The azimuthal dependence of third-order and cascaded second-order nonlinear coupling are used to measure the relative contributions of each to direct third-harmonic generation in -barium borate. This enabled the measurement of the values of 10 (3) , 11 (3) , and 16 (3) relative to the known ij (2) . Finally, conversion efficiencies to 3 of up to 6% from a single crystal were achieved with a femtosecond chirped-pulse-amplification laser with 200 GW/cm 2 in collimated beams