## 3 Single Channel PAM4 Amplification Results  
We create an optical field with 20,000 PAM4 symbols (40,000 bits) at 28 Gbaud encoded into the power waveform. The signals pass through the SOA and are detected in the receiver. The optical input power to the SOA is varied from \(-30\) dBm to 0 dBm, the output of the SOA passes through an optical bandpass filter (OBPF) before the detector block which calculates the BER. The OBPF has a super-Gaussian spectral profile with optical field transfer function  
\[H_{OBPF}(f)=\exp\left(-\frac{1}{4}\bigg{(}\frac{f-f_{0}}{\Delta f_{OBPF}} \bigg{)}^{2}\right). \tag{10}\]  
With \(f_{0}\) being the central frequency of the OBPF, and \(\Delta f_{OBPF}\) = 50 GHz, resulting in a full-width half maximum bandwidth of 108 GHz. This is wide enough to pass the central channel while offering strong rejection of neighboring channels in a multi-channel simulation, more details about the OBPF are given in the following section. Note that the smallest frequency difference to the central channel of interest that we consider throughout this paper is 100 GHz. The OBPF also limits the amount of ASE that reaches the photo-detector and reduces the detrimental spontaneous-spontaneous beat noise in direct detection systems [16]. The BER results are shown in Figure 6 for a single channel scenario. The BER is large for low input powers below \(-30\) dBm because the ASE dominates, and the BER reduces sharply as the power is increased. The BER is just greater than \(10^{-3}\) at \(-20\) dBm which is in-line with experimental results [15]. The multi-section SOA gives a 0.84 dB sensitivity improvement on the lower power side compared to a single-section SOA due to the lower effective NF of the multi-section SOA. As the power increases, the ASE no longer limits performance and BERs \(<\)\(10^{-4}\) are achieved. However, as the power increases above \(-5\) dBm, the BER increases sharply due to signal distortion caused by the SOA gain saturation. The multi-section SOA performs better than a single section SOA because of increased effective \(P_{sat}\). These findings are in line with an experimental study of the saturation characteristics of multisection SOAs that showed picosecond pulses suffer less distortion than regular single section SOAs [20]. We use the IPDR to explicitly quantify the improvement in the signal quality after SOA amplification. The IPDR gives the range of input powers over which the BER remains below that of the forward error correcting algorithm. The calculated IPDR is 13.55 dB for single section SOA and 16.85 dB for a multi-section SOA resulting in a 3.3 dB improvement in the IPDR. To visualize the signal quality at the output of the SOA we plot the eyediagrams of the PAM4 signal  
Figure 5: SOA gain saturation curves for the regular single-section SOA (blue) and multi-section SOA in red. The multi-section SOA is biased so that the \(P_{\text{3 dB}}\) is greater and increases from 8.28 dBm for the single-section SOA to 10.74 dBm for the multi-contact SOA. We find that the results show similar performance to single section and multi section SOAs in [10,11]. The green curve shows the gain saturation characteristic when the bias to the first and third sections are swapped; in this scenario the effective gain saturation is much stronger resulting in a \(P_{\text{3 dB}}\) of 7.1 dB. for different input powers to the multi-section SOA. In Figure 7a, we show the eyediagram for a low input power of \(-21\) dBm, the signal is corrupted by ASE including signal-spontaneous beat noise which is clearly worse for the stronger levels of the PAM4 signal. In Figure 7b, we increase the SOA input power to \(-11\) dBm and we find a clean PAM4 signal at the SOA output and no bit errors were detected for this input power. In Figure 7c, as the power is increasing to \(-6\) dBm, we see that signal distortion begins to occur and when the power is increased further to \(0\) dBm we find that the SOA gain saturation corrupts the PAM4 signal resulting in increased BER.