Fast Computation of Gaussian Window Radiation

A method for the fast computation of radiation by Gaussian windows, with controllable error, is presented. The computation aims to complement beam summation frameworks as an alternative to analytical propagators (e.g., the paraxial Gaussian beam and the complex source beam). Its accuracy in describing the off-axis fields is of particular interest for retaining a correct description of diffraction fields in complex scattering scenarios. The proposed method relies on the efficient sampling and tabulation of the phase- and amplitude-compensated fields produced by Gaussian window distributions, using analytical propagator expressions for designing optimal compensator functions. The reconstruction of the fields from datasets of samples is via low-order local interpolation, followed by restoration of the removed amplitude and phase. The method can be used for constructing a “dictionary” of beams, ranging in tilt and width, in accordance with phase-space lattices of interest, to be naturally integrated into Gaussian beam summation frameworks. Examples that highlight the need for the proposed technique and that demonstrate its performance are provided.