Data driven design of optical resonators

Optical devices lie at the heart of most of the technology we see around us. When one actually wants to make such an optical device, one can predict its optical behavior using computational simulations of Maxwell's equations. If one then asks what the optimal design would be in order to obtain a certain optical behavior, the only way to go further would be to try out all of the possible designs and compute the electromagnetic spectrum they produce. When there are many design parameters, this brute force approach quickly becomes too computationally expensive. We therefore need other methods to create optimal optical devices. An alternative to the brute force approach is inverse design. In this paradigm, one starts from the desired optical response of a material and then determines the design parameters that are needed to obtain this optical response. There are many algorithms known in the literature that implement this inverse design. Some of the best performing, recent approaches are based on Deep Learning. The central idea is to train a neural network to predict the optical response for given design parameters. Since neural networks are completely differentiable, we can compute gradients of the response with respect to the design parameters. We can use these gradients to update the design parameters and get an optical response closer to the one we want. This allows us to obtain an optimal design much faster compared to the brute force approach. In my thesis, I use Deep Learning for the inverse design of the Fabry-P\'erot resonator. This system can be described fully analytically and is therefore ideal to study.