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Impact of objective bandwidth and frequency sampling density on search landscape structure and search performance in design optimization of optical structures

The typical aim of systematic design optimization in optics is to achieve specified performance over a prescribed set of frequencies—single or multiple, narrowly or broadly distributed. While search algorithms capable of efficiently sifting large design spaces have become crucial in such design optimization, the impact of the prescribed set of frequencies on search behavior remains not well understood. This article explores the impact of objective bandwidth and frequency sampling density on design optimization problem structure and search behavior. Particularly, this article explores some intuition—that broadband and/or finely frequency-sampled objectives yield more structured problems than narrowband and/or coarsely frequency-sampled counterparts—and both evidences this intuition and illustrates its practical value in search algorithm design. Specifically, a case study—combinatorial design optimization of a multi-spatial-mode photonic crystal waveguide bend that preserves modal content—evidences the above intuition via search landscape analysis, and illustrates how this intuition informs search algorithm design via comparative performance analysis of a collection of model search algorithms.