Controlling light: Methods for inverse design of nonlinear nanophotonic waveguides on chip

The nonlinear response of optical materials is in general very weak. In order to make use of these nonlinear interactions for optical processes in integrated optical devices, such as optical parametric amplifiers, we often need very long waveguides to achieve appreciable efficiency. These waveguides can have lengths of the order of metres and need to fulfil multiple requirements over a range of wavelengths.Modern advances in manufacturing and nanophotonics have made possible a high degree of tailoring of waveguide geometries for near-field light enhancement to meet these requirements. However, simulating and designing these nonlinear integrated optical devices is challenging.In this thesis, I will present methods for simulating periodic optical waveguide structures with nontrivial unit cells, and how we can use knowledge of the physics to tailor the mesh adaptation in finite-element simulations to electrodynamic problems. I will also present how we can combine machine learning and physics for scattering problems and how we can use inverse design to suggest waveguide cross sections that fulfil multiple design requirements on dispersion characteristics.