Laguerre-Gauss beams versus Bessel beams showdown: peer comparison

Transition from Ince-Gaussian beams to nondiffractive Mathieu beams

We show that under the appropriate conditions, the Ince-Gaussian modes (IGBs) of stable resonators display a behavior very similar to that of the Mathieu beams (MBs), exhibiting nondiffracting propagation and self-healing properties. We show that the high-order IGB propagates in a quasi-nondiffractive manner within the same conical region as any nondiffractive beam, even when their profiles do not match exactly. Our results indicate new, to our knowledge, methods to generate a quasi-nondiffractive MB from spherical resonators and provide more efficient ways to generate them in the Fourier space. These high-order IGBs are an excellent option for applications where a quasi-nondiffractive, but not exact, behavior is required.

Self-healing spiral phase contrast imaging

Spiral phase contrast imaging alleviates the information load by extracting the geometric features of objects and is one of the most representative branches of instant imaging processing. The self-healing capacity of edge detectors can enhance their robustness to obstacles in practical applications. Here, a self-healing spiral phase contrast imaging scheme is proposed and experimentally demonstrated by a liquid crystal edge detector combining a spiral phase, an axicon phase, and a lens phase. The spiral phase is encoded into a liquid crystal by photopatterning. Self-healing contrast imaging is characterized by a series of edge images of both high-contrast amplitude-type and low-contrast phase-type objects. This work extends the self-healing capacity of these detectors to instant imaging processing and paves the way for optical applications with self-healing features.

Observation of Boyer-Wolf Gaussian modes

Stable laser resonators support three fundamental families of transverse modes: the Hermite, Laguerre, and Ince Gaussian modes. These modes are crucial for understanding complex resonators, beam propagation, and structured light. We experimentally observe a new family of fundamental laser modes in stable resonators: Boyer-Wolf Gaussian modes. By studying the isomorphism between laser cavities and quadratic Hamiltonians, we design a laser resonator equivalent to a quantum two-dimensional anisotropic harmonic oscillator with a 2:1 frequency ratio. The generated Boyer-Wolf Gaussian modes exhibit a parabolic structure and show remarkable agreement with our theoretical predictions. These modes are also eigenmodes of a 2:1 anisotropic gradient refractive index medium, suggesting their presence in any physical system with a 2:1 anisotropic quadratic potential. We identify a transition connecting Boyer-Wolf Gaussian modes to Weber nondiffractive parabolic beams. These new modes are foundational for structured light, and open exciting possibilities for applications in laser micromachining, particle micromanipulation, and optical communications.

Shadows of structured beams in lenslike media

The self-healing phenomenon of structured light beams has been comprehensively investigated for its important role in various applications including optical tweezing, superresolution imaging, and optical communication. However, for different structured beams, there are different explanations for the self-healing effect, and a unified theory has not yet been formed. Here we report both theoretically and experimentally a study of the self-healing effect of structured beams in lenslike media, this is, inhomogeneous lenslike media with a quadratic gradient index. By observing the appearance of a number of shadows of obstructed structured wave fields it has been demonstrated that their self-healing in inhomogeneous media are the result of superposition of fundamental traveling waves. We have found that self-healing of structured beams occurs in this medium and, interestingly enough, that the shadows created in the process present sinusoidal propagating characteristics as determined by the geometrical ray theory in lenslike media. This work provides what we believe to be a new inhomogenous environment to explain the self-healing effect and is expected to deepen understanding of the physical mechanism.

Analysis of rotational Doppler shift with multi-ring vortex beams

Vortex beams (VBs) with orbital angular momentum have shown great potential in the detection of transverse rotational motion of spatial targets which is undetectable in the classical radar scheme. However, most of the reported rotational Doppler measurements based on VBs can only be realized under ideal experimental conditions. The long-range detection is still a challenge. The detection distance based on rotational Doppler effect (RDE) is mainly limited by the scattered signal's signal-to-noise ratio (SNR). In this work, we investigated the influence of multi-ring vortex beams (MVBs) on the rotational Doppler frequency spectrum of scattered light from an object based on RDE and proposed a method of SNR enhancement of RDE signal. Firstly, different types of MVBs composed of a set of single-ring VBs with the same topological charge and different radii are designed, including multi-ring Laguerre Gaussian beam (MLGB), multi-ring perfect vortex beams (MPVB), and high-order Laguerre Gaussian beam (HLGB). Then, the influence of the number of rings and radial radius interval on the intensity profiles of MVBs and rotational Doppler frequency spectra under aligned and misaligned conditions is studied in detail. And the reasons why different types of MVBs lead to different SNR enhancement effectiveness with the increase of rings are also analyzed theoretically. Finally, proof-of-concept experiments were conducted to verify the effectiveness of the SNR enhancement method for RDE signals. The results showed that the amplitudes of the Doppler spectra generated by the MLGB and MPVB are improved substantially with the increase of rings, but the enhancement effect caused by the former is superior to the latter. The gain of HLGB on the RDE signal is the lowest. This study provides a useful reference for the optimization of rotational Doppler detection systems and may be of great application value in telemetry, long-range communication and optical imaging.

