1. Introduction

All-optical regeneration technology can effectively improve the communication quality of optical network by improving the quality of the degraded signal [1]. In future transmission networks, amplified spontaneous emission noise (ASE), loss, group velocity dispersion (GVD), polarization mode dispersion (PMD) and nonlinear effects in long-distance transmission will cause significant signal degradation as the data rate increases. In order to regenerate signals directly in the optical domain, it is necessary to develop high-speed all-optical regeneration devices. At the same time, with the comprehensive arrival of the “Internet Plus” era, the amount of network data has exploded, and the expansion of optical communication capacity has become the focus of attention. The demand for information capacity places high demands on network nodes and signal processing technology. Spatial mode multiplexing (SDM) is one of the most effective and important ways to increase the capacity of optical communications. Therefore, it is necessary to study all-optical regeneration of multimode signals.

Various single-mode all-optical signal regeneration schemes based on fast Kerr nonlinearity have been demonstrated, such as self-phase modulation, cross-phase modulation, cross-gain modulation and four-wave mixing (FWM) [2–6]. Among them, FWM is one of the most promising nonlinear effects for high speed and high capacity all-optical regeneration due to its advantages, such as rate transparency and format transparency [7–9]. In order to achieve high-quality multimode FWM all-optical signal regeneration, the core problem lies in nonlinear devices with low loss, strong FWM effect, and small mode crosstalk [10–12]. In various nonlinear devices used for all-optical regeneration, SOA-based solutions are usually difficult to achieve high-speed regeneration, mainly due to the limitation of pattern effects and small conversion bandwidth [2]. Fibre-based systems require long fiber lengths and large volumes [4]. Various nonlinear materials such as silicon-rich nitride, amorphous silicon, AlGaAs, and InGaP have been actively explored and have demonstrated significant advancements [13–21]. Silicon waveguide has the advantages of high nonlinear coefficient, wide band width, mature CMOS manufacturing process, etc. Silicon waveguide has become one of the most potential solutions. The low loss and strong FWM effect of silicon-based waveguides have been extensively studied currently [22–29]. The design of an ultra-thin waveguide reported with very low loss is unsuitable for this regenerator, because the light interacts weakly with the waveguide, resulting in low nonlinearity [25]. At the same time, the reverse bias PIN junction waveguide is reported to reduce the nonlinear loss and enhance FWM effect [27], but the manufacturing process is cumbersome with high cost, which is not conducive to practical applications. Moreover, according to our previous experiments, the problem of doping area technology may increase inter mode crosstalk. Inter-modal FWM is a good scheme for all-optical wavelength conversion, which is not suitable for simultaneous regeneration of multiple modes due to the low conversion efficiency [30–32]. A two-mode division multiplexing circuit has been reported, but its FWM conversion efficiency is too low for regeneration [28]. Therefore, the realization of multimode waveguide regeneration with low-loss and high FWM conversion efficiency is very challenging.

In this paper, we propose and experimentally demonstrate the 40 Gb/s all-optical regeneration of non-return to zero on-off keying (NRZ-OOK) signal in TE0 and TE1 modes via FWM in the low-loss silicon-based nanowaveguide. By optimizing the parameters of the waveguide section to reduce transmission loss and enhance the FWM conversion efficiency of two modes, the transmission loss of the silicon waveguide is 0.3 dB/cm, and FWM conversion efficiency of the multimode regenerator is as high as -9.6 dB (TE0) and -13.0 dB (TE1). The crosstalk between modes is reduced to less than -20 dB by introducing Euler bending. Two modes exhibit an enhanced extinction ratio (ER) of approximately 6 dB following sequential regeneration. This silicon-based all-optical regenerator provides photonic nodes with advanced functions for next-generation large-capacity optical networks, and has broad application prospects in all-optical signal processing (AOSP) networks.

