Higher-order Bessel beams have been demonstrated to have the ability to trap and rotate low- and high-index particles simultaneously [Phys. Rev. A <b>66,</b> 063402 (2002)]. The rotation and trapping is caused by the presence of orbital angular momentum arising from its azimuthal phase variation (that changes at integer multiples of π) and the concentric rings of the Bessel mode. We demonstrate for the first time to our knowledge a branch from the family of higher-order Bessel beams that has fractional azimuthal variation at its beam axis. This new family of laser beams has the ability to perform dynamic optical manipulation with dynamic control of a spatial light modulator. Furthermore, we take the opportunity to explore the propagation characteristics of higher-order Bessel beams for which the azimuthal phase changes at noninteger multiples of 2π .
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