TE and TM beam decomposition of time-harmonic electromagnetic waves

Abstract

The present contribution is concerned with applying beam-type expansion to planar aperture time-harmonic electromagnetic field distribution in which the propagating elements, the electromagnetic beam-type wave objects, are decomposed into transverse electric (TE) and transverse magnetic (TM) field constituents. This procedure is essential for applying Maxwell's boundary conditions for solving different scattering problems. The propagating field is described as a discrete superposition of tilted and shifted TE and TM electromagnetic beams over the frame-based spatial-directional expansion lattice. These vector wave objects are evaluated either by applying differential operators to scalar beam propagators, or by using plane-wave spectral representations. Explicit asymptotic expressions for scalar, as well as for electromagnetic, Gaussian beam propagators are presented as well.

Gaussian Beam Summation Representation of Beam Diffraction by an Impedance Wedge: A 3D Electromagnetic Formulation Within the Physical Optics Approximation

“…The BS of the field is derived in Section V from . A somewhat different procedure for deriving EM-GB expansion is presented in [30].…”

Pulsed Beam Expansion of Electromagnetic Aperture Fields

“…This type of windows gives rise to pulsed-quadratic beam waveobjects which exhibits frequency independent collimation (Rayleigh) distance and therefore are termed iso-diffracting [46]. The iso-diffracting nature makes these waveobjects highly suitable for UWB radiation representations [2,5,10,43,47].…”

“…The propagating waveobjects are localized solutions of Maxwell's equations which carry a Gaussian decay away from the beams' axes. In [43], an EM frame-based expansion was introduced in which the EM field was a priori decomposed into transverse electric and transverse magnetic wave polarizations by processing the transverse field components into novel TE and TM EM beam-type waveobjects. The present investigation extends the time-harmonic representation in [42] for time-dependent EM aperture fields and introduces the time-dependent EM pulsed-beam waveobjects which are requires for the exact expansion as well as their asymptotic evaluation.…”

Time-Dependent Tilted Pulsed-Beams and Their Properties

“…By inserting (29) with (28) into (17), the quadratic phase in (20) is given by (30) By inserting in (28) into (30) with (27) and (17), we find that takes the from of the diagonal matrix (31) for which and are given in (27).…”

“…In order to parameterize the iso-axial tilted PB field, we separate the diagonalized complex curvature matrix into its real and imaginary parts by denoting (32) Then using (31), we obtain (33) and (34) with (35) Finally we separate in (20) into its real and imaginary parts (36) where, using (30) and (32) in (20), we identify (37) and (38) where and are given in (33) and (34), respectively. The real Lorentzian wave-forms are given by (39) and (40) where and are given in (37) and (38), respectively.…”