Abstract
In this work, we present a simple method for the direct retrieval of the effective permittivity and permeability of a bulk semi-infinite metamaterial from variable-angle spectroscopic ellipsometry measurements. Starting from the well-known Fresnel equations, we derive an analytical expression in which unknown coefficients are fitted to the experimental data using a linear regression model. The effective permittivity and permeability are then determined by solving a simple system and the correct solution is selected based on physical criteria. As an example, the method is applied to the case of a self-assembled metamaterial exhibiting strong isotropic optical magnetism.
Highlights
Spectroscopic ellipsometry measures polarized light reflected from the surface of a material or thin-film and lets two polarization directions interfere to produce a measurable signal as a function of wavelength
When light is reflected from a bulk semi-infinite homogeneous material, the reflection coefficients are given by the Fresnel equations and the optical index can be retrieved directly from ρ[1]
We proposed a retrieval method based on variable-angle spectroscopic ellipsometry measurements that overcomes the drawbacks of the celebrated S-parameters retrieval method in the case of an optically thick metamaterial
Summary
Spectroscopic ellipsometry measures polarized light reflected from the surface of a material or thin-film and lets two polarization directions interfere to produce a measurable signal as a function of wavelength. The classical approach to retrieve the optical parameters of metamaterials is the S-parameters retrieval method inherited from microwave research It consists in measuring the normal incidence reflection and transmission coefficients r and t for the electric field (the so-called scattering parameters) in order to calculate the effective electromagnetic constants using simple algebraic equations assuming that the thickness of the sample is known [3,9]. This elegant, simple and powerful method is extensively used by the metamaterial community. The purpose of this paper is to provide a detailed description of the retrieval procedure complemented with a tutorial case using the data previously published by Gomez-Graña et al [8]
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