## 4 Multichannel PAM4 Amplification Results  
Data needs to be multiplexed upon multiple wavelengths to provide for high bit rate connections of 200 Gbit/s and 400 Gbit/s [2; 3; 15], and eight separate wavelengths with 28 Gbaud PAM4 signals modulated on each are required to reach 400 Gbit/s [3]. Our SOA model can handle multiple channels, though there is no inherent wavelength dependence of the SOA gain, refractive index, and saturation power in the model. In the absence of wavelength dependence in the SOA model, we limit ourselves to just four channels. The additional channels with each detuned from each other by a sufficient amount to avoid spectral spillage into neighbouring channels and the frequency detunings must be small enough such that the entire multi-channel bandwidth is smaller than the simulation bandwidth of 1 THz. Though, typically for datacenter applications a coarse wavelength grid of 4.5 nm (-800 GHz) is used allowing for large frequency offsets from the center of each wavelength band [21], here we concentrate on smaller channel spacings because of the limited simulation bandwidth and lack of wavelength dependent gain and gain saturation in our model. In the complex valued optical field representation the total multi-channel field is given by:  
\[E_{tot}=\sum_{0}^{K-1}E_{k}\exp\{j2\pi\Delta f_{k}t\} \tag{11}\]  
where \(E_{k}\) is the optical field of the \(k\)th channel and \(\Delta f_{k}\) is the frequency detuning of the \(k\)th channel from the central frequency channel and \(K\) is the number of channels. We concentrate on gathering BER results for one channel (results already shown in Section 3); for two channels when the detuning frequencies are 0 and 100 GHz; and for four channels when the detuning frequencies are: 0, \(-100\), 120, and \(-220\) GHz. The input spectrum to the SOA is shown for four channels in Figure 8a, and each channel has an average power of 1 mW, the spectral profile of the OBPF is also shown. The filtered signal after amplification is shown in Figure 8b to show strong rejection of neighbouring channels. These channels are well within the 1 THz simulation bandwidth with unequal channel spacings used to avoid signal impairments due to interference from four-wave mixing components. The ASE generated using (7) is already wideband over the entire simulation bandwidth and no further modifications are necessary. Figure 8: (**a**) SOA input spectrum showing four wavelength channels modulated with PAM4 data. The average power per channel is 1 mW. The BER estimates are performed on the channel that has been filtered out using the OBPF shown in red. (**b**) Spectrum of the filtered signal at the SOA output showing strong rejection of neighboring channels. We generate an optical field for one, two, and four channels using (11), a different (uncorrelated) PAM4 signal is applied to each channel and the channels are temporally delayed by a random constant delay such that the symbol transition occurring for each channel are not synchronized, i.e., both waveforms with uncorrelated symbols have non-synchronized symbol transitions, and this helps to average out the optical intensity variations and reduce the signal distortion in the SOA. The SOA gain conditions are the same as in Section 3 for both single-section and multi-section SOAs. The BER results of the multi-channel amplification are shown in Figure 9. For both SOA configurations, the BER performance is the same irrespective of the number of co-propagating channels for low input powers between \(-30\) dBm and \(-18\) dBm, this is unsurprising since there is no gain saturation occurring and the BER is dominated by ASE noise. When the ASE noise limits the performance, the BER of the multi-section SOA is smaller than the BER of the single-section SOA because of the lower effective NF of the multi-section SOA.