Time-resolved dynamical Franz-Keldysh effect produced by an elliptically polarized laser

An analytical formula is reported describing the time-resolved dynamical Franz-Keldysh effect (Tr-DFKE) produced by an elliptically polarized laser at subfemtosecond timescale. The Houston function is assumed as the time-dependent wave function of the parabolic two-band system. For elliptical polarization, the resulting formula exhibits subcycle changes in the optical properties; the modulation of the dielectric function is smaller than that for linear polarization. In contrast, the subcycle modulation of the dielectric function, a significant feature of the Tr-DFKE, disappears for a circularly polarized laser. This analytical formula shows good qualitative agreement with the first-principle calculation employing the time-dependent density functional theory for diamond.