Vortex strength and beam propagation factor of fractional vortex beams

Abstract

Fractional vortex beams (FVBs) with non-integer topological charges attract much attention due to unique features of propagations, but there still exist different viewpoints on the change of their total vortex strength. Here we have experimentally demonstrated the distribution and number of vortices contained in FVBs at Fraunhofer diffraction region. We have verified that the jumps of total vortex strength for FVBs happens only when non-integer topological charge is before and after (but very close to) any even integer number, which originates from two different mechanisms for generation and movement of vortices on focal plane. Meanwhile, we have also measured the beam propagation factor (BPF) of such FVBs, and have found that their BPF values almost increase linearly in one component and oscillate increasingly in another component. Our experimental results are in good agreement with numerical results.PACS numbers:

Precise measurement of trapping and manipulation properties of focused fractional vortex beams

“…This is understandable since the intensity ring of FVBs at the focal plane is bilaterally symmetric and the intensity ripples at the focal plane are only induced by the additional vortex coming from the beam's rim. 40 The three particles trapped at the focal plane of FVBs with fractional TC can keep rotating, but the rotation of the particles is irregular due to the longer stay at intensity breakpoint for focused FVBs with nearly half integers. When the number of trapped microparticles increases a suitable value, see the right column of Fig.…”

“…45 However, for practical FVBs with phase exp(iαθ) embedded in Gaussian beams, recently researchers discovered their novel properties near Fraunhofer-diffraction region or at the focal plane of 2-f lens systems, where the birth of new vortices does not happen at a half-integer TC. 38,40 These new characteristics including bilateral symmetric intensity structures actually also occur in the focal system of optical tweezers. More importantly, there are still lack of quantitative investigations on the rotation and trapping properties of FVBs since they were believed to be hard to rotate microparticles at a half-integer TC due to their low-intensity gap in the intensity ring.…”

“…32,33 Fractional vortex light fields have been drawn attention due to their exotic properties including fractional OAM entanglement, 34,35 topological structured darkness, 36 and quantum entanglement between fractional and integer OAM. 37 Especially, FVBs now are recognized that there are more complex propagation characteristics when propagating close to the focal plane, such as the bilateral symmetric and complicated intensity profiles, [38][39][40][41] the novel birth behavior of new vortices for focused FVBs, 40,41 and the topological competition. 42 The earliest research on optical trapping using FVBs was experimentally performed by Tao et al, who qualitatively ana-lyzed the effect of the radial opening in annular intensity rings on particles' rotation and demonstrated to guide and transport microscopic particles by using FVBs.…”

Observation of multiramp fractional vortex beams and their total vortex strength in free space

“…There is a different mechanism on the birth of vortices for FVBs at Fraunhofer zone, which shows experimentally that total vortex strength for FVBs increases by unit only at a number slightly larger than an integer [17]. Most recently, we reconsidered this issue on the change of total vortex strength for FVBs at Fraunhofer zone, and found both theoretically and experimentally that total vortex strength for FVBs occurs two jumps only when non-integer topological charge is before and after (but very close to) any even integer number [21]. The incident light sources used in Refs.…”

Enhanced Fractional Acoustic Vortices by an Annulus Acoustic Metasurface with Multi‐Layered Rings

“…Fractional‐order vortices with non‐integer topological charges (TCs) have attracted extensive interest in recent years. [ 1–8 ] Compared with the integer‐order vortex, [ 9,10 ] the fractional‐order vortex shows an additional radial discontinuity in phase distribution and thus a low‐intensity strip is observed on the annular intensity pattern of the integer vortex. [ 7,8 ] Meanwhile, the number of the phase singularity depends on the TC‐value of the fractional‐order vortex.…”