Slab waveguides characterized by moments of the index profile

The fundamental mode of a symmetric slab waveguide is described to a high degree of accuracy using only two moments of the refractive index profile rather than its exact form. The two moments can be used to define an equivalent step index slab waveguide, and the fundamental mode propagation constant of an arbitrary profile guide is given by the step index value multiplied by a simple correction factor. The limit to single-mode operation, the second-mode cutoff point, is also given by a simple formula requiring only profile moments. Numerical confirmation of the method is given.