2. Design of low-loss multimode waveguide device

As shown in Fig. 1(a), the low-loss multimode regenerator mainly includes low-loss nonlinear waveguides and mode multiplexers. The low-loss nonlinear waveguide is the medium in which the FWM effect occurs and the mode multiplexer is designed to convert light from a low-order mode to a higher-order mode.

 

Fig. 1. (a) Schematic diagram of the multimode waveguide structure. The device footprint is approximately 4.7 mm × 0.9 mm when the multimode waveguide is 9.5 cm long. (b) Diagram of waveguide bending with constant radius of curvature and evolution of the radius of curvature, i.e. Euler bending. (c-d) Simulated comparison results of TE1 mode transmission in the circular waveguide and Euler curved waveguide. (e) Simulation result of TE1 mode multiplexing.

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The multimode regenerator is required to have low waveguide loss and high FWM conversion efficiency. The cross-section of the low-loss nonlinear waveguide is shown in Fig. 1(a). On the one hand, compared with the strip waveguide, the ridge waveguide has less linear transmission loss, because of the smaller overlap between the optical field and the side wall. On the other hand, the scattering loss of the ridge waveguide mainly depends on the width of waveguide and the height of the slab. With the increase of waveguide width, the transmission scattering loss decreases gradually. With the increase of the slab height, the equivalent refractive index increases, and the scattering coefficient decreases gradually. To achieve low transmission loss, the ridge waveguide needs to have a larger width and a higher slab height, that is, a larger waveguide cross-section. With lower loss, higher optical power is involved in the FWM process, which potentially contributes to higher FWM efficiency. In addition, the main factors affecting the conversion efficiency of waveguide FWM are dispersion and nonlinear effects. The nonlinear coefficient $\gamma = \frac{{\mathrm{2\pi }{n_2}}}{{\lambda {A_{eff}}}}$, where n₂ is the nonlinear refractive index coefficient of the material, $\lambda $ is the central wavelength of light, ${A_{eff}}$ is the effective mode field area, and a large waveguide cross-section will lead to a decrease in the nonlinear coefficient. Therefore, it is necessary to make a trade-off between loss and nonlinear coefficient when designing waveguide cross-section.

Waveguide length is also a factor affecting the conversion efficiency and bandwidth of FWM. On the one hand, based on the expression of maximum conversion efficiency of FWM: $CE = {\gamma ^2}L_{eff}^2P_p^2{e^{ - \alpha L}}$, where L is the length of the waveguide, ${L_{eff}} = ({1 - {e^{ - \alpha L}}} )/\alpha $ is the effective length, $\alpha $ is the waveguide transmission loss, $\gamma $ is the nonlinear coefficient and ${P_p}$ is the pump light power [33], to introduce higher nonlinear effects, it is necessary to design a longer waveguide structure to achieve higher conversion efficiency. On the other hand, the FWM conversion bandwidth $\Delta \omega = 2\sqrt {\frac{\pi }{{L{\beta _2}}}} $, where ${\beta _2}$ is the second-order dispersion at the pump wavelength [34], and the increase in waveguide length will lead to a decrease in conversion bandwidth, so dispersion management is required to make the waveguide have sufficient bandwidth. In order to take these factors into account, a ridge waveguide with a width of 2000nm, a height of 70 nm and a length of 9.5 cm is designed. At the wavelength of 1550 nm, the ${\beta _2}$ of TE0 mode and TE1 mode is 1.727 ps²/m and 1.191 ps²/m, respectively.

