Value Of Topological Charge Research Articles

Perfect Off-Axis Optical Vortex Lattice

Optical vortex lattices (OVLs) with diverse modes show potential for a wide range of applications, such as high-capacity optical communications, optical tweezers, and optical measurements. However, vortices in typical regulated OVLs often exhibit irregular shapes, such as being narrow and elongated. The resulting increase in asymmetry negatively impacts the efficiency of particle trapping. Additionally, the vortex radii expand with an increase in topological charge (TC), limiting the TC value of the vortices and hindering their ability to fully utilize orbital angular momentum (OAM). Herein, we propose an alternative approach to custom OVLs using off-axis techniques combined with amplitude modulation. Amplitude modulation enables the precise generation of an OVL with perfect vortex properties, known as a perfect off-axis OVL. Further, the number of vortices in the perfect off-axis OVL, the off-axis distances, and the TC can be freely modulated while maintaining a circular mode. This unique OVL will promote new applications, such as the complex manipulation of multi-particle systems and optical communication based on OAM.

Spatiotemporal vortex strings.

Light carrying orbital angular momentum (OAM) holds unique properties and boosts myriad applications in diverse fields. However, the generation of an ultrafast wave packet carrying numerous vortices with various transverse OAM modes, i.e., vortex string, remains challenging, and the corresponding detection method is lacking. Here, we demonstrate that a vortex string with 28 spatiotemporal optical vortices (STOVs) with customizable topological charge (TC) arrangements can be generated in one wave packet. The diffraction rules of STOV strings are revealed theoretically and experimentally. Following these rules, the TC values and positions of all STOVs in a vortex string can be simultaneously recognized from the diffraction pattern. Such STOV strings facilitate STOV-based optical communication. As a proof-of-principle demonstration, the transmission of an image is realized with 16-STOV strings. This work provides guidance for revealing the underlying properties of the transverse OAM light and opens up opportunities for applications of the structured light in optical communication, quantum information processing, etc.

Where is the orbital angular momentum in vortex superposition states?

In this paper, we explore the distribution of the orbital angular momentum (OAM) in the coaxial vortex superposition states based on the independent propagation principle of light in this interference process. We find that in this case, some specific singular points exist in the spatial intensity distribution. The first type of singular point is located at the center point of the spatial intensity distribution. The second type of specific singular point is at the critical location of the overlapping area in angular direction. By analogy with the angular momentum superposition of two axially rotating homogeneous disks with different radius in rigid body, We present a suggestion: the center point is located at the overlapping area of all the superposed components. Therefore, the topological charge value in the center point should be doubled by the actual number of superposition field components. The singular point at the critical location of the overlapping area in angular direction should also be co-owned by the superposition components outside the position of the ring (including the corresponding component of the ring). The total OAM is exactly equal to the sum of those two types contained in the superposition states, which is equal to the input OAM of the superposition state components. The conservation of the OAM in the coaxial interference process is demonstrated.

Concentric ring optical traps for orbital rotation of particles

Abstract Optical vortices (OVs), as eigenmodes of optical orbital angular momentum, have been widely used in particle micro-manipulation. Recently, perfect optical vortices (POVs), a subclass of OVs, are gaining increasing interest and becoming an indispensable tool in optical trapping due to their unique property of topological charge-independent vortex radius. Here, we expand the concept of POVs by proposing concentric ring optical traps (CROTs) and apply them to trapping and rotating particles. A CROT consists of a series of concentric rings, each being a vortex whose radius and topological charge can be controlled independently with respect to the other rings. Quantitative results show that the generated CROTs have weak sidelobes, good uniformity, and relatively high diffraction efficiency. In experiments, CROTs are observed to trap multiple dielectric particles simultaneously on different rings and rotate these particles with the direction and speed of rotation depending on the topological charge sign and value of each individual ring. In addition, gold particles are observed to be trapped and rotate in the dark region between two bright rings. As a novel tool, CROTs may find potential applications in fields like optical manipulation and microfluidic viscosity measurements.

