Time-Dependent Tilted Pulsed-Beams and Their Properties

Abstract

Abstract-Novel time-dependent wavepacket equation and its pulsed field solutions are obtained by utilizing a non-orthogonal coordinate system which is a priori matched to the field's planar linearly-delayed pulsed localized aperture distributions. These waveobjects that serve as the building blocks for various time-dependent beam-expansion schemes, are termed tilted pulsed-beams. Iso-axial pulsed-beams are parameterized in term of beam-widths, waist-locations, collimation-lengths, wave-front radii of curvature, and other features. Emphasis is placed on a direct time-domain derivation. A numerical example is presented in which the enhanced accuracy of the tilted pulsed-beams over the conventional (orthogonal coordinates) ones in the well-collimated zone is demonstrated.

Transverse electric and transverse magnetic pulsed-beam decomposition of time-dependent aperture fields

“…(13) and P N r; t is the (shortpulsed) asymptotic evaluation of the scalar PB propagators in Eq. (32).…”

“…(13) and P N r; t is the (shortpulsed) asymptotic evaluation of the PB scalar propagator in Eq. (32) that is given in closed form for ID pulsed-quadratic windows in Eq.…”

“…Nevertheless, these methods are considered as a generic tool for scattering problems or for propagation in complex environments, where other methods fail. Closed-form solutions for beam propagators that are required for the expansions have been derived in homogeneous [11][12][13], anisotropic [14][15][16][17][18], dispersive [19][20][21], and inhomogeneous media [22][23][24][25][26][27][28]. Beam-type expansion methods have been applied for the analysis of large reflector antennas [29][30][31], for rough surface scattering [32][33][34][35], and for various inverse scattering applications [36][37][38][39][40][41][42].…”