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We put forward the existence of localized necklace solitons and ring solitons in a defocusing cubic nonlinear medium with an imprinted Bessel optical lattice. Novel families of necklace solitons are found and their unique properties, including multistable states are revealed. We show that both necklace solitons and ring solitons could reside on any ring of the Bessel lattices. They are dynamically stable provided that the lattice is modulated deep enough. The uncovered phenomena may open a new way for soliton control and manipulation.

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We introduced a kind of novel perfect optical vortex beam, which we termed herein as perfect helical Mathieu vortex (PHMV) beams. The theoretical mechanism regarding the construction of PHMV beams was divided into two parts: generation of helical Mathieu (HM) beams using the stationary phase method and then Fourier transform of HM beams into the PHMV beams. Accordingly, the experimental system for generating PHMV beams was built as follows. Based on the complex amplitude modulation method, HM beams of different orders and ellipticity were generated using an amplitude–type spatial light modulator (SLM) and a radial–helical phase mask. Subsequently, an achromatic Fourier transform lens was illuminated using the HM beams, and the PHMV beams were presented on the focal plane after the Fourier transform lens. The experimental results were consistent with theoretical predictions. Compared with the classical perfect optical vortex (POV) beams, the PHMV beams still retained the property of ring radius independent of topological charge values. The distribution pattern of the PHMV beams can be controlled by the topological charges and elliptical parameters. Furthermore, two important optical properties of the PHMV beams were theoretically elucidated. First, we proved that the PHMV beams carry a fractional order orbital angular momentum (OAM). Second, we found that the complex amplitudes of any two PHMV beams with the same elliptical parameter but different order numbers are orthogonal to each other.