A planar waveguide that has a graded index layer at the core/cladding interface to reduce scattering losses due to core/cladding interface roughness. The refractive index at the core/cladding interface is changed from that of the core to that of cladding gradually by having a graded index layer. The graded index layer reduces the scattering of light traveling in the waveguide by reducing the effect of the roughness at the abrupt interface between the core and the cladding. Using a proper design, the graded index layer also minimizes the modal and polarization dispersion of the optical mode traveling in the waveguide.