Optimization of basis functions in the calculation of weakly inhomogeneous dielectric waveguides

A variational method is developed for calculating weakly inhomogeneous dielectric waveguides whose mode fields are described by the two-dimensional steady-state Schroedinger equation. The solution of the equation is determined in the form of a series in basis functions consisting of the product of two functions each of which depends only on one transverse Cartesian coordinate. For a given number of terms of the series, these functions are constructed optimally for each waveguide examined.