We address the existence of vortex solitons supported by azimuthally modulated lattices and reveal how the global lattice discrete symmetry has fundamental implications on the possible topological charges of solitons. We set a general "charge rule" using group-theory techniques, which holds for all lattices belonging to a given symmetry group. Focusing in the case of Bessel lattices allows us to derive also a overall stability rule for the allowed vortex solitons.Vortex solitons in nonlinear systems (for a review see [1]) characterized by a discrete symmetry have been numerically predicted in two-dimensional arrays of evanescently coupled waveguides [2], harmonic refractive index gratings imprinted in cubic media [3], as well as in photonic crystal fibers with defects [4]. Because of the imprinted refractive-index modulation, such vortices can be made stable in contrast to their ring-shaped counterparts in uniform focusing media. Recently, vortices having unit topological charge have been experimentally observed in optically-induced lattices in photorefractive media [5]. The very refractive index modulation causing the stabilization of vortex solitons simultaneously imposes restriction on the possible topological charges of the vortices dictated by the finite order of allowed discrete rotations [6]. A corollary of such result is that the maximum charge of stable symmetric vortex in two-dimensional square lattices is one.However, square lattices are just one particular example of guiding structures accessible for experimental exploration. Another interesting class of such structures with a new global rotational symmetry is constituted by azimuthally modulated lattices, also offering a wealth of new opportunities. For example, in such lattices the order of rotational symmetry may be higher than 4, in contrast to square lattices, a property that has direct implications in the possible topological charges of symmetric vortex solitons supported by such lattices.In this Letter we explore the connection existing between the lattice discrete symmetry and the topology of the allowed vortex solitons by means of a general grouptheory approach. We find that azimuthally modulated lattices imprinted in focusing medium can support symmetric vortex solitons carrying phase dislocations with topological indices higher that one. The higher the symmetry order of the lattice, the higher the allowed vortex topological charge. We also address the stability of the allowed vortex soliton families, taking as a particular example the case of azimuthally modulated optically-induced Bessel lattices.Optical lattice induction in anisotropic nonlinear materials introduced in [7] opens broad prospects for creation of reconfigurable refractive index landscapes with different types of nondiffracting beams, including Bessel beams [8]. Accurate approximations of Bessel beams can be generated experimentally in a number of ways. Known techniques include illumination of annular slit in the focal plane of a lens, conical axicons, as well as more compli...

We show that two-dimensional photonic Kerr nonlinear lattices can support stable soliton complexes composed of several solitons packed together with appropriately engineered phases. This may open up new prospects for encoding pixellike images made of robust discrete or lattice solitons.

We address azimuthally modulated Bessel optical lattices imprinted in focusing cubic Kerr-type nonlinear media, and reveal that such lattices support different types of stable solitons whose complexity increases with the growth of lattice order. We reveal that the azimuthally modulated lattices cause single solitons launched tangentially to the guiding rings to jump along consecutive sites of the optical lattice. The position of the output channel can be varied by small changes of the launching angle.

We predict the existence of vortex solitons supported by the surface between two optical lattices imprinted in Kerr-type nonlinear media. We find that such surface vortex solitons can exhibit strongly noncanonical profiles, and that their salient properties are dictated by the location of the vortex core relative to the surface. A refractive index modulation forming the optical lattices at both sides of the interface yields complete stability of the vortex solitons in wide domains of their existence, thus introducing the first known example of stable topological solitons supported by a surface.