In order to process multimode signals without crosstalk in low-loss waveguides, the bend of waveguides should be designed to avoid crosstalk between modes. Figure 1(b-e) show the simulation results obtained by using Lumerical FDTD software. Figure 1(c) shows an ordinary circular waveguide with large transmission loss and mode crosstalk. As shown in Fig. 1(d), Euler curved waveguide with gradual curvature is designed, and its curvature is defined as: $\frac{1}{R} = \frac{L}{{{A^2}}} + \frac{1}{{{R_{max}}}}$, where A is a constant given by $A = {[L/({1/{R_{min}} - 1/{R_{max}}} )]^{1/2}}$, L is the length of the curve, ${R_{max}}$ and ${R_{min}}$ are the maximum and minimum radius of curvature on the curve, respectively [35–36]. In order to take into account the small size of the waveguide and the improvement of crosstalk, it is necessary to carefully design the waveguide curvature. After changing to the Euler bending waveguide, the light of each mode is incident on the waveguide respectively. As the simulation result shows in Fig. 1(d), the light field obtained at the output is significantly improved compared with that in Fig. 1(c), which successfully solves the transmission loss and mode crosstalk problems of higher-order modes in the bending waveguide.

The mode multiplexer is an important part of multimode system [37–39]. We design a mode multiplexer based on a directional coupler to realize the conversion of the optical field from TE0 mode to TE1 mode. Optical signals of different modes are multiplexed through different ports, transmitted through multimode waveguides, and then demultiplexed to corresponding output ports. Using the time domain finite difference simulation software, the waveguide width of the coupling area is designed according to the phase matching conditions between different modes, and the structure of the directional coupler is simulated considering the influence of process errors. The width of the single-mode narrow waveguide part in the coupling region of the mode multiplexer is 600 nm, and the width of the wide waveguide part is 1300 nm. The main part of the multimode waveguide is 2000nm wide waveguide. When the coupling distance is 200 nm, the coupling coefficient is calculated, and the excitation from TE0 mode to TE1 mode is maximum when the coupling length is 41 µm. The simulation results in Fig. 1(e) show the light field of this set of parameters.

3. Principle of multimode all-optical regeneration based on FWM

The low-loss multimode waveguide combined with the mode multiplexer can achieve multimode signal regeneration. As mentioned above, The mode multiplexer multiplexes the optical signal into different modes. They are both on the fundamental mode of a single-mode waveguide before the multiplexer. FWM effect occurs between continuous light and original signal light in the same mode in the multimode waveguide, and idler light corresponding to the mode is generated, that is, regenerated signal. Due to the phase mismatch between different modes of light, its FWM processes can be ignored, and the design of Euler bending can effectively avoid crosstalk between modes. Finally, different modes of light are demultiplexed to corresponding output ports, respectively, thus completing the parameter process of multiple modes simultaneously.

The principle of multimode all-optical regeneration based on FWM in silicon waveguide is shown in Fig. 2(a). Input a continuous light whose frequency and field amplitude are ${\omega _1}$ and ${E_1}$, respectively, and an original signal light whose frequency and field amplitude are ${\omega _2}$ and ${E_2}$, respectively, where the original signal acts as the pump light, and a degenerate FWM effect occurs between the two beams. Idler frequency light is generated, that is, the regenerated signal, whose frequency is ${\omega _3} = 2{\omega _2} - {\omega _1}$ and field amplitude is expressed as ${E_3} = C{\gamma ^2}{E_1}E_2^2$, where C is a constant, γ is the nonlinear parameter of the silicon waveguide. It can be seen from the input power and output power curves of FWM regeneration process in Fig. 2(b), in the low power case, that is, when the “0”-level of the input signal is in the region to the left of point A, the “0”-level noise can be compressed. In the high power case, the pump depletion of FWM and the free carrier absorption (FCA) effect of the silicon waveguide will lead to gain saturation, that is, the “1”-level of the input signal reaches the region to the right of point B, and the “1”-level noise can be compressed. As a result, the entire curve is S-shaped. When the regenerator works in the regenerative area between points A and B, ER of the original signal can be expressed as $E{R_2} = 10log\left( {\frac{{{{|{{E_{2\_1}}} |}^2}}}{{{{|{{E_{2\_0}}} |}^2}}}} \right)$, ER of the regenerated signal can be expressed as $E{R_3} = 10log\left( {\frac{{{{|{{E_{3\_1}}} |}^2}}}{{{{|{{E_{3\_0}}} |}^2}}}} \right)$, the subscripts “_1” and “_0” represent the “1”-level and “0”-level of the signal, respectively. Therefore, due to the quadratic transmission relationship of FWM, ER of the regenerated signal can be improved [27]. The regeneration principle of TE0 and TE1 modes is similar. The newly generated regenerated signal is output from the corresponding port of the multiplexer in TE1 mode, so as to achieve multimode multiplexing. Therefore, a reasonable selection of the original signal power makes the all-optical regenerator work in the regeneration area between points A and B, so as to achieve the promotion of the regenerated signal ER, obtain the best regeneration performance, and realize the multimode all-optical signal regeneration.

