Fractional Vortices Research Articles

Precision measurement of the topological charge of a fractional vortex beam based on angular-grating-diffraction OAM spectrum

Precision measurement of the topological charge of a fractional vortex beam based on angular-grating-diffraction OAM spectrum

Quantitative determination of fractional topological charge based on the rotational Doppler effect

The utilization of fractional-order vortex beams extends the diversity of optical field manipulation, permits for more flexible control over beam propagation, and provides novel applications in optical communications, edge enhancement imaging, and particle manipulation. However, compared with the integer-order vortex beams, the topological charge measurement techniques for fractional-order vortex beams are not well developed, impeding the further exploration of its applications. In this paper, the frequency signal of rotational Doppler effect and corresponding broadening behavior under the fractional-order vortex beam illumination were analyzed. When the fractional topological charge approaches a half integer, the broadening is minimized. Leveraging this relationship, we designed a phase-compensated scheme coupled with signal-to-noise ratio detection to realize the real-time fractional topological charge measurement. The single pixel photodetector was used and eliminated the need for two-dimensional image acquisition and analysis, ensuring efficient acquisition and quantitative analysis. Both theoretical and experimental results confirm the feasibility of this method, thereby advancing the comprehension of the optical Doppler effect and potentially paving the way for future investigations into fractional vortex beams.

Characterizing the fractional coherence vortices through the area of the intensity cross-correlation function

We have generated the fractional coherence vortices using the speckle patterns obtained from the scattering of the fractional vortex beams. In this study, we found the topological charge of the fractional vortex beam with a resolution of 0.01 using the area of the coherence function of scattered fractional optical vortex beams. We have also provided accuracy for the measurement of topological charges of fractional vortex beams using the studies of the area of the coherence function. Our experimental results are well matched with the theoretical results. These fractional coherence functions can be used to generate a security key for data authentication and data encryption. In addition, fractional vortex beams have multiple OAM modes and can be used to address the explosive growth in free-space optical communication.

Recognition and information transmission of multiplexed fractional orbital angular momentum

We propose an improved hologram with both phase and amplitude modulation to generate superimposed fractional optical vortices (SFOVs). The modulation of the optical field’s amplitude and phase is achieved through the utilization of controllable diffraction efficiency of the transmission function. The resulting interference fringes of an SFOV with four orbital angular momentum (OAM) modes exhibit a distinctive double-petal-like structure, serving as a distinguishable feature for the beam’s topological charges. Accurate demodulation of the multiplexed OAM modes of 256-ary SFOV is achieved using a residual next neural network based on machine learning. To showcase its practical utility, we employ the coherent OAM multiplexing system to transmit a Newton portrait with 0.01% error rate. Furthermore, the system robustly identifies beams propagating through computer-simulated oceanic turbulence channels to aid in the development of underwater optical communication. These promising results demonstrate the potential to further expand the range of modes and enhance the information processing capabilities in optical communication.

A metalens for detecting fractional-order optical vortices

In this work, a metalens for detecting an incident field with a fractional topological charge ranging from – 2 to 0 is proposed. The metalens is based on a spiral zone plate with a topological charge of 1.5. A change in the topological charge of the incident beam is numerically shown to lead to an off-axis shift of the focal spot from the center, with the intensity maximum value also changing. This results in a 6.9-fold change in the on-axis intensity while the topological charge of the incident beam changes from –0.6 to –1.5. The on-axis intensity at the focus is also shown to be affected by the rotation of the fractional vortex beam. This makes it possible to use the proposed metalens for measuring the angle of rotation of the incident beam in the range from 0 to 110°.

Broadband Generation of Fractional Perfect Optical Vortices via Plasmonic Metasurface

AbstractA fractional perfect optical vortex (FPOV) represents a class of structured light characterized by phase singularities carrying fractional orbital angular momentum (OAM). It manifests a notched annular intensity distribution, and notably, the size of this distribution remains independent of the topological charge. Conventional methods for generating FPOVs involve a series of cascaded bulk components, leading to optical aberrations due to alignment errors and impeding their integration into highly integrated devices. In this work, an experimental demonstration is presented of the broadband generation of FPOVs in the visible spectrum utilizing a monolithic plasmonic metasurface with phase‐only modulation. The metasurface allows for flexible control of various parameters of the FPOVs, including their topological charge, beam radius, ellipticity factor, orientation, and the number of opening gaps. Furthermore, as a proof‐of‐concept, an FPOV pair is utilized to encode a double‐digit hexadecimal number, showcasing the potential of a metasurface array for optical information encryption. This research establishes a highly integrated platform for FPOV generation, with implications for advancing their applications in optical information security.

