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