Wideband Simultaneous Wavelength Conversion of Multiple WDM Channels Using Silicon-Rich Nitride Waveguide

The triple-band (S+C+L) transmission system using only C-band transceivers and all-optical wavelength conversions (AOWCs) without S- and L-band optical transceivers have been proposed. Although an AOWC employs highly nonlinear fibers, it is not applicable to photonic integrated circuits (PICs). For a device with successful wavelength conversion, a silicon-rich nitride (SRN) waveguide provides superior performance, as it is applicable to PIC and facilitates a higher Kerr nonlinearity than conventional stoichiometric silicon nitride waveguides. Thus, in this study, we propose an all-optical simultaneous wavelength conversion method that can be cost-effectively fabricated on a PIC based on four-wave mixing in SRN waveguides. Following an explanation regarding the design of an SRN waveguide for wideband AOWC, the successful operation of a double-stage AOWC of 64-channel 64-Gb/s QPSK signals between the C+L bands and the S-band is demonstrated, which is useful for wideband transmission systems.


I. INTRODUCTION
T HE rapid increase in Internet traffic following the COVID-19 pandemic has resulted in an increased demand for high-capacity optical communication networks. Currently, wavelength-division multiplexing (WDM) technology is applied to optical communication networks to realize the high-capacity transmission of multi-wavelength channels over a single optical fiber. As a technology for future high-capacity communications, ultra-wideband transmission systems, including the conventional C-band and S-and L-band transmission, has been proposed [1]. An experimental demonstration of S+C+L band transmission of 115 Tb/s with 250 wavelength channels over 100 km has been reported [2]. Several studies have been conducted on broadband amplifiers for ultra-wideband transmission systems, such as combining Raman amplifiers with wideband semiconductor optical amplifiers [3]. However, the development and distribution of transmitters and receivers for new wavelength bands, such as the S-band, cannot be considered for realizing low-cost flexible optical transmission systems.
Recently, a triple-band (S+C+L band) transmission system using only C-band transmitters/receivers and all-optical wavelength conversions (AOWCs) was proposed [4], as shown in Fig. 1. In related studies [4], [5], four-wave mixing (FWM) in highly nonlinear fibers (HNLFs) was employed for the simultaneous AOWC technology. However, HNLFs are not applicable to photonic integrated circuits (PICs), and may result in issues of footprint and function integration in the future. Owing to the increasingly widespread use of next-generation optical networks using multi-core fiber-based space-division multiplexing, optical nodes and transmitters/receivers that accommodate a multitude of low-cost optical integrated AOWCs are required. Various device materials have been investigated for use as nonlinear media that can be integrated into PICs. To realize a highly efficient AOWC, highly efficient nonlinear effects in the materials are required. III-V compound semiconductors [6], [7] and periodically poled lithium niobate [8], [9], can provide the required highly efficient nonlinear effects; however, further improvements in the cost and manufacturing process for mass production are required. In recent years, silicon and silicon nitride (SiN) waveguides based on silicon photonics technology, which are employed in CMOS semiconductor platforms to produce low-cost PICs, have attracted attention as promising devices for optical communication [10]. However, although Si waveguides provide highly nonlinear parameters, the input light power is limited by two-photon absorption in the communication This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ wavelength band. On the other hand, SiN waveguides have low nonlinear parameters and inefficient nonlinear optical effects, which requires special structures, such as resonant structures and spiral-shaped waveguide. To address this issue, several studies on prototype Si-rich nitride (SRN) waveguides with higher silicon ratios have been reported [11], [12]. SRN has a higher refractive index and larger nonlinear parameter than SiN, and its bandgap is wider than that of Si. Thus, it can suppress undesired two-photon absorption (TPA) in the communication wavelength band. Although SRN has been actively studied as a new material for optical communication devices, studies on its application to optical communication systems are scarce. For example, the wavelength conversions of continuous-wave light using FWM [13] and return-to-zero on-off keying signals using cross-phase modulation [14] have been reported. There have been no reports on the applicability of SRN waveguides for the wavelength conversion of multiple WDM channels.
In this paper, we propose an all-optical simultaneous wavelength conversion method that can be cost-effectively fabricated on a PIC based on FWM in SRN waveguides. The design of the SRN waveguide for the wavelength converter and the feasibility of the proposed AOWC method are demonstrated via numerical simulations. As an extension of their extant research [15], we describe the SRN waveguide design method in detail for the proposed AOWC along with theoretical and numerical investigations of the basic characteristics. Although the number of wavelength channels was eight in [15], we increased it to investigate the potential performance of wideband simultaneous wavelength conversion and limiting factor for the channel number. In addition, a double-stage AOWC operation is examined for applicability to wideband transmission systems. From the simulation results, we demonstrate that suitable waveguide characteristics for wideband wavelength conversion can be obtained when the core size of the SRN waveguide is 0.51 μm × 0.51 μm. Furthermore, a successful double-stage AOWC of 64-channel × 64-Gb/s quadrature phase-shift keying (QPSK) signals using SRN waveguides with a power penalty <1.4 dB for an S+C+L wideband transmission system was achieved.
The remainder of this paper is organized as follows. Section II describes the design of the SRN waveguide based on the waveguide mode analysis simulation. Section III presents the simulation results of AOWC operation for multichannel 32-GBd QPSK signals. Finally, Section IV presents the major conclusions of this study.

