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A slab waveguide that comprises a linear substrate, an exponentially graded-index guiding layer, and a power-dependent refractive index covering medium is investigated. All layers are assumed dielectric. The guiding film index is described by a function n ( x ) , which changes exponentially from the cover-film interface to the substrate. The solution of the Helmholtz equation in the guiding layer is found as Bessel’s functions of the first and second kinds, the order of which is V b , where V and b are two asymmetry parameters called normalized film thickness and normalized guide index, respectively. The dispersion relation is obtained, and the dispersion properties are investigated. We found that there is no cutoff thickness for small asymmetry coefficient ( a ) values due to the nonlinear covering medium. The properties of the waveguide structure are determined by the graded-index function, and the effect of the cover layer nonlinearity is highly reduced and contributes almost nothing to the dispersion properties for large values of a . The b -values do not exceed unity, which means that the modes carried by the waveguide structure are guided modes.

Graded-index waveguides deserve investigation because they are more practical than those of step-index profiles. In this communication, a three-layer slab waveguide in which the core film has an exponentially graded refractive index is assumed. In this case, the film and substrate layers merge smoothly to form one layer of refractive index n ( x ) which is equal to n f at the cladding–film boundary and n s deep in the substrate layer. The cladding layer is made of a Kerr-type nonlinear material. An exact solution to such a waveguide structure is not possible. Approximation techniques are usually used in these cases. We employ the WKB approximation method to find an approximate dispersion relation of the proposed waveguide in terms of the asymmetry parameters a , b , and V . The universal dispersion curves are studied in detail. A number of interesting features are observed, such as the lack of a cutoff thickness related to the symmetric waveguide structure of a = 0 . The b -values are all less than one, which corresponds to guided modes.

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