Propagation of Few- to Sub-Cycle Pulse in Dispersive Media

Abstract

Propagation of ultrashort electromagnetic pulses of few- to sub-cycle duration is studied. Assuming that the spectrum of the pulse is localized at zero frequency enough to be weakly dispersive, a paraxial equation for the electric field is derived, which has axially symmetric gaussian beam mode solutions. Then, the pulse is found to propagate with its shape unchanged within certain propagation distance determined by dispersion and dissipation strength of the media and the bandwidth of the pulse’s initial spectrum. On the other hand, for the pulse propagating sufficiently long distance, where the dispersion plays a main role, the asymptotic behavior of the oscillatory damped tail of the pulse is investigated. As a possible application, propagation of phonon–polariton pulses in polar crystals including LiNbO₃ is considered.