Topology optimization of periodic layouts of dielectric materials

A topology optimization method is used to design two dimensional periodic structures with desirable transmission properties by distributing two materials of different permittivity over a rectangular representative cell. A plane wave expansion of the electric field at the input and output boundaries is used in the analysis. This allows non-homogeneous material distributions near the boundaries. Numerical examples are used to verify the robustness of the method and to investigate the importance of retaining higher modes in the expansions. It is found that the optimization problem typically admits possibly many local optima and the relevance of higher modes depends on the nature of the solution found. In some instances, higher modes play an important role and using only the dominant mode in the analysis is shown to result in errors in the evaluation of the performance of the design.