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2D and 3D Matrices to Study Linear Invadosome Formation and Activity

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Generalized Jones matrices for anisotropic media.

Noé Ortega-Quijano¹, José Luis Arce-Diego

¹Applied Optical Techniques Group, Electronics Technology, Systems and Automation Engineering Department, University of Cantabria, Avenida de los Castros S/N, 39005 Santander, Cantabria, Spain. ortegan@unican.es

|April 3, 2013

Summary

This study introduces a parametric expression for the 3x3 differential generalized Jones matrix (dGJM) to analyze light beam interactions with optical elements. This versatile method simplifies calculations for anisotropic optical media.

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Area of Science:

Optics and Photonics
Mathematical Physics

Background:

The generalized Jones calculus provides a framework for describing light-optical element interactions.
A need exists for efficient methods to characterize complex optical media with anisotropic effects.

Purpose of the Study:

To derive the parametric expression of the 3x3 differential generalized Jones matrix (dGJM) for arbitrary optical media.
To demonstrate the dGJM's utility in analyzing optical elements with anisotropic properties.

Main Methods:

Derivation of the dGJM using transverse light wave assumptions.
Connection of the dGJM to Gell-Mann matrices for a structured mathematical approach.
Application of the dGJM to derive macroscopic generalized Jones matrices (GJM).

Main Results:

A parametric expression for the dGJM for arbitrary optical media was obtained.
The dGJM was shown to be intimately connected to Gell-Mann matrices.
The dGJM provides a versatile method for characterizing media with sequential or simultaneous anisotropic effects.
Explicit parametric expressions for the GJM of specific optical elements were derived.

Conclusions:

The derived dGJM offers a powerful and versatile tool for analyzing the interaction of light with complex optical systems.
This method simplifies the characterization of optical media exhibiting various anisotropic behaviors.