Coherent Vortex Beams Research Articles

Random sources with rectangular coherence.

A convenient method for modeling partially coherent sources with rectangular coherence is introduced by structuring the degree of coherence as two separable arbitrary functions with arbitrary dependence of variables. The included examples have demonstrated new opportunities of modeling random sources for beam shaping applications by coherence modulation. The first example discusses a class of rectangular sinc-correlated models generating radiating fields with self-focusing features. As a second example, we introduce a new type of partially coherent vortex beams, which has a unique feature of self-rotation around the optical axis upon propagation.

Source coherence-induced control of spatiotemporal coherency vortices.

A novel method to achieve the coherence control of spatiotemporal coherency vortices of spatially and temporally partially coherent pulsed vortex (STPCPV) beams is proposed. The influence of spatial and temporal coherence of the source on the phase distributions and the positions of spatiotemporal coherency vortices of the STPCPV beams propagating through fused silica is investigated in detail, for the first time to our knowledge. It is found that the coherence width and the coherence time of the incident beam can be regarded as a perfect tool for controlling the phase distribution and position of a spatiotemporal coherency vortex. The results obtained in this paper will benefit a number of applications relating to light-matter interaction, quantum entanglement, quantum imaging, optical trapping and spatiotemporal spin-orbit angular momentum coupling.

Structured light in the spatially partially coherent regime

In this work, we present an introduction to the field of spatially partial coherent beams, while keeping in mind the transverse structure of an optical field. We look closely at the concept of spatial coherence and show some strategies to deal with it. We work step–by–step with the reader and construct as an example, a partially coherent vortex beam. Finally, using numerical simulations, the richness in structure of a partially coherent field is revealed through its cross–correlation function.

Radially polarized twisted partially coherent vortex beams

We introduce a new type of partially coherent vector beam, named the radially polarized twisted partially coherent vortex (RPTPCV) beam. Such a beam carries the twist phase and the vortex phase simultaneously, and the initial state of polarization (SOP) is radially polarized. On the basis of the pseudo-modal expansion and fast Fourier transform algorithm, the second-order statistics such as the spectral density, the degree of polarization (DOP) and the SOP, propagation through a paraxial ABCD optical system are investigated in detail through numerical examples. The results reveal that the propagation properties of the RPTPCV beam closely depends on the handedness of the twist phase and the vortex phase. When the handedness of the two phases is same, the beam profile is easier to remain a dark hollow shape and the beam spot rotates faster during propagation, compared to the partially coherent vortex beam or the RPTPCV beam with the opposite handedness of the two phases. In addition, the same handedness of two phases resists the coherence induced de-polarization of the beam upon propagation, and the SOP is also closely related to the handedness, topological charge of the vortex phase and the twist factor of the twist phase, providing an efficient way to modulate the beam's DOP and SOP in the output plane. Moreover, we establish an experiment setup to generate the RPTPCV beam. The average spectral density and the polarization properties are examined in the experiment. The experimental results agree reasonable well with the theoretical predictions. Our results will be useful for particle manipulating, free-space optical communications, and polarization lidar systems.

Scattering of partially coherent vortex beam by rough surface in atmospheric turbulence.

A double-passage propagation model of partially coherent Laguerre-Gaussian (LG) vortex beams with orbital angular momentum (OAM) modes in turbulent atmosphere after scattering from Gaussian rough surfaces was formulated. Rough surface scattering had a weak effect on the spreading of a vortex beam in turbulent atmosphere. However, it severely influenced the phase on this beam, rapidly reducing the original OAM mode's relative intensity. The OAM spectrum information is more useful than the intensity information for rough surface object remote sensing. Additionally, by comparing the scattering intensity in monostatic and bistatic systems, the enhanced backscatter of vortex beams from Gaussian rough surfaces was verified.