 

Fig. 2. The principle of all-optical regeneration using FWM. (a) Spectra of the original signal and regenerated signal distribution. (b) Diagram of nonlinear transfer curve of input power and output power. (c) The simulation curve between input power and output power considering TPA and FCA effects. The blue curve is the result of TE0 mode and the yellow curve is the result of TE1 mode.

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In order to analyze the influence of TPA and FCA on the multimode regeneration performance based on FWM, a theoretical model was established to discuss the change of idler optical power with the input pump power under different modes. Fixed the power of the continuous light, simulation results are shown in Fig. 2(c). When TPA and FCA effects are considered, the regeneration curves of both models are S-shaped. This section provides guidelines for subsequent experiments.

4. System experiment

4.1 High FWM conversion efficiency based on low-loss waveguide

The ridge multimode silicon waveguide is based on a 220 nm-SOI platform, coated with a silica layer of 2 μm thickness, and is manufactured on a standard 8-inch process platform at CUMEC in Chongqing, China. The experimental setup of FWM efficiency measurement is shown in Fig. 3(a). Laser1 generates continuous light with a wavelength of 1547 nm and enters the coupler through polarization controller (PC) as the signal light. Laser2 generates continuous light with a wavelength of 1550 nm and enters the coupler after passing through PC and erbium-doped fiber amplifier (EDFA) as pump light. The function of PC is to optimize the continuous optical polarization state to reduce the on-chip coupling loss and transmission loss. The silicon chip is vertically coupled to the optical fiber array by a grating coupler, which is optimized for TE mode. Here we use 400 um short waveguide to measure the insertion loss. By adjusting the angle and position of the optical fiber, the minimum loss of the incoming light is about 10 dB at 1550 nm, that is, the loss of the grating coupler is about 10 dB (a pair), with a 3 dB bandwidth of about 45 nm. The two optical channels are coupled to a port on the chip to generate FWM in a low-loss waveguide in TE0 mode, resulting in an idler beam of light at wavelength 1553 nm. The output spectrum is measured by an optical spectrum analyzer (OSA). The FWM conversion efficiency of a waveguide is defined as the ratio of the idler optical power at the output to the continuous optical power at the output. Figure 3(b) shows the FWM spectrum of TE0 mode in a 9.5 cm silicon waveguide with a conversion efficiency of -9.6 dB.

 

Fig. 3. (a) Experimental setup of the FWM performance measurement. PC, polarization controller; EDFA, erbium-doped fiber amplifier; OSA, optical spectrum analyzer. (b) Measured spectrum of FWM in TE0 mode under small signal condition. (c) Measured spectrum of the mode multiplexer crosstalk.

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Similarly, when the two light paths are coupled to another port of the chip, FWM will occur in the low loss waveguide in TE1 mode. To evaluate the performance characteristics of the multimode waveguide mode multiplexer, we utilize an apparatus composed solely of a mode mux/demux pair. The broad-spectrum light source is incident at the input port of TE0 and TE1 respectively, and the light in TE0 mode is directly output by the corresponding output port. The TE1 mode light passes through the mode multiplexer and demultiplexer, and is output from the TE1 output port. Figure 3(c) shows the transmission response of different output ports when the light incident at different ports. For instance, the blue curve labeled as TE0-TE0 represents the transmission when light is injected into the TE0 input port and collected from the TE0 output port. The crosstalk between different modes is less than -20 dB.

