Pulsed Beam Propagation in Lossless Dispersive Media

In this paper, we have been concerned with the parameterization of the effects of frequency dispersion on the propagation characteristics of a paraxially approximated pulsed beam (PB) wavepacket in a lossless medium with generic wavenumber profile k(ω). Various nondimensional measures critical parameters have been defined in order to systematically assess and quantify a) the effect of dispersion on various observables associated with the PB field and thereby on the resolution of these observables, and b) the range of validity of the paraxial approximation under these conditions.

After first summarizing the “conventional” spectral synthesis via the previously performed sequence in [4, 5], which begins with the wavenumber superposition in the time harmonic frequency domain (FD), followed by the FD inversion to the time domain (TD), the remaining portion of this paper has dealt with the “unconventional” synthesis whereby the frequency inversion is performed first to yield a wavenumbor spectral distribution of pulsed plane waves which are assembled subsequently to constitute the TD PB field. While the final outcomes from these alternative approaches for a given set of problem conditions coincide, each spectral sequence elucidates its own wave physics. Fur understanding short pulse (i.e., PB) phenomenology at its most fundamental level, the TD spectral plane wave decomposition is the preferred approach. The (k, ω) dispersion profile plays a crucial role in parameterizing all space time observables self-consistently in terms of space-time dependent frequencies and wavenumbers: ω[k(r, l)] or k[ω(r, l)]. Within the condensed format of this paper, details of derivations and extensions to parametric regimes beyond those presented here could not be included. Such material is contained in an article on the “direct TD” approach which is being submitted separately for publication [G].