Topological Charge Of Optical Vortex Research Articles

Generation of variable light fields by radially polarized chirped circular Airy vortex beams

Based on Richards-Wolf vector diffraction theory, the tight focusing properties of radially polarized chirped circular Airy vortex beams (RP-CCAVBs) are theoretically investigated using a high numerical aperture objective lens in the paper. The results shown that super-resolution scalable optical needles, dark channels, elliptical optical cages, and optical oscillations can be obtained by adjusting the scale factor, exponential attenuation coefficient, main ring radius, and topological charge of optical vortex in the incident RP-CCAVBs. The DOF of optical needle and dark channels is exponent dependent on scaling factor ω of RP-CCAVBs. And the position optical needle and dark channels can be moved by changing chirped parameter of RP-CCAVBs. The size of obtained optical cages can be adjusted by changing the radius of main rings in RP-CCAVBs. The intensity distribution of the obtained optical oscillations is intensely affected by parameter a and chirp parameter of RP-CCAVBs.

Influences of edge dislocation on optical vortex transmission

Through theoretical calculation, the analytical expression for the cross-spectral density function of vortex beam with and without edge dislocation during transmission in turbulent atmosphere and free space is obtained. The calculation result is used for researching the influences of edge dislocation on optical vortex transmission. The research shows that due to the edge dislocation, when the optical vortex's topological charge is greater than +1, the optical vortex will no longer carry out steady transmission in the free space transmission. Instead, it will divide into two optical vortices, and the distance between them will gradually increase as the transmission distance increases. Optical vortex will split in turbulent atmosphere propagation. Due to the edge dislocation, when the topological charge of optical vortex is greater than +2, it is found that the distance between one optical vortex and other optical vortices is much larger than that between other optical vortices. Besides, when there's an edge dislocation, the greater the light wavelength and the structure constant are, the smaller the distance between the optical vortex and the edge dislocation on the source plane is, and the evolution of the optical vortex will be accelerated.

Experimental demonstration of acoustically induced polarization-dependent fiber optical vortex inversion.

A recently proposed theoretical model of acousto-optic interaction in optical fibers with a traveling flexural acoustic wave of the fundamental order [M.A. Yavorsky, et al., Opt. Lett.44, 598 (2019)10.1364/OL.44.000598] is experimentally examined. We show the effect of inversion of topological charge of optical vortices, which is governed by the direction of incident linear polarization. This vector effect of a coupling of polarization and orbital degrees of freedom proves the inconsistency of the conventional microbending-based model and confirms the recently suggested approach of the description of acousto-optic interaction that is based on the actual displacement vector. In addition, the obtained results demonstrate the realization of a controlled-NOT gate for orbital angular momentum (OAM) states.

Spin–Orbital Transformation in a Tight Focus of an Optical Vortex with Circular Polarization

In the framework of the Richards–Wolf formalism, the spin–orbit conversion upon tight focusing of an optical vortex with circular polarization is studied. We obtain exact formulas which show what part of the total (averaged over the beam cross-section) longitudinal spin angular momentum is transferred to the total longitudinal orbital angular momentum in the focus. It is shown that the maximum part of the total longitudinal angular momentum that can be transformed into the total longitudinal orbital angular momentum is equal to half the beam power, and this maximum is reached at the maximum numerical aperture equal to one. We prove that the part of the spin angular momentum that transforms into the orbital angular momentum does not depend on the optical vortex topological charge. It is also shown that by virtue of spin–orbital conversion upon focusing, the total longitudinal energy flux decreases and partially transforms into the whole transversal (azimuthal) energy flow in the focus. Moreover, the longitudinal energy flux decreases by exactly the same amount that the total longitudinal spin angular momentum decreases.

Determining the topological charge of optical vortex by intensity distribution of a quasi-Airy vortex beam

Determining the orbital angular momentum state or the topological charge (TC) of a vortex beam is important in exploiting its applications. By analyzing the intensity distribution of the quasi-Airy vortex beam (QAVB) in far field, we find that the number of forked fringes is equal to the TCs of the vortex beam, and the direction of the forked fringes is related to the sign of TCs. Based on this property, a method of measuring the TC of optical vortex by the intensity distribution of QAVB is proposed. The range of initial topological angle (from 0 to 73°) for determining the TC of optical vortex is obtained as well as the relationship between the optimal propagation position and the initial topological angle to observe the forked fringes. In addition, the characteristics of QAVB embedded with multiple optical vortices at different locations would provide a new possibility for improving the confidentiality and the information capacity in free space optical communication.

Constraints on the detection of topological charge of optical vortices using self-reference interferometry

In this paper we investigate the self-reference interferometry of optical vortices using a Michelson interferometer. It is found that the detection of topological charge (TC) for optical vortices is constrained by some physical conditions. We present these conditions through theoretical analyses, numerical simulation and experimental results. The maximal detectable TCs are different for different parameters, which is helpful for the measurement of TC in practical applications. Within the range allowed by the constrained conditions, we also study the detection of TC using the interference pattern of a two-way optical vortex, by changing the inclined angle of one mirror of the Michelson interferometer.

