  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.
