The Berreman matrix method has been previously used to model electromagnetic plane wave propagation through a hyperbolic metamaterial, and to determine transmission and reflection coefficients as a function of wavelength and varying angles of incidence. The Berreman matrix approach is now used to derive the propagation transfer function matrix in such materials. The eigenvalues of the Berreman matrix, which determine the transfer function, depend on the anisotropy. Beam propagation in such anisotropic materials are simulated using the transfer functions of all components of the electric (and magnetic) fields. Implications of this on negative refraction and the self-lensing of beams are explored.
Anisotropic metamaterials are widely used in the field of optics because of their unique electromagnetic properties. These metamaterials can be made from multilayer metallo-dielectric structures. Such stacks can be represented as an anisotropic bulk medium using effective medium theory. Optical properties of anisotropic media are mostly described in terms of effective parameters such as permittivity and permeability, or alternatively, refractive index and characteristic impedance. These properties depend not only on the wavelength and polarization but also the direction of the optical wave-vector. In this work optical wave propagation through such anisotropic media is studied in detail. The Berreman 4 × 4 matrix along with appropriate boundary conditions is used to determine all electric and magnetic fields inside and outside the structure. The overall transmission and reflection are investigated as a function of the thickness of each layer (metal/dielectric), the number of layers, and the wavelength for oblique incidence. The validity of the effective medium theory is also investigated by changing the thickness and number of layers.
The Berreman matrix method is used to analyze the polarization and propagation of electromagnetic waves and beams in anisotropic metamaterials. The metamaterial, comprising a multilayer structure of alternating metal and dielectric layers, is modeled as an effective anisotropic medium. The Maxwell’s equations for electromagnetic propagation are then represented as a set of coupled differential equations using the Berreman matrix. These coupled equations are then solved analytically and cross checked numerically using MATLAB® for plane wave propagation. The analysis can be extended to Gaussian beam propagation through such anisotropic metamaterials using the angular plane wave spectral approach.