Complete azimuthal decomposition of optical fields

We generalize the concept of perfect optical vortices, studying the elliptic perfect optical vortices (EPOVs), which also have diameters independent of the topological charge. A phase-only diffractive optical element is proposed for the efficient generation of such EPOV. The intensity of the EPOV generated by this element is higher than that of the EPOV generated approximately by an elliptical axicon. We obtain exact analytical expressions for the orbital angular momentum (OAM) density and for the total OAM of the EPOV. These expressions show that the normalized OAM of the EPOV is fractional and it exceeds the OAM of the conventional circular perfect optical vortex, which equals the topological charge. It allows continuous controlling of the OAM by changing the ellipticity. We show analytically that the OAM density is maximal on the smaller side of the EPOV. The ratio of the maximal to the minimal OAM density equals the squared ratio of the ellipse dimensions. Using the proposed element, EPOVs that carry different topological charges are generated experimentally with the aid of a spatial light modulator. We experimentally confirm the independence of their size from the topological charge, which is determined interferometrically. Such EPOVs can be used for moving microscopic particles along an ellipse with acceleration, as well as for the generation of OAM-entangled photons.

We propose to generate vortex high harmonics in the extreme ultraviolet (XUV) with a controllable spatial profile by using a Bessel-Gaussian (BG) beam carrying a nonzero orbital angular momentum (OAM). Such BG beam has quite a different intensity profile at the focus compared to the generally used BG beam without carrying the OAM. We show that the BG beam is capable of generating single-ring structured high harmonics, which is quite different from an Laguerre-Gaussian (LG) beam with a similar intensity distribution at the laser focus. We reveal that favorable phase-matching conditions can be achieved off-axis and away from the laser focus because a single-atom intrinsic phase due to the short electron trajectory can be well compensated by a geometric phase of the BG beam. We thus give a general rule that vortex high harmonics with a single annular profile can be efficiently generated when a gas medium is located at 1.5zred to 2.0zred before or after the laser focus of the BG beam, here zred is a reduced length. We also show the validity of this rule when the BG beam carries a higher OAM. This work is expected to be useful for synthesizing attosecond vortex pulses.

We experimentally generated superpositions of higher-order Bessel beams that possess no global orbital angular momentum (OAM), yet exhibit an angular rotation in their intensity profile as the field propagates. The digital holograms encoded on a spatial light modulator (SLM), used for generating such fields, consist of two annular rings of unequal radial wave-vectors where each ring is encoded with an azimuthal mode of equal order but opposite charge. We present experimentally measured angular rotation rates for some example superposition fields, which are shown to be in good agreement with that predicted theoretically. Introducing a second SLM and a Fourier transforming lens, we demonstrate a simple approach to perform an azimuthal decomposition of our generated optical fields. Bounding the match-filter to an annular ring, of varying radius, we are able to perform a scale-independent azimuthal decomposition of our initial field. From the measured weightings of the azimuthally decomposed modes we show reconstruction of the cross-sectional intensity profile and OAM density of our initial field.

Experimental generation and orbital angular momentum properties of focused field for vector vortex beams on Hybrid-order Poincaré sphere

According to the theory of electromagnetic field, the orbital angular momentum density formula of a general beam was deduced. From the electric field intensity of a Gauss Vortex Beam, the orbital angular momentum density calculation formula of a Gaussian vortex beam was also deduced. A MATLAB program was applied to simulate the optical field distributions and the orbital angular momentum density distributions of Gauss Vortex Beams, and found the size and the direction of orbital angular momentum were closely related to the order of a Gaussian vortex beam.

In this paper, the circular Airy derivative beams carrying rotationally-symmetric power-exponent-phase vortices are proposed for the first time, whose evolutionary properties are explored by theoretical analysis as well as experimental verification. The intensity and phase distributions of this kind of beam can be flexibly modulated by controlling its parameters such as derivative order, topological charge, and power order. Intriguingly, the evolution of such beams with different fractional topological charges is also investigated in detail by means of phase singularities distribution. In addition, from the perspective of transverse gradient force, the proposed beam is capable of efficiently protecting the trapped Rayleigh particles located at the beam center from the impact by surrounding particles. Furthermore, the beam width, orbital angular momentum (OAM) density and spiral spectrum are also compared and analyzed under different beam parameters. The proposed beams are expected to be useful for extending applications of optical vortices and autofocusing beam, especially for multi-regional particle gathering and central particle protecting.

We derive new Lorentz invariance and equation of motion relations between twist-three generalized parton distributions (GPDs) and moments in the parton transverse momentum, ${k}_{T}$, of twist-two generalized transverse momentum-dependent distributions (GTMDs), as a function of the parton longitudinal momentum fraction $x$. Although GTMDs in principle define the observables for partonic orbital motion, experiments that can unambiguously detect them appear remote at present. The relations presented here provide a solution to this impasse in that, e.g., the orbital angular momentum density is connected to directly measurable twist-three GPDs. Out of 16 possible equation of motion relations that can be written in the $T$-even sector, we focus on three helicity configurations that can be detected analyzing specific spin asymmetries: two correspond to longitudinal proton polarization and are associated with quark orbital angular momentum and spin-orbit correlations; the third, obtained for transverse proton polarization, is a generalization of the relation obeyed by the ${g}_{2}$ structure function. We also exhibit an additional relation connecting the off-forward extension of the Sivers function to an off-forward Qiu-Sterman term.

