# An Analytical and Rigorous Method for Analysis of an Array of Magnetically-Biased Graphene Ribbons

## TL;DR

This paper introduces an accurate analytical method for analyzing magnetically-biased graphene ribbon arrays, enabling precise prediction of their electromagnetic behavior and Faraday rotation effects, surpassing existing semi-analytical approaches.

## Contribution

It presents a novel, fast, and reliable integral-equation-based analytical technique for periodic graphene ribbon arrays under magnetic bias, including a closed-form solution for Faraday rotation.

## Key findings

- Excellent agreement with full-wave simulations
- Predicts resonant spectral effects not captured by previous methods
- Provides a closed-form expression for Faraday rotation

## Abstract

A sheet of graphene under magnetic bias attains anisotropic surface conductivity, opening the door for realizing compact devices such as Faraday rotators, isolators and circulators. In this paper, an accurate and analytical method is proposed for a periodic array of graphene ribbons under magnetic bias. The method is based on integral equations governing the induced surface currents on the coplanar array of graphene ribbons. For subwavelength size ribbons subjected to normally incident plane waves, the current distribution is derived leading to analytical expressions for the reflection/transmission coefficients. The results obtained are in excellent agreement with full-wave simulations and predict resonant spectral effects that cannot be accounted for by existing semi-analytical methods. Finally, we extract an analytical, closed form solution for the Faraday rotation of magnetically-biased graphene ribbons. In contrast to previous studies, this paper presents a fast, precise and reliable technique for analyzing magnetically-biased array of graphene ribbons, which are one of the most popular graphene-based structures.