Optimization of two-dimensional photonic bandstructure systems using steepest-descent algorithm

Conventionally, perturbation theory is used for the analytical study of small changes in a system. However, it can also be considered as an exact expression in differential form for the gradient of an objective function describing a system. Based on this idea, we have developed an efficient steepest-descent algorithm to optimize particular features of a photonic bandstructure system. We have applied the algorithm to optimize the size of the photonic bandgap at minimal dielectric contrast in two-dimensional photonic crystals on square and hexagonal lattices, obtaining non-zero complete gaps at very low dielectric contrast.