Figure 4(a) shows the FWM conversion efficiency of TE0 mode and TE1 mode at different pump powers in a 9.5 cm long, 2000nm wide waveguide. By adjusting the pump power, the conversion efficiency of TE0 mode and TE1 mode can reach -9.6 dB and -13.0 dB respectively. It can be seen that under the case of low power, the FWM conversion efficiency of the two modes fits well with the theoretical curve. Under the case of high on-chip optical power, the conversion efficiency tends to be saturated due to the presence of two-photon absorption (TPA) and FCA effects. The FWM conversion bandwidth diagram of the silicon waveguide is obtained by changing the operating wavelength of Laser1 with fixed input power unchanged. Figure 4(b) shows that the 3 dB bandwidth of TE0 mode and TE1 mode reaches 10.6 nm and 12.0 nm, respectively, which agrees well with numerical simulations. Experiments are carried out on silicon waveguides with different lengths and widths, and the experimental results are shown in Fig. 4(c-d). Obviously, for waveguides of the same width, as the length of the waveguide increases, the conversion efficiency of all spatial modes increases. For a waveguide with a width of 1412 nm, when the waveguide length increases from 1 cm to 8 cm, the FWM efficiency of TE0 and TE1 can be improved by 8.3 dB and 12.0 dB, respectively. As shown in the Fig. 4(d), for the TE0 mode of a waveguide with a width of 1412 nm, the three points connected here are repeated tests on different waveguides with different lengths, and their losses are slightly different. Along with the increase in the width of the waveguide, the transmission loss per unit length is reduced. Compared with the waveguide with a width of 1412 nm, the loss of TE0 and TE1 of the waveguide with a width of 2000nm can be reduced by about 0.12 dB/cm and 0.35 dB/cm, respectively.

 

Fig. 4. (a) Experimental results of waveguide conversion efficiency under different pump optical power in TE0 and TE1 mode. The blue and yellow lines are the simulation results of conversion efficiency in TE0 and TE1 modes, and the losses are 0.3 dB/cm and 0.42 dB/cm, respectively. (b) Experimental results of conversion bandwidth in TE0 mode and TE1 mode. The curve represents the simulation result of bandwidth. (c) Experimental results of the relationship between waveguide conversion efficiency and waveguide length. The different colored dots indicate waveguides of width 1412 nm, 1793nm and 2000nm, respectively. (d) Experimental results of the relationship between waveguide loss and waveguide width.

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The performance assessment reveals that the TE0 mode benefits from lower propagation loss and a higher nonlinear coefficient, which contribute to a superior conversion efficiency. On the other hand, the TE1 mode, affected by the waveguide's dispersion characteristics, offers an extended conversion bandwidth. It can be seen that when the waveguide is 9.5 cm long and 2000nm wide, the waveguide loss is the smallest and the FWM efficiency is the highest.

4.2 Regeneration experiment of all-optical regenerator

The experimental setup of all-optical regeneration based on low-loss silicon-based nanowaveguide is shown in Fig. 5(a). Laser1 is used as a continuous light, the wavelength is set to 1549.2 nm. After passing through the PC, the continuous light is amplified by EDFA1. Laser2 is used as the pump light, the wavelength is set at 1550.8 nm, and is modulated by the Mach-Zehnder modulator (MZM) to generate 40 Gb/s NRZ-OOK signal. After passing through the PC, the NRZ-OOK signal is amplified by EDFA2. Two beams of light are combined through the coupler and incident on the silicon-based waveguide, and then a light is separated from the beam splitter and enters the spectrum analyzer OSA for the observation of FWM effect. The rest of the light is pre-amplified by EDFA3 and filtered by tunable bandpass filter (TBPF) to obtain idler frequency light, which is the regenerated data signal, and its wavelength is 1552.4 nm. Finally, eye diagram observation and signal quality analysis are performed by an oscilloscope (OSC), and bit error rate (BER) measurement is performed by bit error rate tester (BERT). It is worth mentioning that the powers of the continuous light and pump light are set to maximize the ER of the regenerated signal. The ER of the regenerated signal is measured by the OSC to determine the optimal power levels. When the powers of the continuous light and pump light exceeded 15 dBm and 20 dBm, respectively, there is no significant improvement in the ER of regenerated signal. The continuous optical power is set at 15 dBm and the pump optical power is set at 20 dBm. Figure 5(b-c) shows the FWM spectrum, with a conversion efficiency of -16.1 dB for TE0 mode and -20.7 dB for TE1 mode. Compared with the conversion efficiency in Fig. 3(b), the reduction in conversion efficiency is mainly due to the decrease in the peak power of the modulated signal and the saturation effects induced by the increase in the power of continuous light. Note that this saturation effect is mainly caused by continuous light, which does not contribute to the “1”-level noise compression of signal regeneration.

