Orbital Angular Momentum Density Distribution Research Articles

Generation and characteristics of an Airy vortex beam from the anomalous vortex beam

Hybrid beams have evoked a long-running research upsurge due to its unique properties and extensive application. In this paper, we propose a novel method to generate a kind of hybrid Airy vortex beam (AiVB) with orbital angular momentum (OAM) by imposing a phase modulation on an anomalous vortex beam (AVB), which hybrid AiVB possesses dual characteristics of both optical vortices and Airy beams. According to the integral formula of Airy transform, analytical formula of the AiVB generated from the incident AVB via an optical Airy transform system (OATS) is derived. Eenergy flux density and OAM density of the AiVBs are investigated based on the Maxwell equation and Lorentz force formula, and four representative modes (E11, E12, E13, E14) of the AiVB are selected to elucidated graphically. In addition, dependence of the normalized intensity distribution, OAM density distribution, phase variation, and electric field’s gradient vector of the generated AiVBs on the control parameters δ0x and δ0y of the OATS and topological charge m are also considered. Results obtained here would further enrich the research on the vortex beams and provide theoretical basis for producing versatile optical vortices.

Parametric characterization of vortex cosine-hyperbolic-Gaussian beams

Based on the moments method, the analytical expressions for the beam propagation factor, the kurtosis parameter and the orbital angular momentum density distribution of a vortex cosh-Gaussian beam (vChGB) propagating in free space are derived. According to the obtained expressions, the beam propagation factor is determined by the decentered parameter b and the vortex charge m of the beam. The kurtosis parameter and the orbital angular momentum density are determined by the decentered parameter b, the vortex charge m and the propagation distance. Numerical examples are presented to illustrate and discuss the influences of the parameters b and m on the propagation characteristics of vChGB upon propagation in free space. This research could be beneficial to the applications involving vChGBs in optical communications, beam splitting, and micromanipulation of particles.

Intensity and orbital angular momentum density of nonparaxial anomalous vortex beams

The intensity and the orbital angular momentum density of an anomalous vortex beam beyond the paraxial approximation are studied. By using the vectorial angular spectrum method, analytical expressions of the electric field of the nonparaxial anomalous vortex beam are derived. Based on the expressions, an analytical expression of the orbital angular momentum density of the nonparaxial anomalous vortex beam is deduced. Through the numerical simulation method, the intensity distribution and orbital angular momentum density distribution characteristics are studied, and then the effects of topological charge, beam order, and propagation distance on the distributions of the intensity and orbital angular momentum density are analyzed. The results show that the intensity distribution of an nonparaxial anomalous vortex beam is similar to that of an paraxial anomalous vortex beam, while the orbital angular momentum density distribution is not.

Orbital angular momentum density and spiral spectrum of Lorentz–Gauss vortex beams diffracted by a rectangular aperture

Based on the expansions of the Lorentz distribution and the aperture function, an analytical expression of Lorentz–Gauss vortex beams with a topological charge of ±1 diffracted by a rectangular aperture is derived. One can judge the sign of the topological charge from the normalized intensity and the phase distributions. The effects of the rectangular aperture on the orbital angular momentum density and the spiral spectrum are investigated, respectively. When the length and the width of the rectangular aperture are not equal, the orbital angular momentum density distribution becomes twisted and tilted. When the size of the rectangular aperture increases, the magnitude of the orbital angular momentum density and the weight coefficient of the dominant spectrum both increase, while the weight coefficients of other minor spectra decrease. In addition, the expansion of the spiral spectrum in the case of rectangular aperture is smaller than that in the case of the single slit. The difference between the adjacent spectra in the case of the rectangular aperture is four, which is twice the difference in the case of the single slit. Moreover, the weight coefficient of the dominant spectrum in the case of the rectangular aperture is relatively larger. To measure the topological charge of the diffracted Lorentz–Gauss vortex beam, this research denotes that the rectangular aperture is superior to the single slit.

Observation of orbital angular momentum transfer from bessel-shaped acoustic vortices to diphasic liquid-microparticle mixtures.

