Gaussian beam and pulsed-beam dynamics: complex-source and complex-spectrum formulations within and beyond paraxial asymptotics

Paraxial Gaussian beams (GB's) are collimated wave objects that have found wide application in optical system analysis and design. A GB propagates in physical space according to well-established quasi-geometric-optical rules that can accommodate weakly inhomogeneous media as well as reflection from and transmission through curved interfaces and thin-lens configurations. We examine the GB concept from a broad perspective in the frequency domain (F D) and the short-pulse time domain (TD) and within as well as arbitrarily b eyond the paraxial constraint. For the formal analysis, which is followed b y physics-matched high-frequency asymptotics, we use a (space-time)-(wavenu mber-frequency) phase-space format to discuss the exact complex-source-poin t method and the associated asymptotic beam tracking by means of complex ra ys, the TD pulsed-beam (PB) ultrawideband wave-packet counterpart of the FD GB, GB's and PB's as basis functions for representing arbitrary fields, GB and PB diffraction, and FD-TD radiation from extended continuous aperture distributions in which the GB and the PB bases, installed through windowed transforms, yield numerically compact physics-matched apriori localization in the plane-wave-based nonwindowed spectral representations. (C) 2001 Opti cal Society of America.