A. Wavelength Conversion Operation
We used degenerate FWMs in SRN waveguides for wavelength conversion. Fig. 2 shows an overview of wavelength conversion. When a signal light of frequency ω s and pump light of frequency ω p are launched into the SRN waveguide, an idler light of frequency ω i (= 2ω p − ω s ) is obtained at the SRN waveguide output. The idler light is the phase-conjugate light of the signal light, which can be regarded as a wavelength-converted signal. We assume that the behavior of light in an SRN waveguide is described by the nonlinear Schrödinger equation [16], [17]. When the pump light power is sufficiently larger than the signal light power, and the optical loss in the waveguide is sufficiently small, the idler light output E i (L) is expressed as where E s is the input signal light, P is the input pump light power, γ and L denote the nonlinear parameter and length of the waveguide, respectively. θ denotes the phase that depends on the phase of the input pump light and idler light propagation.
where Δω = ω p − ω s = ω i − ω p and ω 0 is the center frequency. Based on (1)- (3), to obtain high wavelength-converted output power (idler light output power), high nonlinear parameter γ is required. To achieve idler optical output power over a wide bandwidth, the phase-matching condition should be satisfied. In other words, group velocity dispersion (GVD) β 2 and third-order dispersion (TOD) β 3 must be brought close to zero.

B. Waveguide Configuration
In this study, we consider a buried rectangular optical waveguide consisting of an SRN core and silicon dioxide (SiO 2 ) cladding. There are several studies on the fabrication of the SRN based on chemical vapor deposition (CVD), such as inductively coupled plasma CVD (ICP-CVD), plasma-enhanced CVD (PECVD), and low-pressure CVD (LPCVD) [11], [12], [13], [14], [18]. Similar to the growth of stoichiometric silicon nitride (Si 3 N 4 ) films, SRN film growth has been explored with the use of various gas mixtures, including SiH 4 with NH 3 , SiH 4 with N 2 , and dichlorosilane with NH 3 . The film composition and optical properties can be controlled by varying the process conditions, for example, gas ratio, temperature, and radio frequency (RF) power of the plasma source. On the other hand, the process must be designed to reduce the N-H bonds that induce propagation loss at telecommunication wavelengths. Considering Kramers-Kronig and Miller's rule, the Kerr nonlinear refractive index n 2 increases and the bandgap energy decreases as the refractive index increases, namely, the ratio of Si:N increases. However, SRN with a considerably high refractive index and too-low bandgap energy suffers from the TPA effect at telecommunication wavelengths. Fabrication at the highest Si:N ratio of 7:3 with a bandgap of 2.1 eV that avoids the TPA was reported [13], [18]. In this paper, the composition ratio of SRN was set to Si 7 N 3 , and it was assumed to be a compound of amorphous Si and stoichiometric Si 3 N 4 in the ratio of 19:21. The refractive indices of Si and Si 3 N 4 were defined as n Si (ω) and n Si 3 N 4 (ω), respectively, which were calculated using the Sellmeier equations [19], [20]. Subsequently, the refractive index of SRN n Si 7 N 3 (ω) was calculated as follows: Based on the calculations, the refractive indices of the SRN and the cladding at a wavelength of 1530 nm were 2.70 and 1.44, respectively.

C. Mode Analysis
To design a suitable waveguide dimension for AOWC, we performed a mode analysis of the SRN waveguide using the point matching method [21], [22] described in Appendix 1. Because of the large difference in the refractive index between the core and cladding of the SRN waveguides, the weak-guidance approximation cannot be used to calculate the effective mode area. Consequently, the effective mode area A eff and nonlinear parameter γ can be calculated using the following equations [23]: where Z 0 is the characteristic impedance in vacuum, n core (ω) is the refractive index of the core, and c is the speed of light. The Kerr nonlinear refractive index n 2 of the SRN was considered as 2.8 × 10 −13 cm 2 /W [13]. Fig. 3 shows the calculated results for GVD parameter β 2 , TOD parameter β 3 , and nonlinear parameter γ of a quasi-TE  Table I. Three-color graphs indicate the waveguide parameters for different aspect ratios. In this study, we used an aspect ratio of 1:1 to obtain polarization independence. When the core width w = 0.51 μm, β 2 is approximately 0 and γ = 435 W −1 /m is obtained. Even with w = 1.14 μm, we obtain β 2 of 0; however, γ reduces to 154 W −1 /m, which decreases the wavelength conversion efficiency. Therefore, in this study, the SRN waveguides were employed with core sizes 0.51 μm × 0.51 μm for AOWC simulations. Further, the propagation loss was set to 4.5 dB/cm [13], and the waveguide length was set to 1.1 cm to obtain the maximum output power under these conditions.

