Assume Your Neighbor is Your Equal: Inverse Design in Nanophotonics

Abstract

Metasurfaces are optical devices designed for a range of wavelengths. They are subwavelength patterned surfaces with dimensions much larger than the wavelength. These two characteristic length scales are orders of magnitude apart, which makes simulations and optimization of metasurfaces a costly supercomputer scale problem with state-of-the-art solvers. Previously, the community has circumvented this problem by making a local periodic approximation and has simplified the problem into a phase matching problem for fully-known solutions of the Maxwell equations. In this dissertation, I reframe the metasurface design problem as an optimization problem. Based on the local periodic approximation—which I studied analytically, I derived an approximate hybrid solver for metasurfaces which solves orders of magnitude faster than the state of the art. This approximate solver relies on a surrogate model for the solution of each pattern. To find the best surrogate model, I frame the problem as a data-driven artificial intelligence problem. In this research, I designed tangible devices: a lens with extended depth of field and lenses correcting for chromatic aberration in the visible range, with diameters of up to 1 cm. Resulting metasurfaces were fabricated and measured, successfully validating the design framework in both two and three dimensions. This dissertation is a journey at the interface of applied mathematics, applied physics, and artificial intelligence.