CALCULATIONS OF 2ND-ORDER NONLINEAR-OPTICAL SUSCEPTIBILITIES IN III-V-SEMICONDUCTORS AND II-VI-SEMICONDUCTOR HETEROSTRUCTURES

We derive the nonlinear-optical coefficients of insulators using a ful ly quantum-mechanical theory of the electron-photon interaction Using the minimal-coupling interaction, we find an alternative interpretatio n for the absence of the vector-potential-squared (A(2)) term in the s econd-order response. Specializing to the case of up-conversion, we us e the resulting expression, together with empirical tight-binding band -structure calculations, to compute the second-order susceptibility ch i((2)) of bulk semiconductors in the static limit and of semiconductor heterostructures at resonance. These nonlinear-optics calculations ar e based on the empirical tight-binding model without additional pa ram eter fit beyond the band-structure model. The calculated bulk values o f chi((2))(0) are much smaller than available experimental values. Thi s provides an independent and sensitive test on the accuracy of the hi gher tight-binding conduction states and also reveals the need for mor e conduction states. Calculations for the heterostructures were done f or GaAs/AlxGa1-xAs and HgTe/Hg1-xCdxTe quantum wells. The ''macroscopi c'' asymmetry of the quantum structures is reflected in the optical pr operties. Our calculations of intersubband chi((2)) for the AlxGa1-xAs system confirm similar results obtained using one-band calculations a nd agree with recent experimental results. The results predict interes ting differences with respect to the AlxGa1-xAs system due to the inve rted nature of the HgTe band structure. We obtain a nonzero intercondu ction subband c1-c3 optical coupling in a symmetric HgTe quantum well, even at the zone center of the Brillouin cone. Our analysis of ''symm etric'' quantum wells predicts the possibility of second-order nonline arity due to the tetragonal D-2d symmetry. This possibility had been o verlooked in previous discussions of nonlinearity based on the quantum -well picture. The contribution due to interconduction subband transit ions in the symmetric wells is negligible. On the other hand, for the p-doped wells of both material systems, we predict a susceptibility th at is two orders of magnitude larger than typical bulk values and, hen ce, should be amenable to experimental verification.