ONE-DIMENSIONAL PHOTONIC CRYSTAL SELECTIVE FILTERS DESIGN USING SIMULATED ANNEALING OPTIMIZATION TECHNIQUE

Abstract

During the last decade, selective photonic crystal fllters have received much research interest in the flelds of nanotechnology and optical interconnection network. The main focus of this paper consists of an analysis and a synthesis of one-dimensional photonic crystal selective fllters. The optimization is performed by employing the simulated annealing algorithm. The fllters synthesis is obtained by acting on the Bragg grating layer widths. Simulated annealing is applied to solve the PhC-1D fllters synthesis problem in order to reduce the quadratic error and to obtain a desired transmission according to a Gaussian function deflned in advance by the user. Starting from the Maxwell's equations for dielectric nonmagnetic structure, we show the derivation of the Helmholtz equation and flnd its solution for 1D layered structure. In addition, the boundary conditions and equation transformation to set of linear equations which are solved using Cramer's method are described thoroughly. This mathematical technique is then applied for computation of the transmission spectra of 1D perfectly periodic structure and structures with difierent defects. These results can be easily applied for design of selective fllters.