Laguerre-Gaussian Vortex Beams Research Articles

Biaxial Gaussian Beams, Hermite–Gaussian Beams, and Laguerre–Gaussian Vortex Beams in Isotropy-Broken Materials

We have developed the paraxial approximation for electromagnetic fields in arbitrary isotropy-broken media in terms of the ray–wave tilt and the curvature of materials’ Fresnel wave surfaces. We have obtained solutions of the paraxial equation in the form of biaxial Gaussian beams, which is a novel class of electromagnetic field distributions in generic isotropy-broken materials. Such beams have been previously observed experimentally and numerically in hyperbolic metamaterials but have evaded theoretical analysis in the literature up to now. Biaxial Gaussian beams have two axes: one in the direction of the Abraham momentum, corresponding to the ray propagation, and another in the direction of the Minkowski momentum, corresponding to the wave propagation, in agreement with the recent theory of refraction, ray–wave tilt, and hidden momentum [Durach, 2024]. We show that the curvature of the wavefronts in the biaxial Gaussian beams correspond to the curvature of the Fresnel wave surface at the central wave vector of the beam. We obtain the higher-order modes of the biaxial beams, including the biaxial Hermite–Gaussian and Laguerre–Gaussian vortex beams, which opens avenues toward studies of the optical angular momentum (OAM) in isotropy-broken media, including generic anisotropic and bianisotropic materials.

Coded communication study of Laguerre–Gaussian vortex beam and its superposition states in underwater turbulence

Using theoretical and experimental approaches, we have investigated coded communications for the Laguerre–Gaussian (LG) beam and its superposition states in an oceanic turbulent environment. We established an ocean turbulence transmission model and constructed an underwater vortex beam-coded communication experiment, generating light-intensity images of the LG beam and its superposition states transmitted in different simulated ocean turbulence environments. These simulated and experimentally obtained light-intensity images were grayed out, detected and identified, symbol coded, and decoded by the Visual Geometry Group neural network to study the bit error rate (BER) of the LG beam and its superposition states for coded communication in the simulated ocean turbulence environment. The study results show that the BER increases with increasing transmission distance and simulated ocean turbulence intensity. This study provides an important reference for the further development of optical communication and network technology in high-speed data transmission and communication capability enhancement.

Polarization and coherence properties of a partially coherent elegant Laguerre–Gaussian vortex beam in turbulent plasma

The analytical expressions for the cross-spectral density matrix elements of the partially coherent elegant Laguerre–Gaussian (eLG) vortex beam propagating through anisotropic turbulent plasma were derived based on the extended Huygens-Fresnel principle and used to study the changes in the polarization degree and the coherence degree of the partially coherent eLG vortex beam in the turbulent plasma. The numerical results show that the polarization degree of a partially coherent eLG vortex beam reaches a specific value (which is equal to the degree of polarization in the source plane) after a long propagation distance in the turbulent plasma. Moreover, this value is independent of the beam order, topological charge, correlation coefficient, wavelength of the source plane, anisotropy parameter, refractive index fluctuation variance, and outer and inner scales of the turbulent plasma. The results also show that with increasing distance, the coherence degree first decreases from unity and then oscillates around zero. However, this oscillation gradually disappears after traveling a long distance. Our results intuitively present the beam polarization and coherence properties through anisotropic hypersonic turbulence, which can be useful for optical communication in hypersonic turbulent environments.

Tight focusing of azimuthally polarized Laguerre–Gaussian vortex beams by diffractive axicons

This study presents a comprehensive theoretical investigation into the focusing properties of azimuthally polarized Laguerre–Gaussian vortex (APLGV) beams when interacting with different optical elements, including a linear axicon, binary axicon, and lens based on the Debye approximation. The research findings highlight the intriguing combination of polarization and vortex singularities within the APLGV beam, which result in distinctive focal shapes when interacting with these optical elements. The focal shapes achieved include multiple tightly focused spots and optical needles, which can be controlled by adjusting optical system parameters and beam characteristics such as the numerical aperture (NA), truncation parameter, beam order, and annular obstruction. These parameters can be carefully selected to achieve specific focal shapes with applications in multi-optical manipulation, particle acceleration, and trapping. By harnessing the unique properties of APLGV beams and optimizing the optical setup, researchers can explore new possibilities for advanced optical manipulation and control.

Enhancing axial localization with wavefront control.

Enhancing the ability to resolve axial details is crucial in three-dimensional optical imaging. We provide experimental evidence showcasing the ultimate precision achievable in axial localization using vortex beams. For Laguerre-Gauss (LG) beams, this remarkable limit can be attained with just a single intensity scan. This proof-of-principle demonstrates that microscopy techniques based on LG vortex beams can potentially benefit from the introduced quantum-inspired superresolution protocol.

