Quasistatic precursors of ultrashort laser pulses in electro-optic crystals

It was recently predicted [M. I. Bakunov, A. V. Maslov, and M. V. Tsarev, Phys. Rev. A 95, 063817 ( 2017)] that simultaneous optical rectification and multiphoton absorption of an ultrashort laser pulse in an electro-optic crystal can generate a quasistatic electromagnetic precursor propagating ahead of the laser pulse. We explore this phenomenon by finite-difference-time-domain modeling of Maxwell's equations supplemented with the constitutive relations of the optically ionized crystal. In particular, we elucidate the effects of the laser beam width and the pump depletion on the precursor generation. We show that focusing of the laser beam does not destroy the formation of the precursor, and the detrimental effect of the pump depletion can be eliminated by chirping the pump laser pulse.