Designing photonic materials with complete band gaps by topology optimization

Photonic materials may exhibit the band gap, within which the propagation of electromagnetic waves is totally prohibited. To achieve a complete photonic band gap (CPBG) for transverse magnetic (TM) and transverse electric (TE) modes, the bi-directional evolutionary structure optimization (BESO) method originated from structural design is extended for this purpose. The optimization problem is formulated with maximizing the minimum imaginary part of complex wave vectors for TM and TE modes. According to sensitivity analysis, the material distribution within the primitive unit cell of photonic materials is adjusted step by step so as to enlarge the minimum imaginary part of wave vectors. In doing so, the CPBG at the specific frequency is obtained at the desired frequency, and the optimized structures of photonic materials with novel topological patterns are achieved. Numerical examples demonstrate that the effectiveness of the proposed topology optimization method for opening the CPBGs at various specified frequencies, which is of significance in controlling the propagation of electromagnetic waves of any polarization. (paper)