Arbitrary cylindrical vector beam generation enabled by polarization-selective Gouy phase shifter

Experimental investigation on the polarization evolution characteristics of arbitrary cylindrical vector beams in uniaxial crystals orthogonal to the optical axis

A practical direct-view scheme for generating arbitrary high-order cylindrical vector (HCV) beams by cascading vortex half-wave plates (VHPs) is presented. The combination of odd number 2n-1 VHPs for n≥1 can realize (m2n-1-m2n-2+…+m1)-order CV beams, in which m is the order number of VHP and the corresponding subscript 2n-1 represents the arrangement number of VHPs, and the cascading of even number 2n ones can obtain (m2n-m2n-1+…+m2-m1)-order CV beams. All 1-12 order CV beams, including the high-order anti-vortex CV (ACV) beams, are generated only by selectively cascading the VHPs with m=1, 3 and 8. The polarization properties of the generated HCV beams are investigated by measuring the corresponding Stokes parameters. It is experimentally demonstrated that arbitrary HCV beams are effectively achieved by the proposed method. The order numbers of CV beams can be greatly expanded by cascading limited types of VHPs.

A convenient and versatile scheme to generate continuously adjustable cylindrical vector (CV) and vortex beams by multiplexing and cascading passive vortex half-wave plates (VHPs) is proposed. (\ensuremath{-}24)--24 order CV or vortex beams are generated only based on VHPs with m = 1, 3, and 8. The coaxial and small-angle interference are introduced to detect orders. For coaxial interference of ${l}_{1}$-order and ${l}_{2}$-order vortex beams, the intensity distribution is spirally fan shaped. The partition number is N = |${l}_{2}$\ensuremath{-} ${l}_{1}$|, and the spiral direction can distinguish the sign of topological charge with higher value. Fork-shaped fringes appear in the center for small-angle interference between vortex beams with incident angle ${\ensuremath{\beta}}_{1}$ and ${\ensuremath{\beta}}_{2}$. The forking number between two fringes meets N = |${l}_{2}$\ensuremath{-} ${l}_{1}$|, and the forks face upward when (${l}_{2}$\ensuremath{-} ${l}_{1}$)(${\ensuremath{\beta}}_{2}$\ensuremath{-} ${\ensuremath{\beta}}_{1}$) 0, and face downward when (${l}_{2}$\ensuremath{-} ${l}_{1}$)(${\ensuremath{\beta}}_{2}$\ensuremath{-} ${\ensuremath{\beta}}_{1}$) > 0. Particularly, when one of the beams is a Gaussian beam, such as ${l}_{1}$ = 0, the value and sign of the topological charge ${l}_{2}$ can be directly detected. And for the interference between CV and Gaussian plane beams, the partition number N is positively correlated with the polarization order P, with N = |P| or N = 2|P| for coaxial or small-angle interference, respectively, and corresponding sign can be identified by the polarization azimuth distributions measured by Stokes parameters. It is experimentally demonstrated that the proposed scheme can effectively generate continuously adjustable CV and vortex beams by programming limited VHPs, greatly expanding order numbers with low cost, low energy consumption, and high utilization, and the coaxial and small-angle interference method can conveniently detect the corresponding orders without borrowing redundant devices.

Two linked gear wheels in a micromachine can be simultaneously rotated in opposite directions by using a laser beam that has in its section areas the spin angular momentum (SAM) of the opposite sign. However, for instance, a cylindrical vector beam has zero SAM in the focus. We alter a cylindrical vector beam so as to generate areas in its focus where the SAM is of opposite signs. The first alteration is adding to the cylindrical vector beam a linearly polarized beam. Thus, we study superposition of two rotationally symmetric beams: those with cylindrical and linear polarization. We obtain an expression for the SAM and prove two of its properties. The first property is that changing superposition coefficients does not change the shape of the SAM density distribution, whereas the intensity changes. The second property is that maximal SAM density is achieved when both beams in the superposition have the same energy. The second perturbation is adding a spatial carrier frequency. We study the SAM density of a cylindrical vector beam with a spatial carrier frequency. Due to periodic modulation, upon propagation in space, such a beam is split into two beams, having left and right elliptic polarization. Thus, in the beam transverse section, areas with the spin of different signs are separated in space, which is a manifestation of the spin Hall effect. We demonstrate that such light beams can be generated by metasurfaces, with the transmittance depending periodically on one coordinate.

This work presents an investigation of tight focusing of optical vortices, which produce regions where the Poynting vector is directed opposite to the beam's propagation direction-known as areas of reverse energy flow. We study both phase optical vortices and polarization optical vortices (cylindrical vector beams). For phase optical vortices, it is shown that the emergence of reverse energy flow as well as splitting of the initial optical vortex depends on the handedness of the circular polarization and the phase of the initial optical vortex. An optical vortex with an initial topological charge of $m\; \le \; - {3}$ splits into three optical vortices with topological charges $m + {2}$, ${-}{1}$, and ${-}{1}$ when the polarization is right circular. In contrast, under left-hand circular polarization, a vortex with the topological charge $m$ is preserved at the focus. The reverse-flow regions are located between the centers of phase singularities (screw dislocation points). As the topological charge of the phase vortex increases, the region of reverse flow along the radial coordinate widens, and the distance from the vortex center to the optical axis also increases. In the focusing of cylindrical vector beams (polarization optical vortices), the reverse energy flow region is also observed, but screw dislocations are absent.

