PULSED-BEAM REFLECTION AND TRANSMISSION AT A DIELECTRIC INTERFACE - 2-DIMENSIONAL FIELDS

In previous publications it has been shown how highly focused pulsed fields in vacuum can be generated analytically by assigning complex values to the spacetime source coordinates of the conventional transient free-space Green's function. These new wave objects have been called complex source pulsed beams (CSPB). Their utility can be extended to generating new solutions for pulsed beam propagation and diffraction in a perturbed environment by making the spacetime source coordinates in the corresponding Green's function complex. The analytic extension required in this process is performed systematically via the spectral theory of transients (STT). A canonical test case for reflection, including critical angle, lateral (head) wave and evanescent transmission effects, is provided by a dielectric halfspace. The exact solution for CSPB scattering is derived in spectral integral form, evaluated in terms of the time-dependent spatial spectrum singularities in the complex plane, and interpreted physically. Numerical evaluation reveals the detailed spacetime behavior of these physical constituents and their role in establishing the total scattered field. To simplify the analysis, a two-dimensional problem is considered wherein the PB is generated by a complex pulsed line source. Due to the trailing signal that accompanies any two-dimensional transient field, some of the phenomena are less distinct than they would be for three-dimensional CSPB. © 1990 IEEE