Analysis of two-dimensional photonic crystals using a multidomain pseudospectral method

An analysis method based on a multidomain pseudospectral method is proposed for calculating the band diagrams of two-dimensional photonic crystals and is shown to possess excellent numerical convergence behavior and accuracy. The proposed scheme utilizes the multidomain Chebyshev collocation method. By applying Chebyshev-Lagrange interpolating polynomials to the approximation of spatial derivatives at collocation points, the Helmholtz equation is converted into a matrix eigenvalue equation which is then solved for the eigenfrequencies by the shift inverse power method. Suitable multidomain division of the computational domain is performed to deal with general curved interfaces of the permittivity profile, and field continuity conditions are carefully imposed across the dielectric interfaces. The proposed method shows uniformly excellent convergence characteristics for both the transverse-electric and transverse-magnetic waves in the analysis of different structures. The analysis of a mini band gap is also shown to demonstrate the extremely high accuracy of the proposed method.