Wave Objects, Spectra, and Their Role in Analytic Modeling
Modeling of complex wave propagation and scattering relies most generally on a combination of analytical and numerical techniques. How to apportion that combination is problem dependent, with analytical modeling most effective for relatively simple but numerically large portions of a still larger composite. For example, in a large multireflector antenna system, the feed and shaped reflectors constitute complex portions that are separated by long (in terms of wavelengths) propagation paths in free space. While purely numerical treatment of the entire configuration would be prohibitive, a self-consistent parametrization that blends analytical free space propagators with numerical solutions for the feed and reflector portions can render the problem tractable. The most effective analytical models are structured around “observable-based” wave objects tied to the physical phenomena that are operative in establishing the final field. For the propagation links that are most amenable to analytical modeling, “good” wave objects in the frequency domain include ray fields, beams, paraxial propagators, as well as global and local guided mode fields, either separately or in hybrid combinations, that seek to optimize the utility of each for any given propagation environment and input signal. These wave objects and their combinations have direct counterparts under transient conditions. Success in this endeavor requires integrated treatment of input signal, propagation channel, and processing at the receiver so as to unify the entire source-medium-detection process. This is done effectively in a configuration-spectrum phase space representation that treats space-time and wavenumber-frequency simultaneously. It should be noted that the “source” fields here may be actual (directly generated) or virtual (induced on a scatterer surface or an equivalent fictitious surface enclosing a scatterer).
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