On the effect of the thermal cross-talk in a photonic feed-forward neural network based on silicon microresonators

Local heating is widely used to trim or tune photonic components in integrated optics. Typically, it is achieved through the power dissipation of metal microwires driven by a current and placed nearby the photonic component. Then, via the thermo-optic effect, both the amplitude and the phase of the complex optical field propagating in the component can be controlled. In the last decade, optical integrated circuits with a cascade of more than 60 thermo-optical phase shifters were demonstrated for quantum simulators or optical neural networks. In this work, we demonstrate a simple two layers feed-forward neural network based on cascaded of thermally controlled Mach-Zehnder interferometers and microring resonators. We show that the dynamics of a high quality factor microresonator integrated into a Silicon On Insulator (SOI) platform is strongly affected by the current flowing in metal heaters where these last generate both local as well as global heating on the integrated photonic circuit. Interestingly, microheaters, even when they are at distances of a few millimetres from the optical component, influence all the microresonators and the Mach-Zehnder interferometers in the photonic circuit. We model the heat flux they generate and modify accordingly the non-linear equations of a system formed by a microresonator coupled to a bus waveguide. Furthermore, we show experimentally that the use of microheaters can be a limiting factor for the feed-forward neural network where three microresonators are used as non-linear nodes. Here, the information encoding, as well as the signal processing, occurs within the photonic circuit via metal heaters. Specifically, the network reproduces a given non-linear surjective function based on a domain of at most two inputs and a co-domain of just one output. As a result, its training aims to determine the values of the currents to apply to the heaters in the hidden layers, which allows replicating a certain shape. We demonstrate how the network exploits mainly the heat flow generated by the information encoding to reproduce a target avoiding the use of all the hidden layer heaters. This work shows that in large thermally actuated integrated photonic circuit, the thermal cross talk is an issue.