Fresnel coefficients, coherent optical scattering and planar waveguiding

TL;DR

This paper revisits one-dimensional optical waveguiding through electromagnetic derivation of Fresnel formulas, revealing that guided modes are singular solutions linked to poles of Fresnel coefficients, unifying various optical configurations.

Contribution

It provides a unified electromagnetic framework for understanding waveguiding, emphasizing the role of Fresnel coefficient poles as resonance conditions for guided modes.

Findings

Guided modes are singular solutions of the coherent optical scattering problem.

Resonance conditions correspond to poles of Fresnel coefficients.

Shared features across different waveguiding configurations.

Abstract

One-dimensional optical waveguiding is revisited using the electromagnetic deduction of Fresnel formulas relating the incident, reflected, and transmitted waves on the abrupt interface between two different optical media. Throughout the paper, different optical configurations are analyzed from this perspective revealing that, in all cases, those solutions corresponding to waveguiding configurations share common features. These shared characteristics are: firstly, the guided modes always emerge as singular solutions of the associate coherent optical scattering problem and, secondly, the resonance condition that must be satisfied corresponds to the pole of the associated Fresnel Coefficients.