Analytical formulation for modulation of time-resolved dynamical Franz-Keldysh effect by electron excitation in dielectrics

Abstract

Analytical formulation of sub-cycle modulation (SCM) of dielectrics including electron excitation is presented. The SCM is sensitive to not only the time-resolved dynamical Franz-Keldysh effect (Tr-DFKE) [T. Otobe, et al., Phys. Rev. B 93, 045124 (2016)], which is the nonlinear response without the electron excitation, but also the excited electrons. The excited electrons enhance the modulation with even-harmonics of pump laser frequency, and generate the odd-harmonics components. The new aspect of SCM is a consequence of i) the interference between the electrons excited by the pump laser and those excited by the probe pulse laser and ii) oscillation of the generated wave packed by the pump laser. When the probe-and pump-pulse polarizations are parallel, the enhancement of the even harmonics and the generation of the odd harmonics modulation appear. However, if the polarizations are orthogonal, the effect arising from the electron excitations becomes weak. By comparing the parabolic and cosine band models, I found that the electrons under the intense laser field move as quasi-free particles.w n, k ( r, t) = u G n, k+ e c A(t) ( r) exp −i t dt ε G n, k (t )where ε G n, k (t) = ε G n, k+ e c A(t) .

Attosecond electro-optic effect in zinc sulfide induced by a laser field

“…567.-8.9:1-2;<4 respect to ω is similar to that of ∆ε xx (T p , ω). The ω dependent phase shift in ∆ε xx (T p , ω) corresponds to the relative phase of two Floquet states at T p [11][12][13]16 . Therefore, the ω-dependent phase indicates that the Pockelslike effect in the non-adiabatic regime is also the result of the relative phase between the Floquet states.…”

“…The dielectric function observed in an ultrafast pumpprobe experiment can be further considered as a probe time (T p )-dependent function, ε αβ (T p , ω). We determined the sub-cycle change in the optical properties, i.e., the time-resolved dynamical Franz-Keldysh effect (Tr-DFKE), which corresponds to the response of the dressed states and quantum path interference of different dressed states [9][10][11][12][13] . In particular, this ultrafast change exhibits an interesting phase shift that depends on the field amplitude and probe frequency.…”

Electron excitation rate in dielectrics under an intense elliptically polarized laser field

“…The electron excitation dynamics has been numerically studied, employing the time-dependent density functional theory (TDDFT) [21][22][23] as well as analytical models. 15,24) Although the numerical simulation employing TDDFT is one of the most accurate approaches, it needs a sizeable computational resource, and analyzing the details of the physical process is sometimes demanding. The analytical approach is not accurate like TDDFT, although we can use it to study the physics of the interaction in detail.…”