Electromagnetic Wave Energy and Momentum Equations in Transparent, Dispersive, Space- and Time-Varying Media

Abstract

It is shown that the transport equations for the electromagnetic wave energy density W_k and momentum density P_k in transparent, dispersive, space- and time-varying media are given by dW_k⁄dt=ω_k⁻¹∂ω_k⁄∂t W_k+2γ_kW_k and by dP_k⁄dt=−k⁻¹·∂ω_k⁄∂rP_k+2γ_kP_k, respectively, where d⁄dt denotes the total time derivative along the ray trajectory and γ_k is the growth rate. The terms ω_k⁻¹∂ω_k⁄∂t W_k and −k⁻¹·∂ω_k⁄∂rP_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 lincar response theory are valid.