Invariant Imbedding Equations for Electromagnetic Waves in Stratified Magnetic Media: Applications to One-Dimensional Photonic Crystals

TL;DR

This paper develops invariant imbedding equations for electromagnetic waves in stratified magnetic media, enabling exact calculation of reflection, transmission, and internal fields, with applications to one-dimensional photonic crystals exhibiting band gaps.

Contribution

It introduces a novel set of invariant imbedding equations for stratified magnetic media, extending analysis capabilities to arbitrary variations and polarizations.

Findings

Exact reflection and transmission coefficients derived

Photonic band gaps identified in 1D photonic crystals

Applicable to arbitrary polarization and incident angles

Abstract

We derive the invariant imbedding equations for plane electromagnetic waves propagating in stratified magnetic media, where both dielectric and magnetic permeabilities vary in one spatial direction in an arbitrary manner. These equations allow us to obtain the reflection and transmission coefficients of the waves and the field amplitudes inside the media exactly for any polarization and incident angle of the incoming wave by solving an initial value problem of a small number of ordinary differential equations. We apply our results to one-dimensional photonic crystals, where the periodic variations of both dielectric and magnetic permeabilities create photonic band gaps in the frequency spectrum.