Spectral-domain Formulation of Pillar-type Photonic Crystal Waveguide Devices of Infi- Nite Extent

This paper presents a novel formulation for the modeling of electromagnetic wave propagation in pillar-type photonic crystal waveguide devices. The structure under consideration is formed in an infinitely extended pillar-type photonic crystal and the wave propagation is controlled by removing some cylinders from the original periodic structure. The structure is considered as cascade connections of straight waveguides, and the input/output properties of the devices are obtained using an analysis method of multilayer structure. Each layer includes periodic circular cylinder array with defects, and the transfer-matrix is obtained by using a spectral-domain approach based on the recursive transition-matrix algorithm with the lattice sums technique and the pseudo-periodic Fourier transform.