Dispersion curves of a slab waveguide with a nonlinear covering medium and an exponential graded-index thin film (transverse magnetic case)

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.