Retrieval of material parameters for uniaxial metamaterials

TL;DR

This paper introduces a comprehensive method to accurately retrieve the tensorial permittivity and permeability of uniaxial metamaterials, including hyperbolic types, using spectroscopic ellipsometry and generalized dispersion equations.

Contribution

It presents a novel approach that relaxes previous assumptions, enabling direct measurement of global material parameters and verification through experiments and comparisons.

Findings

Hyperbolic metamaterials exhibit strong diamagnetic response in visible regime.

The method accurately retrieves permittivity and permeability tensors.

Experimental verification confirms the effectiveness of the approach.

Abstract

We present a general method for retrieving the effective tensorial permittivity of any uniaxially anisotropic metamaterial. By relaxing the usually imposed condition of non-magnetic metal/dielectric metamaterials, we also retrieve the permeability tensor and show that hyperbolic metamaterials exhibit a strong diamagnetic response in the visible regime. We obtain global material parameters, directly measurable with spectroscopic ellipsometry and distinguishable from mere wave parameters, by using the generalized dispersion equation for uniaxial crystals along with existing homogenization methods. Our method is analytically and experimentally verified for Ag/SiO2 planar metamaterials with varying number of layers and compared to the effective medium theory. We also propose an experimental method for retrieving material parameters using methods other than ellipsometry.