Femtosecond time-resolved dynamical Franz-Keldysh effect

Abstract

We theoretically investigate the dynamical Franz-Keldysh effect in femtosecond time resolution, that is, the time-dependent modulation of a dielectric function at around the band gap under an irradiation of an intense laser field. We develop a pump-probe formalism in two distinct approaches: first-principles simulation based on real-time time-dependent density functional theory and analytic consideration of a simple two-band model. We find that, while time-average modulation can be reasonably described by the static Franz-Keldysh theory, a remarkable phase shift is found to appear between the dielectric response and the applied electric field.

Multi-Scale Simulation for Transient Absorption Spectroscopy under Intense Few-Cycle Pulse Laser

“…On the other hand, the peaks shift forward as the photon energy decreases and increases. This behavior is similar to the case of CW pump laser [24]. Figure 4 shows the case of a more intense pump laser (4 × 10 11 W/cm 2 ).…”

“…The calculated optical band gap by the mBJ is 6 eV, which is improved from that by the LDA (5.5 eV) [24,28], and close to the experimental value (7 eV). We approximate the time-evolution operator by its Taylor series expansion up to 4th order…”

“…The negative value in ∆Ab indicates photo-emission. According to previous theoretical work, DFKE can be understood via the response of the dressed states [24]. The response of the dressed states includes all optical paths, i.e.…”

“…In the case of the continuous wave (CW) pump laser, Tr-DFKE can be analytically understood from the general dressed state picture, as we reported [24,25]. However, for a few-cycle laser pulse, numerical simulation is indispensable because the dressed state is not a good picture.…”

“…In previous work, we determined the sub-cycle change of the optical propertiescite, i.e., time-resolved DFKE (Tr-DFKE), which corresponds to the beat and quantum path interference between the different dressed states [24,25]. In particular, this ultra-fast change exhibits an interesting phase shift that depends on the field intensity and probe frequency.…”