Application of Deterministic Optimization Methods for the Design Photonic Crystal Waveguide Fragments with Bends

Abstract

Various bends type of photonic crystal waveguides (by 120°, 60° and 45°) is designed in this paper using various deterministic optimization methods (coordinate descent method, Hook-Jeeves method and gradient descent). Application of zero-order optimization methods (coordinate descent and Hook-Jeeves) to bends by 120°, 60° on a crystal with a hexagonal lattice and air holes in the silicon layer made it possible to reduce the computation time by an average of 16 times compared to the genetic algorithm. The application of gradient descent to the design of a 45° bend on a crystal with a square lattice and silicon rods in air made it possible to achieve an increase in efficiency from 10 to 99%, and the number of calls to the target function during the algorithm’s operation is significantly lower compared to the genetic algorithm. Particular attention is paid to the consideration of the “partial search” method. Using the example of a photonic crystal waveguide bending by 120°, it is shown that the element designed by this method is characterized by radiation transmission practically without losses, while the computational complexity of the calculation is 1.5 times less than that of the genetic algorithm.