Azimuthally modulated vortex solitons in bulk dielectric media with a Gaussian barrier

By means of the variational approach, three classes of azimuthally modulated vortex solitons are constructed for the (2+1)-dimensional nonlinear Schrödinger equation with a type of transverse nonperiodic modulation. These solutions include numerical single layer azimuthal vortex solitons in the medium with Gaussian type modulation and analytical azimuthons in medium with the anharmonic potential. We present the results for two types of nonlinearities which are common in optical materials. The properties of vortex solitons, which are characteristic of the topological charge m, propagation constant k0, angular velocity ω and radial quantum number L, are studied. The numerical simulations are used to verify the propagation properties of these vortex solitons.