Topological Optimization for Photonic and Phononic crystals problems

Abstract. In this paper, we propose a numerical method to study phononic and photonic crystal problems. The proposed method is based on topological optimization tools. In fact, after modeling crystal photonics and phononic problems, we use topological optimization tools to build a numerical method for getting optimal design. Here the optimal design is the one in which all frequencies near the reference frequency corresponding to the reference wave length a can pass.