Effective photons in weakly absorptive dielectric media and the Beer-Lambert-Bouguer law

TL;DR

This paper derives effective photon modes in weakly absorptive dielectrics, providing an intuitive framework for photon dynamics and deriving a formula for the Beer-Lambert-Bouguer law in structured media.

Contribution

It introduces effective photon modes with associated line-widths in weakly absorbing dielectrics, linking them to absorption laws in structured dispersive media.

Findings

Effective photon modes with decay rates are derived.

An expression for the Beer-Lambert-Bouguer law in structured media is obtained.

The framework simplifies understanding photon behavior in weakly absorptive materials.

Abstract

We derive effective photon modes that facilitate an intuitive and convenient picture of photon dynamics in a structured Kramers-Kronig dielectric in the limit of weak absorption. Each mode is associated with an effective line-width which determines the temporal decay rate of the photon. These results are then applied to obtain an expression for the Beer-Lambert-Bouguer law absorption coefficient for unidirectional propagation in structured media consisting of dispersive, weakly absorptive dielectric materials.