Physical source realization of complex source pulsed beams

A more stable transition matrix for acoustic target scattering by highly oblate elastic objects

In previous work, a variant of Waterman's transition (T) matrix utilizing an ansatz for problematic outgoing basis functions in standard formulations was proposed and demonstrated to improve the stability of free-field acoustic scattering calculations for elongated axisymmetric elastic objects. The ansatz replaced the basis causing instability with one consisting of low-order spherical functions made complete by distributing the functions along the axis within the object. Unfortunately, these bases are not as useful for expanding outgoing source fields along oblate axisymmetric surfaces. However, related work by Doicu, Eremin, and Wriedt, [Acoustic & Electromagnetic Scattering Analysis Using Discrete Sources, Academic Press, London (2000)], suggests using an alternate basis of low-order spherical functions made complete by analytically continuing them into the complex plane of the object's axial coordinate, distributing them along the imaginary axis of this plane. This paper will show that this alternative does extend the range of stability of our T-matrix formulation for highly oblate axisymmetric objects to frequencies attainable with competing spheroidal-basis T-matrix formulations. Nevertheless, the range is not as great as achieved for prolate shapes and an analysis of the residual noise sources suggest more optimal basis sets are possible that further stabilize scattering computations for such shapes.

High-aperture beams: comment

Clarifications are provided for the proper choice of the branch of a square-root function that is connected with the singularity on the focal plane occurring in the treatment by Sheppard on 'High-aperture beams' [J. Opt. Soc. Am. A18, 1579 (2001)]. The author's claim that the singularity is nonphysical is disputed.

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.