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

Abstract

An ultrafast anisotropic electro-optic effect of the zinc sulfide crystal is predicted employing a numerical pump-probe simulation. The numerical results indicate that the time-dependence of the anisotropic response of ZnS exhibits a phase shift with respect to the pump laser field. The phase shift coincides with the time-resolved dynamical Franz-Keldysh effect, which is the modulation of the isotropic part of the dielectric function. While the probe frequency dependence around the band gap is not intense, it becomes intense at higher photon energies of approximately 42 eV.In the last two decades, advances in laser sciences and technologies have led to the availability of intense coherent light sources with different characteristics. Ultrashort laser pulses can be as short as few tens of attoseconds, leading to the development of the new field of attosecond science 1 . Intense laser pulses of mid-infrared (MIR) or terahertz (THz) frequencies have also recently become available 2,3 . By employing these extreme sources of coherent light, investigating the optical response of materials in real-time with sub-optical cycle resolution is possible 1,4-8 .The dielectric function ε αβ (ω) is the most fundamental quantity characterizing the optical properties of matter. 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 9-13 . In particular, this ultrafast change exhibits an interesting phase shift that depends on the field amplitude and probe frequency. By utilizing this phenomenon, we can develop an ultrafast optical modulator or an ultrafast optical switch.Recently, the Tr-DFKE was experimentally observed by a near-infrared (NIR)-pump extreme ultraviolet (EUV)-probe with attosecond time resolution for polycrystalline diamond 14,15 . A similar effect was also observed in an excitonic state in a GaAs quantum well by THz-pump NIR-probe spectroscopy 16 . However, because the signal by the Tr-DFKE is small, the high precision measurement or intense pump field is required.The diagonal parts represent ε αα the isotropic response, whereas the off-diagonal parts ε αβ (α = β) represent the anisotropic response. Because the anisotropic response can be detected as the polarization direction, it is sensitive to the change of signal. The magnetic field and electric field can induce anisotropic properties in isotropic materials. An ultrafast optical Faraday effect induced by the circularly laser field has been theoretically proposed 17 Under the electric field, some material shows an intense electro-optic effect, e.g., the Pockels effect and the Kerr effect. The electro-optic effect is utilized to probe the waveform of the THz field, and ultrafast phenomena such as laser-accelerated electron bun...