Band gap optimization of finite photonic structures using apodization method

In this paper, the photonic band diagram and the density of states in finite photonic structures are analyzed and optimized for broad bandwidths using the apodization method. Based on the effective propagation constant, the group refractive index can be computed for the finite structures, which is adopted to reveal the physical explanation on the optimal band gaps. The surface states of the finite photonic crystal and the mode matching at the interfaces are also considered. It is found that the high group index of the photonic structures can obtain broad bandwidths and also enhance the mode matching at the interfaces. By slowly varying the radii of the cylinders monotonously in two dimensions, the first band gap can be increased from 10.6% to 20.04%. This work provides a useful tool for the optimal design of finite photonic crystals.