In this paper, a method of analysis of dielectric waveguides using a variational method is presented. This method can be applied to dielectric waveguides with any general permittivity distribution. As examples, numerical calculations for dielectric waveguides with rectangular cross-sectional shape and quadratic inhomogeneous permittivity distribution are given.
M. Matsuhara, "Analysis of TEM modes in dielectric waveguides, by a variational method," J. Opt. Soc. Am. 63, 1514-1517 (1973)