A rigorous supermode solution method in a strong absorption slab multilayer waveguide is performed. The method is directed toward finding solutions for a sophisticated complex determinant in a complex plane. The rigorous results are applied to design a waveguide photodetector that has a configuration of a vertical directional coupler. Absorption lengths of the supermodes and coupling length of the coupler are calculated based on an effective index approach by using the rigorous results of the strong absorption slab multilayer waveguide to optimize the directional coupling waveguide photodetector.