Stability of light beams in nonlinear antiwaveguides

We consider the standard models of the nonlinear light-guiding systems in the form of a core sheathed by a cladding with a different refractive index, the Kerr coefficient being the same in both media. Recently, it has been demonstrated that this system may support a light beam localized near the core not only in the case of the usual waveguide configuration, when the core is optically denser than the cladding, but also in the opposite case (the antiwaveguide). In this work, we compute the effective Hamiltonian of the localized beam (normalized to the number of quanta) versus the refractive index difference. We demonstrate that, while this dependence is trivial in the waveguide case, for the antiwaveguide it reveals nontrivial minima at special values of the parameters. These minima may be a strong argument in favor of stability of the corresponding antiwaveguide states. We compare the loci of the minima with the possible stability regions predicted recently by means of another heuristic criterion. The comparsion yields an additional argument in favor of the stability.