 

Fig. 5. (a) Experimental setup of the all-optical regenerator in silicon waveguide. MZM, Mach-Zehnder modulator; BPG, bit pattern generators; TBPF, tunable bandpass filter; ATT, attenuator; OSC, oscilloscope; BERT, bit error rate tester. (b-c) Measured FWM spectra of all-optical regeneration in TE0 mode and TE1 mode.

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In order to analyze the regeneration performance of the all-optical regenerator based on the waveguide, the bias voltage of MZM is adjusted to obtain signals with different degrees of deterioration. It should be noted that here the regeneration experiments for the TE0 and TE1 modes are executed in a sequential manner due to the limitations of the experimental setup. As shown in Fig. 6(a) and Fig. 6(c), the grey curve is the original signal, while the blue and yellow curves correspond to the regenerated signals of TE0 and TE1 modes, respectively. EDFA3 and attenuator (ATT) are used to control the signal on the OSC to receive constant optical power. The measurement of the ER and the signal to noise ratio (SNR) is achieved directly by the OSC. It can be seen that with the decrease of bias voltage, the ER and the SNR of the original signal are gradually decreased. After the all-optical regenerator, compared with the original signals of different qualities, the ER of TE0 and TE1 mode regenerated signals is improved to a certain extent, while the SNR is decreased to a certain extent. Figure 6(b) shows the increase in ER of regenerated signals of TE0 and TE1 modes. It can be seen that when the original signal ER is between 6.6 dB to 12.5 dB, the increase in ER of regenerated signals of both modes is greater than 4 dB, and the regeneration effect is good. Meanwhile, as shown in Fig. 6(d), when the SNR of the original signal is less than 9.2 dB, the SNR of the regenerated signal suffers from less degradation. In conclusion, in order to further analyze the performance of the all-optical regenerator, the signal with ER of 8.7 dB and SNR of 7.5 dB is selected as the degraded signal.

 

Fig. 6. (a) (c) ER and SNR of the signal under different MZM bias voltages. (b) (d) The amount of ER and SNR change of the regenerated signal corresponding to different original signals. ΔER = ER_regenerated – ER_original, ΔSNR = SNR_regenerated - SNR_original.

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In order to evaluate the performance of the regenerator under different optical power conditions, the OSC receives signals of different powers by adjusting the EDFA3 and ATT. Figure 7 shows the eye diagrams of the degraded signals selected above and the regenerated signals of TE0 and TE1 modes for received power from -6 dBm to 0 dBm. It can be seen that, compared with the degraded signal, the eye diagram quality of the regenerated signal is significantly improved, the “0”-level noise is significantly reduced, and the regenerated signal ER is increased by above 5 dB. However, the signal input power is difficult to fully reach the ideal regeneration area in Fig. 2(b), which makes it difficult to improve the noise performance of the “1”-level.

 

Fig. 7. Eye diagrams and ER of degraded signals, regenerated signals in TE0 mode and TE1 mode of different optical power.