Phase discontinuities induced scintillation enhancement: coherent vortex beams propagating through weak oceanic turbulence

Under the impact of an infinitely extended edge phase dislocation, optical vortices (screw phase dislocations) with tight spacing induce scintillation enhancement. As the simplest case, the scintillation index of an interfering beam consisting of two Gaussian vortex beams with topological charges through weak oceanic turbulence is researched via derivation and phase screen simulation to present this phenomenon. Different combinations of two types of phase discontinuities can be obtained by changing the overlapping degree and the phase difference of two coherent Gaussian vortex beams. The scintillation indexes for them verify that the formation condition of the phenomenon is the coexistence of two types of phase discontinuities. And the enhanced scintillation index can be several orders of magnitude larger than that of a plane wave under weak perturbation (Rytov variance). This phenomenon could be useful for both optical vortex detection and perturbation measurement.

Influence of Source Parameters and Non-Kolmogorov Turbulence on Evolution Properties of Radial Phased-Locked Partially Coherent Vortex Beam Array

Partially coherent optical vortices have been applicated widely to reduce the influence of atmospheric turbulence, especially for free-space optical (FSO) communication. Furthermore, the beam array is an effective way to increase the power of the light source, and can increase the propagation distance of the FSO communication system. Herein, we innovatively report evolution properties of the radial phased-locked partially coherent vortex (RPLPCV) beam array in non-Kolmogorov turbulence. The analytical expressions for the cross-spectral density and the average intensity of an RPLPCV beam array propagated through non-Kolmogorov turbulence are obtained. The numerical results reveal that the intensity distribution of the RPLPCV array propagated in the non-Kolmogorov turbulence is gradually converted to a standard Gaussian distribution. In addition, the larger the radial radius, radial number and waist radius are, the smaller the coherence length is. Moreover, the longer the wavelength is, the shorter the propagation distance required for the intensity distribution of the RPLPCV beam array to be converted into a Gaussian distribution in the non-Kolmogorov turbulence. The research in this paper provides a theoretical reference for the selection of light sources and the suppression of turbulence effects in wireless optical communication.

Partially coherent perfect vortex beam generated by an axicon phase

Vortex beams are structured light fields with a helical phase of the form exp (ilϕ) that carries an optical angular momentum (OAM) of lℏ per photon. Such beams typically have a ring-shaped intensity with a radius that varies with l. Perfect vortex (PV) beams are designed to have a radius that is approximately uniform over a certain OAM range. Here, we report how spatial coherence can be used to maintain a fixed ring shape over a larger propagation distance and for a greater OAM range than is possible for fully coherent vortex beams. Our work is relevant for the application of PV beams in areas such as trapping, tweezing, and optical communications.

Propagation factor of partially coherent radially polarized vortex beams in anisotropic turbulent atmosphere.

We skillfully combined the cosine theorem with the second moment theory and the Wigner distribution function and derived the analytical expressions of the propagation factor (M2-factor) of a partially coherent radially polarized vortex beam (PCRPVB) in atmospheric turbulence. Then, we comparatively studied the propagation factors of a PCRPVB and a partially coherent electromagnetic vortex beam (PCEVB) in atmospheric turbulence. The results show that a PCRPVB has a smaller value of a relative M2-factor than a PCEVB, which means that a PCRPVB has a stronger ability to resist atmospheric turbulence than a PCEVB. To confirm our theoretical studies, the hyperbolic fitting method is combined with the random phase screen (RPS) to simulate the M2-factor of a PCRPVB and a PCEVB through atmospheric turbulence. The study results indicate that the theoretical values agree well with the simulated values. Our results may find applications in free-space optical communications and remote sensing.

Propagation of partially coherent vortex beams in gain media

In this paper, the propagation of partially coherent vortex beams in gain media was investigated based on the generalized Huygens-Fresnel principle. Our research focused on the influences of topological charge (m) and coherence length (σ0) on light intensity distribution, phase and spectral degree of coherence during the propagation. The results show that partially coherent vortex beams can maintain their initial dark hollow intensity distributions for a longer distance with larger m and σ0 as the gain and diffraction effects appear simultaneously. The decay of the maximum value of light intensity caused by diffraction is more obvious with a smaller σ0. On the other hand, the larger σ0 is, the more obvious the gain effect on the maximum value of light intensity is. We also observe that the coherence vortex with topological charge equals to m will split into m coherence vortices with topological charges are 1, and the coherence vortices with negative topological charge will generate at the same time. Some phenomena also appear with a larger coherence length, for example, a larger distance between coherence vortices with negative topological charge, a bigger splitting of the coherence vortices, and a slower damping of spectral degree of coherence, et al. This study can be used in the research and application of vortex beams in the materials field.

