Nonlinear dynamics in neuromorphic photonic networks: physical simulation in Verilog-A

Advances in silicon photonics technology have enabled the field of neuromorphic photonics, where analog neuron-like processing elements are implemented in silicon photonics technology. Accurate and scalable simulation tools for photonic integrated circuits are critical for designing neuromorphic photonic circuits. This is especially important when designing networks with recurrent connections, where the dynamics of the system may give rise to unstable and oscillatory solutions which need to be accurately modelled. These tools must simultaneously simulate the analog electronics and the multi-channel (wavelength-division-multiplexed) photonics contained in a photonic neuron to accurately predict on-chip behaviour. In this paper, we utilize a Verilog-A model of the photonic neural network to investigate the dynamics of recurrent integrated circuits. We begin by reviewing the theory of continuous-time recurrent neural networks as dynamical systems and the relation of these dynamics to important physical features of photonic neurons such as cascadability. We then present the neural dynamics of systems of one and two neurons in the simulated Verilog-A circuit, which are compared to the expected dynamics of the abstract CTRNN model. Due to the presence of parasitic circuit elements in the Verilog-A simulation, it is seen that there is a topological equivalence, but not an exact isomorphism, between the theoretical model and the simulated model. The implications of these discrepancies for the design of neuromorphic photonic circuits are discussed. Our findings pave the way for the practical implementation of large-scale silicon photonic recurrent neural networks.