ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06

1aPA1. On local versus global parametrization of short-pulse-excited scattering and spectra: Poisson summation revisited.

Leopold B. Felsen

Dept. of Aerospace and Mech. Eng., Boston Univ., 110 Cummington St., Boston, MA 02215

Poisson summation has conventionally been employed for conversion of local scatterings due to individual elements in an infinite periodic array into global Bragg spectra that characterize the collective phenomena due to the entire array. In a recent generalization, time harmonic and transient local--global phenomena in finite periodic and quasiperiodic arrays have been related via finite Poisson summation, with the global outcome interpreted as radiation from equivalent sources distributed over the finite array aperture [L. B. Felsen and L. Carin, 638--649 (1994)]. This analysis is now re-examined in the context of multiple scatter scenarios under short-pulse time-domain excitation. Since short enough pulsed incident fields can time-gate individual scattered field arrivals, the early time response at the observer is necessarily parametrized locally. As multiple interaction develops, one may reparametrize any finite number of these collectively in terms of spectra associated with equivalent sources that are smoothly distributed over the corresponding multipass finite space-time aperture. This results in global algorithms based partly in the configuration domain and partly in the spectral domain. These concepts are developed and examined rigorously and asymptotically with respect to the time evolution of global spectra from highly resolved early scatters under short-pulse time-domain conditions. Corresponding statistical aspects, when the scattering hierarchy is randomly perturbed, are explored as well. [Work supported by AFOSR and ONR.]