DISPERSION OF BOUND ELECTRONIC NONLINEAR REFRACTION IN SOLIDS

A two-band model is used to calculate the scaling and spectrum of the nondegenerate nonlinear absorption DELTA-alpha(omega-1; omega-2). 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 n2 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 n2 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.