Numerical Analysis of Two-Dimensional Photonic Crystal Waveguide Devices Using Periodic Boundary Conditions and Multilayer Technique

This paper presents a formulation of two-dimensional photonic crystal wave guide devices formed by circular cylinders in triangular lattice. Decomposing the structure into layers of the cylinder arrays, the input/output properties of the devices are obtained using an analysis method of multilayer structure. We introduce periodic boundary conditions in the direction perpendicular to the wave propagation, and the Floquet-modes of each layer are calculated by the Fourier series expansion method with the help of the recursive transition-matrix algorithm. Then, the input/output properties of the devices are obtained by recursive calculation of scattering matrix with each layer.