Approximate solutions for modal propagation in channel dielectric waveguides

A method allowing the approximate modal solutions of a truly two-dimensional-channel, dielectric waveguide to be evaluated easily is presented. In principle, the approximation can be applied iteratively until an arbitrary numerical accuracy is achieved. The application of the method to planar optical waveguides is illustrated; the results obtained for a step semicircular channel guide are presented as an example. It is shown that, within its limitations, the method provides an approximation that lies within 1% of the converged value