Time-domain theory of forerunners

Abstract

The time-domain theory of forerunners (precursors) in temporally dispersive, nonmagnetic, isotropic materials is developed using the propagator technique. Specifically, the impulse response at a (comparatively) large propagation depth is expanded in two different ways: (a) with respect to the wave-front and (b) with respect to slowly varying field components. A few numerical examples illustrating the theory are given.

Time-domain Green dyadics for temporally dispersive, simple media

“…which can be proved by mathematical induction, the propagator kernel is seen to satisfy the temporal Volterra integral equation of the second kind [6],…”

“…The second term on the right-hand side of (9.5) is interpreted as 6) where the integrals exist as principal value integrals. Using the Maxwell equations (6.2) and the fact that ∇ S · (u n × Q − ) = −u n · (∇ × Q − ), both equations (9.5) reduce to (r ∈ S)…”

Electromagnetic Wave Propagation in Dispersive and Complex Material with Time-Domain Techniques

“…The wave propagator is closely related to the causal fundamental solution of the dispersive wave operator, see [13].…”

“…In the following, Brillouin's forerunner is defined for materials for which the refractive coefficients n 1 , n 2 < 0, and n 3 are finite. The Debye model indicates that the restriction on the numerical signature (5.6) can be relaxed [13].…”

“…The leading behavior of the hyper-Airy functions of odd indices are oscillating but only weakly attenuated for large negative arguments. The frequencies, the phase angles, and attenuating functions can be obtained explicitly in each separate case [13].…”