Dispersion Equations of Transverse Electromagnetic Waves Narrowly Localized Near the Interface between the Media with Different Graded-Index Profiles

"Combinations of three pairs of contacting media with linear, exponential, and parabolic profiles of dielectric permittivity are described theoretically. Three new types of narrowly localized transverse electric waves propagating along the interfaces between the considered graded-index media are found. The exact dispersion equations for each type of the waves determining the effective refractive index in dependence on optical and geometric characteristics are obtained. The influence of the thicknesses of the graded-index layers on dispersion equation solutions is analyzed. It is found that the effective refractive index increases with an increase in the thickness of the gradedindex layers in all considered combinations of the contacting media. The thickness of the parabolic graded-index profile has the least significant effect on the effective refractive index, compared to the linear and exponential ones. "