We observe distinct regimes of orbital angular momentum (OAM) transfer from two-dimensional Bessel-shaped acoustic vortices to matter. In a homogeneous diphasic mixture of microparticles and water, slow swirling about the vortex axis is seen. This effect is driven by the absorption of OAM across the mixture, the motion following the OAM density distribution. Larger particles are formed into clusters by the acoustic radiation force, making the mixture nonhomogeneous. Here, the OAM transfer to the microparticle clusters dominates and they spin at high speeds entraining the surrounding fluid.

Propagation property of a Lorentz–Gauss vortex beam in a strongly nonlocal nonlinear media

An analytical expression of a Lorentz–Gauss vortex beam with one topological charge propagating in a strongly nonlocal nonlinear media is derived. The analytical expressions of the beam width, the curvature radius, and the orbital angular momentum density for the Lorentz–Gauss vortex beam with one topological charge have been also presented. The normalized intensity distribution, the relative beam width, the curvature radius, and the orbital angular momentum density distribution of the Lorentz–Gauss vortex beam with one topological charge are demonstrated in the strongly nonlocal nonlinear media, respectively. The normalized intensity, the beam width, the curvature radius, and the orbital angular momentum density versus the axial propagation distance are all periodic and the period is T=πz0/η. The evolution of the propagation property of the Lorentz–Gauss vortex beam with one topological charge has been exhibited in the strongly nonlocal nonlinear media. When the parameter η reaches the critical value, the beam width keeps invariant upon propagation, and the corresponding curvature radius is infinite. The propagation of Lorentz–Gauss vortex beams with larger topological charge propagating in the strongly nonlocal nonlinear media can be analyzed by the same procedure as here.

ORBITAL ANGULAR MOMENTUM DENSITY OF A HOLLOW VORTEX GAUSSIAN BEAM

Here the hollow vortex Gaussian beam is described by the exact solution of the Maxwell equations. By means of the method of the vectorial angular spectrum, analytical expressions of the electromagnetic fields of a hollow vortex Gaussian beam propagating in free space are derived. By using the electromagnetic fields of a hollow vortex Gaussian beam beyond the paraxial approximation, one can calculate the orbital angular momentum density distribution of a hollow vortex Gaussian beam in free space. The overall transverse components of the orbital angular momentum of a hollow vortex Gaussian beam are equal to zero. Therefore, the influences of the topological charge, beam order, Gaussian waist size, and linearly polarized angle on the distribution of longitudinal component of the orbital angular momentum density of a hollow vortex Gaussian beam are numerically demonstrated in the reference plane. The outcome is useful to optical trapping, optical guiding, and optical manipulation using the hollow vortex Gaussian beams.

Fractional Fourier transform of Lorentz-Gauss vortex beams

An analytical expression for a Lorentz-Gauss vortex beam passing through a fractional Fourier transform (FRFT) system is derived. The influences of the order of the FRFT and the topological charge on the normalized intensity distribution, the phase distribution, and the orbital angular momentum density of a Lorentz-Gauss vortex beam in the FRFT plane are examined. The order of the FRFT controls the beam spot size, the orientation of the beam spot, the spiral direction of the phase distribution, the spatial orientation of the two peaks in the orbital angular momentum density distribution, and the magnitude of the orbital angular momentum density. The increase of the topological charge not only results in the dark-hollow region becoming large, but also brings about detail changes in the beam profile. The spatial orientation of the two peaks in the orbital angular momentum density distribution and the phase distribution also depend on the topological charge.

Propagation of a Lorentz–Gauss vortex beam through a paraxial ABCD optical system

Based on the Collins integral, an analytical expression of a general Lorentz–Gauss vortex beam passing through a paraxial ABCD optical system is derived by means of the mathematical technique. As a numerical example, the normalized intensity distribution, the phase distribution, and the orbital angular momentum density distribution of Lorentz–Gauss vortex beams propagating in free space are graphically demonstrated. The influences of Gaussian waist, the width parameters of Lorentzian part, and the topological charge on the normalized intensity distribution, the phase distribution, and the orbital angular momentum density distribution of Lorentz–Gauss vortex beams propagating in free space are discussed in detail. This research is useful to the optical trapping, guiding, and manipulation of microscopic particles involved in the single mode diode laser beams.