Polarized Vortex Beams Research Articles

Polarization evolution on the higher-order Poincaré sphere via photonic Dirac points

In this work, we report a general reflection model to describe the reflected behaviors of a Gaussian beam near photonic Dirac point at the optical interface. With spin polarized electromagnetic waves strikes near the single Dirac point on Dirac material interface, vortical phase distribution and spin inversion are demonstrated for reflected state, and we further develop a higher-order Poincar\'e sphere to describe the evolution of polarization states. It is possible to generate any desired Poincar\'e vortex beam on the sphere by modulating the incident polarization state of light. Moreover, we discuss the case of normal incidence around two adjacent Dirac points, reflection spectrum involves a couple of spin flip vortices corresponding to two points with the corresponding topological invariants, which are consistent with the Berry curvature and topological charge. These results can be extended to similar hyperbolic metamaterials with degenerate point, and inspire a different perspective for manipulating polarized vortex beam with photonic Dirac point.

Orientational imaging of single fluorescent molecules: What laser beam can provide azimuth-rotation-invariant image shape?

In some areas of orientational fluorescence microscopy of single quantum emitters, exploiting tightly focused laser beams, the following property of single quantum emitter images is desirable: Rotations of an emitter’s transition dipole moment around a microscope objective axis leads to similar rotations of the emitter’s image but not to modifying a shape of this image. Here, we derive mathematically a generalized structure of an entrance laser beam that can provide this property. It was discovered that the only and the most possibly generalized kind of beam satisfying this requirement is a beam expressed mathematically as a linear complex superposition of a circularly polarized vortex beam with a spin angular momentum s=1 and an integer orbital angular momentum l and a circularly polarized vortex beam with a spin angular momentum s=−1 and an orbital angular momentum l+2.

Experimental observation of the orbital Hall effect of light through pure orbit–orbit interaction for randomly and radially polarized vortex beams

The orbit–orbit interaction of light leads to fundamentally rich optical phenomena whose experimental exploration and theoretical understanding remain challenging. Here, we investigate polarization-independent vortex-induced beam shifts for light beams possessing random polarization and radial polarization. The experiments reveal an intriguing manifestation of the orbital Hall effect of light as a consequence of orbit–orbit interactions and resulting conservation of total angular momentum. An interferometric scheme is experimentally implemented to quantify the change in the phase structure of the orbital angular momentum carrying beam as signatures of the orbital Hall effect of light arising due to partial reflection at a dielectric interface. We also demonstrate, and thus corroborate, the conservation of total angular momentum for such vortex-induced beam shifts.

Generation of needle beams through focusing of azimuthally polarized vortex beams by polarization-insensitive metasurfaces

Needle beams are widely used in advanced applications due to their high intensity, high resolution, and extended depth of focus. In this work, the generation of needle beams through transmitting azimuthally polarized beams to polarization-insensitive metasurfaces is presented. Defocus phase profiles and annular apertures were adopted to obtain needle beams, respectively. A relatively long depth of focus ( 16.9 λ ) with subdiffraction beam size ( 0.41 λ ) was obtained. The introduction of metasurfaces can significantly simplify an optical system compared with traditional methods utilizing complex optical elements. This study may contribute to photolithography, microscopy, particle manipulation, and acceleration.

Generation of pure longitudinal magnetization focal spot with a triplex metalens.

A pure longitudinal magnetization focal spot is greatly desired by all-optical magnetic recording. In this Letter, a triplex metalens is proposed and demonstrated to possess triple functions of an azimuthal polarization converter, a helical phase plate, and a focusing lens. The three-in-one combination enables conversion of linearly polarized incident light to the first-order azimuthally polarized vortex beam and focusing into a diffraction-limited spot. The state of polarization of the focal spot is measured to be pure circular polarization implying that a pure longitudinal magnetization field can be induced by the inverse Faraday effect. The lateral full width at half-maximum of the focal spot is 1.9 µm, and the experimental conversion efficiency of the metasurface is about 19.3%.

