A good justification for gallium nitride on silicone is the potential for integrated optoelectronic circuits and for the low cost bring by growth of GaN on a large size wafers. Actually, the application interest for GaN/Si is power electronics. This work focused on the optimization of the growth process for GaN/Si and the relation between the structure and the optical properties. Using the guided wave prism coupling technique, we have fully established the index dispersion of GaN at room temperature and its temperature dependence in the wavelength range 0.4 to 1.5μm. We report a slightly low temperature dependence. Results demonstrated excellent waveguide properties of GaN on silicon with optical propagation loss below 1dB/cm. We compared trhe results on Si with those on sapphire. This opens a real opportunity of future device using this technology.