First-order statistics of intensity and phase in Laguerre-Gauss speckles

Laguerre-Gaussian (LG) beams are characterized by an azimuthal index or topological charge (m), associated with the orbital angular momentum, and by a radial index (p), which represents the number of the rings in the intensity distribution. We present a detailed, systematic study of the first-order phase statistics of the speckle fields created when LG beams of different order interact with random phase screens with different optical roughness. The phase properties of the LG speckle fields are studied in both the Fresnel and the Fraunhofer regimes using the equiprobability density ellipse formalism such that analytical expressions can be derived for the phase statistics.

ABCD transfer matrix model of Gaussian beam propagation in Fabry-Perot etalons

A numerical model of Gaussian beam propagation in planar Fabry-Perot (FP) etalons is presented. The model is based on the ABCD transfer matrix method. This method is easy to use and interpret, and readily connects models of lenses, mirrors, fibres and other optics to aid simulating complex multi-component etalon systems. To validate the etalon model, its predictions were verified using a previously validated model based on Fourier optics. To demonstrate its utility, three different etalon systems were simulated. The results suggest the model is valid and versatile and could aid in designing and understanding a range of systems containing planar FP etalons. The method could be extended to model higher order beams, other FP type devices such as plano-concave resonators, and more complex etalon systems such as those involving tilted components.

Product of Two Laguerre–Gaussian Beams

We show that a product of two Laguerre–Gaussian (pLG) beams can be expressed as a finite superposition of conventional LG beams with particular coefficients. Based on such an approach, an explicit relationship is derived for the complex amplitude of pLG beams in the Fresnel diffraction zone. Two identical LG beams of the duet produce a particular case of a “squared” Fourier-invariant LG beam, termed as an (LG)2 beam. For a particular case of pLG beams described by Laguerre polynomials with azimuthal numbers n − m and n + m, an explicit expression for the complex amplitude in a Fourier plane is derived. Similar to conventional LG beams, the pLG beams can be utilized for information transmission, as they are characterized by orthogonal azimuthal numbers and carry an orbital angular momentum equal to their topological charge.

Phase memory of optical vortex beams

Optical vortex beams are under considerable scrutiny due to their demonstrated potential for applications ranging from quantum optics to optical communications and from material processing to particle trapping. However, upon interaction with inhomogeneous material systems, their deterministic properties are altered. The way these structured beams are affected by different levels of disturbances is critical for their uses. Here, for the first time, we quantify the degradation of perfect optical vortex beams after their interaction with localized random media. We developed an analytical model that (1) describes how the spatial correlation and the phase variance of disturbance affect the phase distribution across the vortex beams and (2) establishes the regimes of randomness for which the beams maintain the memory of their initial vorticity. Systematic numerical simulations and controlled experiments demonstrate the extent of this memory effect for beams with different vorticity indices.

Generation of perfect optical vortex by Laguerre-Gauss beams with a high-order radial index

Perfect optical vortex (POV) beams have attracted extensive attention because they have the advantage of a radial profile that is independent of orbital angular momentum. To date, it is usually obtained by means of the Fourier transform performed by a lens on Bessel beams. We theoretically and experimentally demonstrate that POV can be generated by performing the Fourier transform on Laguerre-Gauss beams with a high-order radial index. Furthermore, we derive an analytical expression for the increase in vortex radius, which is beneficial to compensate for the influence of the radius change in actual experiments. Our results may shed new light for a variety of research utilizing POV.

