Dispersion Properties, Nonlinear Waves and Birefringence in Classical Nonlinear Electrodynamics

TL;DR

This paper investigates how quantum corrections influence electromagnetic wave propagation in nonlinear electrodynamics, revealing effects like reduced wave speed, polarization-dependent birefringence, and wave behavior akin to cnoidal waves.

Contribution

It derives a nonlinear wave equation accounting for quantum corrections and analyzes polarization-dependent birefringence and wave speed reduction in classical nonlinear electrodynamics.

Findings

Electromagnetic waves propagate with reduced speed proportional to initial wave intensity.

Two polarization states propagate independently at different frequencies.

Wave behavior resembles cnoidal waves in shallow water.

Abstract

Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the electromagnetic vector potential is solved perturbatively about the known exact plane wave solution in both the free vacuum case, as well as when a constant magnetic field is applied. A nonlinear wave equation with nonzero convective part for the (relatively) slowly varying amplitude of the first-order perturbation has been derived. This equation governs the propagation of electromagnetic waves with a reduced speed of light, where the reduction is roughly proportional to the intensity of the initial pumping plane wave. A system of coupled nonlinear wave equations for the two slowly varying amplitudes of the first-order perturbation, which describe the two polarization states, has been obtained for the case of constant magnetic field background. Further, the slowly varying wave amplitude behavior is shown to be similar to that of a cnoidal wave, known to describe surface gravity waves in shallow water. It has been demonstrated that the two wave modes describing the two polarization states are independent, and they propagate at different wave frequencies. This effect is usually called nonlinear birefringence.