Scattering of partially coherent vortex beams by a $\mathcal {PT}$-symmetric dipole.

We investigated the statistical properties of partially coherent optical vortex beams scattered by a $\mathcal {PT}$ dipole, consisting of a pair of point particles having balanced gain and loss. The formalism of second-order classical coherence theory is adopted, together with the first Born approximation, to obtain the cross-spectral density of the scattered field. It is shown that the radiated pattern depends strongly on the coherence properties of the incident beam and on the non-Hermitian properties of the dipole. The spectral density for the scattered radiation is ruled by two terms, one associated to the vortex structure and the other independent of the topological charge, and the competition between these terms dictates the directional properties of the scattered radiation. When they have same order of magnitude, the scattered profile resembles that of an incoherent system, with radiation being emitted in all directions in the three-dimensional space, regardless of the dipole's gain and loss properties. Depending on the gain and loss present in the dipole, the system may scatter light in some preferable directions. All of these effects are accompanied by a change in the spectral degree of coherence of the scattered field.

Influence of gain or absorption media on transmission of partially coherent vortex beams.

The results show that the larger the real part of the wave number is, the farther the transmission of PCVBs with hollow distribution will be. The expression of partially coherent vortex beams passing through a gain/absorption medium is derived in this paper based on the generalized Huygens-Fresnel principle. The influences of the refractive index (related to the real part of the wave number) and the gain/absorption characteristics (related to the imaginary part of the wave number) on the transmission of partially coherence vortex beams are investigated. The results show that the larger the real part of the wave number is, the farther the transmission of PCVBs with hollow distribution will be. In gain media, the light power keeps increasing; on the other hand, in absorption media, the light power keeps decreasing. The diffraction effect of the media on the intensity distribution also is mentioned. We discover that, during the transmission, the evolutions of the spectral degree of coherence relate to the real and imaginary parts of the wave number, and the coherence vortices can split and generate. We believe the results of this study are important to the fields of singular optics and optical communications.

Recovery of the topological charge of a vortex beam propagated through a scattering layer.

Coherent vortex beams have shown great potential in many applications including information transmission under non-ideal conditions, as information can be encoded in the orbital angular momentum. However, inhomogeneity of atmosphere tends to scramble the vortex structure and give rise to speckle. It is therefore of great interest to reconstruct the topological charge of a vortex beam after it propagates through a scattering medium. Here, we propose a feasible solution for this. The proposed method measures holographically the scattered field and reconstructs the spiral phase from it by taking advantage of both the deterministic nature and the ergodicity of the scattering process. Our preliminary experiments show promising results and suggest that the proposed method can have great potential in information transmission under non-ideal conditions.

Young's double-slit experiment with a partially coherent vortex beam.

We perform a Young's double-slit experiment with a partially coherent vortex beam (PCVB) and explore its cross-spectral density (CSD) at the focal plane after passing through a double-slit. Our results reveal that the phase of the CSD distribution with respect to an on-axis reference point can simultaneously quantitatively characterize the sign and magnitude of the topological charge (TC) carried by such a beam. In particular, the magnitude of the TC is half of the number of coherence singularities and the sign of the TC is determined by the phase winding of the coherence singularities (i.e., counterclockwise- and clockwise increases correspond to positive and negative, respectively). Based on this property, we present and demonstrate experimentally a simple technique to measure the sign and magnitude of the TC of a PCVB through its CSD distribution after a double-slit. Our method allows for easy measurement of the TC by being conceptually simpler than other methods.

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.

Shaping the focal intensity distribution using a partially coherent radially polarized beam with multiple off-axis vortices.

A new kind of partially coherent vector vortex beam, namely, the partially coherent radially polarized (PCRP) beam with multiple off-axis vortices, is introduced, and the average intensity distributions of such vortex beam focused by a thin lens are investigated theoretically. It is novelty that the off-axis vortices will induce the focal intensity redistribution and reconstruction, while this remarkable characteristic will be vanished in the case of a very low coherence. In view of this distinctive feature, a new method has been put forward to shape or modulate the focal intensity distribution by elaborately tailoring the multiple off-axis vortices as well as the coherence length. More importantly, some peculiar focal fields with novel structures, such as bar-shaped, triangle-shaped, square-shaped, and pentagon-shaped hollow profiles or flat-top foci, are obtained. Our results indicate that modulating the multiple off-axis vortices provides an additional degree of freedom for focus shaping.