Next generation PON architecture using PD-NOMA employing OAM and WDM multiplexing

In this paper, we propose and experimentally demonstrate the efficacy of a next-generation passive optical network (PON) architecture for free space optical link, which utilizes power domain (PD) non-orthogonal multiple access (NOMA) along with simultaneous orbital angular momentum (OAM) mode and wavelength-division multiplexing (WDM) techniques. In this proposed architecture, many optical network units (ONUs) are accommodated by clustering them based on their power budgets and their data streams are allocated with different powers accordingly. The clustered ONUs are served with multiple OAM modes over multiple wavelengths to maintain high capacity, low latency, and increased reliability. As a proof-of-principle experimental demonstration of the proposed architecture, we have experimentally emulated two ONU clusters having a power ratio of (near:far)−3.17dB for implementing the PD-NOMA system for downlink. Each ONU cluster uses three 50 GHz spaced WDM channels, where each WDM channel carries two multiplexed OAM modes having opposite topological charge (l=±1 and ±2) values. Each cluster’s six ONUs is delivered with a 10 Gbps On-Off Keying (OOK) signal. We have demonstrated that all users can achieve a pre-forward error correction (pre-FEC) bit error rate (BER) below the 7% overhead-FEC (OH-FEC) BER limit of 3.8×10−3. We have also measured the x-talk due to WDM and mode multiplexing, and it has been revealed that the main contribution to the power penalty (relative to the no cross-talk condition) comes from OAM mode cross-talk.

Topological Charge Measurement of a Partially Coherent Vortex Beam Using Dual Cylindrical Lenses with an Arbitrary Angle

For a partially coherent Laguerre–Gaussian (PCLG) vortex beam, information regarding the topological charge (TC) is concealed in the cross-spectral density (CSD) function phase. Herein, a flexible method for the simultaneous determination of the sign and magnitude of the TC for a PCLG vortex beam is proposed based on the measured CSD amplitude and phase after the beam propagates through a dual cylindrical lens with adjustable angles. Both the stripes in the CSD amplitude and phase exhibit quantitative relationships with the value of TC, that is, N=2l+1. Meanwhile, the angle adjustability of cylindrical lenses allows flexible measurements, thus rendering the scheme effective for both high and extreme coherences.

Mode Conversion Between Beams Carrying Orbital Angular Momentum With Opposite Topological Charges Using Two-Dimensional Multimode Interference Waveguides

Recently, the implementation of rectangular waveguides for generation and manipulation of orbital angular momentum (OAM) modes, has been developed to exploit the outstanding features of these modes in more complex integrated devices. Multimode interference (MMI) structures have been widely used in both one and two dimensions as the basic elements in many integrated optical devices like optical beam splitters, mode converters, couplers, wavelength-division (de)multiplexers, and switches. According to the various applications of OAM modes in quantum and classical communications, the study of their propagation properties in MMI waveguides is useful in order to facilitate the way into higher security and capacity systems. This paper presents the results of numerical investigation of a proposed integrated optical OAM mode converter which is performed based on the mode decomposition properties of propagating OAM modes in 2D MMI waveguides, as well as the fact that any order of OAM mode can be represented as superposition of an odd mode and a quarter-wave shifted even mode. The proposed device, which consists of two MMI waveguides connected by phase shifters and linear waveguides, provides mode conversion between beams carrying OAM with odd opposite topological charges. The design procedure is performed for OAM modes with topological charge values of l = ±1 and l = ±3 using beam propagation method. The proposed device is passive with reciprocal behavior and has the output mode purity of 94% and 82% for beams carrying l = ±1 and l = ±3, respectively.

Tight Focus Vector Light Field of Hybrid Double Circularly Polarized Beams

Based on the Richard-Wolf diffraction theory, we demonstrate the tightly focused optical field distribution with two beams circularly polarized light. We deduced the expression of the double-beam superimposed vortex light intensity of left-handed circularly polarized light and right-handed circularly polarized light under the focusing condition of a high numerical aperture objective lens. Based on the different vortex topological charge values, amplitudes and initial phases of the dual beams, we numerically simulated the light intensity distribution of the superimposed hybrid focused light field. It is found that a variety of peculiar vortex spots can be obtained through the tight focus stacking of the double beams. These complex hybrid focused light fields with different polarizations can be used in fields such as optical field micro-manipulation or nonlinear fluorescence microscopy imaging.

Topological electrostatics

We present a theory of optimal topological textures in nonlinear sigma-models with degrees of freedom living in the Grassmannian manifold. These textures describe skyrmion lattices of N-component fermions in a quantising magnetic field, relevant to the physics of graphene, bilayer and other multicomponent quantum Hall systems near integer filling factors ν > 1. We derive analytically the optimality condition, minimizing topological charge density fluctuations, for a general Grassmannian sigma model on a sphere and a torus, together with counting arguments which show that for any filling factor and number of components there is a critical value of topological charge above which there are no optimal textures. Below a solution of the optimality condition on a torus is unique, while in the case of a sphere one has, in general, a continuum of solutions corresponding to new non-Goldstone zero modes, whose degeneracy is not lifted (via a order from disorder mechanism) by any fermion interactions depending only on the distance on a sphere. We supplement our general theoretical considerations with the exact analytical results for the case of , appropriate for recent experiments in graphene.

Generalized Newton's rings with vortex beams.

