Gaussian beams representation based on periodic frames for radiation from cylindrical apertures

A formulation is introduced for periodic windowed Fourier transform (WFT) frames. Such frames are then used to represent fields on cylindrical surfaces. Through phase matching at the surface, fields radiated from localized Gaussian windows are expressed in the form of general Gaussian beams, leading to a representation of radiated fields as sums of beam propagators. Such representations are presented on test cases, and can be most useful in representing fields in complex environments, around linear sources or obstacles.