Poles and zeros of the scattering matrix associated to defect modes

TL;DR

This paper investigates the relationship between defect modes and the poles and zeros of the scattering matrix in one-dimensional periodic media, providing explicit dispersion equations for mode calculation.

Contribution

It introduces an explicit dispersion equation and links defect modes to scattering matrix poles and zeros, advancing understanding of wave propagation in periodic media with defects.

Findings

Derived an explicit dispersion equation for defect modes

Established a connection between modes and scattering matrix poles and zeros

Enhanced methods for analyzing electromagnetic wave propagation in periodic structures

Abstract

We analyze electromagnetic waves propagation in one-dimensional periodic media with single or periodic defects. The study is made both from the point of view of the modes and of the diffraction problem. We provide an explicit dispersion equation for the numerical calculation of the modes, and we establish a connection between modes and poles and zeros of the scattering matrix.