Pulsed beam reflection and transmission at a planar interface: exact solutions and local models

Pulsed beams (PB) are collimated space-time wavepackets that propagate along ray trajectories. Because they are localized in spacetime, they are useful in modeling applications addressing highly focused energy transfer, local (high resolution) probing of the propagation environment, etc. An important class of PB are the complex source PB (CSPB) which are modeled mathematically by a pulsed source located at a complex coordinate point. Their properties, physical realization and application have been explored extensively in recent years. A whole new class of wavepacket scattering problems can therefore be modeled by substituting complex source coordinates into the time-dependent Green's function of the environment. The response to the PB input can be evaluated exactly via the previously introduced spectral theory of transients (STT). This procedure is applied here for the canonical problem of a PB scattering at a planar interface separating two homogeneous half spaces. Exact field solutions are derived in closed form via the STT while extension to more general interface configurations is addressed by deriving approximate scattering models that depend on the local properties of the interrogation wavepacket and of the interface. Depending on the PB angle, these models involve PB reflection and refraction, evanescent wavepackets and local excitation of a head-wavepacket. Via numerical examples and parametrical studies, we emphasize both the physical phenomena and the new mathematical procedures of the full 3D solution.