Electromagnetic wave energy and momentum equations in transparent, dispersive, space- and time-varying media

It is shown that the transport equations for the electromagnetic wave energy density W sub(k) and momentum density P sub(k) in transparent, dispersive, space- and time-varying media are given by dW sub(k)/dt = ωsub(k)sup(-1)deltaωsub(k)/delta t W sub(k) + 2γsub(k)W sub(k) and by dP sub(k)/dt = -k-1.deltaωsub(k)/delta r P sub(k) + 2γsub(k)P sub(k), respectively, where d/dt denotes the total time derivative along the ray trajectory and γsub(k) is the growth rate. The terms ωsub(k)sup(-1)deltaωsub(k)/delta t W sub(k) and -k-1.deltaωsub(k)/delta r P sub(k) result from the fact that the wave energy and momentum density are not adiabatic invariants in space- and time-varying media. It is assumed that the geometric optics approximation and the nonlocal linear response theory are valid. (author)