Pulsed-beam propagation in dispersive media via pulsed plane wave spectral decomposition

This paper is concerned with the behavior of transient wavefields due to a pulsed-beam (PB) wavepacket launched obliquely from a hypothetical aperture plane in a medium with generic dispersion k(ω) where k and ω are wavenumber and frequency, respectively. This generalizes our previous investigation of a PB launched normally from the hypothetical aperture plane. The problem is solved through spectral decomposition into plane waves in the frequency (ω) and spatial wavenumber (E) domains, followed by asymptotics on the spectral inversion integrals, with ω synthesis performed before ξ synthesis. Special attention in the transient spectral domain is given to paraxial PB approximations and to criteria for their range of validity, which are expressed in terms of critical nondimensional estimators that contain the beam parameters as well as the dispersion parameters of the medium. The resulting PBs can be used to synthesize transient wavefields excited by arbitrary space-time source distributions of finite support on a specified aperture plane in the medium