Spirally rotating particles with structured beams generated by phase-shifted zone plates

The emerging field of structured beams has led to optical manipulation with tremendous progress. Beyond various methods for structured beams, we use phase-shifted zone plates known as beam-shaping diffractive optical elements to generate beams whose phase exclusively or both phase and intensity are twisted along a curve. These beams can trap and guide particles on open curved trajectories for continuous motion, not necessarily requiring a closed symmetric intensity distribution. We show the feasibility and versatility of the proposed method as a promising technique in optical manipulation in which the trajectory of the spiral rotation and the rate of rotation of trapped particles can be controlled.

Customizing structured light beams with a differential operator

We show that structured light beams can be customized with a differential operator in Fourier space. This operator is represented as an algebraic function that acts on a seed beam for adjusting its shape. If the seed beams are perfect Laguerre-Gauss beams (PLGBs) and Bessel beams (BBs) without orbital angular momentum, we demonstrate that the custom beams generated on the seed-PLG preserve their distribution a longer distance than the propagation-invariant custom-caustic light fields obtained with the seed-Bessel, where both beams have similar initial conditions. In this sense, the custom-PLGBs can be a better option for many applications where the propagation-invariant light fields are used. We show some beam distributions-astroid, deltoid, and parabolic-generated with both seeds.

Modal description of paraxial structured light propagation: tutorial

Here we outline a description of paraxial light propagation from a modal perspective. By decomposing the initial transverse field into a spatial basis whose elements have known and analytical propagation characteristics, we are able to analytically propagate any desired field, making the calculation fast and easy. By selecting a basis other than that of planes waves, we overcome the problem of numerical artifacts in the angular spectrum approach and at the same time are able to offer an intuitive understanding for why certain classes of fields propagate as they do. We outline the concept theoretically, compare it to the numerical angular spectrum approach, and confirm its veracity experimentally using a range of instructive examples. We believe that this modal approach to propagating light will be a useful addition to the toolbox for propagating optical fields.

What are the traveling waves composing the Hermite-Gauss beams that make them structured wavefields?

To the best of our knowledge, at the present time there is no answer to the fundamental question stated in the title that provides a complete and satisfactory physical description of the structured nature of Hermite-Gauss beams. The purpose of this manuscript is to provide proper answers supported by a rigorous mathematical-physics framework that is physically consistent with the observed propagation of these beams under different circumstances. In the process we identify that the paraxial approximation introduces spurious effects in the solutions that are unphysical. By removing them and using the property of self-healing, that is characteristic to structured beams, we demonstrate that Hermite-Gaussian beams are constituted by the superposition of four traveling waves.

Spatial properties and propagation dynamics of apodized Hermite-Gauss beams

Hermite-Gauss beams (HGBs), which have been presented as exact solutions to the paraxial wave equation in Cartesian coordinates, are natural resonating modes in stable laser resonators. In this work, we demonstrate that the apodized Hermite-Gauss beam (ApHGB), by a decaying exponential function exp⁡(γx) (γ is the decaying or apodization parameter), is equivalent, under certain circumstances, to the apodized Airy beam (ApAiB). Based on the asymptotic treatment of the Hermite polynomials, we provide analytical expressions to describe their propagation dynamics in free space, then we investigate their similarity as a function of the apodization parameter. Moreover, by combining symmetric ApHGBs, we build dual and quad ApHGBs. The obtained numerical simulations confirm our analytical predictions. We believe that the ApHGB could be used as an alternative to the Airy beam in many applications.

Rotational Doppler effect detection by LG beams with a nonzero radial index

The capability to detect the rotational speed of non-cooperative targets in a long distance is a difficult problem to be solved. In recent years, vortex light provides a feasible solution for the measurement of rotational speed for its spiral phase and the orbital angular momentum. Laguerre-Gaussian (LG) mode, as the typical vortex beam, has been widely employed in rotational Doppler effect (RDE) experiments. Here, we show that the nonzero radial index LG beam not only has a specific physical meaning but also can enhance the light intensity and the amplitude of RDE frequency signal relative to a zero radial index LG beam. To this end, we theoretically analyze the reason of intensity enhancement of a nonzero radial index beam and verify the conclusion in a variable control experiment. Our study provides a new aspect of LG beams that can be considered in rotational speed detection based on RDE. It may produce an improvement of the detection range of rotating targets in practical applications.