Focusing fractional-order cylindrical vector beams

By numerically simulating the sharp focusing of fractional-order vector beams (0≤m≤1, with azimuthal polarization at m=1 and linear polarization at m=0), it is shown that the shape of the intensity distribution in the focal spot changes from elliptical (m=0) to round (m=0.5) and ends up being annular (m=1). Meanwhile, the distribution pattern of the longitudinal component of the Poynting vector (energy flux) in the focal spot changes in a different way: from circular (m=0) to elliptical (m=0.5) and ends up being annular (m=1). The size of the focal spot at full width at half maximum of intensity for a first-order azimuthally polarized optical vortex (m=1) and numerical aperture NA=0.95 is found to be 0.46 of the incident wavelength, whereas the diameter of the on-axis energy flux for linearly polarized light (m=0) is 0.45 of the wavelength. Therefore, the answers to the questions: when the focal spot is round and when elliptical, or when the focal spot is minimal -- when focusing an azimuthally polarized vortex beam or a linearly polarized non-vortex beam, depend on whether we are considering the intensity at the focus or the energy flow. In another run of numerical simulation, we investigate the effect of the deviation of the beam order from m=2 (when an energy backflow is observed at the focal spot center). The reverse energy flow is shown to occur at the focal spot center until the beam order gets equal to m=1.55.

Goos–Hänchen and Imbert–Federov shifts of vortex beams near critical incidence

We investigate the Goos–Hänchen and Imbert–Federov shifts of linearly polarized vortex beams undergoing internal reflection in a glass prism in the critical region of incidence. Beam shifts are numerically calculated based on a wavenumber-space representation. The influences of the beam’s topological charge, angle of incidence, and propagation distance on the beam shifts are investigated. We find that in the critical region, the Goos–Hänchen and Imbert–Federov shifts are coupled by the vortex beam’s orbital angular momentum. While the Goos–Hänchen increases with propagation distance, the Imbert–Federov shift is invariant with propagation. We show that both shifts exhibit a dependence on the beam’s topological charge beyond a simple linear proportionality.

Donut-like photonic nanojet with reverse energy flow

Photonic nanojets (PNJs) are subwavelength jet-like propagating waves generated by illuminating a dielectric microstructure with an electromagnetic wave, conventionally a linearly polarized plane wave. Here, we study the donut-like PNJ produced when a circularly polarized vortex beam is used instead. This novel PNJ also has a reverse energy flow at the donut-like focal plane depending on both the optical vortex topological charge and microsphere size. Our tunable PNJ, which we investigate numerically and analytically, can find applications in optical micromanipulation and trapping.

Nonlinear accelerated orbiting motions of optical trapped particles through two-photon absorption.

Vortex beams carrying optical angular momentum (AM) could drive the orbital motion of a small particle around the optical axis. In general, the orbital rotation speed of trapped particles increases linearly with the increasing laser power. Beyond the linear optics regime, in this work, we investigate both the optical force and torque on a two-photon absorbing Rayleigh particle produced by the tightly focused femtosecond-pulsed circularly polarized vortex beam. Different from the trapping dynamics of particles without two-photon absorption (TPA), it is shown that the orbital motion of trapped particles with TPA accelerates nonlinearly as the laser power increases. Moreover, the orbital motion acceleration of trapped particles is proportional to the TPA coefficient. The corresponding underlying mechanism is discussed in detail. Our results may find interesting applications in the characterization of the optical nonlinearity of a single nanoparticle, and AM manipulation and particle transportation in the nonlinear optics regime.

Vector polarizability of an atomic state induced by a linearly polarized vortex beam: External control of magic, tune-out wavelengths, and heteronuclear spin oscillations

Experiments with vortex beams have shown a surge of interest in controlling cold atoms. Most of the controlling protocols are dominated by circularly polarized light due to its ability to induce vector polarization at atoms, which is impossible for paraxial linearly polarized light. Here we develop a theory for frequency dependent polarizability of an atomic state interacting with a focused linearly polarized vortex beam. The naturally induced spin-orbit coupling in this type of linearly polarized beam produces vector component of the valence polarizability to an atomic state, obeying the total angular-momentum conservation of the beam. The theory is employed on $^{87}\mathrm{Sr}^{+}$ to accurately calculate the magic wavelengths for the clock transitions and tune-out wavelengths for the clock states using the relativistic coupled-cluster method. The induced vector component in the dynamic polarizability due to the linearly polarized focused vortex beam promotes a fictitious magnetic field to the atomic state. We demonstrate that this fictitious magnetic field, depending on the focusing angle and orbital angular momentum of the beam, improves the flexibility of the coherent heteronuclear spin oscillations in a spin-1 mixture of $^{87}\mathrm{Rb}$ and $^{23}\mathrm{Na}$ atoms.

