The growing number of near- and mid-infrared laser and parametric sources with ultrashort pulse duration and high pulse energy opens up new possibility for many applications [1,2]. For example, the current direction of developing more efficient Terahertz (THz) sources needs infrared pump sources with sufficiently long wavelength to surpass the low order multiphoton absorption [3-5]. It is challenging to design new experiments for this infrared region in lack of available data of the crystal properties like the four-photon absorption (4PA) coefficient (β4). A commonly used technique to measure the two- (2PA) and three-photon absorption (3PA) of optical materials, is the z-scan method with which the anisotropy of 2PA and 3PA in GaAs was possible to measure [6,7]. In contrast, little is known about the nonlinearities of still higher order, although they can be important in the infrared region.