  Gallium-nitride (GaN) is a promising material platform for integrated
electro-optic devices due to its wide direct bandgap, pronounced nonlinearities
and high optical damage threshold. Low-loss ridge waveguides in GaN layers were
recently demonstrated. In this work we provide a first report of four-wave
mixing in a GaN waveguide at telecommunication wavelengths, and observe
comparatively high nonlinear propagation parameters. The nonlinear coefficient
of the waveguide is measured as 1.6 +/- 0.45 [W*m]-1, and the corresponding
third-order nonlinear parameter of GaN is estimated as 3.4e-18 +/- 1e-18
[m^2/W]. The results suggest that GaN waveguides could be instrumental in
nonlinear-optical signal processing applications.