The Newton's rings are interference patterns with concentric rings, and Newton's rings experiment is one of the most famous classic optics experiments. Here, we show that if we use a vortex beam, we can obtain generalized Newton's rings. Unlike traditional Newton's rings, the generalized ones are no longer concentric rings but spiral arms, and fork-shaped dislocations appear in spiral arms. More interesting, we reveal that both the number of spiral arms and the number of fork-shaped dislocations are equal to the value of topological charge of incident vortex beams. Our theoretical results are demonstrated experimentally. This novel interference pattern can be used for measuring the topological charge of vortex beams.

Controlling spacing of double-ring perfect optical vortex using the Fourier transform of Bessel beam with axicon phase

The perfect optical vortex (POV) has additional potential uses in optical trapping and optical communication, due to its diameter being independent of its topological charge. In this study, we demonstrate a double-ring vortex beam with adjustable spacing between the two rings; its size is also only minimally affected by the change of topological charge. To our knowledge, the beam satisfies the double-ring POV concept. The Fourier transform of a Bessel beam embedded with an axicon phase can theoretically produce such a beam. The experimental findings support the numerical results, demonstrating that the ring spacing between two rings can be modulated via the conical parameter, expanding the superposition of double-ring beams and that the two rings always keep the same topological charge value. We also consider the vortex array created by the double-ring beam, as well as the beam’s shape. Optical trapping, orbital angular momentum multiplexing, and optical communication could all benefit from the changeable ring spacing of a double-ring vortex beam.

Topology of critical points and Hawking-Page transition

Using the Bragg-Williams construction of an off-shell free energy we compute the topological charge of the Hawking-Page transition point for black holes in AdS. A computation following from a related off-shell effective potential in the boundary gauge dual matches the value of topological charge obtained in the bulk. We also compute the topological charges of the equilibrium phases of these systems, which follow from the saddle points of the appropriate free energy. The locally stable and unstable phases turn out to have topological charges opposite to each other, with the total being zero, in agreement with the result obtained from a related construction [arXiv:2208.01932].

Evolution Properties of a Partially Coherent Twisted Laguerre-Gaussian Pulsed Beam Propagating through Anisotropic Atmospheric Turbulence

Analytical expressions for the cross-spectral density matrix of a partially coherent twisted Laguerre-Gaussian pulsed (PCTLGP) beam in anisotropic atmospheric turbulence are derived based on the extended Huygens–Fresnel principle. Numerical results indicate that the atmospheric turbulence induces the degeneration of the spectral intensity distribution of the PCTLGP beam, and the PCTLGP beam also shows different evolution properties on propagation in weaker turbulence and stronger turbulence. The PCTLGP beam with a negative twisted factor exhibits an advantage over the Laguerre-Gaussian pulsed beam for reducing the atmospheric turbulence-induced degeneration, and this advantage is further strengthened with increasing the topological charge, mode order and absolute value of the twisted factor. In addition, we also find that the pulse duration will affect the spectral intensity of the PCTLGP beam in turbulence. This kind of beam will show potential application value in free-space optical communications and remote sensing.

How convolutional-neural-network detects optical vortex scattering fields

Light scattering through disordered media is a critical topic in optical engineering as its ubiquity in natural and artificial systems. Recent progress has shown that deep learning is capable to recognize topological charge values carried by orbital angular momentum (OAM) waves with ultra-fine resolution under scattering environment. However, the physical mechanism of how a deep learning convolutional neural network (CNN) fulfills such tasks remains unclear. In this paper, in perspective of optical vortex scattering field detection, we studied the basic physical mechanism of the CNN on recognizing scattered vortex beams carrying OAMs. It has been demonstrated that a CNN uses statistical invariance of both spatial phase front of an incident OAM wave and intrinsic features of a specific disordered medium across large-scale datasets to identify the OAM topological charge values from speckles. This work can provide insightful reference for CNN-assisted OAM-based scattering detection.

Identification of Orbital Angular Momentum by Support Vector Machine in Ocean Turbulence

With the advancement of underwater communication technology, the traditional modulation dimension has been introduced, developed and utilized. In addition, orbital angular momentum (OAM) is utilized as the modulation dimension for optical underwater communication to obtain larger spectrum resources. The OAM features are extracted using a histogram of oriented gradient and trained using the support vector machine method with a gradient direction histogram feature. The topological charge value of the OAM was used to identify the classification labels, and the ocean turbulence caused by different temperatures and salinity were analyzed. Experimentation results showed that the recognition accuracy for the OAM under the Laguerre–Gaussian beam rates of 1~5, 1~6, 1~7, 1~8, 1~9, and 1~10 was 98.93%, 98.89%, 97.33%, 96.66%, 95.40%, and 95.33%, respectively. The proposed method achieved a high recognition accuracy and performed efficiently under strong turbulence. Our research explored a new technique that provides a new idea for the demodulation of OAM in optical underwater communication.

