Creating Composite Vortex Beams with a Single Geometric Metasurface.

Most of the reported vortex beam generators generate vortex beams at a fixed frequency, which limits the practical applications. Therefore, it is inevitable to explore a vortex beam generator, which can actively control the operating frequency. We propose a switchable frequency terahertz vortex beam metasurface, it is freely switchable under single-frequency mode and dual-frequency mode by changing the external temperature, the phase state of vanadium dioxide (VO<sub>2</sub>) is also changeable. External temperature changes will cause VO<sub>2</sub> to transform from insulating state to metallic state. Generally, VO<sub>2</sub> conductivity can increase by several orders of magnitude as operating temperature changes. By using the phase change property of VO<sub>2</sub>, we can obtain a metasurface with switchable operating frequencies. For operating at room temperature, the proposed metasurface behaves as a single-frequency terahertz vortex generator. When (left-handed circularly polarized, LCP) terahertz wave is vertically incident on the metasurface, it generates vortex beams with different topological charge numbers at a frequency of 1.1 THz, and the mode purity is above 85%. The simulation results show that the mode purity of the vortex beam with the topological charge <i>l</i> = 1 is 90%, and the mode purity is about 91.1% for the vortex beam with <i>l</i> = 2, and 85.4% for the vortex beam with <i>l</i> = 3. When the external temperature is of 68 ℃, the designed metasurface becomes a dual-frequency vortex beam generator. At this time, the operating frequencies of vortex beams with different topological charges (<i>l</i> = 1, 2, 3) are 0.7 and 1.23 THz, whose mode purities are both above 60%. That is to say, the corresponding mode purities at topological charge with<i> l</i> = 1 for two operating frequencies are 89.1% and 71.6%, respectively. The mode purities are 83.2% and 94.4% with topological charge <i>l</i> = 2, respectively. The mode purities are 62.4% and 68.2% with topological charge<i> l</i> = 3, respectively. Therefore, the proposed switchable frequency terahertz vortex generator provides a new design idea for working frequency modulation in wireless terahertz communication.

The paper reports the intensity characteristics of fractional vortex beam, and controls the coupling between photon orbital angular momentum and spin angular momentum by coherently manipulating Laguerre–Gaussian vortex beam with linearly polarized plane light and its conjugate beam. By comparing theory with experiment, fractional vortex beams with different topological charges are generated by using pure phase liquid crystal spatial light modulator, and their intensity characteristics and interference characteristics are observed. The results show that the radial notch size of the spot is related to the fractional part of the topological charge value, and the closer the fractional part of the topological charge value is to the half integer, the more obvious the radial notch is. With the increase of integer part of topological charge, the spot radius also increases. In addition, interference with linearly polarized plane light reveals that the number of branches is equal to the number of topological charges. Interfere with its conjugate beam, and judge the topological charge number of vortex beam by the relationship between petal number and topological charge number. The petal number of integer vortex beam is twice the topological charge number, and fractional order vortex beam destroys the ring structure of Laguerre–Gaussian beam.

Cylindrical vector vortex (CVV) beam, which possesses both helical phase front and spatially inhomogeneous polarization, is a promising structured light for its various applications ranging from optical communication to optical field manipulation and optical microscopy. However, approaches to generate CVV beams with switchable and tunable polarization order and topological charge are still immature, which hinders the wide application of CVV beams. In this paper, we have experimentally demonstrated that order-controllable CVV beams can be produced by using spatial light modulator (SLM) and equivalent <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -plate system at wavelength of 1550.8 nm. It is shown that the topological charge of the CVV beam can be switched by directly programming the SLM. We have also demonstrated that the polarization order of the CVV beam can be tuned to as high as eight by employing an equivalent <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -plate system, which consists of two cascaded metasurfaces and a half-wave plate. To further verify the helical phase of the CVV beam, we have proposed a novel measurement method based on first removing the vector property and then interfering the remaining helical phase with plane wave or spherical wave.

This work investigates the joint effects of jet engine exhaust‐induced turbulence and atmospheric turbulence on the propagation of a partially coherent Gaussian Schell‐model Array (GSMA) vortex beam. Using the two‐process propagation method, analytical formulae are derived for the cross‐spectral density, spectral density, degree of coherence, and beam width of the considered beam. The results show that the considered beam takes different shapes; when the spatial coherence is large, the spectral density of the GSMA vortex beam takes an elliptical shape, whereas when the spatial coherence is smaller, the spectral density remains a Gaussian shape. The evolution profile of the degree of coherence weakens gradually when the propagation distance, topological charge, and turbulence strength increase. Moreover, the profile of the degree of coherence takes the Gaussian profile when the propagation distance is longer or turbulence atmospheric is stronger. Furthermore, the results reveal that the corresponding beam spreads faster with a larger propagation distance, lower spatial coherence, and high‐strength turbulence. This study also concludes from the results that the beam is affected more when its propagation is near the jet engine exhaust, which means that this latter has a significant impact.

