Non-linear Faraday Precession of Light Polarization in Time-Reversal Invariant Materials

TL;DR

This paper explores how electromagnetic waves experience a non-linear Faraday-like precession of polarization in materials with a non-linear Hall effect, revealing oscillatory behavior linked to wave intensity and Berry dipole dynamics.

Contribution

It introduces a theoretical framework mapping Maxwell-Boltzmann equations to pendulum-like equations, predicting polarization precession and oscillations in non-linear Hall materials.

Findings

Polarization precesses back and forth around Berry dipole direction.

Oscillation frequency increases linearly with wave intensity.

Observable effects include thickness-dependent Faraday rotation and emitted radiation.

Abstract

We investigate the propagation of electromagnetic waves through materials displaying a non-linear Hall effect. The coupled Maxwell-Boltzmann equations for traveling waves can be mapped onto ordinary differential equations that resemble those for the motion of a pendulum. In the weakly non-linear regime relevant for most experiments, we find that the polarization of light displays a Faraday-like precession of its polarization direction that swings back and forth around the direction of Berry dipole vector as the light beam traverses the material. This occurs concomitantly with an oscillation of its degree of polarization, with a characteristic frequency that increases linearly with the intensity of the traveling wave. These effects could be observed by measuring thickness dependent Faraday rotations as well as the emission of lower frequency radiation associated with the polarization oscillations in materials displaying the non-linear Hall effect.