1. Introduction

During the last years, the quasi-phase matched (QPM) periodically poled lithium niobate (PPLN) waveguide has been widely used for various all-optical signal processing applications, such as wavelength conversion [1–4], add/drop [5], pulse reshaping and compression [6], switching [7], NOT gate [8], etc. It offers several distinct advantages of ultra-fast nonlinear optical response, strict transparency, independence of bit rate and data format, negligible spontaneous emission noise and no intrinsic frequency chirp. However, up to now, PPLN waveguide has not been applied to all-optical format conversion, which is an essential function to enhance the optical network flexibility. All-optical format conversion from nonreturn-to-zero (NRZ) to return-to-zero (RZ) is an important interface technology for connecting metro/access and core optical networks. Different schemes have been employed to perform NRZ-to-RZ format conversion, showing impressive conversion performance [9, 10], nevertheless, most of them are difficult to be operated at 40 Gbit/s and only single-to-single channel format conversion is demonstrated. In this paper, by exploiting the cascaded sum- and difference-frequency generation (SFG+DFG) in a PPLN waveguide placed in a Sagnac interferometer structure, we report, for the first time to our knowledge, simultaneous single-to-triple channel NRZ-to-RZ format conversion. The conversion performance is simulated, including the conversion efficiency, duty cycle, pulse width ratio, Q-factor, extinction ratio (ER) and tunability.

2. Operating principle

 

Fig. 1. Schematic illustration for PPLN-based all-optical NRZ-to-RZ format conversion. TF: tunable filter.

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Figure 1 shows the schematic diagram for all-optical NRZ-to-RZ format conversion exploiting SFG+DFG in a PPLN-based Sagnac interferometer structure. The NRZ data signal (λ_S) and continuous-wave control (λ_C) combined by a wavelength-division-multiplexed fiber coupler (WDM FC) are launched into port ① and divided into two counter-propagating waves at ports ③ and ④ by a 3dB FC. A pulsed pump (λ_P) synchronized at a clock of the same period as the data signal is injected into the Sagnac interferometer in the clockwise (CW) direction by another WDM FC [9]. Ports ① and ② are known as the reflected and transmitted port of the Sagnac interferometer, respectively [11]. In the absence of pulsed pump, there are no outputs from port ② due to destructive interference [11]. In the presence of pulsed pump, the CW data signal, control, and pulsed pump co-propagate along the PPLN waveguide, in which the SFG+DFG nonlinear interactions take place under the QPM condition [4]. Here we pay attention to the changes induced on the CW data signal and control during the SFG+DFG processes, which can be briefly described as follows. In the SFG interaction, one photon from the signal wave and another photon from the pump wave are annihilated to create one photon at the wavelength of the sum-frequency wave (λ_SF), at the same time, one sum-frequency photon is annihilated to generate one photon of the control wave and the other photon of the idler wave (λ_i) by the subsequent DFG process. At the output of the PPLN waveguide (Point A in Fig. 1), it is noted that the generated idler wave is RZ format. Moreover, within the region when pulsed pump is on in the time domain, the CW data signal is depleted and the CW control is amplified during the generation of the sum-frequency and idler waves, i.e. notches in the data signal wave and overshoots in the control wave can be observed [4]. On the contrary, for counter-clockwise (CCW) data signal and control which are opposite to the CW pulsed pump, they experience negligible SFG+DFG nonlinear interactions according to the following explanations. First, the CCW data signal and CW pulsed pump propagate in the different directions and can not interact with each other effectively. Second, when the co-propagating SFG+DFG associated with CW signal, control and pump satisfies the QPM condition with phase mismatching for SFG Δk_CW=k_SF-k_S-k_P-2π/Λ=0 (k_SF,S,P denote propagation constant of sum-frequency, signal, pump waves and Λ is the microdomain period of PPLN), the counter-propagating SFG+DFG relative to CCW signal, control and CW pump is severely phase mismatched for SFG with Δk_CCW=k_SF-k_S+k_P-2π/Λ≠0. Therefore, no CCW idler wave is generated and the CCW data signal and control undergo negligible changes after passing through the PPLN waveguide (Point B in Fig. 1). As a result, at port ② of the Sagnac interferometer, in addition to the output RZ idler wave, the RZ signal output can be obtained by the interference between CW and CCW signal waves, and the interference between CW and CCW control waves generates the RZ control output. Thus simultaneous single-to-triple channel NRZ-to-RZ format conversion can be implemented. Note that, as the role of PPLN is to introduce changes on the CW signal and control waves without affecting the CCW signal and control waves, the position of the PPLN waveguide placed into the Sagnac interferometer could be arbitrary, which is an advantage compared with other Sagnac interferometers requiring accurate location of the optical element inside the loop.

