Berreman Approach to Optical Propagation Through Anisotropic Metamaterials

Date of Award


Degree Name

Ph.D. in Engineering


Department of Electrical and Computer Engineering


Advisor: Partha Banerjee


This dissertation investigates the propagation of all electromagnetic fields inside anisotropic metamaterials using the Berreman 4 x 4 matrix method. Specifically, the Berreman matrix is used to derive the forward and backward propagating electric fields inside anisotropic metamaterials for all polarizations. Results from the Berreman method are compared with those obtained from the transfer matrix method and finite element methods. Examples include transmissivity and reflectivity as a function of wavelength and angle of incidence for multi-layer metallo-dielectric stacks and dielectric-phase change material stacks, modeled using effective medium theory for Berreman matrix calculations. It is shown that the Berreman matrix method used along with effective medium theory provides a fast and reliable estimate of the optical characteristics of the composite material. The Berreman technique also readily leads to the transfer function matrix for beam propagation in anisotropic materials. The eigenvalues of the Berreman matrix, which determine the transfer function, depend on the anisotropy. Beam propagation in anisotropic materials is analyzed both theoretically and numerically. It is shown that for transverse magnetic polarization, self-lensing of beams occur in a hyperbolic metamaterial. Finally, the transmission coefficient, which is a function of the spatial frequency, is used to determine the spatial shifts of beams propagating through anisotropic metamaterials. Again, for transverse magnetic polarization, negative refraction is observed. The results should prove useful for the analysis of arbitrary beam profiles through composite metamaterials.


Electrical Engineering, Electromagnetics, Optics, Physics, Berreman matrix method, Transfer matrix method, Finite element method, Effective medium, Metamaterials, Anisotropic metamaterials, Multilayered, Beam propagation, Negative refraction, Transfer function

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