Phase variation of Laguerre-Gaussian vortex beams in a homogeneous atmospheric medium under finite amplitude acoustic wave perturbation

In this article, we have derived the acoustic pressure and medium refractive index expressions in a homogeneous atmospheric medium perturbed by a planar finite amplitude acoustic wave. In a planar finite amplitude acoustic wave perturbation, we developed a Laguerre–Gaussian vortex beam transmission model in a homogeneous atmospheric medium. We investigated the effects of different acoustic source parameters on the phase of the Laguerre–Gaussian vortex beam transmission, considering the atmospheric medium’s viscous effect. The results show that acoustic waves of finite amplitude distort the refractive index distribution of a homogeneous atmospheric medium. At a given distance, the amplitude of the refractive index gradually increases with increasing acoustic wave transmission distance. At the same time, the phase of the Laguerre–Gaussian vortex beam is rotated by the perturbation of the finite-amplitude acoustic wave, and the phase always returns to its initial position. Unlike linear acoustic waves, changes in the homogeneous atmospheric refractive index distribution and the homogeneous phase of the Laguerre–Gaussian vortex light no longer satisfy the periodic variation when perturbed by finite-amplitude acoustic waves. Under the same conditions, the effect of finite-amplitude acoustic waves on the phase of the Laguerre–Gaussian vortex light is stronger than that of linear acoustic waves. Finally, the effects of different acoustic pressure and frequency of the source on the phase of the Laguerre–Gaussian vortex beam transmission are calculated. The results show that different acoustic parameters at the source can be used to achieve phase modulation at different distances and intensities.

Angular width and beam quality of a partially coherent standard Laguerre-Gaussian vortex beam in turbulent plasma.

Analytical formulas for the angular width and propagation factor of a partially coherent standard Laguerre-Gaussian (sLG) vortex beam through anisotropic turbulent plasma were derived based on the extended Huygens-Fresnel integral and the second-order moments of the Wigner distribution function. The evolution properties of the angular width and propagation factor of partially coherent sLG vortex beams propagating in anisotropic turbulent plasma were investigated numerically. The numerical results demonstrate the influence of the source and turbulence parameters on the normalized angular width and normalized propagation factor of the partially coherent sLG vortex beams. It can be observed that in a partially coherent sLG vortex beam with a lower beam order, topological charge, and wavelength, or a higher correlation coefficient of the source plane, and with increasing propagation distance and refractive index fluctuation variance or decreasing anisotropy parameters, the outer and inner scales of the turbulent plasma have a large angular width and propagation factor (i.e.,the beam quality is worse). The results of this study will be beneficial for applications in remote sensing and optical communications.

Efficient post-processing of electromagnetic plane wave simulations to model arbitrary structured beams incident on axisymmetric structures

The study of an optical beam interacting with material structures is a fundamental of nanophotonics. Computational electromagnetic solvers facilitate the rapid calculation of the scattering from material structures with arbitrary geometry and complexity, but have limited efficiency when employing structured excitation fields. We have developed a post-processing method and package that can efficiently calculate the full three-dimensional electric and magnetic fields for any optical beam incident on a particle or structure with at least one axis of continuous rotational symmetry, called an axisymmetric body (such as a sphere, cylinder, cone, torus or surface). Provided an initial batch of plane wave simulations is computed, this open-source package combines data from computational electromagnetic solvers in a post-processing fashion using the angular spectrum representation to create arbitrarily structured beams, including vector vortex beams. Any and all possible incident beams can be generated from the initial batch of PWSs, without the need for further simulations. This allows for efficiently performing parameter sweeps such as changing the angle of illumination or translating the particle position relative to the beam, all in post-processing, with no need for additional time-consuming simulations. We demonstrate some applications by numerically calculating optical force and torque maps for a spherical plasmonic nanoparticle in a tightly focused Gaussian beam, a plasmonic nanocone in an azimuthally polarised beam and compute the fields of a non-paraxial Laguerre–Gaussian vortex beam reflecting on a multilayered surface. We believe this package, called BEAMS, is a valuable tool for rapidly quantifying electromagnetic systems that are beyond traditional analytical methods.

