Phase-space beam summation for time-harmonic radiation from large apertures

Analytical modeling of high-frequency time-harmonic and transient radiation from extended aperture sources and of propagation of the resulting fields through perturbing environments is facilitated by simultaneous use of configurational (space-time) and spectral (wave number–frequency) information for suitably defined synthesizing wave objects. Such a bilateral approach can be embodied within a configuration-spectrum phase space. The present investigation deals with radiation from extended aperture sources, with emphasis on alternative uses of the phase space at high frequencies, on promising wave objects as basis elements for field synthesis, and on extraction of physical information from exact wave solutions by asymptotic methods. Of special interest are beam-type wave objects that exhibit localization in the phase space because localized wave fields have favorable propagation characteristics in complex external environments. In this paper, alternative phase-space parameterizations are applied to time-harmonic plane aperture distributions and to the corresponding fields radiated into a homogeneous half-space. The parameterizations include nonwindowed continuum versions, in which localization occurs asymptotically through constructive interference; windowed continuum versions, in which localization is embedded inherently; and windowed discretized versions, in which the basis elements are situated on a self-consistent configuration–wave number lattice. By analysis and illustrative examples, it is shown how these alternative formulations are interrelated, how the localization around well-defined regions in the phase space takes place in each formulation, and how these localization properties, through the beam propagators, influence the synthesis of the radiation field. Transient phenomena will be addressed in separate publications.

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