Transmission–Reflection-Integrated Metasurfaces Design for Simultaneous Manipulation of Phase and Amplitude

A kind of transmission–reflection-integrated elements and metasurfaces (MSs) are proposed to achieve full-space manipulation of amplitudes, phases, and polarization states of electromagnetic (EM) waves. The elements of MSs are designed to control the reflection and transmission under the same incident wave. By introducing an amplitude–phase regulation structure to each element, the amplitudes, phases, and polarization states of reflection and transmission can be simultaneously controlled by three geometric parameters of the proposed elements, respectively. To demonstrate the abilities of elements to regulate EM waves, the MSs working in the reflection mode, transmission mode, and transmission–reflection-integrated mode are designed and simulated, and their simulation results verify the designs. The transmission–reflection-integrated MS is also fabricated and experimentally measured. Its simulation and measurement results show that deflective vortex beams with different values of topological charge can be generated simultaneously and independently in both the reflection and transmission modes.

Propagation of a multi-vortex beam: far-field diffraction of a Gaussian beam from a multi-fork phase grating.

In this work, the far-field propagation of multi-vortex beams is investigated. We consider diffraction of a Gaussian wave from a spatial light modulator (SLM) in which a multi-fork grating is implemented on it at the waist plane of the Gaussian wave. In the first-order diffraction pattern a multi-vortex beam is produced, and we consider its evolution under propagation when different multi-fork gratings are implemented on the SLM. We consider two different schemes for the phase singularities of the implemented grating. A topological charge (TC) equal to l1 is considered at the center of the grating, and four similar phase singularities all having a TC equal to l2=l14 (or l2=-l14) are located on the corners of a square where the l1 singularity is located on the square center. Some cases with different values of l1, and consequently l2, are investigated. Experimental and simulation results show that if signs of the TCs at the corners and center of the square are the same, the radius of the central singularity on the first-order diffracted beam increases, and it convolves the other singularities. If their signs are opposite, the total TC value equals zero, and at the far-field, the light beam distribution becomes a Gaussian beam. For determining the TCs of the resulting far-field beams, we interfere experimentally and by simulation the resulting far-field beams with a plane wave and count the forked interference fringes. All the results are consistent.

Supercontinuum Induced by Filamentation of Bessel-Gaussian and Laguerre-Gaussian Beams in Water

In this paper, we study the characteristics of the supercontinuum (SC) induced by the filamentation of two typical vortex beams (i.e., Laguerre-Gaussian (LG) and Bessel-Gaussian (BG) beams) in water. By moving the cuvette filled with water along the laser propagation path, we measure the SC induced by the filamentation of the two vortex beams at different positions in water. The results show that the degree of spectral broadening induced by the filamentation of LG beams hardly changes with the change of position, while for BG beams, the spectral broadening induced by filamentation is weak on both sides and strong in the middle. The value of topological charge (TC) affects the length of the filament formed by BG beams; however, its effect on the spectral broadening induced by the filamentation of LG and BG beams is negligible.

Topological charge of two parallel Laguerre-Gaussian beams

We analytically, numerically, and experimentally determine a topological charge (TC) of the sum of two axisymmetric off-axis Laguerre-Gaussian (LG) beams with the indices (0, m) and (0, n). In particular, we find that at m = n, the combined beam has TC = n, which suggests that the sum of two identical off-axis LG beams has the TC of an individual constituent LG beam. At m < n, the TC of the sum is found to take one of the following four values: TC1 = (m + n)/2, TC2 = TC1 + 1, TC3 = TC1 + 1/2, and TC4 = TC1 – 1/2. We also establish rules for selecting one of the four feasible values of TC. For the sum of two on-axis LG beams, TC of the superposition equals the larger constituent TC, i.e. TC = n. Meanwhile following any infinitesimally small off-axis shift, TC of the sum either remains equal to the pre-shift TC or decreases by an even number. This can be explained by an even number of optical vortices (OV) with TC = –1 instantly ‘arriving’ from infinity that compensate for the same number of OV with TC = +1 born in the superposition. We also show that when two LG beams with different parity are swapped in the superposition, the topological charge of the superposition changes by 1. Interestingly, when superposing two off-axis LG beams tilted to the optical axis so that their superposition produces a structurally stable beam, an infinite number of screw dislocations with TC = +1 are arranged along a certain line, with the total TC of the superposition equal to infinity.

Intensity interference characteristics of fractional Laguerre–Gaussian optical vortex

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.