Partially coherent vortex beams: Fundamentals and applications

It has been over 30 years since the concept of optical vortices was first proposed by Coullet et al. in 1989, and the field of structured beams has grown extremely. In the last two decades, partially coherent vortex beams (PCVBs) have received increasing interest in the fields of optical manipulation, optical communication, optical imaging, etc., and great progress has been made in the area of the coherence singularities, generation methods, topological charge measurements, and promising applications of PCVBs. In this review, we firstly outline the basic concepts of PCVBs. We explicate the relationship between the coherence vortices and optical vortices, and the evolution behavior of optical vortices to coherence vortices is summarized in detail. We discuss a special form of coherence singularity, ring dislocation, mathematically and physically. The ring dislocation in the correlation functions under low coherence is dependent on the mode indices, which provide a feasible approach to measure mode indices of PCVBs. Subsequently, we summarize the various methods for measuring the topological charge of PCVBs, highlight the measurement method based on the cross-correlation function, and a physical explanation on the relation between ring dislocation and topological charge is given. After that, we review the recent advances on experimental generation of several kinds of PCVBs. Lastly, we give an overview on the potential applications of PCVBs.

Statistical characteristics of speckle field and orbital angular momentum of partially coherent superposition vortex beams

The rotating speed of a target is usually measured using superposition vortex beams with opposite topological charges. Based on angular spectrum representation and Goodman’s speckle theory, the speckle characteristics of superposition vortex beams after passing through a rotating ground glass disk (RGGD) were studied. The statistical characteristics of the speckle field were analyzed using the theory of the orbital angular momentum (OAM) spectrum. The analysis determined the relationship between the spatial coherence length and the topological charge of a superimposition vortex beam and its speckle field. Moreover, the study explored the relationship between the speed of the ground glass disk (GGD) and the speckle field of the superposition vortex beam. Results show that the rotating speed of the GGD increases and the intensity distributions of generated partially coherent superposition vortex beams become increasingly uniform after passing through the RGGD. The speckles gradually disappear but the OAM spectrum becomes increasingly dispersive with increased rotating speed. These results might be useful for practical applications of the rotational Doppler effect in remote sensing and metrology.

Generation and regulation of electron vortices in an underdense plasma by Laguerre-Gaussian laser pulses

An analytical model is presented to control the angular momentum of electrons by impinging Laguerre-Gaussian (LG) laser beam in an underdense warm plasma. During intense laser-plasma interaction, radiative effects of intense long laser pulses become important, which are analyzed under quasi-static approximation. It is shown that the spot size of the laser beam controls the depth of doughnut-shaped ion-channel created in the plasma. Due to inhomogeneity of plasma density, the nonlinear beating of two fast-time-scale laser fields results in the generation of slow-time-scale “dc” magnetic fields. These fields confine the fast electrons in relativistic laser channel and support their direct coupling with the lasers’ fields. Inside the doughnut-shaped channel, the electrons are found to execute transverse betatron oscillations. At resonance, the laser field efficiently transfers the energy and momentum to the plasma electrons which can be controlled by the lasers and plasma parameters. The angular momentum of the electrons is also found to be dependent on the magnitude of the quasi-static axial magnetic field. Moreover, regulation of the electron angular momentum can explore various interesting areas including coherent vortex beam generation via synchrotron radiation process.

Beam wander of partially coherent twisted elliptical vortex beam in turbulence

Based on the generalized Huygens–Fresnel theorem, the characteristics of beam wander in partially coherent elliptical vortex beams in anisotropic non-Kolmogorov turbulence are studied. Considering not only the vortex phase but also the twisted phase modulation in the partially coherent beams, the study of twisted phase modulation is carried out based on the content of the partially coherent elliptical vortex beam in order to research the relationship between the beam wander and the twisted phase modulation factor. It is found that twisted phase modulation and coherent modulation have a saturation region, and outside the saturation region, the twisted phase modulation can restrain the beam wander effectively.