Comparison of the spectral method of calculation of open dielectric waveguides beam method and the partial areas

We compare three methods of calculating the dispersion characteristics of open dielectric waveguides. We consider the spectral method, implying the expansion of the autonomous components of the field. Numerical results obtained by this method are compared with the results given by the method of partial areas, which when applied to the analysis of the open circular dielectric waveguides allows you to find the exact solution. The question of the correctness of the application of the ray method for calculation of the strip of dielectric waveguides.