Second-harmonic generation of single-mode Laguerre-Gaussian beams with an improved quasi-phase-matching method

In the second-harmonic generation processes involving Laguerre-Gaussian (LG) beams, the generated second-harmonic wave is generally composed of multiple modes with different radial quantum numbers. To generate single-mode second-harmonic LG beams, a type of improved quasi-phase-matching method is proposed. The Gouy phase shift has been considered in the optical superlattice designing and an adjustment phase item is introduced. By changing the structure parameters, each target mode can be phase-matched selectively, whose purity can reach up to 95%. The single LG mode generated from the optical superlattice can be modulated separately and used as the input signals in the mode division multiplexing system.

Elegant Gaussian beams: nondiffracting nature and self-healing property

Alongside the well-known solutions of standard beams, elegant Gaussian beams (eGBs) have been presented as alternative solutions to the paraxial wave equation. In this work, we show that the eGBs in cartesian (elegant Hermite-Gauss) and cylindrical (elegant Laguerre-Gauss) coordinates are asymptotically equivalent to pseudo-nondiffracting beams (pNDBs) in the same coordinates (cosine-Gauss and Bessel-Gauss, respectively). A theoretical comparison of their intensity distributions at different planes without and with obstruction is given, allowing to revisit and discuss the diffraction-free nature and self-healing property. The obtained results demonstrate that both families of beams are indistinguishable and have similar propagation features, which means that the eGBs class can be used as an alternative to pNDBs.

Cosine beam: diffraction-free propagation and self-healing

In this paper we revisit the nondiffracting properties of the cosine beam (CB). Since the CB is of infinite extension and not physically realizable, we use two apodization pupils to manage its transverse extent: the first one is a Gaussian apodized pupil, giving rise to the cosine-Gauss (CG) beam, and the second one is a window (aperture) apodized pupil, giving rise to the cosine-windowed beam. Based on the second-order intensity moments, we demonstrate analytical expressions for the CG beam width and its nondiffracting range as a function of some key parameters. By considering the CG beam a standing wave resulting from the superposition of two oppositely oblique traveling Gaussian beams, we extend the study to higher-order CG beams. The latter is generated by the superposition of two oppositely oblique Hermite-Gauss (HG_n) beams of order n, giving birth to a standing nondiffracting Hermite-cosine-Gauss (HCG_n) beam of order n. We also demonstrate the expressions of the higher-order CG beam width and its nondiffracting range z_max. After demonstrating the nondiffracting nature of the HCG beam family, we test their ability to self-heal and recover against obstacles, and we show the limit distance from which HCG_n beams self-heal as a function of obstruction size and CG parameter. The results of this paper are of big interest in fields involving structured light such as particle manipulation, imaging, and light sheet microscopy.

The non-diffracting nature of truncated Hermite-Gaussian beams

Using the asymptotic formula of the Hermite polynomials for higher-orders n≫1, an elegant mathematical expression that makes Hermite-Gaussian beams and cosine beams equivalent is obtained. Two factors of merit, the similarity and the power content ratio, are used to quantify the degree of equivalence between the two beams. These results yield a new nondiffracting Hermite-Gaussian beam in one dimension (1D) and that is easily extended to 2D.

Far-field modeling of obstructed Laguerre-Gauss beams

It was shown in the paper Opt. Lett.40, 3739 (2015)OPLEDP0146-959210.1364/OL.40.003739 that Laguerre-Gauss beams (LGB_n) of order n and Bessel beams (BB) are asymptotically equivalent for n≫1. Here we demonstrate that an LGB_n and a BB are equivalent just in the inner multiring parts of the two beams. However, the outer multiring parts are completely different, and this leads us to apply a truncation on the two beams to make them indistinguishable. Since the LGB_n could be approximated by a BB only in the inner multiring part, we suggest another beam that could replace its outer multiring part. By considering the LGB_n as a sum of n rings having different radii and widths, we model the LGB_n outer multiring part by a sum of what we call in this paper "ring shifted-Gaussian beams." The peer-to-peer comparison of the LGB_n with the two cited beams allowed us to provide a new analytical description of the obstructed LGB_n far field. These results will be very useful to study many aspects related to the LGB_n diffraction by apertures and stops. As an example, we show at the end of this paper how the self-healing ability of an obstructed LGB_n could be studied analytically.

