One-dimensional Photonic Crystal Selective Filters Design Using Simulated Annealing Optimization Technique

During the last decade, selective photonic crystal filters have received much research interest in the fields 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 filters. The optimization is performed by employing the simulated annealing algorithm. The filters synthesis is obtained by acting on the Bragg grating layer widths. Simulated annealing is applied to solve the PhC-1D filters synthesis problem in order to reduce the quadratic error and to obtain a desired transmission according to a Gaussian function defined in advance by the user. Starting from the Maxwell’s equations for dielectric nonmagnetic structure, we show the derivation of the Helmholtz equation and find 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 different defects. These results can be easily applied for design of selective filters. Received 25 May 2013, Accepted 6 July 2013, Scheduled 11 July 2013 * Corresponding author: Hadjira Abri Badaoui ([email protected]). 108 Badaoui and Abri