The Angular Spectrum Representation of Pulsed Electromagnetic Beam Fields

Abstract

A completely general representation of the propagation of a freely-propagating electromagnetic field into the half-space z ⩾ z₀ > Z > 0 of a homogeneous, isotropic, locally linear, temporally dispersive medium is now considered. The term “free” is used here¹ to indicate that there are no externally supplied charge or current sources for the field present in this half-space, the field source residing somewhere in the region ∣z∣ ⩽ Z. It is unnecessary to know what this source is provided that the pair of electromagnetic field vectors are known functions of time and the transverse position vector r_T = î _x x + î_yy in the plane z = z₀, as illustrated in Fig. 4.1. The rigorous, formal solution of this planar boundary value problem for the electromagnetic field in the half-space z ⩾ z₀ forms the basis of investigation for a wide class of pulsed electromagnetic beam field problems.