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Experimental setup with Mach-Zehnder interferometer: the laser is a HeNe laser of wavelegnth 633 nm, M1, M2, M3 are flat mirrors, L1 and L2 are lenses within the spatial filter, L3 is a bi-convex lens with focal length of 1m, Ph is a pinhole (of the spatial filter), P1 and P2 are two polarizers used to attenuate intensity of light, BS1 and BS2 are beam splitters, SLM is a spatial light modulator and BP is a beam profiler camera.
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The behavior of the optical vortices with fractional topological charges in the far-field is assessed through numerical modeling and confirmed by experimental results. The generation of fractional topological charge variations of the phase within a Gaussian beam was achieved by using a liquid crystal spatial light modulator (LCoS SLM). It is shown...
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Citations
... In the experiment, a Gaussian beam is commonly selected to generate fractional-order vortex beams, which can be expressed as 21,22 ...
Fractional vortex beams have attracted increasing attention due to their complex yet intriguing physical properties, such as radial notch intensity distribution and higher degrees of modulation in orbital angular momentum. In this study, we experimentally investigated and compared the beam spread and beam wander characteristics of fractional-order vortex beams with those of integer-order vortex beams after passing through a turbulent atmosphere simulator with varying turbulence intensities. Our results revealed that the beam spread of both fractional-order and integer-order vortex beams increased in a stepwise manner with the topological charge number, indicating that a larger topological charge number resulted in more severe beam spread. Interestingly, we observed that the beam radius of fractional-order vortex beams between two adjacent integer orders initially grew slowly and then rapidly before finally stabilizing into a curvilinear growth trend. This is in contrast to the linear growth trend exhibited by the beam radius of integer-order vortex beams. Furthermore, we found that the growth of the beam radius of half-integer-order vortex beams followed the linear growth trend of the beam radius of integer-order vortex beams. When the integer part of the topological charge was fixed, we observed that stronger turbulence resulted in more severe beam wander for both integer-order and fractional-order vortex beams, with the variance of the center-of-mass drift following the same growth curve. However, when the turbulence intensity is constant, both integer-order and fractional-order vortex beams exhibit a weaker beam wander effect with increasing topological charge. Our findings may provide valuable insights for applications such as optical communication and optical measurement using fractional-order vortex beams.
... A Gaussian beam with a finite beam width is usually preferred in practice over a plane wave with infinite energy. The fractional phase azimuthal variation hosted within a Gaussian beam can be expressed as [79,80] ...
... vortices along the direction of the initial radial discontinuity [47]. Furthermore, the visualization process of the formation and evolution of a vortex with an increase in the fractional TC has been reported [79,80,89], even at the submicron scale [105]. However, in a demonstration of fractional vortex beams generating new TC through the Hilbert Hotel mechanism, Gbur [46] showed that an adjustable multi-ramp SPP, with M (M = 1, 2, 3…) ramps in the azimuthal direction instead of one, could cause a jump of M in TC as the source charge increased, corresponding to M rooms being simultaneously freed in Hilbert's Hotel. ...
As an indispensable complement to an integer vortex beam, the fractional vortex beam has unique physical properties such as radially notched intensity distribution, complex phase structure consisting of alternating charge vortex chains, and more sophisticated orbital angular momentum modulation dimension. In recent years, we have noticed that the fractional vortex beam was widely used for complex micro-particle manipulation in optical tweezers, improving communication capacity, controllable edge enhancement of image and quantum entanglement. Moreover, this has stimulated extensive research interest, including the deep digging of the phenomenon and physics based on different advanced beam sources and has led to a new research boom in micro/nano-optical devices. Here, we review the recent advances leading to theoretical models, propagation, generation, measurement, and applications of fractional vortex beams and consider the possible directions and challenges in the future.
... The wavefront of beams with an initial fractional topological charge has the form of a mixed screw-edge dislocation. These dislocations are unstable and, upon propagation, decay into unit-charged optical vortices in the far field [5,[17][18][19][20], e.g. the strength of the central phase singularity ...
... The phase of optical vortex repeats itself every pl 2 turns on the closed loop around a singularity, i.e. it has a pl 2 phase step, where | | l -is the integer. The phase step of beams with the initial strength of phase singularity = | | l 1 2 is proportional to π. Linear propagation of beams with embedded fractional phase step, i.e. when l is fractional, has been analyzed in [5,17,18,20,26,30]. It was shown that the central part of such beams, in the far field, transforms into an optical vortex of integer charge. ...
We demonstrate collinear second harmonic generation performed with a beam with an embedded initial phase singularity of strength ∣l∣ = 1 2. We examine the law of topological charge conservation during this process. Despite the instability of the initial singularity, we observe a counterintuitive topological charge doubling. In the second harmonic, we observe an optical vortex of strength (topological charge) ∣l∣ = 1. The conservation of topological charge is confirmed by both numerical simulations and the experiment. We also provide a qualitative explanation of the process.
