Mueller matrices for anisotropic metamaterials generated using 4x4 matrix formalism

TL;DR

This paper develops a comprehensive 4x4 matrix formalism to model Mueller matrices of anisotropic metamaterials with magnetic properties, providing analytic solutions for complex reflection coefficients and demonstrating separation of magnetic and dielectric effects.

Contribution

It introduces a general 4x4 matrix approach for calculating Mueller matrices of dielectric-magnetic materials with arbitrary symmetry and orientation, including analytic solutions for specific cases.

Findings

Derived analytic formulas for reflection and transmission coefficients.

Demonstrated separation of magnetic and dielectric contributions.

Provided general solutions for complex reflection coefficients.

Abstract

Forward models for the Mueller Matrix (MM) components of materials with relative magnetic permeability tensor {\mu} \neq 1 are studied. 4x4 matrix formalism is employed to produce general solutions for the complex reflection coefficients and MMs of dielectric-magnetic materials having arbitrary crystal symmetry and arbitrary laboratory orientation. For certain orientations of materials with simultaneously diagonalizable {\epsilon} and {\mu} tensors (with coincident principal axes), analytic solutions to the Berreman equation are available. For the single layer thin film configuration of these materials, analytic formulas for the complex reflection and transmission coefficients are derived for orthorhombic or higher crystal symmetry. The separation of the magnetic and dielectric contributions to the optical properties of a material are demonstrated using measurements of the MM at varying angles of incidence.