Determination of the characteristics of diffused waveguides by the method of approximating functions

A quantitative criterion is derived for the accuracy of the approximating functions. This criterion is based on calculation of the overlap integrals of the mode fields corresponding to the "true" and approximating distributions of the refractive index. An estimate of the accuracy of the approximating function method is estimated for smooth (Epstein) and nonsmooth (step) functions. It is shown that the error in the determination of the field characteristics does not exceed 0.25%.