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Discretized Beam Methods For Focused Radiation From Distributed Apertures

In the analysis of focused radiation from large aperture systems, and especially for the generation of "bullet-like" strongly collimated fields under transient conditions, it is suggestive to employ field representations in terms of focused basis elements. Possible basis functions in the frequency domain include Gaussians and Hermite or Laguerre Gaussians, and, directly in the time domain, complex source pulsed beams and focus wave modes. Some difficulties concerning the excitability of the focus wave modes will be discussed. The basis elements are next embedded in a discretized phase space spanning the space-time and spatial-temporal frequency domains to yield a rigorous field representation. Using space-time Gaussians, the phase space representation has been implemented for radiation from a space-time truncated aperture distribution. The results reveal the effectiveness of this approach to charting the near to far zone evolution of the emitted pulse.