Dissociation of composite Abrikosov vortices in two-band superconductors in a strong rf field

In several theoretical works, it was argued that under certain conditions Abrikosov vortices in multiband superconductors can split and exist in the form of fractional vortices, formed separately in superfluid condensates of different electron bands. Such vortices possess a fractional flux quantum, and these fractional vortices attract each other, trying to join into a composite vortex with the whole flux quantum ϕ0=h/2e. In the present work, we solve numerically the nonlinear dynamic equation for the composite vortex, settled in the pinning potential well of the columnar defect within a two-band superconductor, and exerted the rf Lorentz force action. We demonstrate that at high enough rf current amplitudes such composite Abrikosov vortices will dissociate into fractional ones and escape from the pinning potential well. The sequence of these events depends on the character of the pinning potential well, e.g., the radius of the pinning potential well. The possible manifestation of such kind transitions in rf electrodynamic characteristics, such as a complex rf resistivity and harmonics generation is calculated.

The Rossiter equation: Improving the fractional vortex speed and defining an effective length to depth ratio for cavity flows

This paper first reviews well known analytical techniques for predicting the Rossiter modes of a cavity in compressible flow. We combine existing methods to improve the performance in compressible flow. Second, we introduce a method based on an effective length to depth ratio of the cavity from experimental results for predicting frequencies across Mach numbers. Finally, the fractional vortex speed used in the Rossiter equation and its derivatives is calculated from high subsonic (M 0.55) to supersonic (M 2.3) for use in future cavity mode prediction.

Propagation of integral and fractional perfect vortex beams in a gradient-index medium.

The analytical expressions for the complex amplitude of integral and fractional perfect vortex (PV) beams propagating in a gradient-index (GRIN) medium are derived. The intensity and phase distributions, propagation trajectories, Poynting vectors, and the effects of topological charge and refractive index at the medium axis on the intensity of both beams in the medium are numerically investigated. It is shown that both beams propagate periodically in the GRIN medium with alternating spot focusing and reconstruction. Unlike the integral PV beam, the fractional PV beam has a dark line in intensity profiles and a line edge dislocation in phase distributions along the positive x-axis. These properties persist during the beam propagation in the GRIN medium. Moreover, the topological charge and the refractive index at the medium axis have little effect on the intensity of the PV beam propagating in the GRIN medium. The results presented in this paper may be useful for the application of integral and fractional PV beams in optical guiding and optical communications.

The Propagation Characteristics of Circular Airy Beams with Propagational Fractional-Order Optical Vortices

We investigate the propagation properties of circular Airy beams (CABs) with propagational fractional-order optical vortices (OVs). The superposition of the phase singularity and polarization singularity from a vortex vector beam (VVB) plays a significant role in creating a propagational fractional vortex beam. Propagational fractional vortex beams can be considered as a superposition of left and right circularly polarized vortex beams with different integer topological charges (TCs). We study the propagation characteristics of two kinds of propagational fractional vortex CABs, and the results show that both of the two kinds of beams can stably propagate in free space, and they exhibit an “abruptly auto-focusing” property and “self-healing” property during the propagation. The intensity distribution of the first kind of propagational fractional vortex CAB has an odd number of petals (2m + 1), while the second kind of beam has a crescent-shaped intensity distribution. The influence of turbulence on the beam propagation through atmosphere under different turbulence strengths is also numerically studied in this paper. A fractional vortex CAB with an initial radius r0 = 10 mm can retain its shape after propagating 20 m when the atmospheric refractive-index structure constant CN2=0.2×10−12m−2/3. Our results are expected to broaden the application of CABs.

