Permittivity and Permeability Tensor Extraction Technique for Arbitrary Anisotropic Materials

Abstract

Computing the permittivity and permeability of complex materials has previously relied on a series of simplifying assumptions to enable analysis. The most restricting requirement is that the optical axes of the material must align with the laboratory frame of reference. This requirement cannot be met for a large group of materials, including crystalline structures and metamaterials such as tilted nanorods. Currently, designing the optical characteristics of these structures would require ellipsometric analysis, which uses an error-correction-based technique. Here, a new technique built upon the underlying physics of ellipsometry is proposed to extract arbitrary permittivity and permeability tensors using a set of off-axis measurements. This new permittivity and permeability tensor extraction technique allows all 18 elements of the permittivity and permeability tensors to be nonzero and extracts them, given a set of reflectance and transmittance measurements. Several materials are analyzed here, including a) an isotopic plane of known permittivity, b) an anisotropic aligned structure, and c) a tilted-nanorod-based sample that cannot be measured using traditional methodologies. The isotropic plane shows very low error $( in the $x$ and $y$ tensor measurements and around 1% error in the $z$ tensor measurement at higher (metallic) permittivities. The aligned structure's characteristics are compared to measurements made with traditional techniques and show excellent agreement between the techniques. The tilted nanorod characteristics are analyzed and used to predict the reflection and transmission coefficients at other angles. The predictions compare very well with the computational electromagnetic simulations, showing at most 5% error over the range examined.