# Numerical Simulation of an InP Photonic Integrated Cross-Connect for Deep Neural Networks on [PERSON] Shi
## 4 Implementation of Weight Calibration and Weighted Addition  
For the operation of the SOA-based photonic neural network, a calibration of the weighting is required for correctly assigning the given weight factors to the input data. For this simulation implementation, the weight-SOAs are identical for all the input channels so that we demonstrate the weight calibration on one of the input channels. For the weight calibration, the input can be a non-return-to-zero on-off keying (NRZ OOK) signal or multi-level data input. As the weighting of \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Parameters** & **Value** & **Unit** & **Parameters** & **Value** & **Unit** \\ \hline Device Section Length & \(1000\times 10^{-6}\) & m & Nonlinear Gain Coefficient & \(1.0\times 10^{-23}\) & m\({}^{3}\) \\ Active Region Type & MQW & Nonlinear Gain Time Constant & \(5.00\times 10^{-13}\) & s \\ Active Region Width & \(2.0\times 10^{-6}\) & m & Carrier Density Transparency & \(1.0\times 10^{24}\) & m\({}^{-3}\) \\ Active Region Thickness & \(250\times 10^{-6}\) & m & Linear Recombination & \(1.0\times 10^{8}\) & s\({}^{-1}\) \\ Active Region Thickness MQW & \(100\times 10^{-6}\) & m & Bimolecular Recombination & \(1.0\times 10^{-16}\) & m\({}^{3}\)/s \\ Active Region Thickness SCH & \(200\times 10^{-6}\) & m & Auger Recombination & \(2.1\times 10^{-41}\) & m\({}^{6}\)/s \\ Current Injection Efficiency & 1 & Carrier Capture Time Constant & \(3.0\times 10^{-11}\) & s \\ Nominal Frequency & 193.7 & THz & Carrier Escape Time Constant & \(1.0\times 10^{-10}\) & s \\ Group Index & 3.52 & & Initial Carrier Density & \(8.0\times 10^{23}\) & m\({}^{-3}\) \\ Polarization Model & TE & & Chirp Model & Linewidth Factor & \\ Internal Loss & 3000 & m\({}^{-1}\) & Linewidth Factor & 3 & \\ Confinement Factor & 0.3 & & Linewidth Factor MQW & 3 & \\ Confinement Factor MQW & 0.07 & & Differential Index & \(-1.0\times 10^{-26}\) & m\({}^{3}\) \\ Confinement Factor SCH & 0.56 & & Differential Index MQW & \(-1.0\times 10^{-26}\) & m\({}^{3}\) \\ Gain Shape Model & Flat & & Differential Index SCH & \(-1.5\times 10^{-26}\) & m\({}^{3}\) \\ Gain Model & Logarithmic & Carrier Density Ref. Index & \(1.0\times 10^{24}\) & m\({}^{-3}\) \\ Gain Coefficient Linear & \(4.00\times 10^{-20}\) & m\({}^{2}\) & Noise Model & Inversion Parameter & \\ Gain Coefficient Logarithmic & \(6.9\times 10^{4}\) & m\({}^{-1}\) & Inversion Parameter & 1.2 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The parameters used in the simulation of SOA. Figure 2: Photonic deep neural network (PDNN) simulation scheme on software _VPlphotonics_. (a) System for examining the PDNN. (b) Arbitrary waveform generator. (c) Lasers and modulators. (d) Receiver. (e) One photonic weighted addition unit (part of the matrix multiplication unit, MMU). the input data is performed after the AWG, the fixed optical crosstalk from the AWG will influence the output optical signal. We consider two extreme conditions for the optical crosstalk level: when switching ON (injection current at 70 mA) all the weight-SOAs, the optical crosstalk coming from the adjacent channels is expected to be maximum (XTalk\({}_{\text{max}}\)), while when all the weight-SOAs are OFF (zero injected current), the induced optical crosstalk by that the corresponding channels will be the minimum (XTalk\({}_{\text{min}}\)). Due to the complexity of operation conditions, we consider the average between these two scenarios in order to generate the weight control curve, in order to minimize the error induced by the optical interference. The crosstalk in the AWG in the photonic MMU (see Figure 2e) is set at \(-20\) dB, as experimentally measured in [33]. Firstly, when all the weight-SOAs are set to OFF (XTalk\({}_{\text{min}}\)), but one of these weight-SOAs is injected with currents from 0 mA to 70 mA, we record the signal peak power at channel 1, 193.1 THz, from the monitoring power meter as shown in Figure 2a.