Efficient pixel-by-pixel optimization of photonic devices utilizing the Dyson's equation in a Green's function formalism: Part I. Implementation with the method of discrete dipole approximation

摘要

Here, we introduce an efficient method to perform pixel-by-pixel optimization of photonic devices, based on the Dyson equation in the Green's function formalism. Unlike continuous optimization techniques widely used for photonic device optimization, pixel-by-pixel optimization automatically results in structures consisting of a discrete set of permittivities, and it incorporates the constraint of a minimum feature size throughout the optimization process. Thus pixel-by-pixel optimizations automatically result in structures amenable to lithographic nanofabrication. We show that the use of a Green's function formalism enables an efficient pixel-by-pixel update of the structure, where each update is guaranteed to improve the performance of the structure. (C) 2019 Optical Society of America