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 ∂ω
S
/∂k
S
where k
S
, ω
S
are the saddle-point values of the propagation vector and the angular frequency. The imaginary part of ∂ω
S
/∂k
S
can physically be interpreted in terms of v and derivatives of Re k
S
ċ σ, Re ω
S
τ in the direction of v, where σ
^1/2
and τ
^1/2
are beam-width and pulse duration, respectively.