Calculations of second-order nonlinear optical susceptibilities in III-V and II-VI semiconductor heterostructures

We derive the nonlinear-optical coefficients of insulators using a fully quantum-mechanical theory of the electron-photon interaction. Using the minimal-couping interaction, we find an alternative interpretation for the absence of the vector-potential-squared (${\mathit{A}}^2$) term in the second-order response. Specializing to the case of up-conversion, we use the resulting expression, together with empirical tight-binding band-structure calculations, to compute the second-order susceptibility ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$ of bulk semiconductors in the static limit and of semiconductor heterostructures at resonance. These nonlinear-optics calculations are based on the empirical tight-binding model without additional parameter fit beyond the band-structure model.