Optical rectification and shift currents in GaAs and GaP response: Below and above the band gap

We present a full band structure scheme to calculate the electronic contribution to the second order susceptibility coefficient pertinent to optical rectification, χ₂ᵃᵇᶜ(-ω_∑;ω_β,ω_γ) where ω_∑≈0, within the independent particle approximation for the electron dynamics, and in the dipole limit. This allows us to determine the electronic response of a bulk semiconductor to a femtosecond optical pulse over a range of central frequencies, both below and above the band gap frequency. Particularly interesting is the limit χ₂ᵃᵇᶜ(0;ω,-ω). In addition to the usual near-dc interband rectification current, shift and injection currents, associated with actual divergences in χ₂ᵃᵇᶜ(0;ω,-ω), are taken into account. Calculations for GaAs and GaP, in which injection currents are forbidden, are performed. The band energies and matrix elements are computed with the full potential linearized augmented plane wave method. For frequencies above the band gap, and for typically available pulse widths, we demonstrate that the shift current dominates the current response, being approximately two orders of magnitude larger than the rectification current. For very narrow pulse widths, on the order of a femtosecond, the rectification current becomes comparable to the shift current.