An intense laser pulse can transiently turn a dielectric into a conducting medium by exciting electron-hole pairs. If the pulse is as short as a few optical cycles, and the excitation process is highly nonlinear, then injected charge carriers form a highly non-equilibrium state. We investigate the optical conductivity of such transient states. Understanding the electrical properties of these states is important to utilize a fast change of optical conductivity for ultrafast metrology. We find that the average effective mass of laser-excited electrons and holes significantly increases with the peak intensity of the laser pulse. Also, we find that the optical conductivity induced by an intense pulse is sensitive to its carrier-envelope phase.
We performed simulations using our recently developed numerical model where the time-dependent Schrödinger equation (TDSE) or semiconductor Bloch equations (SBE) are solved in three spatial dimensions using the basis of Kohn-Sham orbitals . As the input, our code uses band energies and momentum matrix elements obtained from DFT codes (Abinit, Wien2k, GPAW). The equations of motion are solved in the velocity gauge within the independent-particle approximation. Evaluating the polarization response, we benefit from our method for correcting artifacts typical to velocity-gauge simulations .
As an example, the average effective mass of charge carriers excited by a 750-nm 4-fs laser pulse in diamond increases by a factor of 1.7 as the amplitude of the laser pulse increases from 0.5 V/Å to 1.4 V/Å. For SiO2, this is a factor of 3.9. This result is important for interpreting pump-probe measurements designed to study the temporal dynamics of strong-field charge-carrier injection, where a probe pulse accelerates electrons and holes generated by an intense few-cycle pump pulse. Also, the significant increase of the effective mass for intense pulses must be taken into account when the Drude model is applied to describe excitation-induced changes of optical properties of dielectrics and semiconductors.
The effects that we study two main origins: First, a stronger field populates a larger number of bands. Second, multiphoton and tunneling transitions driven by a strong field populate a large part of the Brillouin zone, especially if the amplitude of the vector potential is comparable to or exceeds the size of the Brillouin zone.
 Wismer, M.S., M.I. Stockman, V.S. Yakovlev. Ultrafast optical Faraday effect in transparent solids. arXiv:1612.08433 [cond-mat.other], 2016.
 V. S. Yakovlev, M. Wismer. Adiabatic corrections for velocity-gauge simulations of electron dynamics in periodic potentials. Comp. Phys. Comm. 217, 82 (2017).
Vladislav S. Yakovlev and Michael S. Wismer, "The optical conductivity of dielectrics after ultrafast multiphoton excitation (Conference Presentation)," Proc. SPIE 10673, Advances in Ultrafast Condensed Phase Physics, 106730D (Presented at SPIE Photonics Europe: April 24, 2018; Published: 29 May 2018); https://doi.org/10.1117/12.2309294.5788740836001.
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