On the propagation of light waves in a multilayer planar dielectric waveguide

Dispersion equations for the eigenvalues of effective refractive index β of a planar dielectric waveguide supporting an optic TE wave are investigated. A relation between the traditional dispersion equation obtained on the basis of the characteristic-matrix method and the so-called multilayer equation is revealed. It is shown that all of the roots of the traditional dispersion equation are roots of the multilayer equation for the same problem. It is found that the roots of the multilayer equation may include the values of the refractive indices of inner layers of the waveguide and that these values are not the eigenvalues of quantity β.