A. Simulation Model
We investigated the applicability of an SRN-waveguide-based AOWC in wideband transmission systems. Fig. 4 shows the simulation model. We generated 1-128 channels × 32-GBd QPSK signals using a random bit sequence with a length of 32768 symbols. The QPSK signal was wavelength-multiplexed (1-128 channels) over a wavelength range in the C and L bands with a wavelength spacing of 37.5 GHz. Further, the input signal power per wavelength channel in the AOWC was set to −3 to +9 dBm. We assume that the fiber-waveguide coupling loss was 7.0 dB per facet [13], [17]. A pump light with an input power of 17 dBm at a wavelength of 1530 nm was launched into the SRN waveguide along with the QPSK signal. We assumed that the complex envelope amplitude of the electric field E(z, t) in the SRN waveguide satisfied the following nonlinear Schrödinger where z is the propagation distance, t is the time, and α is the propagation loss. The output optical field was calculated using the split-step Fourier method [16]. The WDM signal was converted from the C+L band to the S band by AOWC. Subsequently, the wavelength-converted signal light at the waveguide output was extracted using an optical bandpass filter, and then amplified using an optical amplifier with a noise figure of 8 dB.
We assumed that an ultra-wideband semiconductor optical amplifier (SOA) was used for the optical amplification of the S-band converted signal [24], [25]. Ultra-wideband SOA can amplify the high-speed-modulated S-band signal, for example, with NF < 7 dB for the full S-band [24] and NF < 8 dB for 1508-1611 nm [25]. In this simulation, the waveform distortion in SOA was not considered except amplified spontaneous emission (ASE) noise.
The wavelength-converted signal light was then received by the optical coherent receiver and demodulated. Moreover, to prevent inter-symbol interference, the signal was passed through the RRC filter after QPSK modulation and before demodulation, with roll-off factor and tap length of 0.01 and 1000, respectively. First, we calculate the wavelength dependence of the output power of the wavelength-converted signal for a single-channel QPSK signal. Subsequently, the maximum number of WDM channels for wavelength conversion in first-stage AOWC was investigated. Finally, an operation including the second-stage AOWC that converts back to the C+L band was demonstrated with bit error rate (BER) results. Fig. 5 shows the waveguide length dependence on the output power of converted signal after a first-stage AOWC for a single-channel QPSK signal, input signal power of 0 dBm, and core width w = 0.51 μm. Although the idler (converted signal) light grew through the propagation, the output power decreased with an increase in the waveguide length L owing to the propagation loss in the SRN waveguide for L > 1.1 cm. The maximum output power balancing the idler light growth and the propagation loss was achieved for a length of approximately  1.1 cm. Hereafter, in this paper, the waveguide length L is set to 1.1 cm. Fig. 6 shows the power diagram from the input signal to the output converted signal. The input signal to the SRN waveguide was attenuated owing to the fiber-to-waveguide loss of 7 dB. In the SRN waveguide, although the input signal light decayed by the propagation loss of 4.5 dB/cm, the idler (converted signal) light grew owing to the FWM effect. At the output, the converted signal was attenuated by the waveguide-to-fiber loss of 7 dB. Fig. 7 shows the wavelength dependence of the idler light output power after a first-stage AOWC for a single-channel QPSK signal, input signal power of 0 dBm, and various waveguide dimensions. We varied the wavelength of the QPSK signal light in the range 1530-1570 nm. As described in (2) and (3), the wavelength (frequency) dependence of the parametric gain g depends largely on the GVD parameter β 2 . Therefore, perfect-zero dispersion characteristics lead to flat gain spectrum. For β 2 = ±0.4 ps 2 /m, the output power of the idler light decreased rapidly with increase in the wavelength difference between the pump and the signal light. In contrast, a flat output optical power characteristic of −35.9 dBm was obtained when β 2 = ±0 ps 2 /m and the core width w of 0.51 μm. Although a flat output spectrum was obtained for w = 1.14 μm, the output power was reduced to −44.9 dBm owing to the low nonlinear parameter. Thus, the SRN waveguide with core width w = 0.51 μm and β 2 = ±0 ps 2 /m facilitated broadband wavelength conversion between different wavelength bands. In mass production, the core width slightly shifts from the target (w = 0.51 μm), owing to dimensional variability. When the core width was shifted ±0.01 μm, the differences in the output power between the wavelengths of 1490 and 1528 nm were 0.2 (w = 0.52 μm) and 1.6 dB (w = 0.50 μm), respectively. Hereafter, the core width w is set to 0.51 μm, unless otherwise noted. Fig. 8 shows the spectra after first-stage AOWC for the input optical power of 0 dBm with 64 and 128 WDM channels. In case of 64 WDM channels, it is evident that a flat WDM signal spectrum is obtained after the wavelength conversion by optimizing the waveguide size. However, for 128 channels, interference between the pump light component spread by the FWM and conversion signal was observed. Fig. 9 shows the spectra for the above simulation when only the β 3 value is changed. The results show that the spread of the pump light component depends on |β 3 | and the propagation distance z. Compared with Fig. 8, the interference effect of the pump light component in Fig. 9(c) becomes smaller. This study focused on β 2 for the waveguide design; however, it is expected that tuning β 3 will also enable the conversion of multiple wavelengths. Fig. 10 shows the error vector magnitude (EVM) of the WDM signal after the wavelength conversion and optical amplification while varying the number of WDM channels and input signal power. When the input power was 6 and 9 dBm, EVM increased with the number of WDM channels owing to the cascade FWM among the WDM channels. Moreover, when the input signal power was −3 dBm, the EVM increased even in single-channel operation, owing to the effect of spontaneous emission lights    amplified in the optical amplifier. For 64-channel operation, the optimum input power was 3 dBm, with an average EVM of 16.7%. Inter-channel crosstalk due to FWM resulted in a slight increase in EVM at the center channel. However, for the 128channel operation, the signal quality was significantly degraded owing to the interference, as shown in Fig. 8. Fig. 11 shows the EVM characteristics for each channel in 64-channel operation when the input signal powers were 3 and 6 dBm. It is evident that the influence of the FWM increases, and the cascade FWM effect is emphasized around the center channel for an input power of 6 dBm. Thus, based on the results, we have demonstrated that 64-channel simultaneous wavelength conversion using SRN waveguides is feasible through the appropriate setting of the waveguide dimensions and input signal light power. Fig. 12 shows the BER characteristics before wavelength conversion and after double-stage AOWC. The input signal light power was set to 3 dBm and the number of WDM channels was set to 64. The BER characteristics of the representative channels for β 2 = −0.4 ps 2 /m (w = 0.57 μm) are shown in Fig. 12 for comparison. The BER characteristics of the QPSK signal after the double-stage wavelength conversion at an input signal power of 3 dBm for β 2 = 0 ps 2 /m (w = 0.51 μm) were similar to those of the signal before conversion. When β 2 = −0.4 ps 2 /m, the farther the signal light was from the pump light, the worse was the conversion efficiency, resulting in critical BER degradation in both the center (ch. 31-33) and outer channels (ch. 62-64, BER > 0.1). For a signal power of 3 dBm and β 2 of 0 ps 2 /m, the optical signal-to-noise ratio penalty owing to the double-stage AOWC at the input was less than 1.4 dB, assuming the use of a hard decision forward error correction with an overhead of 7 % [26]. Thus, successful wavelength conversion of 64×64 Gb/s QPSK signals using a double-stage AOWC was demonstrated.

