Phase-space beam summation for time-harmonic and time-dependent radiation from extended apertures: 3D formulation

This paper is concerned with a general mathematical framework for the modeling and analysis of pulsed radiation from an extended source distribution. The radiated field is expressed as a continuous superposition of pulsed beam (PB) propagators which emanate from all points in the source plan and in all directions and initiation times. This phase-space distribution of PB is matched rigorously to the given time-depended source distribution via the new "local Radon transform", which extracts the local space-time spectral (directional) properties of the source distribution. The representation integral emphasizes a priori the local radiation properties of the source distribution, thereby improves numerical efficiency and enhances physical interpretation. The basic concepts have been introduced recently for two-dimensional configurations. The present paper extends the representation to three dimensions, derives expressions for relevant transforms and propagators and discusses the additional phenomena introduced by the three dimensionality. This phase-space formulation should be contrasted with the alternative Hermite pulsed beam expansion scheme presented elsewhere in this issue, which applies only for well collimated radiation.