Beams Propagation Modelled by Bi-filters

TL;DR

This paper introduces a bi-filter model with four linear invariant filters to accurately represent wave propagation in media where polarization effects are significant, extending traditional scalar models to bi-dimensional wave fields.

Contribution

It proposes a novel bi-filter model for wave propagation that accounts for polarization exchanges, generalizing the Beer-Lambert law for electromagnetic beams in continuous media.

Findings

Model accurately represents polarization effects in wave propagation.

Generalized Beer-Lambert law applicable to bi-dimensional waves.

Applicable to optical devices and free space propagation.

Abstract

In acoustic, ultrasonic or electromagnetic propagation, crossed media are often modelled by linear filters with complex gains in accordance with the Beer-Lambert law. This paper addresses the problem of propagation in media where polarization has to be taken into account. Because waves are now bi-dimensional, an unique filter is not sufficient to represent the effects of the medium. We propose a model which uses four linear invariant filters, which allows to take into account exchanges between components of the field. We call it bi-filter because it has two inputs and two outputs. Such a circuit can be fitted to light devices like polarizers, rotators and compensators and to propagation in free space. We give a generalization of the Beer-Lambert law which can be reduced to the usual one in some cases and which justifies the proposed model for propagation of electromagnic beams in continuous media.