Kepler's law for optical beams

It is well known that optics and classical mechanics are intimately related. One of the most important concepts in classical mechanics is that of a particle in a central potential that leads to the Newtonian description of the planetary dynamics. Within this, a relevant result is Kepler's second law that is related to the conservation of orbital angular momentum, one of the fundamental laws in physics. In this paper, we demonstrate that it is possible to find the conditions that allow us to state Kepler's second law for optical beams with orbital angular momentum by analyzing the streamlines of their energy flow. We find that the optical Kepler's law is satisfied only for cylindrical symmetric beams in contrast to the classical mechanics situation that is satisfied for the other conic geometries, namely, parabolic, elliptical and hyperbolic. We propose a novel approach to confirm our analytic results: we observe the propagation of the Arago's spot created by a beam with orbital angular momentum as a local "light-tracer" instead of looking at the propagation of the whole beam. The observed patterns fully agree with the prediction of our formalism.

Perfect Laguerre-Gauss beams

Perfect vortex beams (PVBs) have intensity distributions independent of their topological charges. We propose an alternative formulation to generate PVBs through Laguerre-Gauss beams (LGBs). Using the connection between Bessel and LGBs, we formulate a modified LGB that mimics the features of a PVB, the perfect LGB (PLGB). The PLGB is closer to the ideal PVB, maintaining a quasi-constant ring radius and width. Furthermore, its number of rings can be augmented with the order of the Laguerre polynomial, showing an outer ring independent of the topological charge. Since the PLGB comprises a paraxial solution, it is closely related to an experimental realization, e.g., using spatial light modulators [Phys. Rev. A100, 053847 (2019)PLRAAN1050-294710.1103/PhysRevA.100.053847].

Generation of light beams with custom orbital angular momentum and tunable transverse intensity symmetries

We introduce a novel and simple modulation technique to tailor optical beams with a customized amount of orbital angular momentum (OAM). The technique is based on the modulation of the angular spectrum of a seed beam, which allows us to specify in an independent manner the value of OAM and the shape of the resulting beam transverse intensity. We experimentally demonstrate our method by arbitrarily shaping the radial and angular intensity distributions of Bessel and Laguerre-Gauss beams, while their OAM value remains constant. Our experimental results agree with the numerical and theoretical predictions.

Extending a set of well-focused beams described by gamma and gamma-coupled functions

A set of rotationally symmetric, paraxial gamma and gamma-coupled beams [introduced in Appl. Opt.57, 3653 (2018)APOPAI0003-693510.1364/AO.57.003653] is extended with other well-focused higher-order beams described by the gamma and gamma-coupled functions with extra free parameters. A computer simulation of the propagation characteristics of some new parametrically optimized higher-order beams with a sharp central peak demonstrates that, in relation to the previous gamma and gamma-coupled beams, most of the new beams have elevated levels of sidelobes in the waist plane. At the same time, the new beams have far more propagation stability over an extended depth of field. In relation to similar Bessel-Gauss beams, these beams have a much better spatial localization of their energy.

Self-healing high-dimensional quantum key distribution using hybrid spin-orbit Bessel states

Using spatial modes for quantum key distribution (QKD) has become highly topical due to their infinite dimensionality, promising high information capacity per photon. However, spatial distortions reduce the feasible secret key rates and compromise the security of a quantum channel. In an extreme form such a distortion might be a physical obstacle, impeding line-of-sight for free-space channels. Here, by controlling the radial degree of freedom of a photon's spatial mode, we are able to demonstrate hybrid high-dimensional QKD through obstacles with self-reconstructing single photons. We construct high-dimensional mutually unbiased bases using spin-orbit hybrid states that are radially modulated with a non-diffracting Bessel-Gaussian (BG) profile, and show secure transmission through partially obstructed quantum links. Using a prepare-measure protocol we report higher quantum state self-reconstruction and information retention for the non-diffracting BG modes as compared to Laguerre-Gaussian modes, obtaining a quantum bit error rate (QBER) that is up to 3× lower. This work highlights the importance of controlling the radial mode of single photons in quantum information processing and communication as well as the advantages of QKD with hybrid states.

