Phase space methods for radiation from apertures

Development of new concepts for time-harmonic and transient electromagnetic radiation in general, and for directed energy transfer in particular, requires detailed understanding of the spectral as well as the configurational behavior of the fundamental wave constituents employed in field synthesis. The simultaneous treatment of these aspects can be effected in a phase space covering configurational and spatial wavenumber variables for the time-harmonic regime, with the addition of time and frequency variables for the transient regime. The full phase space constructed in this manner is generally not the most convenient for tracking physical observables. Instead, it is desirable to employ reduced or partial phase space representations based on the spectral decomposition of only some of the space-time variables. Various choices in the reduction lead to alternative representations with different physical content, and to corresponding alternative parametrizations of the radiation process. The relation between these alternative forms, their evolution in the phase space, and their manifestation in real space-time, is explored in general terms. Special attention is given to incorporating spatial or spectral windows in the formulation, thereby effecting localization in the form of beams. In this brief summary, only the formulation is presented. Full versions of the theory will be published separately.