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A discrete phase‐space Gaussian beam summation representation for electromagnetic radiation from a planar source is presented. The formulation is based on the theory of frames and removes the inherent difficulties of the Gabor representation for both monochromatic and ultra wideband (UWB) fields. For monochromatic fields the frame‐based representation leads to an efficient and flexible discrete Gaussian beam representation with local and stable expansion coefficients. For UWB fields a novel scaling of the frame overcompleteness parameter is introduced, leading to a new expansion that utilizes a discrete frequency‐independent set of beams over the entire relevant spectrum. It is demonstrated that the isodiffracting Gaussian beams provide the snuggest frame representation over the entire spectrum. The rules for choosing the “optimal” frame and beam parameters for a given problem are discussed and demonstrated on application examples.
Lugara et al. (Tue,) studied this question.