Synthesis of two-dimensional photonic crystals for large band gaps

For a photonic crystal, the larger the photonic band gap (PBG), the greater the bandwidth for manipulating the optical wave propagation. Therefore, to enlarge the photonic band gaps would be an important research topic. In this paper, we adopt the simulated annealing (SA) algorithm to synthesize two-dimensional photonic crystals for large band gaps. The SA is an iterative procedure and its probabilistic nature provides an opportunity to escape from the local minima and to reach the global minimum in a nonlinear optimization problem. To speed up the numerical calculations, we also use the fast plane wave expansion method for calculating the band diagram of a photonic crystal at each iteration step of the SA procedure. Numerical simulations are carried out to demonstrate the feasibility and effectiveness of our synthesis algorithms.