The propagation of wave packets in inhomogeneous anisotropic media with moderate absorption

Hamilton's equations for geometric optics contain the quantity ∂ω/∂k which is complex in absorbing media. To investigate its physical meaning, the field of a wave packet (a pulsed beam) in a homogeneous medium with moderate absorption is calculated using the saddle-point method. The packet velocity v is approximately equal to the real part of ∂ωS/∂kSwhere kS, ωSare the saddle-point values of the propagation vector and the angular frequency. The imaginary part of ∂ωS/∂kScan physically be interpreted in terms of v and derivatives of Re kSċ σ, Re ωSτ in the direction of v, where σ1/2and τ1/2are beam-width and pulse duration, respectively.