(20 pts) Design a step index Bragg grating with uniformly spaced layers of GaAs and Al,Ga1-As to satisfy following requirements: the Bragg peak should be at 950 nm with maximum reflectivity of 5% (a weak grating), and the first zero reflection near the Bragg peak is located at 1000 nm. GaAs refractive index is n = 3.5, but the refractive index of the AlGal- As layers is a function of Al composition. Determine (a) the spacing between layers, (b) the number of layers, and (c) the required refractive index of the Al,Gaj-As layers