A two-band model is used to calculate the scaling and spectrum of the nondegenerate nonlinear absorption Aa(w,; wJ. From this, the bound electronic nonlinear refractive index n2 is obtained using a Kramers-Kronig transformation. We include the effects of two-photon and Raman transitions and the ac Stark shift (virtual band blocking). The theoretical calculation for n, shows excellent agreement with measured values for a five order of magnitude variation in the modulus of n2 in semiconductors and wide-gap optical solids. We also present new measurements of n, in semiconductors using the Z-scan method. The observed change of sign of n2 midway between the two-photon absorption edge and the fundamental absorption edge is also predicted. Thus, we now have a comprehensive theory that allows a determination of n2 at wavelengths beneath the band edge, given only the bandgap energy and the linear index of refraction. Such information is useful for a variety of applications including optical limiting, laser-induced damage, and all-optical switching. Some consequences for all-optical switching are discussed, and a wavelength criterion for the observation of switching is derived.

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An algorithm is presented for the calculation of the nondegenerate two-photon absorption coefficient by using second-order perturbation theory and a Kane band-structure model, including the effects of nonparabolicity and nonzone-center wave functions. The polarization dependence is included by correctly accounting for the symmetry of the electronic wave functions. A comparison is made with degenerate two-photon absorption data in various zinc blende semiconductors, and excellent agreement is found without the use of fitting parameters. Comparisons are also made with nondegenerate two-photon absorption spectra measured in ZnSe and ZnS by using a picosecond continuum and with some polarization-dependent measurements obtained by a two-color Z-scan measurement.