L B Felsen | PubMed Health

PubMed2001

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 (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 a priori localization in the plane-wave-based nonwindowed spectral representations.

Journal Article↗

PubMed1992

Multiple reflected beam synthesis of fields excited by a high-frequency oblique beam input in an elastic plate.

Transducer-excited beams provide important diagnostic tools for ultrasonic nondestructive evaluation (NDE) of elastic materials. For bonded multilayer elastic plates, an obliquely injected high-frequency compressional (P) beam creates interior dynamic fields that are sensitive to weak debonding between the layers. In an effort to clarify the wave phenomena that are operative under these conditions of excitation, a highly idealized model has been chosen wherein a lossless plate in vacuum is insonified by an internal oblique P-beam source. This problem was analyzed in a previous investigation [Lu, Felsen, and Klosner, J. Acoust. Soc. Am. 87, 42-53 (1990)] by expressing the total field in terms of a sum of P-S (vertically polarized or in-plane) coupled normal modes. While the resulting field assumed oscillatory modal patterns at interior cross sections far from the source region, the modally synthesized field near the source clearly outlined profiles interpretable as incident and singly or multiply reflected P-S coupled beams. The problem is therefore studied here directly by Gaussian beam tracing as implemented via our previously employed complex ray field algorithm. The results clarify the observed phenomena by revealing the successive buildup from initially well-resolved beams into oscillatory mode patterns synthesized by overlapping multiples. For the same idealized model, the beam algorithm has been applied elsewhere to the detection and identification of weak debonding in a layered plate [Felsen and Zeroug, J. Acoust. Soc. Am. 90, 1527-1538 (1991)]. With an understanding of the physical mechanisms that arise in the beam-to-mode conversion, one may now explore how their utility is affected under realistic NDE conditions.

Algorithms↗