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We study the anisotropic nature of the Kerr nonlinear response in abeta-barium borate (\beta-BaB2O4, BBO) nonlinear crystal. The focus is ondetermining the relevant $\chi^{(3)}$ cubic tensor components that affectinteraction of type I cascaded second-harmonic generation. Various experimentsin the literature are analyzed and we correct the data from some of theexperiments for contributions from cascading as well as for updated materialparameters. We find that the Kerr nonlinear tensor component responsible forself-phase modulation in cascading is considerably larger than what has beenused to date. We evaluate the impact of using such a cubic anisotropic responsein ultrafast cascading experiments.

The anisotropic Kerr nonlinear refractive index of the beta-barium borate (\beta-BaB2O4) nonlinear crystal