Two-photon indirect optical injection and two-color coherent control in bulk silicon

Using an empirical pseudopotential description of electron states and an adiabatic bond charge model for phonon states in bulk silicon, we theoretically investigate two-photon indirect optical injection of carriers and spins and two-color coherent control of the motion of the injected carriers and spins. For two-photon indirect carrier and spin injection, we identify the selection rules of band edge transitions, the injection in each conduction band valley, and the injection from each phonon branch at 4 and 300 K. At 4 K, the TA-phonon-assisted transitions dominate the injection at low photon energies and the TO-phonon-assisted transitions at high photon energies. At 300 K, the former dominates at all photon energies of interest. The carrier injection shows anisotropy and linear-circular dichroism with respect to the light propagation direction. For light propagating along the $\ensuremath{\langle}001\ensuremath{\rangle}$ direction, the carrier injection exhibits valley anisotropy, and the injection into the $Z$ conduction band valley is larger than that into the $X$ and $Y$ valleys. For ${\ensuremath{\sigma}}^{\ensuremath{-}}$ light propagating along the $\ensuremath{\langle}001\ensuremath{\rangle}$ ($\ensuremath{\langle}111\ensuremath{\rangle}$) direction, the degree of spin polarization gives a maximum value about $20%$ ($6%$) at 4 K and $\ensuremath{-}10%$ ($20%$) at 300 K, and at both temperature shows abundant structure near the injection edges due to contributions from different phonon branches. For two-color coherent current injection with an incident optical field composed of a fundamental frequency and its second harmonic, the response tensors of the electron (hole) charge and spin currents are calculated at 4 and 300 K. We show the current control for three different polarization scenarios: For cocircularly polarized beams, the direction of the charge current and the polarization direction of the spin current can be controlled by a relative-phase parameter; for the collinearly and cross-linearly polarized beams, the current amplitude can be controlled by that parameter. The spectral dependence of the maximum swarm velocity shows that the direction of the charge current reverses under an increase in photon energy.

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