  We report, for the first time, the characterizations on optical
nonlinearities of beta-phase gallium oxide (\b{eta}-Ga2O3), where both (010)
\b{eta}-Ga2O3 and (-201) \b{eta}-Ga2O3 were examined for two-photon absorption
(TPA) coefficient, Kerr refractive index, and their polarization dependence.
The wavelength dependence of the TPA coefficient and Kerr refractive index was
estimated using a widely used analytical model. \b{eta}-Ga2O3 exhibits a TPA
coefficient of 1.2 cm/GW for (010) \b{eta}-Ga2O3 and 0.58 cm/GW for (-201)
\b{eta}-Ga2O3. The Kerr refractive index is -2.14*10^(15) cm2/W for (010)
\b{eta}-Ga2O3 and -2.89*10^(15) cm2/W for (-201) \b{eta}-Ga2O3. In addition,
\b{eta}-Ga2O3 shows stronger nonlinear optical anisotropy on the (-201) plane
than on the (010) plane, possibly due to highly asymmetric crystal structure.
Compared with that of gallium nitride (GaN), the TPA coefficient of
\b{eta}-Ga2O3 is 20 times smaller, and the Kerr refractive index of
\b{eta}-Ga2O3 is also found to be 4 to 5 times smaller. These results indicate
that \b{eta}-Ga2O3 has the potential for use in ultra-low loss waveguides and
ultra-stable resonators and integrated photonics, especially in the UV and
visible wavelength spectral range.
