Synthesis of novel all-dielectric grating filters using genetic algorithms

The feasibility of novel all-dielectric waveguide grating filters is demonstrated, using a genetic algorithm (GA) to solve for material dielectric constants and geometric boundaries separating homogeneous regions of the periodic cell. In particular, the GAs show that simple geometries (not previously reported) utilizing a small number of layers and/or gratings can be found to yield bandpass or stop-band filters with user defined linewidth. The evaluation of the fitness of a candidate design entails the solution of an integral equation for the electric field in the cell using the method of moments (MoM). Our implementation is made efficient by using only very few design frequency points and accurately approximating a given filter transfer function by a quotient of polynomials as a function of frequency. Additionally, the problem impedance matrices are conveniently represented as the product of a material independent matrix and a vector of dielectric constants, thus allowing us to fill the matrices only once. Our code has been parallelized for the Cray T3D to take advantage of the intrinsic parallelization efficiencies offered by the GAs. Solutions are illustrated for a very narrow-band single-grating transmission filter and a relatively broad-band double grating reflection filter. Additionally, a solution for a five homogeneous layers Fabry-Perot filter is also presented.