3. Theoretical results and discussions

Similar to the theoretical analyses on the wavelength conversion of picosecond pulses in [4], the above NRZ-to-RZ format conversion process can be simulated based on the well-known coupled-mode equations describing the SFG+DFG nonlinear interactions [4]. In the following calculations, a super-Gaussian type, 2⁷-1, 40 Gbit/s pseudorandom bit sequence (PRBS) NRZ data signal is adopted and a continuous-wave control is considered. The synchronized pulsed pump is assumed as a hyperbolic-secant pulse sequence with a repetition rate of 40 GHz and a pulse width of 5 ps. The peak power of input data signal and input control power are both assumed to be 200 mW, and the peak power of input pulsed pump is set at 100 mW. A typical PPLN waveguide with a length of 60 mm and a waveguide area of 50 μm² is used in the simulations. The uniform microdomain period of the PPLN waveguide is assumed to be 18.8 μm in order to meet the QPM SFG process for the sum-frequency wavelength of 0.772 μm at room temperature. The central wavelengths of the signal and pump are set at 1550.0 and 1538.0 nm, respectively. The control wavelength is tuned at 1555.0 nm, thus the idler wavelength is generated at about 1533.2 nm. The group-velocity mismatch (GVM) and group-velocity dispersion (GVD) in the SFG+DFG processes are taken into consideration.

Figure 2 presents the calculated temporal waveforms (20 bits) of different optical waves. It can be seen clearly from Fig. 2(d)(e) that the CW signal and control at the output of the PPLN waveguide are respectively depleted and amplified, which is in good agreement with Point A in Fig. 1. By comparing Fig. 2(f)(g)(h) with Fig. 2(a), it is found that single-to-triple channel NRZ-to-RZ format conversion is successfully realized, including one channel NRZ-to-RZ format conversion with wavelength unchanged and single-to-dual channel simultaneous NRZ-to-RZ format conversion and wavelength conversion. The peak powers of output idler, signal and control at port ② are 20.3, 8.8 and 1.7 mW, respectively. Thus the conversion efficiency for single-to-triple channel NRZ-to-RZ format conversion, defined as the ratio of the peak power of the converted RZ wave to that of the input NRZ signal, is approximately - 9.94, -13.59 and -20.69 dB, respectively, corresponding to Fig. 2(f)(g)(h). It is expected that the conversion efficiency can be improved by appropriately increasing the powers of the pump and control waves and the length of the PPLN waveguide.

 

Fig. 2. Temporal waveforms of different optical waves: (a) input NRZ signal, (b) input pulsed pump, (c) input continuous-wave control, (d) clockwise output signal from PPLN, (e) clockwise output control from PPLN, (f) output RZ idler at port ②, (g) output RZ signal at port ②, (h) output RZ control at port ②.

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Figure 3 depicts the simulated optical spectra of different optical waves. As shown in Fig. 3(f), the output idler spectrum from interferometer is different from the input NRZ signal in Fig. 3(a) but similar to the referenced RZ signal in Fig. 3(i). Remarkably, the clockwise signal spectrum at the output of the PPLN waveguide shown in Fig. 3(d) contains both NRZ and RZ information, which can be explained with the fact that the signal waveform shown in Fig. 2(d) simultaneously carries the information of NRZ and RZ. Similarly, the clockwise output control waveform from PPLN shown in Fig. 2(e) can be regarded as the combination of RZ and continuous-wave, thus the corresponding spectrum shown in Fig. 3(e) includes the RZ information as well as the Fourier Transform of the continuous-wave component. After undergoing interference at the output of interferometer, the NRZ information in Fig. 3(d) and the continuous-wave component in Fig. 3(e) are removed, leading to the RZ outputs shown in Fig. 3(g)(h) which also resemble the referenced RZ signal in Fig. 3(i).

