Polarisation effects in reflection of ultrashort single-cycle pulses from semiconductors and metals

A model, capable of providing an analytic solution, is proposed for describing the reflection and refraction of polarised ultrashort single-cycle pulses (i.e. pulses with durations as short as one or several oscillations of the field) with an asymmetric nonsinusoidal envelope on the surfaces of dispersive and conducting media. The fields excited by single-cycle pulses in these media are represented by novel transient solutions of the Maxwell equations, obtained directly in the time domain without separation of variables and without Fourier expansions. This approach yields simple formulas for the reflection coefficients of s- and p-polarised single-cycle pulses with Laguerre envelopes, incident at arbitrary angles. The Fresnel, Snell, and Brewster formulas are generalised. It is shown that the reflection coefficients and the angles of refraction of a single-cycle pulse depend on the characteristic duration of the envelope of such a pulse and on the relaxation time of the field in the investigated medium.