Direct generation of a narrow-linewidth Laguerre-Gaussian vortex laser in a monolithic nonplanar oscillator

Vortex laser beams carrying orbital angular momentum have been attracting a lot of interest in recent years. Here we demonstrate the direct generation of a vortex laser in a monolithic nonplanar ring cavity. The unidirectional and single-frequency operation of Laguerre-Gaussian modes is observed and characterized. Fork interferograms have been obtained using a simple interferometer based on a plano-concave lens, and the topological charge of vortex beam is determined. A spectral linewidth as narrow as 2.3 kHz is measured by beating with a reference laser. We believe that such a high coherent vortex laser can be beneficial for numerous applications, including precision measurements and optical communications.

Goos-Hänchen and Imbert-Fedorov shifts of higher-order Laguerre-Gaussian beams reflected from a dielectric slab

We consider reflection of the Laguerre-Gaussian light beams by a dielectric slab. In view of the unified operator approach, the higher-order Laguerre-Gaussian beams represent a parametric family with the transverse beam profile given by an arbitrary generating parameter. Relying on the Fourier expansion in the focal plane of the beam, we compute the Goos-Hänchen and the Imbert-Fedorov shifts for light beams with non-zero order and azimuthal index. It is demonstrated that both shifts exhibit resonant behavior as functions of the angle of incidence due to the interference between the waves reflected from the upper and lower interfaces. The centroid shifts strongly depend on the order and azimuthal index of the beam. Most interestingly, it is found that the generating parameter of the higher-order beam families strongly affects the shifts. Thus, reshaping of the incident wavefront with fixed order and azimuthal index changes the linear Goos-Hänchen shift up to one half of the beam radius, both negative and positive.

Fields of a Bessel-Bessel light bullet of arbitrary order in an under-dense plasma

Considerable theoretical and experimental work has lately been focused on waves localized in time and space. In optics, waves of that nature are often referred to as light bullets. The most fascinating feature of light bullets is their propagation without appreciable distortion by diffraction or dispersion. Here, analytic expressions for the fields of an ultra-short, tightly-focused and arbitrary-order Bessel pulse are derived and discussed. Propagation in an under-dense plasma, responding linearly to the fields of the pulse, is assumed throughout. The derivation stems from wave equations satisfied by the vector and scalar potentials, themselves following from the appropriate Maxwell equations and linked by the Lorentz gauge. It is demonstrated that the fields represent well a pulse of axial extension, L, and waist radius at focus, w0, both of the order of the central wavelength λ0. As an example, to lowest approximation, the pulse of order l = 2 is shown to propagate undistorted for many centimeters, in vacuum as well as in the plasma. As such, the pulse behaves like a "light bullet" and is termed a "Bessel-Bessel bullet of arbitrary order". The field expressions will help to better understand light bullets and open up avenues for their utility in potential applications.

Are Bessel beams resilient to aberrations and turbulence?

It is understood from the conical wave picture that Bessel beams may self-heal after certain opaque obstructions, but the extrapolation to transparent phase screens is not self-evident. Here we consider the propagation of Bessel beams through aberrated obstacles and show that the self-healing is not guaranteed, but rather a function of the severity of the aberration. Paradoxically, we explain why strong aberrations may show self-healing while weak aberrations will not, and highlight the parameters that influence this. Finally, we combine aberrations to pass the Bessel beam through turbulence, and debunk the myth that Bessel beams are resilient to such perturbations.

Three-Dimensional Speckle Light Self-Healing-Based Imaging System

Recently new methodologies for imaging have been achieved making use of multiple light scattering. Here we present the self-healing effect using a speckled light field. We present an experiment that constitutes a useful application for a three-dimensional light sheet-based imaging system through an inhomogeneous medium. Each layer can be imaged independently of the others. The axial resolution basically depends on the coherence length, which can be sub-wavelength and controllable. This allows for a simple and direct technique for imaging through scattering layers with axial resolution improvement. Our results may find applications not only in bio-microscopy systems but also in data transmission.

Sorting Photons by Radial Quantum Number

The Laguerre-Gaussian (LG) modes constitute a complete basis set for representing the transverse structure of a paraxial photon field in free space. Earlier workers have shown how to construct a device for sorting a photon according to its azimuthal LG mode index, which describes the orbital angular momentum (OAM) carried by the field. In this paper we propose and demonstrate a mode sorter based on the fractional Fourier transform to efficiently decompose the optical field according to its radial profile. We experimentally characterize the performance of our implementation by separating individual radial modes as well as superposition states. The reported scheme can, in principle, achieve unit efficiency and thus can be suitable for applications that involve quantum states of light. This approach can be readily combined with existing OAM mode sorters to provide a complete characterization of the transverse profile of the optical field.