A Systematic Summary and Comparison of Scalar Diffraction Theories for Structured Light Beams

Structured light beams have recently attracted enormous research interest for their unique properties and potential applications in optical communications, imaging, sensing, etc. Since most of these applications involve the propagation of structured light beams, which is accompanied by the phenomenon of diffraction, it is very necessary to employ diffraction theories to analyze the obstacle effects on structured light beams during propagation. The aim of this work is to provide a systematic summary and comparison of the scalar diffraction theories for structured light beams. We first present the scalar fields of typical structured light beams in the source plane, including the fundamental Gaussian beams, higher-order Hermite–Gaussian beams, Laguerre–Gaussian vortex beams, non-diffracting Bessel beams, and self-accelerating Airy beams. Then, we summarize and compare the main scalar diffraction theories of structured light beams, including the Fresnel diffraction integral, Collins formula, angular spectrum representation, and Rayleigh–Sommerfeld diffraction integral. Finally, based on these theories, we derive in detail the analytical propagation expressions of typical structured light beams under different conditions. In addition, the propagation of typical structured light beams is simulated. We hope this work can be helpful for the efficient study of the propagation of structured light beams.

Complete transport of intensity equation for phase retrieval of optical vortex beams

We derive the complete form of the transport of intensity equation (TIE) for an arbitrary wave field, in which additional terms describing the effect of optical vortices are included. The Poynting vector of optical vortices goes in a spiral around the vortex core through space. Consequently, the intensity variation is not observable in the manner of wave propagation, thereby precluding the possibility of phase retrieval via near-field intensity measurements. This difficulty is elegantly overcome by introducing a hard-edged aperture, as a common procedure to produce the required Neumann boundary signal, to break the azimuthal symmetry of the propagation, and visualize the rotation of the beam’s local Poynting vector around the aperture boundary. The basic principle, numerical solution, and practical implementation of how to use this new version of TIE for phase retrieval of arbitrary wave fields including optical vortices are developed. Based on the new approach, we present the first experimental demonstration of non-interferometric phase retrieval of Laguerre–Gaussian vortex beams of different orders using only two near-field intensity measurements. Our results consummate the basic theoretical framework of TIE and represent an important step towards phase retrieval of arbitrary wave fields carrying phase singularities.

Laguerre–Gaussian vortex beam for reduced thermal effects in nonlinear optical studies

Interaction of an intense laser beam with a material induces many thermal effects. In this work, thermo-optic effects induced by fundamental Gaussian and Laguerre–Gaussian vortex (LGV) laser beams in a sample in nonlinear optical (NLO) experiments are compared and their impact on the accuracy of determining the nonlinear susceptibility is examined. A solution of saturable absorber dye IR 26 in dichloroethane with the technique of z-scan to determine its third order nonlinear susceptibility was used as a model system. The LGV beams were generated by passing the Hermite–Gaussian beams from an Ar-ion laser through a cylindrical lens mode converter. Pump–probe setup was used to study the thermo-optic effects. Experiments and simulations suggest that the LGV beam is advantageous to reduce the thermal effects.

Generation of vortex beams with nonuniform phase jumps in azimuthal locations

The phase angle of the vortex beam along a closed loop centered on the optical singularity changes by 2πℓ, where ℓ is the number of phase jumps (PJs) from 0 to 2π and indicates the topological charge of the vortex beam. In this paper, the generation and specification of a new type of vortex beam, in which their PJs are asymmetrically embedded in the phase pattern, are reported. In contrast to Laguerre–Gaussian vortex beams, where PJs are equally spaced azimuthally around the optical singularity, the presented vortex beams have PJs embedded at arbitrary azimuthal angles. By designing a particular forked grating and displaying it on a spatial light modulator, this type of vortex beam is experimentally generated. As with conventional forked grating, the designed grating produces vortex beams with the opposite orbital angular momentum (OAM) sign in the first diffraction order. By measuring the relative orientation of the intensity profile of these OAM beams in the first diffraction order, the position of the PJs on the wavefront of a vortex beam with ℓ = 2 can be determined. This type of vortex beam could have potential applications in various fields of photonics, especially in optical communications based on optical vortices.

Coherence singularity and evolution of partially coherent Bessel-Gaussian vortex beams.

For a partially coherent Bessel-Gaussian (PCBG) vortex beam, information regarding the topological charge (TC) is hidden in the phase of the cross-spectral density (CSD) function. We theoretically and experimentally confirmed that during free-space propagation, the number of coherence singularities is equal to the magnitude of the TC. In contrast to the Laguerre-Gaussian vortex beam, this quantitative relationship only holds for the case with an off-axis reference point for the PCBG vortex beam. The phase winding direction is determined by the sign of the TC. We developed a scheme for CSD phase measurement of PCBG vortex beams and verified the aforementioned quantitative relationship at different propagation distances and coherence widths. The findings of this study may be useful for optical communications.

