Nonlinear Faraday Rotation of Light Polarization in Time-Reversal-Invariant Materials

We investigate the propagation of electromagnetic waves through materials displaying a nonlinear 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 nonlinear regime relevant for most experiments, we find that the polarization of light displays a Faraday-like rotation when it propagates inside a metal above its plasma frequency. In contrast to the conventional Faraday effect, however, the polarization direction 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 in materials displaying the nonlinear Hall effect.