Optical misalignment between transmitter and receiver leads to power loss and mode crosstalk in a mode division multiplexing (MDM) free-space optical (FSO) link. We report both numerical simulations and experimental results on the propagation performance of two typical vector beams, C-point polarization full Poincaré beams (FPB), and V-point polarization cylindrical vector beams (CVB), compared to homogeneous polarization scalar vortex beams (SVB) under optical misalignment. The FSO communication performance under misalignment using different transmit beams is evaluated in terms of power loss, mode crosstalk, power penalty, etc. Vector beams are shown to have superior misalignment tolerance compared to the corresponding SVBs, with the FPBs in particular being the most robust for small topological charges. At the same mode spacing, the CVBs have a larger misalignment tolerance, which causes the MDM-FSO communication systems with narrower mode spacing to have a smaller power penalty. Furthermore, moderately increasing the transmitted beam size could improve the system tolerance of lateral displacement while reducing that of tilt error.

Cylindrical vector beams (CVB) with large topological charges extend their potential applications on high security optics communications, microparticle manipulation and high-resolution imaging, which are sensitive to laser wavelength. CVBs operating at new laser wavelengths converted with stimulated Raman scattering effect in Raman solid-state lasers fulfill requirements of these potential applications. Here, CVBs in form of Laguerre-Gaussian (LG<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0,</sub><italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">_l</i>) with tunable topological charges have been generated directly in an annular pumped Raman microchip laser constructed with Yb<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup>:Y<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub>Al<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub>O<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sub> crystal and vanadate crystal. The topological charge is tuned from 3 to 6 by changing applied pump power. Stable LG<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0,6</sub> CVB is obtained in Raman microchip laser when pump power is in the range from 4 to 6.1 W. Maximum output power of 420 mW is obtained for LG<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0,6</sub> vortex Raman laser at input pump power of 6.1 W, the optical conversion efficiency is 6.8%. The state of polarization of generated CVBs with topological charge <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> is <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0,</sub><italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">_l</i>(<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">φ</i>,<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i>) = <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E_φ</i> × sin[(<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i>-1)<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">φ</i>]+ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E_r</i> × cos[(<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i>-1)<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">φ</i>], <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E_φ</i>, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E_r</i> are unit vectors along azimuthal and radial directions. LG<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0,3</sub> vortex laser oscillates in multi-longitudinal-mode around 1050 nm. LG<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0,4</sub> and LG<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0,5</sub> vortex lasers oscillate in 1050 nm and 1076 nm two-wavelengths. LG<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0,6</sub> vortex laser oscillates in multi-longitudinal-mode. Polarization purity is over 95% for LG<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0,</sub><italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">_l</i> (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> = 3, 4, 5, 6) CVBs generated in the Raman microchip laser. High beam quality is achieved for CVBs with measured M<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> nearly equal to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> +1.

We show that continuous and spin-lattice models of chiral ferro- and antiferromagnets provide the existence of an infinite number of stable soliton solutions of any integer topological charge. A detailed description of the morphology of new skyrmions and the corresponding energy dependencies are provided. The considered model is general, and is expected to predict a plethora of particlelike states which may occur in various chiral magnets including ultrathin films, e.g., PdFe/Ir(111), rhombohedral ${\mathrm{GaV}}_{4}{\mathrm{S}}_{8}$ semiconductor, B20-type alloys as ${\mathrm{Mn}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x}\mathrm{Ge}$, ${\mathrm{Mn}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x}\mathrm{Si}$, ${\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x}\mathrm{Si}$, ${\mathrm{Cu}}_{2}{\mathrm{OSeO}}_{3}$, and acentric tetragonal Heusler compounds.

Vortex beams characterized by helical phase wavefronts enable innovative explorations of optical and physical interactions. This work experimentally realizes longitudinally polarized vortices with arbitrary topological charges in terahertz (THz) frequencies using a silicon ring resonator integrated with a second-order diffraction grating. The implemented configuration enables flexible topological charge manipulation in longitudinally polarized electric fields through the excitation of quasi-transverse-magnetic (TM) waveguide modes with different frequencies. By employing a terahertz near-field measurement system, the spatial intensity patterns and phase characteristics of emitted waves are quantitatively analyzed via a precision probe. This strategy shows promising potential for applications in particle manipulation techniques and advanced imaging technologies.

