Mueller matrices for anisotropic metamaterials generated using 4 × 4 matrix formalism

Forward models for the Mueller Matrix (MM) components of materials with relative magnetic permeability tensor μ ≠ 1 are studied. 4 × 4 matrix formalism can be used to calculate the complex reflection coefficients and the MMs of dielectric-magnetic materials having arbitrary crystal symmetry. For materials with simultaneously diagonalizable ε and μ tensors (with coincident principal axes), analytic solutions to the Berreman equation are available. For the single layer thin film configuration, analytic formulas for the complex reflection and transmission coefficients are derived for orthorhombic symmetry or higher. The separation of the magnetic and dielectric contributions to the optical properties as well as the ability to distinguish materials exhibiting negative index of refraction are demonstrated using simulations of the MM at varying angles of incidence.