AbstractThe analysis of propagation characteristics of TE waveguiding in linear/self‐focusing nonlinear/self‐focusing nonlinear, three‐layer slab waveguide with a symmetric linear dielectric distribution is presented. In this analysis, the electric field inside the film is expressed in terms of Jacobi's cn function with a constant amplitude, and the equation to determine the transverse wavenumber inside the film is derived by considering the relation between this amplitude and the electric field on both sides of the film.By introducing the maximum optical power density divided by the dielectric constant difference between the film and the substrate as a measure for nonlinearity, this equation contains only three parameters (nonlinearity parameter, normalized thickness and relative nonlinear coefficient difference).By changing the values of these parameters and restricting the numerical calculation for TEo modes, the number of TEo modes with its peaks in the substrate or in the film or at the boundary between the film and the substrate is examined. These results are illustrated in a plane in which we take the normalized thickness along the vertical axis and nonlinearity parameter along the horizontal axis.Moreover, it is shown that for the waveguide with nonlinear coefficient of the substrate greater than the film, there is a possibility of existence of TEo mode for which the values of the normalized guide index and the change of the electric field profile are discontinuous for the change of the nonlinearity parameter.