Figure 4 further displays the simulated eye diagrams of different optical waves. The Q-factor and ER defined as Q=20log₁₀ [(μ ₁-μ ₀)/(σ ₁+σ ₀)] and ER=10log₁₀(μ ₁/μ ₀) are used to describe the performance of the converted RZ, where μ ₁ and μ ₀ are the average power of logical “1” and “0” of the eye diagrams at the sampling time, while σ ₁ and σ ₀ are the corresponding standard deviations. As illustrated in Fig. 4(c)(d)(e), the nice eye opening, high Q-factor and ER of the converted RZ idler, signal and control at the output of interferometer indicate the successful single-to-triple channel format conversion form NRZ to RZ. In comparison to the ideal referenced RZ shown in Fig. 4(f), the performance degradation from NRZ to RZ can be mainly ascribed to the walk-off effects caused by the GVM between the sum-frequency wave in the 0.77-μm band and the signal, pump, control, idler waves in the 1.55-μm band [4]. Note that, the pulse widths of output RZ idler, signal and control are 6.8, 3.5 and 4.9 ps, corresponding to the duty cycles of 0.27, 0.14 and 0.20, respectively. Moreover, the converted RZ signal and control are compressed compared with the pulsed pump shown in Fig. 4(b), while the converted RZ idler is broadened.

 

Fig. 3. Simulated optical spectra of different optical waves: (a) input NRZ signal, (b) input pulsed pump, (c) input continuous-wave control, (d) clockwise output signal from PPLN, (e) clockwise output control from PPLN, (f) output RZ idler at port ②, (g) output RZ signal at port ②, (h) output RZ control at port ②, (i) referenced 2⁷-1, 40 Gbit/s PRBS RZ data signal of hyperbolic-secant type with a pulse width of 5 ps.

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Fig. 4. Simulated eye diagrams of different optical waves: (a) input NRZ signal, (b) input pulsed pump, (c) output RZ idler at port ②, (d) output RZ signal at port ②, (e) output RZ control at port ②, (f) referenced 2⁷-1, 40 Gbit/s PRBS RZ data signal of hyperbolic-secant type with a pulse width of 5 ps.

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Figure 5 theoretically plots the changes of duty cycle, pulse width ratio of converted RZ to pulsed pump, Q-factor and ER against pump pulse width for the converted RZ idler, signal and control. As shown in Fig. 5(a), the duty cycle can be adjusted by varying the pulse width of the pump. In fact, the duty cycle increases with the pump pulse width. Meanwhile, with the increase of the pump pulse width, it is found that the converted RZ signal is compressed and its pulse width ratio almost keeps unchanged with the fluctuation less than 0.1. The converted RZ idler is broadened and its pulse width ratio decreases as increasing the pump pulse width. The converted RZ control is broadened as the pump pulse width is less than 5 ps, while compressed with the pump pulse width larger than 5 ps. Remarkably, the walk-off effects are accelerated and become severe during the increase of the pump pulse width, as a result of which, both the Q-factor and ER degrade as shown in Fig. 5(b).

Figure 6 depicts the simulated tunable performance of the SFG+DFG-based NRZ-to-RZ format conversion. As shown in Fig. 6(a), keeping the signal and pump wavelengths at 1550.0 and 1538. 0 nm, respectively, the 3 dB bandwidths of the control and idler wavelengths are about 61.5 nm for the converted RZ idler and 89 nm for the converted RZ control. Furthermore, the conversion efficiency fluctuation of the converted RZ signal is always kept less than 2.2 dB during the tunable operation of the control. When the control wavelength is set at 1555.0 nm and the sum-frequency wavelength is kept at 772.0 nm, the idler wavelength is about 1533.2 nm, as shown in Fig. 6(b), the signal and pump wavelengths can be also tuned in a wide wavelength range of 62.5 nm for the converted RZ idler, 78 nm for the converted RZ control, and 116 nm for the converted RZ signal. Therefore, flexible NRZ-to-RZ format conversion with great tunability can be performed with the proposed scheme.

 

Fig. 5. Dependence of (a) duty cycle, pulse width ratio and (b) Q-factor, extinction ratio on the pump pulse width for the converted RZ idler, signal and control.

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Fig. 6. Dependence of conversion efficiency on (a) control wavelength, idler wavelength and (b) signal wavelength, pump wavelength for the converted RZ idler, signal and control.

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4. Conclusion

A novel all-optical NRZ-to-RZ format conversion scheme at 40 Gbit/s is proposed and numerically simulated by use of SFG+DFG in a PPLN waveguide, which is inserted into a Sagnac interferometer structure. The optical spectra and eye diagrams show the successful implementation of simultaneous single-to-triple channel NRZ-to-RZ format conversion. The conversion efficiency, duty cycle, pulse width ratio, Q-factor and extinction ratio of the converted RZ are calculated. It is attractive that tunable operation can be readily realized with great flexibility. With further improvement, single-to-multiple channel (multicasting) NRZ-to-RZ format conversion will be investigated by employing multiple continuous-wave controls.