A self-consistent formulation of the exchange energy density, effective exchange field, and Poynting vector is carried out, for a general ferrimagnet, in terms of the spin and orbital angular momentum densities. When there is more than one magnetic lattice or when the gyromagnetic ratios are tensor quantities, this formulation leads to an exchange energy density and Poynting vector that differ from those commonly employed. The associated boundary conditions at a surface of passive discontinuity are also discussed; power flow considerations lead to the conclusion that one of these is a dynamic boundary condition. With the help of the correspondence principle and a quasi particle interpretation of spin waves, a small-signal energy density, momentum density, and stress tensor are postulated for a ferromagnet. The associated small-signal force density (postulated to equal the divergence of the stress tensor minus the time rate of change of the momentum density) is found to be the negative of the force density that accelerates the envelope of the spin wave packet and is interpreted as a reaction force density acting upon the lattice. A prediction is made that a magnon incident upon a surface of discontinuity such as a material—air interface, will exert an exchange-radiation pressure on it.

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.

Bandwidth-limited orbital angular momentum mode of Bessel Gaussian beams in the moderate to strong non-Kolmogorov turbulence

Modal analysis of in-duct fan broadband noise via an iterative Bayesian inverse approach

In this paper, we have performed experimental, analytical, and numerical studies of beams with topological charges of $\ifmmode\pm\else\textpm\fi{}1$ and $\ifmmode\pm\else\textpm\fi{}2$ formed by silicon binary phase axicons (BPAs) with spiral zone structures. The axicons were illuminated with the Novosibirsk free electron laser radiation (a continuous stream of 100-ps pulses at $f=5.6$ MHz). The cw power of the beams produced reached 30 W and can by doubled via antireflection coating of the axicons. The intensity distribution in the beam cross sections was in good agreement with the Bessel functions and was kept constant within a distance of about $L/r\ensuremath{\approx}190$ and 100, where the first ring radii of the beams r were 0.9 and 1.5 mm for the Bessel beams of the first and second orders, respectively. Although the characteristics of the beams (Bessel cross section, ``diffraction-free'' propagation, self-recovery after passing obstacles, and randomly inhomogeneous media) corresponded to the properties of ideal Bessel beams, their spatial Fourier spectrum (the image in the focal plane of the lens) was, instead of an ideal ring, intertwined segments of arcs with phases shifted by $\ensuremath{\pi}$, the number of which was equal to the double value of the topological charge. This feature can be used, for example, in a demultiplexing unit of a free vortex-wave communication system or for identification of beam topological charge. We also revisited Young's double-slit diffraction and rotation of beams obstructed by a half-plane, previously applied to Laguerre-Gaussian beam characterization, in the case of the Bessel beams. The Young diffraction pattern demonstrated in this case a complicated intensity-phase distribution. It was shown that the Bessel beams formed by BPAs have two important advantages, which can be used in applications, in comparison with other methods of generation, e.g., a combination of an axicon lens with a spiral phase plate. Although the phase jumps of the axicons are designed for a determined wavelength (141 $\ensuremath{\mu}\mathrm{m}$ in our case), the BPAs can form the beams at incident radiation with any wavelength, albeit with a reduced diffraction efficiency, and their cross section is the same for any wavelength.

Spin angular momentum (SAM) and orbital angular momentum (OAM) are two important fundamental degrees of freedom of light and play crucial roles in various light–matter interactions. SAM usually makes the microparticle rotate around its axis, while OAM causes orbital motion of the microparticles around the beam axis. For an optical field with only SAM, the spin-to-orbit conversion may occur under the tightly focused condition, leading to the orbital motion of probing particles. However, it is invalid for weakly focused conditions. Here, we generated an annular optical field without intrinsic OAM by weakly focusing (i.e., negligible spin-to-orbit conversion) a circularly polarized light with a linearly varying radial phase and then observed a kind of dual orbital motion of asymmetric probing particles (Janus particles) in the focal plane. The two orbital motions have opposite directions on both sides across the strongest ring of the annular optical field. In addition to the SAM, the local angular momentum (AM) density also depends on the radial intensity gradient. The radial intensity gradient has the opposite signs on both sides across the strongest ring of the annular optical field, which results in the opposite orbital motions of trapped particles. The manipulation of the local AM density and the resulting novel dual orbital effect in the absence of intrinsic OAM provide a new scene to understand the physics underlying the light–matter interaction, paving the way to some new applications involving the sorting and delivery of microparticles.

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.

A circularly polarized electromagnetic plane wave carries an electric field that rotates clockwise or counterclockwise around the propagation direction of the wave. According to the handedness of this rotation, its longitudinal spin angular momentum (AM) density is either parallel or antiparallel to the propagation of light. However, there are also light waves that are not simply plane and carry an electric field that rotates around an axis perpendicular to the propagation direction, thus yielding transverse spin AM density. Electric field configurations of this kind have been suggestively dubbed ‘photonic wheels’. It has been recently shown that photonic wheels are commonplace in optics as they occur in electromagnetic fields confined by waveguides, in strongly focused beams, in plasmonic and evanescent waves. In this work we establish a general theory of electromagnetic waves propagating along a well defined direction, and carrying transverse spin AM density. We show that depending on the shape of these waves, the spin density may be either perpendicular to the mean linear momentum (globally transverse spin) or to the linear momentum density (locally transverse spin). We find that the latter case generically occurs only for non-diffracting beams, such as the Bessel beams. Moreover, we introduce the concept of meridional Stokes parameters to operationally quantify the transverse spin density. To illustrate our theory, we apply it to the exemplary cases of Bessel beams and evanescent waves. These results open a new and accessible route to the understanding, generation and manipulation of optical beams with transverse spin AM density.