Search landscape analysis in design optimization of optical structures
Keywords: Applied Physics.

Systematic design optimization of optical structures is opening new and advancing existing frontiers in the control of light. To exploit systematic design optimization's full potential in optics, search methods capable of efficiently sifting large design spaces are critical. The degree to which a search method exploits problem structure determines its efficacy. Thus, in the methodical analysis that is often key to understanding, and thereby ultimately improving, search behavior, analysis of problem structure --- or search landscape analysis --- is a crucial component. Despite this, search landscape analysis is largely absent from the otherwise-rapidly-growing literature on search methods in design optimization of optical structures. In this dissertation, we first illustrate how search landscape analysis can provide insight into both search behavior and underlying problem structure in design optimization in optics. To this end, we present a case study in which search landscape analysis sheds light on the surprisingly good performance of a simple search method on a challenging problem. In the process, this case study also reveals that design optimization problems in optics possess much more structure than conventional reasoning might suggest, and thereby yields insight potentially valuable in design optimization of a broad class of optical structures. Having observed the former, we then ask how the important parameters in design optimization problems in optics impact search landscape structure, and how understanding that impact informs choice or design of search methods: Achieving specified performance over a prescribed set of frequencies --- single or multiple, narrowly or broadly distributed --- is the typical aim of systematic design optimization in optics; despite the importance of this objective function characteristic, its impact on search behavior remains not well understood. Accordingly, we next explore how bandwidth and band sampling density of objective functions in design optimization problems in optics impact problem structure, and how understanding that impact informs choice or design of search methods. Particularly, we explore some intuition --- that broadband and/or finely frequency-sampled objectives yield more structured problems than narrowband and/or coarsely frequency-sampled counterparts --- and both evidence this intuition and illustrate its practical value in search method design. Capitalizing on insight developed through search landscape analyses of various design optimization problems like those involved in the above investigations, we then introduce a metaheuristic, or high-level strategy, for tailoring general purpose search methods to design optimization problems in optics, and demonstrate its implementation and value via a concrete example. Prior to closing with a discussion of future directions, we pivot slightly to methods that enabled the analysis in the preceding work. Specifically, we describe a broadly applicable method for accelerating simulation of ensembles of locally-differing optical (and other) structures via domain decomposition.