Fig. 1. Schematic structure of the experimental setup for generating the modulated Bessel-like beams with a phase imprinting: PPM - programmable phase modulator; PBS - polarizing beam splitter; λ/2 - half-wave plate; L - lenses; M - mirrors; BS - beam splitter; FF - Fourier filter; SBN -photorefractive crystal, Strontium Barium Niobate; CCD - camera. Inset on the left: Images of the Bessel lattice, localized state, and its interferogram.

Fig. 2. Experimental images: (a) Intensity profile of the generated third-order Bessel lattice; (b) linear diffraction of the probe beam without the ilattice, the outer radius of the black circle shows the size of the input beam at the crystal front facet; (c-h) linear diffraction (top row) and nonlinear self-focusing (bottom row) of the input beam positioned (c,d) at the lattice center, (e,f) between two cites, and (g,h) at one site of the first lattice ring.

Fig. 3. Results of numerical simulations with the anisotropic nonlocal model Eqs. (3)–(5): (a) Intensity of the azimuthally modulated Bessel beam and (b) corresponding induced refractive index profile ~ ∂ _x φ; parameters are A = 2.5 and γ = 2. (c,d) Examples of the ring-like and single-site solitons corresponding to the experimental data shown in Figs. 2(d) and (h), respectively. The soliton with β = 0.13 and the peak intensity max|E|² = 0.05 in (c) is close to the bifurcation point from the corresponding linear guided wave, while the soliton in (d) with β = 0.3 and max |E|² = 0.97 is essentially in the nonlinear regime.