Rigorous modal analysis of two-dimensional photonic crystal waveguides

A rigorous approach for modal analysis of two-dimensional photonic crystal waveguides consisting of layered arrays of circular cylinders is presented. The mode propagation constants and the mode field profiles can be accurately obtained by a simpler matrix calculus, using the one-dimensional lattice sums, the T matrix of an isolated circular cylinder, and the generalized reflection matrices for a multilayered system. Numerical examples of the dispersion characteristics and field distributions are presented for lowest even and odd transverse electric modes of a coupled two-parallel photonic crystal waveguide with a square lattice of dielectric circular cylinders in a background free space.