Propagation theory of Laguerre–Gaussian vortex beams in nonlinear Kerr media

The propagation theory of Laguerre–Gaussian (LG) vortex beams in nonlinear Kerr media is studied. The analytical formulae of the amplitude, Gouy phase and orbital angular momentum (OAM) of LG vortex beams propagating in nonlinear Kerr media are derived. It is shown that the inverse rotation of the vortex field can be achieved due to the self-focusing nonlinearity. It is found that the influence of Kerr nonlinearity on OAM can be ignored for a situation without filamentation. Furthermore, the gradient force increases because of the self-focusing nonlinearity.

Transmission Characteristics of Underwater Laguerre-Gaussian Vortex Beam and Its Superposition States

Transmission Characteristics of Underwater Laguerre-Gaussian Vortex Beam and Its Superposition States

Research on propagation characteristic of Laguerre–Gaussian vortex beams with Far-field scattering Electric Monte Carlo method

A Far-field Scattering Electric field Monte Carlo (FSEMC) method is proposed to investigate the propagation and imaging characteristics of Laguerre–Gaussian Beams (LGB) with different Orbital Angular Momentum (OAM) in long-distance (relative to wavelength) scattering environment. As an extension of the Electric field Monte Carlo (EMC) method, the electric field transport mode is simulated to properly analyze the fading effect of scattering. The mean free path and total transmission length in the simulation are equivalent to the environment parameters of experiment. The beam transmission modes, intensity attenuation and effects on imaging quality through different turbidity media are analyzed. It is observed that vortex beams with different topological charges play a subtle role in transmission through turbid media, showing strong correlations with total transmission intensity, retention of ballistic light, and penetration depth. The experimental results fitting well with the FSEMC simulation results, validating the proposed method for far-field propagation characteristic of vortex beams in turbid media.

Vortex chaoticons in thermal nonlocal nonlinear media.

This paper numerically investigates the propagation of Laguerre-Gaussian vortex beams launched in nonlocal nonlinear media, such as lead glass. Our results show that the propagation properties depend on the selection of beam parameters m and p, which represent the azimuthal and radial mode numbers. When p=0, these profiles can be stable solitons for m≤2, or break up and then form a set of single-hump profiles for m≥3, which are unbounded states with scattered remnants of the energy. However, for p≥1, the broken beams can evolve into vortex chaoticons, which exhibit both chaotic and solitonlike properties. The chaotic properties are determined by the positive Lyapunov exponents and spatial decoherence, while the solitonlike properties are demonstrated by the invariance of beam width and the interaction of beams in the form of quasielastic collisions. In addition, the power and orbital angular momentum of unbounded beam states both decay in propagation, while those of the chaoticons maintain their values well.

Completely revealing the amplitude properties of Laguerre-Gaussian vortex beams.

In this paper, the amplitude properties of the Laguerre-Gaussian (LG) vortex beams are analyzed theoretically and demonstrated experimentally. Firstly, the ring width of the LG vortex beam is almost a constant, which can be considered to be independent of the topological charge (l) and only determined by the waist radius ω(z), and its general expression is derived via investigating Lambert W function. On this basis, concise expressions for inner and outer ring radii, ratio of inner and outer ring radius, ring area and beam divergence are also given out. Moreover, modification functions are added to obtain more accurate expressions. In the experiment, a spatial light modulator is employed to generate the LG vortex beams with l = 1∼20 at ω0 = 0.3mm and ω0=0.4mm, and the LG vortex beams with l=10 at different propagation distances. The experimental results are in good agreement with the theoretical values. This work may help researchers to better understand the LG vortex beam and provide a useful guideline for its further applications.

Scattering of Laguerre-Gaussian Vortex Beams by Underwater Suspended Spherical Algal Particle Swarms

Scattering of Laguerre-Gaussian Vortex Beams by Underwater Suspended Spherical Algal Particle Swarms

On-chip orbital angular momentum detection using a catenary grating metasurface

Vortex lights with optical orbital angular momentum have shown great promise in the areas of optical communication, optical manipulation and quantum optics. However, traditional methods for detecting the topological charge of vortex beams, such as interference and diffraction, are still challenging in miniaturization of the detection system and perfect matching of wave vectors. Here, a detection approach is proposed for measuring the topological charge of Laguerre–Gaussian (LG) vortex beams based on a catenary grating metasurface. According to the wave vector matching principle, the LG vortex beam can be coupled into surface plasmon polariton (SPP) waves propagating in different directions by using the well-designed catenary grating structure. The positive and negative topological charges can be distinguished by different arrangement of the catenary gratings. Additionally, the propagation angle of the launched SPP waves increases with the value of the topological charge. We believe that the proposed device would have broad application prospects in high compact photonic integrated circuits.