Dispersion properties of a slab waveguide with a graded-index core layer and a nonlinear cladding using the WKB approximation method

Abstract

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.