We present a full band-structure calculation of the electronic contribution to the second-order susceptibility in the limit of a sum frequency that vanishes. We give a sum-over-states expression for the optical rectification coefficient χrect(ω)≡χrect(0;ω,-ω), which includes intraband contributions. Intraband transitions additionally lead to shift and injection currents, which we identify in the total response and separate from the optical rectification. The approach applies to all crystal classes and over a wide range of applied optical frequencies. We apply our results to a full band-structure calculation of the optical rectification, shift current, and injection current susceptibilities for wurtzite CdS and CdSe.
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Nastos et al. (2010) studied this question.