Bidirectional multi-mode microwave vortex beam generation enabled by spoof surface plasmon polaritons

The microwave spectrum has become more and more crowded, motivating the investigation of new techniques to increase the communication capacity. Vortex beams carrying orbital angular momentum (OAM) have the capability for providing an extra degree of freedom to increase the channel and capacity of the wireless communication system. In this Letter, we demonstrate an effective route to achieving efficient bidirectional multi-mode microwave circularly polarized vortex beam generation enabled by spoof surface plasmon polariton (spoof SPPs, SSPPs). According to the dispersion relation of the SSPP waveguide and the radiation principle for a leaky-wave antenna, multi-OAM-mode vortex beams with different topological charges can be generated by changing the operating frequency without changing the structure. Interestingly, the emitter simultaneously radiates the right-hand circularly polarized and the left-hand circularly polarized vortex beams with opposite topological charge values upward and downward, respectively. Simulation and experimental results show that this planar SSPP vortex emitter has the advantages of single-fed, bidirectional, multi-mode, and integration compatibility.

Broadband and high-efficiency ultrathin Pancharatnam-Berry metasurfaces for generating X-band orbital angular momentum beam

Vortex beams have been extensively investigated for their major applications in wireless communications. To obtain practical applications, vortex beam generators with high performance and simple structure are of vital importance. Here, we present a novel metasurface-based device to generate high-performance vortex beams. This device is a four-layer Pancharatnam-Berry metasurface with ultrathin thickness. The unit cell of each metasurface is composed of a cross dipole and a square ring resonator. The simulated and experimental results show that the proposed meta-device can convert a right-hand circularly polarized wave into a left-hand circularly polarized vortex beam in a broadband from 9.3 to 12 GHz. Moreover, the device has high transmission efficiency up to 79% and ultrathin thickness of 0.2λ (λ is the central frequency of operation frequency band).

Statistical properties of a partially coherent radially polarized vortex beam propagating in a uniaxial crystal.

Free-space propagation and experimental generation of a partially coherent radially polarized (PCRP) vortex beam were studied recently [Opt. Express24, 13714 (2016)OPEXFF1094-408710.1364/OE.24.013714]. In this work, we explore the statistical properties of such a PCRP vortex beam propagating in a uniaxial crystal. We show that the anisotropy of the refractive index of the uniaxial crystal induces the asymmetrical distribution of the intensity, the degree and the state of polarization, as well as the degree of coherence of the beam during propagation. Further, by comparing the asymmetrical distribution of the statistical properties of the PRCP vortex beam with those of a PRCP beam without a vortex phase, we find that the asymmetrical features can be used for determining whether a PCRP beam carries the vortex phase. Further, we show that from the far-field distribution of the degree of coherence, we could quantify the topological charge and distinguish the handedness of the vortex phase. Our findings provide a novel approach for measuring the phase information of the partially coherent vortex beams.

Non-dipole effect in vortex high-order harmonic generation

We discuss the non-dipole effect in high-order harmonic generation from atoms driving by a linearly polarized vortex beam. Different from the selection rule under the dipole approximation, where only odd high harmonics are allowed, both even and odd harmonics are generated in the vortex beam. Moreover, the polarization states of the harmonics are modulated. Elliptically polarized high harmonics can be directly generated with a linearly polarized vortex beam. We show that these non-dipole effects arise from the orbital angular momentum and spin angular momentum of the vortex beam.

High numerical aperture metalens to generate an energy backflow

Using electronic beam lithography and reactive ion beam etching, a metalens is manufactured in a thin layer of amorphous silicon of a 130-nm depth, a 30-µm diameter, and a 633-nm focal length (equal to the illumination wavelength). The metalens is composed of 16 sectored subwavelength binary gratings with a 220-nm period. The uniqueness of this metalens is that when illuminated by left-handed circularly polarized light, it is capable of generating a left-handed circularly polarized vortex beam with a topological charge of 2, generating a second-order cylindrical vector beam when illuminated by linearly polarized light. Both for linear and circular incident polarization, an energy backflow is found to be generated in the vicinity of the tight focus. Transverse intensity distributions measured with a scanning near-field optical microscope near the focus of the metalens are in qualitative agreement with the intensity distributions calculated by the FDTD method. This confirms that a backward energy flow takes place at the focus of the metalens. A metalens generating an energy backflow near its focus is fabricated and characterized for the first time.

Symmetric spin splitting of elliptically polarized vortex beams reflected at air-gold interface via pseudo-Brewster angle.

