Optical propagation through layered anisotropic materials using effective medium theory

Abstract

Anisotropic materials can be multilayer stacks made from isotropic-isotropic, uniaxial-uniaxial or uniaxial-isotropic layers. Under certain conditions, these multilayer stacks can be modeled as a bulk anisotropic medium using effective medium theory. In this work, the effective permittivity tensor of arbitrary anisotropic layers is first derived using effective medium theory. Thereafter the Berreman matrix method is used to analyze electromagnetic propagation in this effective bulk medium. The overall transmittance and reflectance are investigated as a function of the thickness of the layers, number of layers, wavelength and the incident angle. Illustrative examples of stacks made from uniaxial-uniaxial layers and uniaxial-isotropic layers are provided. The uniaxial layers are, in turn, made from a sandwich of two isotropic layers. An example of a transmission filter comprising a multilayer stack on a substrate is also discussed, along with comparison with experimental observations.