IV. CONCLUSION
We proposed an all-optical simultaneous wavelength conversion method using an SRN waveguide. First, we performed a mode analysis of the SRN waveguide and showed that suitable parameters of the AOWC, such as the GVD parameters β 2 = 0 ps 2 /m and nonlinear parameters γ = 435 W −1 /m, were obtained when the core size was 0.51 μm × 0.51 μm. Consequently, using the designed SRN waveguide, a wavelength conversion simulation of a 64-channel QPSK signal was performed at an optimized input-signal power of 3 dBm. For 64 channel operation, the power penalty of the double-stage AOWC could be maintained below 1.4 dB. Thus, the successful operation of the proposed AOWC for 64-channel×64-Gb/s QPSK signals between the C+L-and S-bands was demonstrated.

IV. APPENDIX
The direction of propagation is along the z-axis, and the waveguide cross-section is the r-θ plane. The electromagnetic field components in the z-axis direction at points (r, θ) in each region are represented by a linear combination of Bessel functions J n (·) or modified Bessel functions of the second kind, K n (·) as expressed in the following equation: E z, core = ∞ n=0 a n J n (hr) sin (nθ + φ n ) exp {i (βz − ωt)} where a n , b n , c n , and d n are the expansion coefficients determined by the boundary conditions, h and p are propagation constants in the cross-sectional direction, φ n and ψ n are arbitrary phase angles, and β is the propagation constant in the z-axis direction. Subsequently, the electromagnetic field problem is approximately solved by considering a finite number of matching points on the core and cladding boundaries and satisfying the boundary conditions at these points.