Impact of phase modulation on the performance of photonic delay-based reservoir computing with semiconductor lasers

Semiconductor lasers with delayed feedback have demonstrated to be able to efficiently solve difficult and time-consuming problems for photonic reservoir computing. In these systems the input data is often injected optically into the reservoir. We numerically show that the performance of specific prediction tasks is strongly affected by the way that information is encoded on the optical injection signal. We compare various input configurations consisting of Mach-Zehnder modulators and phase modulators for injecting the signal in our simulations and evaluate their performances by using a one-step ahead prediction task. We show that using an unbalanced Mach-Zehnder modulator as input configuration outperforms the balanced Mach-Zehnder modulator. We therefore find that modulating the phase of the injected field with the input data strongly improves the performance of optical reservoir computing. This observation has led us to investigate input signals which are only phase modulated and no longer intensity modulated. This results in an improved performance compared to the other modulation types. We are able to retain the same performance between phase modulated and intensity modulated input signals, while reducing the amount of nodes in the reservoir computer. We can therefore conclude that using only a phase modulator as input configuration, with well-chosen modulation amplitude, is ideal for one-step ahead prediction tasks, both performance-wise as well as in simplicity of implementation. Additionally, we have investigated how the memory capacity depends on the phase modulation amplitude. These results indicate that the phase modulation amplitude can be carefully chosen such that many higher order non-linear capacities are available for computation. This leads us to conclude that phase modulation will also have beneficial effects on the performance for other computational tasks, and that such phase modulated injection signals lead to optimal performance of delay-based reservoir computing systems using semiconductor lasers and optical data-injection.