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.Comment: 11 pages, 3 figure