Recent studies on orbital angular momentum (OAM) states in the surface plasmon polariton (SPP) field have primarily focused on the generation of single OAM modes and the evolution of OAM states with various topological charges. However, achieving coherent superposition of two OAM states with well-defined phase relations through precise nanostructure design remains challenging. In this work, we propose a plasmonic nanostructure consisting of paired rectangular slits arranged along circular or segmented Archimedes spiral. The Archimedean spiral of various radii in azimuthal angle provides a geometry-dependent helical phase; coupled with a rotated nanoslit pair, it introduces a geometric phase of twice the rotated angle. By combining chiral spiral with nanoslit pair units, the design both generates plasmonic OAM eigenstates with arbitrary topological charges and enables their coherent superposition. The amplitudes of the two constituent OAM states are continuously tunable through the degree of polarization of the incident light, and their relative phase difference is controlled by the polarization angle, enabling arbitrary superposition of the plasmonic OAM states with continuously variable amplitude ratios and phase differences. Theoretical analysis and numerical simulations demonstrate that circularly polarized illumination produces distinct OAM pure states, whereas linearly polarized light leads to equal-amplitude superposition states with structured field distributions. Moreover, rotating the polarization angle continuously adjusts the relative phase between the eigenstates and produces a predictable rotation of the resultant interference pattern. These results provide a new approach for coherent control of plasmonic OAM states and offer design guidelines for multifunctional on-chip optical field manipulation devices.

Quantum oscillations of response functions in high magnetic fields tend to reveal some of the most interesting properties of metals. In particular, the oscillation phase shift is sensitive to topological band features, thereby helping to identify the presence of Weyl fermions. In this work we predict characteristic parameter dependence of the phase shift for Weyl fermions with tilted and overtilted dispersion (type I and type II Weyl fermions) and an arbitrary topological charge (multi-Weyl fermions). For type-II Weyl fermions our calculations capture the case of magnetic breakthrough between the electron and the hole part of the dispersion. Here the phase shift turns out to depend only on the quantized topological charge due to cancellation of non-universal contributions from the electron and the hole part.

Topological charge plays a significant role in a range of physical systems. In particular, observations of real-space topological objects in magnetic materials have been largely limited to skyrmions - states with a unitary topological charge. Recently, more exotic states with varying topology, such as antiskyrmions, merons, or bimerons and 3D states such as skyrmion strings, chiral bobbers, and hopfions, have been experimentally reported. Along these lines, the realization of states with higher-order topology has the potential to open new avenues of research in topological magnetism and its spintronic applications. Here, real-space imaging of such spin textures, including skyrmion, skyrmionium, skyrmion bag, and skyrmion sack states, observed in exfoliated flakes of the van der Waals magnet Fe3-x GeTe2 (FGT) is reported. These composite skyrmions may emerge from seeded, loop-like states condensed into the stripe domain structure, demonstrating the possibility to realize spin textures with arbitrary integer topological charge within exfoliated flakes of 2D magnets. The general nature of the formation mechanism motivates the search for composite skyrmion states in both well-known and new magnetic materials, which may yet reveal an even richer spectrum of higher-order topologicalobjects.

Nested skyrmion bags, as magnetic solitons with arbitrary integer topological charges (Q), hold potential for applications in data encoding. A crucial issue is the local manipulation of skyrmions within nested skyrmion bags to control the total Q. In this study, we explore different possible ground states and resonant excitation spectra of nested skyrmion bags through micromagnetic simulations. More importantly, we demonstrate that the manipulation of the Q of nested skyrmion bags can be achieved by using microwave magnetic fields, i.e., the inner, middle, and outer skyrmions within the nested skyrmion bags are selectively excited by using the diverse out-of-plane excitation modes. By calculating the energy of skyrmions, we further analyze the relationship between the annihilation of skyrmions at different positions and the out-of-plane microwave magnetic fields. Our findings present a promising approach for manipulating the Q of nested skyrmion bags, potentially advancing their application in storage and logic devices.

The generation of surface plasmon vortices with arbitrary higher order vortex topological charges with novel plasmonic vortex lens is experimentally demonstrated. It is shown that the polarization sensitivity of the plasmonic vortex lens can be utilized for the dynamic switching of the surface plasmon vortices with different topological charges. A simple algebraic rule related to the vortex topological charge change in the dynamic switching is formulated, and its proof is provided with theory and experiment. The synthesis and dynamic switching of higher order surface plasmon vortices have profound potential in optical trapping, optical data storage, and other related fields.

The broadband spin-decoupled metasurface is highly desirable for wireless communication applications, which possesses the independent control of dual-circularly polarized microwaves. In this work, a group of double arrow-shaped meta-atoms is designed for generating orbital angular momentum(OAM) vortex beams with arbitrary topological charges and dual-circularly polarized vortex waves. The proposed meta-atoms have a broad bandwidth ranging from 12.67 to 19.20 GHz (41%), which realize conversion efficiency higher than 0.8 and a reflection phase coverage of 360 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sup> . Based on the Pancharatnam- Berry(PB) phase theory and the spin decoupling concept, they can also realize spin-decoupled phase change in dual-circular polarization by simultaneously manipulating the geometrical parameters and rotation angle of the meta-atom. Then, the helical phase profile is analyzed as a blueprint for the design of the metasurface array, which generates different order vortex beams under left-handed and right-handed circularly polarized (LCP/RCP) wave excitations. The corresponding energy weight and far-field electric field distribution of dual-circularly polarized vortex waves are achieved by numerical computation to verify the high performance of the proposed metasurfaces. This paper demonstrates that the proposed meta-atoms can actualize wide- band with separate control of the dual-circularly polarized vortex wave.