Laguerre-Gaussian modal q-plates

We propose space-variant uniaxial flat optical elements designed to generate pure Laguerre-Gaussian modes with arbitrary azimuthal and radial indices l and p from an incident Gaussian beam. This is done via the combined use of the dynamic and the geometric phases. Optimal design protocol for the mode conversion efficiency is derived, and the corresponding characteristics are given for -6≤l≤6 and 0≤p≤5. The obtained "modal q-plates" may find many applications whenever the radial degree of freedom of a light field is at play.

Study of propagation of vortex beams in aerosol optical medium

A theoretical and experimental study of the propagation of vortex laser beams in a random aerosol medium is presented. The theoretical study is based on the extended Huygens-Fresnel principle with the generation of a random field, using the fast Fourier transform. The simulation shows that the stability of vortex beams to fluctuations of an optical medium falls with rising order of optical vortices. Moreover, a coherence length (radius) of the random medium is of great importance. The coherence radius extension affects adversely the conservation of a beam structure in the random medium. During further free-space propagation, increasing coherence enables reduction of the negative effects of fluctuations for beams with high-value topological charges. Experimental studies in the random aerosol medium have shown that at small distances vortex beams mostly demonstrate lower stability than a Gaussian beam. However, at considerable distances, vortex beams start to demonstrate greater stability that may be explained by their capacity to be regenerated after they passed obstacles.

Laguerre-Gauss and Bessel-Gauss beams propagation through turbulence: analysis of channel efficiency

As a means of increasing the channel capacity in free-space optical communication systems, two types of orbital angular momentum carrying beams, Bessel-Gauss and Laguerre-Gauss, are studied. In a series of numerical simulations, we show that Bessel-Gauss beams, pseudo-nondiffracting beams, outperform Laguerre-Gauss beams of various orders in channel efficiency and bit error rates.

Self-mode-locked Laguerre-Gaussian beam with staged topological charge by thermal-optical field coupling

A light beam with a helical phase is associated with an optical vortex and carries optical orbital angular momentum. Mode-locked optical vortex pulses impart orbital angular momentum to photons in short pulses and have attractive applications. However, due to the conflict between mature mode-locking and the generation of optical vortices, directly generated mode-locked optical vortex short pulses seem to be unavailable, thus constraining the development and applications of optical vortex short pulses. Laguerre-Gaussian (LG) modes are eigenfunctions for a laser cavity. Besides carrying optical orbital angular momentum, LG beams also have self-healing and quasi-nondiffracting properties. Here, we report the realization of a self-mode-locked LG lasers with tunable orbital angular momentum. By coupling between the thermal and optical fields, the orbital angular momentum was found to be staged. These results verify the possibility of direct mode-locking of optical vortices, and may open the way for several applications of short pulses. Moreover, mode-locked pulses with high-repetition rates also have particularly attractive applications such as optical frequency comb spectroscopy, high capacity optical networks, spectroscopy of metallic nanoparticles, arbitrary waveform generation, etc..

Mode-Division-Multiplexing of Multiple Bessel-Gaussian Beams Carrying Orbital-Angular-Momentum for Obstruction-Tolerant Free-Space Optical and Millimetre-Wave Communication Links

We experimentally investigate the potential of using 'self-healing' Bessel-Gaussian beams carrying orbital-angular-momentum to overcome limitations in obstructed free-space optical and 28-GHz millimetre-wave communication links. We multiplex and transmit two beams (l = +1 and +3) over 1.4 metres in both the optical and millimetre-wave domains. Each optical beam carried 50-Gbaud quadrature-phase-shift-keyed data, and each millimetre-wave beam carried 1-Gbaud 16-quadrature-amplitude-modulated data. In both types of links, opaque disks of different sizes are used to obstruct the beams at different transverse positions. We observe self-healing after the obstructions, and assess crosstalk and power penalty when data is transmitted. Moreover, we show that Bessel-Gaussian orbital-angular-momentum beams are more tolerant to obstructions than non-Bessel orbital-angular-momentum beams. For example, when obstructions that are 1 and 0.44 the size of the l = +1 beam, are placed at beam centre, optical and millimetre-wave Bessel-Gaussian beams show ~6 dB and ~8 dB reduction in crosstalk, respectively.