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

Abstract

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.

Using Hocker and Burns numerical method to analyze the dispersion properties of a planar waveguide with an exponentially graded-index core layer for s-polarized light

“…Despite the fact that these structures are more realistic, only a small number of papers [5][6][7][8][9] have sought to explore them as compared to the majority of publications that have reported step-index structures. To determine the modal characteristics of graded-index structures with various profiles, analytical and numerical approaches were developed [10][11][12][13][14][15]. Treating particular profiles analytically is challenging.…”

Surface waves propagating along the interface between a parabolic graded-index medium and a self-focusing nonlinear medium: exact analytical solution

“…The unique properties of surface waves arise along the interfaces between media with fundamentally different mechanisms for the formation of optical properties, in particular, spatially distributed or nonlinear optical properties. Composite waveguides combining graded-index and nonlinear intensitydependent layers can be considered the most promising from the point of view of technical application [57][58][59].…”