The special spiral phase structure of an optical vortex leads to an intriguing study in modern singular optics. This paper proposes a real-time phase measurement method of vortex beam based on pixelated micropolarizer array (PMA). Four phase-shifting fringe images can be obtained from a single interference image, thus the vortex beam phase can be obtained in real-time. The proposed method can achieve full-field phase measurement of the vortex beam with the advantages of lower computation and vibration resistance. In the experiments, the typical phases of vortex with different topological charges are loaded on a spatial light modulator (SLM) to generate diffraction vortex beam, and the phase distribution of vortex beam is obtained in real-time, which confirm the robustness of this method. This method is of great significance in promoting the study of optical vortices.

Propagation characteristics study of radially polarized Gaussian vortex beam in ocean turbulence

In recent years, vanadium dioxide (VO2) has drawn enormous attention in dynamic electromagnetic (EM) manipulation, owing to its mild phase change condition and prominent diversity of optical characteristics. In this paper, anisotropic meta-atoms integrating VO2 are proposed to obtain four polarization-multiplexing channels. The meta-atom is composed of two stacking metal–insulator–metal (MIM) structures. For the modulation of EM wavefront in desired manners, a meta-atom database composed of 256 meta-atoms is elaborately designed. Applying the meta-atom database and the degree of freedom in interfacial phase distribution, two metasurfaces are demonstrated in the verification of four-channel polarization-multiplexed vortex beams. The firstly proposed metasurface realizes the generation of four vortex beams with different topological charges. Each channel is dependent on the polarization of the incident wave and VO2 state. The further investigated metasurface achieves simultaneous control over the reflection direction, quantity, and mode of vortex beams under different VO2 states and polarization states of incident wave. In addition, designed metasurfaces exhibit wideband effect for over 100 GHz. The proposed design method enables four-channel generation of vortex beams using a single metasurface, and may have potential applications in dynamic and integrated terahertz communication.

We present a model based on the Fresnel diffraction scheme for the spatial coherence function of random fields created by scattering optical vortex and perfect vortex beams. By using the spatial coherence function we showed analytically, numerically, and experimentally the dependence and independence of the speckle size of an optical vortex and perfect optical vortex (POV) with a topological charge, respectively. We also showed in both cases the linear dependence of speckle size on the distance of propagation. Furthermore, we describe a regime in which the spatial coherence function is nonevolving for the optical vortex beam and the POV beam with the propagation distance.

Optical vortices have special wave front structures and determined orbital angular momentum, which have huge prospect to apply. In this paper, a vortex beam with different topological charges is generated by using reflected type phase only liquid crystal spatial light modulator (LCSLM), and the interference characters of a vortex beam and a plane wave and a spherical wave are analyzed. Then, a radially polarized beam and azimuthally polarized beam are experimentally obtained. Experimental results show that, using the LCSLM, vortex beams with different topological charges can be generated dynamically in real time. Energy conversion efficiency is up to 60%.

This paper utilizes the stepwise phase screen method to study the intensity distribution and axial scintillation factor evolution characteristics of double-elliptical vortex beams with varying polarization directions and topological charges during turbulent atmospheric transmission at different intensities. The research reveals that the axial scintillation factor of a double-elliptical vortex beam is smaller than that of a single-elliptical vortex beam. As the polarization angle between the inner and outer elliptical vortex beams increases from 0 to π/2, the axial scintillation factor decreases gradually. The study also finds that for double-elliptical vortex beams with perpendicular polarization directions for the inner and outer rings, when the topological charge of the inner elliptical vortex beam is one and that of the outer elliptical vortex beam is even, the scintillation factor decreases significantly with increasing transmission distance in weak turbulence conditions and is lower than that of double-elliptical vortex beams with identical inner and outer polarization parameters. However, as turbulence intensifies, the automatic compensation effect of light intensity cannot mitigate the disturbances caused by turbulence, leading to an increased scintillation factor. When the topological charge of the outer ring is odd, the axial scintillation factor does not decrease with increasing transmission distance and exhibits high fluctuations. For double-elliptical vortex beams with an inner-beam topological charge of two and perpendicular polarization directions for the inner and outer rings, the axial scintillation factor is smaller than that of a beam with an inner-ring topological charge of one. As the transmission distance increases, the scintillation factor gradually increases. The evolution of the scintillation factor is less influenced by the outer ring's topological charge and remains lower than that of a double-elliptical vortex beam with identical inner and outer polarization parameters. The rate of change is slower, but the trend of increasing scintillation factor becomes more pronounced with increasing turbulence. Therefore, by optimizing the topological charge and ensuring perpendicular polarization between the inner and outer elliptical vortex beams, the ability of the double-elliptical vortex beam to suppress turbulence-induced disturbances can be further enhanced.

