Hybrid Wavefront-Resonance Representation for Transient Scattering by an Open Cavity Part III: Analytical Models for the Late Time Oscillations

The numerical results of the second portion of this three part sequence dealing with transient scattering by an open ended plane-parallel waveguide cavity, clearly reveal the existence of a distinct late-time observable in the form of a slowly decaying, aspect-independent typical waveform that carries the signature of a cluster of high-Q resonances that occur near the cavity's mode cutoff frequencies. In this paper, we derive analytic approximations for the resonance frequencies, for the late-time waveform, and for the low-frequency "beats" that appear in this late-time waveform. These observables are related to the cavity dimensions. It is shown that the late-time waveform is essentially independent of the incidence angle and of the excitation pulse.