# Cascaded Nonlinear-Optical Loop Mirror-Based All-Optical PAM Regenerator
## 4 Cascaded NOLM-Based Regeneration Scheme
To give a performance comparison we test the transmission results in an un-regenerative link, i.e., bypassing the regenerator in the inset of Figure 7. Figure 7 depicts the BER improvement achieved at every input SNR points, which confirms the regeneration behavior obtained by the proposed cascaded two-NOLMs subsystem. We observe a 2.69 dB SNR improvement at lg(BER) = -3, 1.69 dB higher than the conventional PAM-4 regenerator [12]. Figure 5: The schematic diagram of the PAM regeneration system. Figure 6: **(a)**The level distribution of input and output signal; **(b)** waveforms of PAM-4 signals before and after regeneration and **(c)** the relation curve between input SNR and NRR. By appropriately designing the structure parameters of two NOLMs in series, we can also obtain a PAM-8 regenerator with \(\rho=0.989\) and \(\rho=0.975\), whose optimal WPs correspond to the eighth level (first stage) and the fourth level (second stage), respectively. The inter-stage matching amplifier has a gain of 1.62 dB. To reduce the operational power we double the nonlinear coefficient \(\gamma\) compared to the former discussion. Figure 8a shows the simulated waveforms of the PAM-8 signals before and after regeneration, in which the input SNR is 20.86 dB. Numerical simulation shows that the Q-factor improvement is up to 21.18 dB and the noise over all eight levels can be suppressed to certain extent, with NRRs of 15.22 dB, 19.57 dB, 25.56 dB, 31.22 dB, 28.27 dB, 25.21 dB, 23.19 dB, and 21.51 dB, respectively. The transmission system of PAM-8 with and without regenerator is also tested as shown in Figure 8b. The BER results in the cascaded-NOLM transmission link are significantly lower than the un-regenerative case, achieving over 3.04 dB improvement. Comparing with the PAM-4 case, the better transmission performance is obtained by using the higher-order modulated format, confirming the regeneration results in other scheme [8; 20]. Furthermore, we carry out the cascaded transmission test by placing the proposed regenerator in each 80 km-fiber span, the system scheme depicted in Figure 9. In the span, the EDFA is used to compensate the fiber loss and also introduces the ASE noise consequently. We sweep the input SNR of the PAM-4 signal at a fixed transmission distance, i.e., a fixed loop number N, and collect the required input SNR, i.e., SNRin, corresponding to the output BER of \(\lg(\text{BER})=-3\). Then, we plot the dependence of the required SNRin on the number of loop, as depicted in Figure 10a. The red line and the blue  
Figure 8: (**a**) The input and output waveforms of PAM-8 signals of regenerator; (**b**) BER and SNR of PAM-8 transmission system with and without NOLM. Figure 7: BER and SNR of PAM4 transmission system with and without NOLM. line correspond to the left coordinate axis, and the green symbol corresponds to the right coordinate axis. When there is no all-optical regenerator in the transmission link, i.e., an un-regenerative case, the required input SNR becomes even higher with the increase of the loop number N due to the accumulation of ASE noise. For the loop number of 10, i.e., 800 km fiber transmission, we calculated the required input SNR of around 23 dB, close to the input SNR of 26 dB demonstrated in a PAM-4 800 km-fiber transmission experiment [21]. After placing the proposed cascade-NOLM regenerator in each span, the amplitude noise is effectively suppressed in the regenerative range, and consequently a lower SNR is needed for the regenerative transmission link, see the red-circular mark in Figure 10a. The SNR improvement of around 2.79 dB is observed by comparing the un-regenerative and regenerative links. We also investigated the transmission performance of PAM-8 signal with or without cascaded-NOLM regenerator; results are depicted in Figure 10b. The similar behavior is observed as the PAM-4 case. Almost the same SNR improvement, i.e., 2.63 dB for PAM-8 signals, was obtained because of the optimized multilevel amplitude regeneration achieved in the cascaded-NOLM scheme.