Observation of a triangular-lattice pattern in nonlinear wave mixing with optical vortices

Preparation, control, and measurement of optical vortices are increasingly important, as they play essential roles in both fundamental science and optical technology applications. Spatial light modulation is the main approach behind the control strategies, although there are limitations concerning the controllable wavelength. It is therefore crucial to develop approaches that expand the spectral range of light modulation. Here, we demonstrate the modulation of light by light in nonlinear optical interactions to demonstrate the identification of the topological charge of optical vortices. A triangular-lattice pattern is observed in light beams resulting from the spatial cross modulation between an optical vortex and a triangular shaped beam undergoing parametric interaction. Both up- and downconversion processes are investigated, and the far-field image of the converted beam exhibits a triangular lattice. The number of sites and the lattice orientation are determined by the topological charge of the vortex beam. In the downconversion process, the lattice orientation can also be affected by phase conjugation. The observed cross modulation works for a large variety of spatial field structures. Our results show that modulation of light by light can be used at wavelengths for which solid-state devices are not yet available.

Topological charge of optical vortices in the far field with an initial fractional charge: optical "dipoles"

In this work, using the Rayleigh-Sommerfeld integral and the Berry formula, the topological charge (TC) of a Gaussian optical vortex with an initial fractional TC is calculated. It is shown that for different fractional parts of the TС, the beam contains a different number of screw dislocations, which determine the TС of the entire beam. With a small fractional part of the TС, the beam consists of the main optical vortex centered on the optical axis with the TС equal to the nearest integer (let be n), and two edge dislocations located on the vertical axis (above and below the center). With an increase in the fractional part of the initial TC, a "dipole" is formed from the upper edge dislocation, consisting of two vortices with TC+1 and –1. With a further increase in the fractional part, the additional vortex with TC+1 is displaced to the center of the beam, and the vortex with TC–1 is displaced to the periphery. With a further increase in the fractional part of the TC, another "dipole" is formed from the lower edge dislocation, in which, on the contrary, the vortex with TC–1 is displaced to the optical axis (to the center of the beam), and the vortex with TC+1 is displaced to the beam periphery. When the fractional part of the TC becomes equal to 1/2, the "lower" vortex with TC–1, which was displaced to the center of the beam, begins to shift to the periphery, and the "upper" vortex with TC+1 moves closer and closer to the center of the beam and merges with the main vortex when the fractional part approaches 1. Such dynamics of additional vortices with upper TC+1 and lower TC–1 determine the whole TC the beam have (n or n+1) for different values of the fractional part from the segment [n, n+1].

Topological Charge of Multi-Color Optical Vortices

The topological charge of an optical vortex is a quantity rather stable against phase distortions, for example, turbulence. This makes the topological charge attractive for optical communications, but for many structured beams it is unknown. Here, we derive the topological charge (TC) of a coaxial superposition of spatially coherent Laguerre–Gaussian beams with different colors, each beam with its own wavelength and its own TC. It turns out that the TC of such a superposition equals the TC of the LG beam with a longer wavelength, regardless of the weight coefficient of this beam in the superposition and regardless of its TC. It is interesting that the instantaneous TC of such a superposition is conserved on propagation, whereas the time-averaged intensity distribution of the colored optical vortex changes its gamut; if, in the near field, the colors of the light rings arrange along the radius according to their TCs in the superposition from lower to greater, then, on space propagation, the colors of the light rings in the cross-section are arranged in reverse order from the greater TC to the lower TC. We also demonstrate that, by choosing appropriate wavelengths (blue, green, and red) in a three-color superposition of single-ringed LG beams, it is possible to generate, at some propagation distance, a time-averaged light ring of the white color. If all the beams in a three-color superposition of single-ringed LG beams have the same TC, then there is a single ring of nearly white light in the initial plane. Then, on propagation in space, light rings of different colors acquire different radii: a smaller ring radius for a shorter wavelength.

Measuring the topological charge of optical vortices with a single plate

Measuring the topological charge of optical vortices with a single plate

Revealing the Topological Charge of Optical Vortices Through the Geometry of the Autocorrelation Intensity Profile

Revealing the Topological Charge of Optical Vortices Through the Geometry of the Autocorrelation Intensity Profile

Determining the Topological Charge of Optical Vortex by Intensity Distribution of a Quasi-Airy Vortex Beam

Determining the Topological Charge of Optical Vortex by Intensity Distribution of a Quasi-Airy Vortex Beam

Measurement of topological charges of optical vortices by antiphased semicircular slit pair

Determination of orbital angular momentum (OAM) states is a subject of crucial importance for their applications in areas ranging from classical physics to quantum information. Here, we propose the antiphase semicircular slit pair (ASSP) as a novel approach to determine the topological charge of OAM states. The ASSP contains two semicircular slits with a diameter increment and symmetrically arranged in upper and lower circle. It converts an incident OAM state into light field with two bright spots, of which the relative shift is twice as spot shift for a semicircular slit. Physically, we introduce the two models of equivalent spiral slit and the Young’s-like interference, obtaining two approximate linear relations between the shift and the incident topological charge. Analytically, the antiphase of the diffracted fields for the two semicircular slits cancels a main Bessel vortex term, and doubles the complement fields contained in that for a single semicircular slit, realizing the field with two bright intensity spots with the relative shift doubled. The diffracted field is fundamentally approximated as the weighted superposition of finite Bessel vortex eigenstates. Using shift between the bright spots, the determination of topological charge of OAM states becomes a feasible and convenient, and the experimental measurement conforms to the theory with satisfying accuracy.

