Mode dispersion in diffused channel waveguides by the effective index method

The effective index method for calculating waveguide mode dispersion is reviewed and applied to uniform rectangular optical waveguides with both small and large index differences. The results are shown to be at least as accurate as other approximate techniques. The effective index method is then applied to channel waveguides assuming 1-D and 2-D diffusion. Channel waveguides without sideways diffusion are shown to be described by the method using a normalized notation and previously published universal dispersion curves. Two-dimensional diffusion theory is applied to treat the case of isotropic sideways diffusion. A new, normalized, 1-D universal chart is obtained which in conjunction with previous results defines waveguide mode dispersion in isotropically diffused 2-D channels.