Simple solutions for modeling symmetric step-index dielectric waveguides

An approximate analytic solution for the guided wave in a planar step index waveguide is derived. It is shown that a solution can be chosen for the longitudinal and transverse propagation constants which is accurate to a few percent from cutoff to highly confined modes. This result is of importance for analytic modeling of step-index waveguides for problems such as directional couplers and nonlinear devices. It also provides a simple formula which can be used on a personal computer to model expected behavior.>