Time-resolved dynamical Franz-Keldysh effect under elliptically polarized laser

The analytical formula for the time-resolved dynamical Franz-Keldysh effect (Tr-DFKE) under an elliptically polarized laser in sub-femtosecond time-scale is reported. The Houston function is assumed as the time-dependent wave function of the parabolic two-band system. The resulting formula shows the sub-cycle change of the optical properties for elliptically polarization; the modulation of the dielectric function becomes smaller than that of linear polarization. On the other hand, the subcycle modulation of the dielectric function disappears for a circularly polarized laser, which is a significant feature of the Tr-DFKE. This analytical formulas show good qualitative agreement with the first-principle calculation employing the time-dependent density functional theory for diamond.