MEASUREMENT OF THE ANISOTROPY OF 2-PHOTON ABSORPTION-COEFFICIENTS IN ZINCBLENDE SEMICONDUCTORS

The imaginary parts of all of the independent two-photon-resonant susc eptibility tensor elements in GaAs and CdTe are determined by using a two-beam coupling technique to measure the anisotropy of the two-photo n absorption coefficient beta as a function of crystal orientation and probe polarization. Anisotropy parameters of -0.76 and -0.46 are meas ured for GaAs and CdTe, respectively, at a wavelength of 950 nm. These correspond to a 45% variation in beta for GaAs, between 19 and 30 cm/ GW, for radiation polarized along the [001] and the [111] crystallogra phic axes, respectively, and a 25% variation between 14 and 18 cm/GW f or CdTe. By invoking intrinsic and zincblende symmetry, we present mac roscopic expressions that accurately account for the dependence of sin gle-beam two-photon absorption on the orientation of the crystal with respect to the polarization of the light and also expressions that des cribe 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 aniso tropy 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 band. This simple theory produces magnitudes consistent with experimental results and predicts that the anisotropy scales linearly with the ratio of th e lower bandgap to the higher bandgap: E(g)/E(g)'.