Bessel-Modal Method for Finite-Height Two-Dimensional Photonic Crystal

By applying the dyadic Green function, the dispersion relation of two-dimensional photonic crystal can be expressed as the cylindrical wave expansions of eigenmodes. With the aid of Green’s theorem, the plane-wave coefficients of eigenmodes are reconstructed and employed to formulate the scattering matrix of finite-height two-dimensional photonic crystal. These operations make the convergence rate very rapid, and reduce the dimension of the scattering matrix. As a demonstration, we present the transmission and electromagnetic field distributions for an InGaAsIn photonic crystal, and investigate their convergence.