Reflectivity of multidielectric coatings deposited on the end facet of a weakly guiding dielectric slab waveguide

The reflectivity of a multilayer dielectric coating deposited upon the end facet of a symmetrical dielectric slab waveguide is investigated for both TE and TM waves. The integral equation satisfied by the field in the junction plane is solved numerically through a Fourier representation and an iteration process. The process converges rapidly and can easily provide a solution of as many as five or six exact digits in the case of problems involving semiconductor optical waveguides. In this case of sufficiently weak guidance, the integral equation can be simplified considerably, leading to an explicit solution for the Fourier transform of the field. This approximation greatly simplifies the computation of the reflectivity but is accurate enough to meet the current needs for the design of antireflection coatings.