Beam decomposition of time-harmonic electromagnetic waves

The present contribution is concerned with extending the scalar frame-based beam summation to include electromagnetic fields in which an exact beam expansion of planar initial time-harmonic electromagnetic field is presented. The propagating electromagnetic field is described as a discrete superposition of tilted and shifted electromagnetic beam propagators over the frame spatial-directional spectral lattice. The propagating wave objects are localized solutions of Maxwell´s equations which carry a Gaussian decay away from the beams´ axes. Moreover, the EM field is a priori decomposed into transverse electric (TE) and transverse magnetic (TM) wave constituents by processing (expanding) the transverse field components into a novel TE and TM EM beam-type waveobjects.