Coherence phase spectrum analyzer for a randomly fluctuated fractional vortex beam

Fractional vortex beams exhibit a higher degree of modulation dimensions than conventional vortices, thus inheriting superior anti-turbulent transmission properties through the incorporation of additional coherence modulation. However, aliasing the mixed modes induced by coherence degradation makes the quantitative measurement of the topological charge in fractional vortex beams challenging. In this study, a coherence phase spectrum was introduced, and experimental demonstrations to quantitatively determine the fractional topological charge of partially coherent fractional vortex beams were performed. By leveraging the four-dimensional measurement of a partially coherent light field, the source coherence function was inversely reconstructed, and fractional topological charges were determined with high precision by extracting the phase spectrum of the coherence function. Laguerre–Gaussian, elliptical Gaussian, and plane-wave-fraction vortex beams with various degrees of coherence were used to demonstrate measurement precision. The proposed method is applicable to X-rays and electron vortices. It has potential applications in optical encryption, high-capacity optical communication, and quantum entanglement.

Generating the 1.5 kW mode-tunable fractional vortex beam by a coherent beam combining system.

As an essential component of the vortex beam, the fractional vortex beam has significantly advanced various applications, such as optical imaging, optical communication, and particle manipulation. However, practical applications face a significant challenge as generating high average power fractional vortex beams remains difficult. Here, we proposed and experimentally demonstrated a high average power mode-tunable fractional vortex beam generator based on an internally sensed coherent beam combining (CBC) system. We presented the first, to the best of our knowledge, successful generation of a 1.5 kW continuous wave fractional vortex beam. Moreover, real-time tuning of the topological charge (TC) from -2/3 to +2/3 was easily achieved using the programmable liquid crystals (LCs). More importantly, the fractional vortex beam copier was presented as well, and the generated fractional vortex beam could be easily transformed into a fractional vortex beam array by changing the fill factor of the laser array. This work can pave the path for the practical implementation of high average power structured light beams.

Observation of spatial self-phase modulation excited by off-axis integer and fractional vortex beams

Spatial self-phase modulation (SSPM) is widely used to characterize the nonlinear refractive index of two-dimensional layered materials and design passive nonlinear photonic devices. In this work, we investigate the SSPM phenomena of black phosphorus dispersed in agarose solid under the excitation of on-axis and off-axis integer and half-integer vortex beams. It is found that with the increase of the off-axis distance of the Gaussian vortex beam, the pattern of the far-field self-diffraction intensity gradually breaks from the initial ring and finally evolves into a tail outside the self-diffraction ring. Moreover, for half-integer vortex beams, the size of the innermost tail of the self-diffraction ring is nearly half smaller than that of the second outer tail. The underlying mechanism of the observed SSPM phenomenon is also analyzed. Interestingly, the trailing number and rotation direction of the self-diffraction ring pattern quantitatively reflect the magnitude and sign of the topological charge (TC) of the off-axis vortex beam, respectively. This work provides a novel method to measure the TC of off-axis vortex beam in the nonlinear optics regime.

Generation of integer and fractional vortex beams based on liquid crystal electronically reconfigurable spiral phase plates.

The manufacturing and characterization of a large-size 72-electrode liquid crystal-based reconfigurable spiral phase plate (SPP) is presented. The SPP is addressed by a custom-made driver with 72 independent channels, which allows for the generation of any arbitrary integer or fractional optical vortex beam with topological charges ranging from -24 to +24. The 25 mm diameter device is fabricated using direct laser writing, leading to a fill factor over 99%. The device performance and flexibility exceed previous transparent reconfigurable SPP in terms of size, tuning range, and fill factor. The device and the light path have been simulated using the angular spectrum propagation method, showing excellent correspondence.

Experimental study of the transport characteristics of fractional-order vortex beams in a turbulent atmosphere simulator

Fractional vortex beams have attracted increasing attention due to their complex yet intriguing physical properties, such as radial notch intensity distribution and higher degrees of modulation in orbital angular momentum. In this study, we experimentally investigated and compared the beam spread and beam wander characteristics of fractional-order vortex beams with those of integer-order vortex beams after passing through a turbulent atmosphere simulator with varying turbulence intensities. Our results revealed that the beam spread of both fractional-order and integer-order vortex beams increased in a stepwise manner with the topological charge number, indicating that a larger topological charge number resulted in more severe beam spread. Interestingly, we observed that the beam radius of fractional-order vortex beams between two adjacent integer orders initially grew slowly and then rapidly before finally stabilizing into a curvilinear growth trend. This is in contrast to the linear growth trend exhibited by the beam radius of integer-order vortex beams. Furthermore, we found that the growth of the beam radius of half-integer-order vortex beams followed the linear growth trend of the beam radius of integer-order vortex beams. When the integer part of the topological charge was fixed, we observed that stronger turbulence resulted in more severe beam wander for both integer-order and fractional-order vortex beams, with the variance of the center-of-mass drift following the same growth curve. However, when the turbulence intensity is constant, both integer-order and fractional-order vortex beams exhibit a weaker beam wander effect with increasing topological charge. Our findings may provide valuable insights for applications such as optical communication and optical measurement using fractional-order vortex beams.

