8.1 ps and 11-tone quasi-rectangular-shaped frequency combs of 10-GHz frequency spacing with 0.9-dB flatness fluctuation is achieved. By adjusting the wavelength of the CW light from 1535.2 nm to 1565.2 nm, ~8.1 ps nearly chirp-free Nyquist pulses at all wavelengths are obtained, which indicated that the performance of the Nyquist pulses at each wavelength is almost the same. In addition, simultaneous dual-channel Nyquist pulse generation is also demonstrated.

## Acknowledgment

This work is supported by “973” Major State Basic Research Development Program of China (No. 2011CB301703), the National Natural Science Foundation of China (No. 61275032), and Tsinghua University Initiative Scientific Research Program.

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