About the Bidimensional Beer-Lambert Law

TL;DR

This paper generalizes the Beer-Lambert law to account for electromagnetic wave polarization, modeling the medium with four linear invariant filters to describe the evolution of electric field components.

Contribution

It introduces a novel model for electromagnetic wave propagation that incorporates polarization effects using a system of four linear invariant filters.

Findings

Modeling of medium with four LIFs enables detailed polarization analysis

Generalization of Beer-Lambert law for polarized electromagnetic waves

Potential applications in complex medium characterization

Abstract

In acoustics, ultrasonics and in electromagnetic wave propagation, the crossed medium can be often modelled by a linear invariant filter (LIF) which acts on a wide-sense stationary process. Its complex gain follows the Beer-Lambert law i.e is in the form exp [-\alphaz] where z is the thickness of the medium and \alpha depends on the frequency and on the medium properties. This paper addresses a generalization for electromagnetic waves when the beam polarization has to be taken into account. In this case, we have to study the evolution of both components of the electric field (assumed orthogonal to the trajectory). We assume that each component at z is a linear function of both components at 0. New results are obtained modelling each piece of medium by four LIF. They lead to a great choice of possibilities in the medium modelling. Particular cases can be deduced from works of R. C. Jones on deterministic monochromatic light. keywords: linear filtering, polarization, Beer-Lambert law, random processes.