PROPAGATION OF ELECTROMAGNETIC PULSES THROUGH THE SURFACE OF DISPERSIVE BODIES

The motion of an electromagnetic pulse (signal) through the surface of a semiinfinite (half-space) polarizable body is investigated. The incident pulse of electromagnetic radiation propagating in vacuum is assumed to be of finite duration and finite spatial extension. As regards its extension along the transverse directions, two cases are considered. First, we assume a large (infinite) extension (in comparison with the wavelength), as for a plane wave (beam, ray); second, a very narrow pulse is assumed (zero thickness, close to the diffraction limit). In its motion the pulse encounters the plane surface of a semi-infinite polarizable body (a half-space) and penetrates into the body. The body reacts through its polarization degrees of freedom, which obey the well-known Drude-Lorentz (plasma) equation of motion. It is shown that the beam obeys the well-known refraction law (Fresnel equations), with a specific discussion, which is provided. For the narrow pulse, both the normal and oblique incidence are analysed. It is shown that far away from the incidence direction (large transverse distance r) the motion is governed by the polaritonic eigenmodes, which yields a pulse, approximately of the same shape as the original one, propagating with the group velocity and with an amplitude which decreases as 1/r(2). The group velocity is always smaller than the speed of light in vacuum c. In the vicinity of the propagation direction (small distance r), the original pulse is almost entirely preserved, including its propagation velocity c, with a distorted amplitude, which depends on the transverse direction. This picture is in fact the diffraction limit of the narrow pulse. The transmitted coefficient is computed for normal incidence. The reflected pulse is also computed, as well as the refracted pulse for oblique incidence. While the reflection law is preserved (reflection angle is equal to the incidence angle), the refraction law is different from Snell's law of refraction of a plane wave, in the sense that the highly localized (narrow) pulse along the transverse direction preserves its propagation direction on entering into the body.