Modeling of electromagnetic wave propagation and spectra of optical excitations in complex media using 4x4 matrix formalism

Using 4x4 matrix formalism we analyzed electromagnetic wave propagation and Jones matrix components for reflectivity and transmittivity in bi-anisotropic materials. Analytic formulas for complex reflection and transmission coefficients for bi-anisotropic materials in both semi-infinite and thin-film configurations have been derived. The obtained results are applicable for analysis of the optical spectra of multiferroic crystals and metamaterials. The Adjusted Oscillator Strength Matching Condition (AOSM) for hybrid magnetic- and electric-dipole excitations in anisotropic multiferroics is derived for oblique angles of incidence. Mueller Matrices are used to simulate spectra of magneto-electric and chiral excitations and methods to distinguish them are discussed.