First Principles Metalens Design

Metasurfaces and metadevices are names given to materials whose electromagnetic properties are tuned to a set of desired ones by (usually) manipulating microstructures that, individually, have very different properties. However, when interacting in bulk, the net effect can be tuned to, for example, focus light or mimic non-physical negative index materials. The recent progress in fabrication of these so-called metasurfaces and metadevices for controlling electromagnetic waves (e.g. light propagation) has been largely based on (1) single-scatterer approximations and (2) low-order finite-difference time-domain simulations of Max-well's equations. The first approach ignores the complicated multiple scattering effects, and the latter is often not very numerically accurate. In this thesis, we present several tools that are needed for a full high-order accurate simulation and design of a specific class of metasurfaces: metalenses. We first develop a multiple-scattering framework based on a boundary integral equation formulation of the problem. Then, we construct a fast multipole-accelerated multi-particle scattering algorithm for the forward simulation of the scattering of electromagnetic waves by many inclusions. Next, we derive an adjoint formulation of an optimization problem to compute an optimal configuration of inclusions. Finally, we construct various translation operators needed in order to apply adjoint operators using fast multipole methods for the Helmholtz equation in three dimensions