Pulsed beam reflection and transmission at a dielectric interface: two-dimensional fields

Highly focused pulsed fields in vacuum can be generated analytically by assigning complex values to the space-time source coordinates of the conventional transient free-space Green´s function. These new wave objects have been named 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 space-time 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. A canonical test case for reflection, including critical angle, lateral (head) wave and evanescent transmission effects, is provided by a dielectric half-space. 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 space-time 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 pulsed beam is generated by a complex pulsed line source