Genetic algorithm for design of reflective filters: Application to AlxGa1-xN based Bragg reflectors

Abstract

A genetic algorithm (GA) with adaptive mutations has been employed for the design of Bragg reflectors. The algorithm enables three different design types a) composition and thickness of two layers are chosen and the pair is repeated b) two compositions are chosen for the two alternating materials, and thickness of each layer is optimized c) composition and thickness of each layer are optimized. In all cases, the wavelength and composition dependence of the index of refraction is taken into account. Also, it is possible to impose constraints on the composition difference of the neighbouring layers, either with a penalty function or with narrowing the boundaries for possible compositions. This feature is important because the large lattice mismatch between GaN and AlN can cause poor surface morphology, so measured reflectivity would be lower than the calculated one due to the surface roughness. The algorithm enables finding the optimal design for two chosen incident and final media, and it is capable of taking into account the existence of a finite, optically thick substrate. We have investigated two systems: air/sapphire/AlxGa1-xN reflector/GaN and GaN/AlxGa1-xN/air.