Nanophotonic reservoir computing with photonic crystal cavities to generate periodic patterns

Reservoir computing (RC) is a technique in machine learning inspired by neural systems. RC has been used successfully to solve complex problems such as signal classification and signal generation. These systems are mainly implemented in software, and thereby they are limited in speed and power efficiency. Several optical and optoelectronic implementations have been demonstrated, in which the system has signals with an amplitude and phase. It is proven that these enrich the dynamics of the system, which is beneficial for the performance. In this paper, we introduce a novel optical architecture based on nanophotonic crystal cavities. This allows us to integrate many neurons on one chip, which, compared with other photonic solutions, closest resembles a classical neural network. Furthermore, the components are passive, which simplifies the design and reduces the power consumption. To assess the performance of this network, we train a photonic network to generate periodic patterns, using an alternative online learning rule called first-order reduced and corrected error. For this, we first train a classical hyperbolic tangent reservoir, but then we vary some of the properties to incorporate typical aspects of a photonics reservoir, such as the use of continuous-time versus discrete-time signals and the use of complex-valued versus real-valued signals. Then, the nanophotonic reservoir is simulated and we explore the role of relevant parameters such as the topology, the phases between the resonators, the number of nodes that are biased and the delay between the resonators. It is important that these parameters are chosen such that no strong self-oscillations occur. Finally, our results show that for a signal generation task a complex-valued, continuous-time nanophotonic reservoir outperforms a classical (i.e., discrete-time, real-valued) leaky hyperbolic tangent reservoir (normalized root-mean-square errors=0.030 versus NRMSE=0.127).