Spectral-Domain Formulation of Pillar-Type Photonic Crystal Waveguide Devices of Infinite Extent

Abstract

Abstract-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.

Microwave Analysis of Scattered and Absorbed Powers of Semiconductor and Metamaterial Cylinder Structures

“…Scattering, diffraction, and propagation problems concerning cylindrical obstacles play a significant role, even today. There are functional devices of great importance, such as antennas, switches, electromagnetic (EM) band gap structures with multiple applications, reflectors, polarizers, resonators, splitters, and so on made on the basis of cylindrical arrays [1,2,3,4,5].…”

“…It is popular enough to have an array of similar obstacles in the microwave range and thus to name also a photonic (or electromagnetic) crystal by analogy with structures in the optical range [2]. In the last article, it is mentioned that splitters, couplers, and filters can be performed on the basis of photonic crystal waveguide devices (PCWD).…”

“…The wave propagation is controlled by removing some cylinders (i.e., there is a periodic cylinder array with defects). The reflected and transmission powers vice versa to the wavelength in free space are presented in [2].…”