Baby skyrmion in two-component holographic superfluids

In the two-component Ginzburg-Landau theory of superfluidity, a pair of fractional vortices form a composite type of topological defect, usually referred to as a baby skyrmion. In this paper, we initiate the construction of such a baby skyrmion in the holographic model of two-component superfluids. As a result, two types of baby skyrmion configurations are found, where the monopole-type of one is constructed directly by solving the static equations of motion while the dipole-type of one is obtained by resorting to the time evolution method. In addition, we find that the existence of these two types of baby skyrmion depends on the inter-component coupling, reminiscent of the situation in the baby skyrmion model.

Second-Harmonic Generation of the Vortex Beams with Integer and Fractional Topological Charges

The single-pass second-harmonic generation (SHG) of a vortex beam under low fundamental wave depletion is systematically studied. Vortex modes at 1064 nm with integer topological charges from ±1 to ±9 and fractional ones at ±0.75 are generated by modulating the fundamental Gaussian beam with different spiral phase plates. The frequency doubling of these fundamental vortex modes is realized via single-pass SHG through the KTP. A detailed theoretical model is set up in the single-pass SHG of the vortex beams. Theoretical analysis indicates that the higher the order of the vortex beams, the lower the SHG efficiency, when the beam waists and fundamental power are given. The experimentally measured SHG output characteristics verify those obtained via theoretical analysis. Conservation of the orbital angular momentum during the SHG process is also verified, regardless of the fractional or integer vortex beams. SH LG0,2l vortex beams with high mode purity are obtained. The beam waists of fundamental/SH in KTP measured using a 4f system demonstrate that the Rayleigh ranges of the fundamental wave and SH wave are the same. The paper comprehensively presents some basic laws in the single-pass SHG of a vortex beam. In addition, it also indicates that SHG is an effective method to improve the mode purity of vortex beam.

Energy Backflow in Tightly Focused Fractional Order Vector Vortex Beams with Binary Topological Charges

Using the Richards–Wolf diffraction integral, the longitudinal energy evolution on the focal plane of the fractional order vector vortex (FOVV) beams was studied. These beams possessed a vortex topological charge n and a polarization topological charge m, and were subjected to tight focusing through a larger numerical aperture. Our investigation revealed the existence of backflow energy when the binary topological charges n and m satisfied the conditions of n + m = 2 or n − m = −2. The component circularly polarized vortex beams of e−i2ϕe^+ (i.e., the minus second-order vortex right circularly polarized beam) and ei2ϕe^− (i.e., the second-order vortex left circularly polarized beam) played significant roles in the generation of reverse energy flux at the focal region. For FOVV beams with binary topological charges n and m, whose sum and difference were integers, the longitudinal energy on the focal plane exhibited axial symmetry. If the sum or the difference of the topological charges n and m was not an integer, the axisymmetric longitudinal energy on the focal plane was disrupted.

Reconstruction of fractional vortex phase evolution by generative adversarial networks.

Digital signal coding based on the combination of vortex beam orbital angular momentum (OAM) and vortex optical phase information has made many achievements in optical communication. The accuracy of the vortex optical phase is the key to improving the efficiency of communication coding. In this regard, we propose a depth learning model based on the generative adversarial network (GAN) to accurately recover the phase image information of fractional vortex patterns at any diffraction distance, thus solving the problem that it is difficult to determine the phase information of fractional vortex patterns at different transmission distances due to the phase evolution. Compared with other depth learning methods, the phase recovery result of GAN is not affected by the diffraction distance, which is the first time we know that this method is applied to the fractional order optical vortex. Our work provides a new idea for the accurate identification of multi-singular structured light.

Observation of fractional vortices and π phases in Josephson junctions involving periodic magnetic layers

Observation of fractional vortices and <i>π</i> phases in Josephson junctions involving periodic magnetic layers