Spectral-domain formulation of photonic crystal waveguide devices formed by circular cylinders

This paper shows a spectral-domain approach of the pillar-type photonic crystal waveguide device with infinite extent. The structure is here treated as a multilayer of imperfectly periodic arrays the circular cylinders, and the scattering-matrix representation for each layer is derived by the recursive transition-matrix algorithm with the use of the pseudo-periodic Fourier transform. Then the scattering-matrix propagation algorithm is applied to obtain the input/output properties of the composite structure.