In order to determine the third order of the nonlinear susceptibility chi((
3)) of GaN, we perform degenerate four-wave mixing measurements in a two-be
am configuration at low temperature on a GaN epilayer on sapphire substrate
. We measure the excitation spectrum of chi((3)) close to the exciton reson
ances. Besides the chi((3)) contribution, higher orders of the nonlinear su
sceptibility show already up around 10 kW cm(-2), leading to a saturation o
f the signal. Results are complemented by a study of the influence of a ban
d-to-band excitation ((h) over bar omega(P) = 4.02 eV) on the nonlinear sus
ceptibility. (C) 1999 American Institute of Physics. [S0003-6951(99)02810-7
].