About the Bidimensional Beer-Lambert Law

Source: arXiv


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.

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