Atomic-size vortex beams have great potential in probing the magnetic moment of materials at atomic scales. However, the limited depth of field of vortex beams constrains the probing depth in which the helical phase front is preserved. On the other hand, electron channeling in crystals can counteract beam divergence and extend the vortex beam without disrupting its topological charge. Specifically, in this article, we report that atomic vortex beams with topological charge ±1 can be coupled to the 2pcolumnar bound states and propagate for more than 50 nm without being dispersed and losing its helical phase front. We give numerical solutions to the 2pcolumnar orbitals and tabulate the characteristic size of the 2pstates of two typical elements, Co and Dy, for various incident beam energies and various atomic densities. The tabulated numbers allow estimates of the optimal convergence angle for maximal coupling to 2pcolumnar orbital. We have also developed analytic formulae for beam energy, convergence angle, and hologram-dependent scaling for various characteristic sizes. These length scales are useful for the design of pitch-fork apertures and operations of microscopes in the vortex-beam imaging mode.

The propagation of Riemann-Silberstein (RS) vortices for Gaussian vortex beams with topological charges m=+1 through a lens is studied. It is shown that if there is an ideal lens, a RS vortex and a circular edge dislocation appear for Gaussian on-axis vortex beams, while only RS vortices take place for Gaussian off-axis vortex beams. In the presence of an astigmatic lens, there exist RS vortices but no edge dislocations for both Gaussian on-axis and off-axis beams. By varying the astigmatic coefficient, the off-axis parameter, and the propagation distance, the motion, creation, and annihilation of vortices may take place, and in the process, the total topological charge of RS vortices remains unchanged.

Based on the mathematical framework of the partially coherent Gaussian Schell model vortex (PCGSMV) beam and the Huygens-Fresnel integral, we conducted a study to analyze the intensity distribution and depth of focus (DOF) of the PCGSMV beam as it propagates through a classical axicon. Our numerical results indicate the influence of factors such as the beam width, spatial degree of coherence, topological charge, and axicon base angle on the intensity distribution and DOF. In addition, we investigated the relationship between the beam spot size and propagation distance, as well as the effects of the spatial degree of coherence and propagation distance on the intensity profile. Our findings highlight the importance of the intensity values along the DOF for various applications, including the optical trapping and manipulation of micro particles.

ABSTRACTPerfect optical vortex (POV) beam is a special kind of vortex beam, whose radius is independent of its topological charge. In this paper, we propose a two-dimensional multiplexing scheme with a ring radius and topological charge of POV beam. A communication system using the proposed multiplexing scheme with a two-step detection method is presented, and on–off keying modulation is applied to demonstrate the bit error rate (BER) performance under atmospheric turbulence. The numerical results show that the BER performance of the proposed scheme is better than that when only topological charge is multiplexed with the same conditions. The two-dimensional multiplexing scheme has an anti-interference capability since the ring radius is only concerned in magnitude. At the same time, the capacity and the spectral efficiency of the system are improved since both ring radial and topological charge of POV beam are used.

This work presents a detailed analytic approach to the diffraction of vortex beams from 2D orthogonal periodic structures. Using the presented formulation, the diffraction of vortex beams from 2D sinusoidal and Ronchi gratings is investigated. For these gratings, the Talbot self-healing effect under vortex beam illumination is examined. In the illumination of a 2D grating with a vortex beam, we refer the Talbot self-healing effect to the filling of the null area of the incident beam under propagation. We show that, for an incident vortex beam having odd value of topological charge, the generated Talbot self-images over the self-healing area are a 2D array of optical vortices, in which each of the individual self-images gets the form of an optical vortex with a topological charge of l=1 regardless of the topological charge of the incident beam. Both the Talbot self-healing effect and generation of the 2D array of optical vortices occur optimally between a definite interval of propagation distance. Using an intuitive approach based on the interference of the diffracted orders of the grating, we determine the self-healing interval. We show that a 2D array of optical vortices can be generated directly in the interference of eight copies of a vortex beam having proper lateral shifts and relative tilts. Easy tuning and energy preservation are two main advantages that the interference-based method has over the above-mentioned diffraction-based method for generating a 2D array of optical vortices. However, setup and implementation of the diffraction-based method are very simple. We believe that both the diffraction-based and interference-based methods for creating vortex beam arrays might find applications in optical tweezers, micromanipulations, and microfluidics.