# Direct retrieval method of the effective permittivity and permeability of bulk semi-infinite metamaterials by variable-angle spectroscopic ellipsometry

## TL;DR

This paper introduces a straightforward spectroscopic ellipsometry-based method to directly determine the effective permittivity and permeability of bulk semi-infinite metamaterials, simplifying characterization processes.

## Contribution

It provides an analytical approach using Fresnel equations and linear regression to accurately retrieve metamaterial parameters from experimental data.

## Key findings

- Successfully applied to a self-assembled metamaterial with strong isotropic optical magnetism.
- Demonstrates the method's effectiveness and simplicity in characterizing complex metamaterials.
- Offers a practical tool for rapid and direct metamaterial property measurement.

## 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.