Method for simultaneous optimization of the material composition and dimensions of multilayer photonic nanostructures

摘要

While several approaches have been proposed to optimize the geometrical dimensions of multilayer photonicnanostructures with a given material composition, very few works have considered simultaneously optimizingthe material composition and dimensions of such nanostructures. Here, we develop a hybrid optimization algo-rithm as a method to design optimal multilayer photonic structures. Leveraging recent progress in metaheuristicoptimization, we develop an optimization method consisting of a Monte Carlo simulation, a continuous adaptivegenetic algorithm, and a pattern search algorithm. We first perform a Monte Carlo simulation over the entire de-sign space. Structures are ranked according to the chosen fitness function. We find that this method yields viablematerial compositions. The material compositions of the best structures are used to parameterize the geneticalgorithm in the next stage. A number of genetic algorithm populations are generated, one for each materialcomposition, to optimize the thicknesses. These populations are run in parallel for a number of generations,evaluating the structures of each generation and using the characteristics of those that best satisfy the fitnessfunction to improve other structures. The resulting populations converge towards the optimum of their solutionspace typically after a few thousand generations. The genetic algorithm used is continuous because parametersare treated as real numbers rather than bit strings as in classical genetic algorithms, and adaptive because thealgorithm uses characteristics of the population pool to guide optimization. Finally, we apply a pattern searchlocal optimization algorithm to the best result from each population to nd the exact optimum.