Measurement of the refractive index of Al_xGa_1-xAs and the mode indices of guided modes by a grating coupling technique

We have determined the index of refraction of Al_xGa _-xAs over the wavelength range 0.76-1.15 μm, and the composition range 0≤x<0.33, using a grating to couple light into waveguides. We find the mode indices of multimode slab waveguides from the coupling angle and grating period, then calculate the bulk indices of the core and cladding materials by a root searching technique using the analytical formula for the effective index of a guided mode. The method gives the core index within ±0.001, and the cladding index within ±0.01. We are in agreement with high precision index values for GaAs in the literature, confirming the method. We are in substantial agreement with literature values for AlGaAs but find a significant systematic difference in the composition dependence. An analysis of measurement uncertainties shows that the determination of composition is the dominant variable.