Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors

The imaginary parts of all of the independent two-photon-resonant susceptibility tensor elements in GaAs and CdTe are determined by using a two-beam coupling technique to measure the anisotropy of the two-photon absorption coefficient p as a function of crystal orientation and probe polarization. Anisotropy parameters of -0.76 and -0.46 are measured for GaAs and CdTe, respectively, at a wavelength of 950 nm. These correspond to a 45% variation in β for GaAs, between 19 and 30 cm/GW, for radiation polarized along the [001] and the [111] crystallographic axes, respectively, and a 25% variation between 14 and 18 cm/GW for CdTe. By invoking intrinsic and zincblende symmetry, we present macroscopic expressions that accurately account for the dependence of single-beam two-photon absorption on the orientation of the crystal with respect to the polarization of the light and also expressions that describe the two-photon absorption of a probe when it is polarized either perpendicular or parallel to the pump in degenerate-four-wave-mixing experiments. Finally, we discuss the microscopic origins of this anisotropy of two-photon absorption in terms of simple k·p models of the band structure, and we find the anisotropy to be caused predominantly by the mixing of the valence band with a higher conduction hand. This simple theory produces magnitudes consistent with experimental results and predicts that the anisotropy scales linearly with the ratio of the lower bandgap to the higher bandgap: E_g/E´_g