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Advances in silicon photonics technology have enabled the field ofneuromorphic photonics, where analog neuron-like processing elements areimplemented in silicon photonics technology. Accurate and scalable simulationtools for photonic integrated circuits are critical for designing neuromorphicphotonic circuits. This is especially important when designing networks withrecurrent connections, where the dynamics of the system may give rise tounstable and oscillatory solutions which need to be accurately modelled. Thesetools must simultaneously simulate the analog electronics and the multi-channel(wavelength-division-multiplexed) photonics contained in a photonic neuron toaccurately predict on-chip behaviour. In this paper, we utilize a Verilog-Amodel of the photonic neural network to investigate the dynamics of recurrentintegrated circuits. We begin by reviewing the theory of continuous-timerecurrent neural networks as dynamical systems and the relation of thesedynamics to important physical features of photonic neurons such ascascadability. We then present the neural dynamics of systems of one and twoneurons in the simulated Verilog-A circuit, which are compared to the expecteddynamics of the abstract CTRNN model. Due to the presence of parasitic circuitelements in the Verilog-A simulation, it is seen that there is a topologicalequivalence, but not an exact isomorphism, between the theoretical model andthe simulated model. The implications of these discrepancies for the design ofneuromorphic photonic circuits are discussed. Our findings pave the way for thepractical implementation of large-scale silicon photonic recurrent neuralnetworks.

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