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 (FD) and the short-pulse time domain (TD) and within as well as arbitrarily beyond the paraxial constraint. For the formal analysis, which is followed by physics-matched high-frequency asymptotics, we use a (space–time)–(wavenumber–frequency) phase-space format to discuss the exact complex-source-point method and the associated asymptotic beam tracking by means of complex rays, 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 <i>a priori</i> localization in the plane-wave-based nonwindowed spectral representations.
© 2001 Optical Society of America
(080.1510) Geometric optics : Propagation methods
(080.2710) Geometric optics : Inhomogeneous optical media
(130.2790) Integrated optics : Guided waves
(350.7420) Other areas of optics : Waves
Ehud Heyman and Leopold B. Felsen, "Gaussian beam and pulsed-beam dynamics: complex-source and complex-spectrum formulations within and beyond paraxial asymptotics," J. Opt. Soc. Am. A 18, 1588-1611 (2001)