Polarization interferometric prism: A versatile tool for generation of vector fields, measurement of topological charges, and implementation of a spin–orbit controlled-Not gate

Optical vortex and vector field are two important types of structured optical fields. Due to their wide applications and unique features in many scientific realms, the generation, manipulation, and measurement of such fields have attracted significant interest and become very important topics. However, most ways to generate vector fields have a trade-off among flexibility, efficiency, stability, and simplicity. Meanwhile, an easy and direct way to measure the topological charges, especially for a high order optical vortex, is still a challenge. Here we design and manufacture a prism: a polarization interferometric prism (PIP) as a single-element interferometer, which can conveniently convert an optical vortex to vector fields with high efficiency and be utilized to precisely measure the topological charge (both absolute value and sign) of an arbitrary optical vortex, even with a high order. Experimentally, we generate a variety of vector fields with global fidelity ranging from 0.963 to 0.993 and measure the topological charge of an optical vortex by counting the number of petals uniformly distributed over a ring on the output intensity patterns. As a versatile tool to generate, manipulate, and detect the spin-orbital state of single photons, PIP can also work in the single-photon regime for quantum information processing. In the experiment, the PIP is utilized as a spin–orbit controlled-Not gate on the generated 28 two-qubit states, achieving the state fidelities ranging from 0.966 to 0.995 and demonstrating the feasibility of the PIP for single photons.

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.

Measuring the Topological Charge of Optical Vortices Using Elliptical Airy Phase Mask

Measuring the topological charge(TC) of optical vortices is of great importance in applications of vortex beams. A flexible and convenient method to determine the TC of an optical vortex is proposed by using an elliptical airy phase mask (EAPM). The mask can be embedded into a typical vortex generation setup, in which no additional optical elements are required. The number and the sign of TC are respectively obtained by analyzing the number and the direction of dark stripes in the far-field diffraction patterns of the vortex beam companied with EAPM. It is experimentally demonstrated that this method is able to measure TCs of both conventional and perfect vortex up to ±120.

Topological charge of optical vortices and their superpositions

An optical vortex passed through an arbitrary aperture (with the vortex center found within the aperture) or shifted from the optical axis of an arbitrary axisymmetric carrier beam is shown to conserve the integer topological charge (TC). If the beam contains a finite number of off-axis optical vortices with different TCs of the same sign, the resulting TC of the beam is shown to be equal to the sum of all constituent TCs. For a coaxial superposition of a finite number of the Laguerre-Gaussian modes (n, 0), the resulting TC equals that of the mode with the highest TC (including sign). If the highest positive and negative TCs of the constituent modes are equal in magnitude, then TC of the superposition is equal to that of the mode with the larger (in absolute value) weight coefficient. If both weight coefficients are the same, the resulting TC equals zero. For a coaxial superposition of two different-amplitude Gaussian vortices, the resulting TC equals that of the constituent vortex with the larger absolute value of the weight coefficient amplitude, irrespective of the relation between the individual TCs.

Inverted field interferometer for measuring the topological charges of optical vortices carried by short pulses

In this work, we present an improved technique for measuring both the magnitude and sign of the topological charge of input optical vortex beams carried by short laser pulses. Numerical simulations and experimental evidences for the interference signal obtainable at the output of an inverted field interferometer (IFI) valid for both continuous wave and femtosecond optical vortex beams and pulses with an eventual pulse front tilt are in an excellent agreement. An IFI also appears to be a valuable tool for calibrating a built-in variable delay line and for estimating an eventual pulse front tilt of the input ultrashort laser pulses without any realignments. As a trivial side effect, by blocking alternatively one of the two arms of the interferometer, one can use OV beams/pulses of opposite TCs, which are well located in the plane of a desired target, eventually — at precisely known time delays.

Measuring the topological charge of optical vortices with a twisting phase.

We analyzed the propagation characteristics of the intensity of a vortex beam after it passes through a twisting phase. It was found that the doughnut-like intensity pattern of a vortex beam would separate into several bright and dark fringes. The number of dark fringes between two bright spots is equal to the topological charge (TC) of the vortex beam. Meanwhile, the intensity pattern varies with the sign of the TC. Based on this property, we proposed a convenient method to measure the TC of a vortex beam by observing its intensity pattern after passing through a twisting phase. This detection technique is mainly based on the use of a twisting phase, and the effect of parameters in the twisting phase is demonstrated and clearly studied. By choosing proper parameters in the twisting phase, the separation speed of a vortex beam's intensity could be controlled in the experiment. The experimental results are in good agreement with the theoretical analyses.

Detection of an optical vortex topological charge and coordinates by analyzing branches of an interference pattern

Detection of an optical vortex topological charge and coordinates by analyzing branches of an interference pattern