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The ER and SNR curves under different received optical power are shown in Fig. 8(a-b). Compared with the degraded signal (the green curve), the ER of the regenerated signal in TE0 and TE1 mode has a 5-6 dB improvement. The ER increase of TE0 mode regenerated signal can reach 5.85 dB. The ER increase of TE1 mode regenerated signal can reach 6.21 dB. When the recevied power of the OSC changes from -6 to 0 dBm, the SNR of the two modes varies within 1.5 dB.

 

Fig. 8. (a-b) ER and SNR curves of degraded signals, TE0 mode and TE1 mode regeneration signals at received power from -6 dBm to 0 dBm, which are given by green, blue and yellow curves, respectively.

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The BER of the original signal (the grey curve), degraded signal and the regenerated signal is measured as shown in Fig. 9. The curve slope change of the regenerative signal in the figure is caused by the different changes of the signal “1” and “0” level noise, which is the nonlinearity of the regeneration process [40–41]. The essence of this optical regeneration is to make the eye diagram open much wider, and when the signal power is low, the quality improvement caused by this opening effect is more important, and the overall quality of the signal is better. For TE0 mode regenerated signal, when the received power is less than -7.1 dBm, the signal quality is better than the original signal. As can be seen from the blue dashed line, BER below 10⁻⁷ is achieved when the received power is -4.3 dBm. When the optical power of the degraded signal is below -4.3 dBm, TE0 and TE1 mode regenerated signals obtain a notable regeneration effect. When the target BER is the hard decision forward error correction (HD-FEC) threshold of 3.8 × 10⁻³ [42], the receiver sensitivity is improved by 3.85 dB and 1.85 dB for TE0 and TE1 mode, respectively.

 

Fig. 9. BER curves of original signal, degraded signal, TE0 mode and TE1 mode regenerated signal under different received power, which are given by grey, green, blue and yellow curves, respectively.

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Multimode signal regeneration using FWM in the passive silicon waveguide chip bas been experimentally demonstrated. As shown in Table 1, most of the previous work was reported on single-mode signals using various nonlinear effects [2,3,4,23,27]. Comparing with other work, the transmission loss of our silicon waveguide devices is as low as 0.3 dB/cm; As a passive device, the FWM conversion efficiency of -9.6 dB is also high. In terms of all-optical regeneration, the proposed scheme has advantages in the number of regeneration modes, the improvement of ER and receiver sensitivity. It is noteworthy that the regeneration of the two modes in this study is performed sequentially. Looking forward, simultaneous regeneration of multiple modes may lead to more effective applications.

Table 1. Performance comparison of advanced all-optical regenerators at present.

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Besides, the geometric parameters of the waveguide in this scheme affect the waveguide loss, dispersion and nonlinear coefficient, and then affect the conversion efficiency and bandwidth of FWM, which requires careful design and trade-off. By optimizing the waveguide cross-section parameters, the loss of the multimode nonlinear waveguide can be further reduced, and the conversion efficiency and bandwidth of the waveguide can be better balanced, so that the multimode all-optical regenerator can meet different application scenarios. For example, the optimized design of dispersion engineering can be used to realize nonlinear waveguides with very large FWM conversion bandwidth [20]. In addition, the number of regenerator modes can be increased by the optimal design of the mode multiplexer considering the process tolerance, thus further expanding the all-optical communication capacity.

5. Conclusion

In summary, we have proposed and experimentally demonstrated all-optical regeneration operation of 40 Gb/s NRZ-OOK signals in two spatial modes by using the low-loss silicon-based multimode waveguide. The linear transmission loss of the multimode silicone-based waveguide is as low as 0.3 dB/cm, and the conversion efficiency of FWM is as high as -9.6 dB. The ERs of the regenerated signal carried by the TE0 and TE1 modes increase by 5.85 dB and 6.21 dB, respectively. The proposed silicon-based all-optical regenerator shows good regenerative performance and is expected to be used for all-optical signal regeneration of large-capacity AOSP systems in the near future.