A simple expression of the transverse spatial spin splitting of light-carrying intrinsic orbital angular momentum (IOAM) is theoretically derived for reflections at strong absorbing media surfaces. By introducing an asymmetric spin splitting (ASS) factor, the transverse spatial symmetric spin splitting (SSS) and ASS of an arbitrary polarized vortex beam can be distinguished. Here, the transverse spatial SSS of an elliptically polarized vortex beam with a phase difference of 90° is predicted when the incident angle is close to the pseudo-Brewster angle. Remarkably, the larger transverse spatial SSS reaches 1100 nm for the incident circularly polarized LG beam with l=3. It is noteworthy that the transverse spatial SSS can be flexibly manipulated by changing the polarized angle, meaning it is theoretically possible to realize fully polarization-controllable transverse spatial SSS for elliptically polarized incident vortex beams. These results could potentially be applied to precision polarization metrology and edge-enhanced imaging.

Spin-orbit and orbit-spin conversion in the sharp focus of laser light: Theory and experiment

Based on the Richards-Wolf theory, it is strictly shown that in the sharp focus of a linearly polarized laser beam, the flux of a spin vector has only transverse components (the effect of photonic wheels or a photonic helicopter). For a linearly polarized optical vortex, the orbit-spin conversion leads to the appearance of both longitudinal and transverse components of the spin angular momentum (SAM) vector in the focus. We show that in the strong focus of a circularly polarized Gaussian beam, the longitudinal component of the SAM is maximal on the optical axis, with the longitudinal component of the orbital angular momentum (OAM) being maximal on a ring. In this way, the effect of SAM and OAM on the motion of a trapped microparticle can be evaluated separately. Spin-orbit conversion is experimentally demonstrated for a circularly polarized Gaussian beam when transverse energy flux (orbital angular momentum) arises in the focus, which is transmitted to a microparticle and causes it to rotate. Switching the handedness of circular polarization (from left to right) switches the direction of microparticle rotation. It is also shown here that an azimuthally polarized vortex beam with an arbitrary integer topological charge generates in the focus a SAM vector with only an axial component (pure magnetization), whereas there is no transverse spin flux.

Orbital angular momentum density characteristics of tightly focused polarized Laguerre-Gaussian beam.

The orbital angular moment (OAM) of light has been proved to be useful in plenty of applications. By transmitting the OAM of the focused light field to a particle, it will be orbited around the optical axis. Therefore, it is necessary to study the OAM distribution of the focused light field used to manipulate the particles. In this application, the widely used paraxial approximation is no longer sufficient due to the tightly focused beam. We employ the higher-order Poincaré sphere to represent the Laguerre-Gaussian (LG) beams with arbitrary polarization. Then the Rayleigh-Sommerfeld integral method and the q-parameter method are used to derive the analytical expression of the light field on the focal plane. Based on this, the OAM density expression of the tightly focused LG beam is derived. In the numerical simulation, we study and analyze the unique intensity distributions and OAM distributions of tightly focused linear polarized, radial polarized, and circular polarized LG beams. The results could be leveraged to further explore the applications of the polarized vortex beam.

Deuterogenic Plasmonic Vortices.

The optical vortex on a chip is of extreme importance for many applications in nanoscience, and as well-known, the chiral metallic nanostructures like plasmonic vortex lenses (PVLs) can produce a spin-dependent plasmonic vortex (PV) which is governed by plasmonic spin-orbit coupling. The well-established nanophotonic theory and various experimental demonstrations all show a single PV mode in one PVL, when the excitation is fixed. Here, counterintuitively, we report the existence of the nontrivial deuterogenic PVs, besides the one predicted previously. We theoretically reveal a general spin-to-orbit coupling and experimentally demonstrate the surprising existence of multiple PVs in a single PVL even when excited by a fixed circularly polarized vortex beam. This work provides a deeper fundamental understanding of the dynamics and the near-field spin-orbit coupling in nanophotonics, which promises to flexibly manipulate the PV for emerging optical vortex-based nanotechnologies and quantum optical applications on a chip.

Transfer of spin angular momentum to a dielectric particle

We show here that in the sharp focus of a linearly polarized laser beam the spin vector flux has only transverse components (the effect of photonic wheels or photonic helicopter). For a linearly polarized optical vortex, the orbit-spin conversion leads to the appearance of both longitudinal and transverse components of the spin density vector in the focus. Spin-orbit conversion is experimentally demonstrated for a circularly polarized Gaussian beam when a transverse energy flux (orbital angular momentum) arises in the focus, which is transmitted to a microparticle and makes it rotate. Switching the handedness of circular polarization (from left to right) switches the microparticle rotation direction. It is also shown here that an azimuthally polarized vortex beam with an arbitrary integer topological charge generates in the focus a spin density vector that only has an axial component (pure magnetization), while the transverse spin flux is absent.