The behavior of electromagnetic localized waves at a planar interface

In this paper, we investigate the behavior of electromagnetic localized waves [LW's], which are concentrated moving pulses of energy, at an interlace between two electrically different media. We employ a previously given Fourier transform domain representation of LW's that is geometric in nature; the Fourier transform of an LW consists of a support line on a particular surface together with a weighting associated with this line. The behavior of electromagnetic LW's at an interface is somewhat involved owing to their broadband nature, but this behavior has a lucid pictorial representation in terms of the transform domain geometry and, in this paper, we exploit this representation. If an LW strikes the interface obliquely then a different LW is reflected, but the pulse transmitted into the second medium is not a LW. We give analytical and graphical evidence of this behavior. Moreover, we show that if one desires a particular LW to be propagated into the second medium, one can in some cases design the necessary non-LW pulse one needs to launch at the interface to achieve this goal.