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Dynamic focusing of electromagnetic (EM) waves is a cornerstone in various applications, encompassing aerospace communication, sensing, and high‐resolution imaging. Recently, the advent of intelligent metasurfaces, hailed as the next evolutionary step, has revolutionized self‐adaptive functionalities. However, their extensive embeddings of active components pose a great challenge associated with escalated costs, heightened power consumption, and increased complexity, thus hindering large‐scale implementation. Here, a cost‐effective approach for dynamic EM focusing utilizing a twisted metasurface is introduced, which integrates a transmissive layer with a reflective layer in a cascade fashion. This innovative design leverages the mutual rotation between two layers to enable the precise manipulation of beam propagation and scanning area, allowing for the flexible localization of the focal point across a wide range, spanning −44.17° to 44.17° in elevation and 0° to 360° in azimuth. This capability is underpinned by the strategic fusion of multiple phase profiles, including gradient and Gaussian phase. In the experiment, a goal‐oriented system is built up whose outcomes demonstrate a striking alignment with the simulated results, achieving a correlation coefficient of 96.7%. This work presents a streamlined pathway toward dynamic EM focusing and the related applications constrained by space and power limitations. [ABSTRACT FROM AUTHOR]

Cross Polarization in anisotropic Gaussian light beams is derived within the framework of the Maxwell optics using the elegant Mukunda–Simon–Sudarshan matrix substitution rule for transition from Helmholtz scalar wave optics to the Maxwell vector wave optics. It is seen that the electromagnetic field components have certain interesting relations to each other. Other properties such as the intensity distribution are also presented. [ABSTRACT FROM AUTHOR]

In this paper, evolution properties of a generalized Hermite cosh-Gaussian (GHchG) beam propagating through a chiral medium are investigated. By using the Huygens–Fresnel integral formula, analytical expression of a GHchG beam in a chiral medium is obtained. We numerically simulate the corresponding beam under both chiral and beam parameters. By controlling these parameters, we can exhibit the GHchG beam in many different intensity modes. Results demonstrate that the chiral factor of the medium and the source beam parameters during beam propagation affect the spatial properties of the GHchG beam in the chiral medium. The results of this work could be shown the helpfulness in understanding the interaction between the GHchG beam and a chiral medium. [ABSTRACT FROM AUTHOR]

A model of the generalized dark hollow sine-Gaussian beam (GDHsGB) is proposed to uniformly describe both conventional dark hollow beams (DHBs) and anomalous dark hollow beams (ADHBs) with circular or elliptic geometrical patterns. Using the Collins formula, we derive the analytical expression for GDHsGBs propagating in ABCD paraxial optical systems. We analyze the evolution of the intensity pattern and beam width of circular ADHBs, as well as the ellipticity of elliptic ADHBs, providing mathematical expressions for these physical quantities. The results reveal various evolution forms based on beam parameters, with elliptic ADHBs exhibiting more intricate propagation behavior compared to circular ADHBs. By controlling parameters, the intensity pattern of elliptic ADHBs undergoes a transformation into a petal-like distribution in the near field, later reverting to its original elliptic configuration but rotated 90° from its initial orientation on the source plane in the far field.

In this paper, diffraction of scalar waves by a screen with a circular aperture is explored, considering the incidence of either a collimated beam or a focused wave, a historical review of the development of the theory is presented, and the introduction of the Fresnel approximation is described. For diffraction by a focused wave, the general case is considered for both high numerical aperture and for finite values of the Fresnel number. One aim is to develop a theory based on the use of dimensionless optical coordinates that can help to determined the general behaviour and trends of different system parameters. An important phenomenon, the focal shift effect, is discussed as well. Explicit expressions are provided for focal shift and the peak intensity for different numerical apertures and Fresnel numbers. This is one application where the Rayleigh–Sommerfeld diffraction integrals provide inaccurate results. [ABSTRACT FROM AUTHOR]

Optical beam propagation through the atmosphere is suffering from turbulence condition and scattering due to the refractive index effects on propagation. In this paper, we study optical beam propagation under the UAE's weather conditions. An outdoor test was carried out to gather the atmosphere parameters (temperature, wind, humidity, and refractive index) and feed them to a beam propagation model. The beam centroid was determined to study and predict the effects on it at different periods of the day. [ABSTRACT FROM AUTHOR]

The annular array Airy beam (AAAB) possesses excellent optical properties, and it exhibits great potential in optical particle manipulation, light bullet, and so on. When the power of the laser system is relatively high, the B-integral greatly affects the generation and transmission of AAABs. We numerically study the nonlinear propagation of AAABs based on the Schrödinger equation. The variation of the maximum peak intensity of the AAAB with the nonlinear coefficient at different parameters are discussed. The influence of the truncation coefficient, lateral offsets, scale factor, and rotation factor on the AAAB affected by B-integral are also taken into consideration. We show that the AAAB gradually evolves into solitons in the transmission process as the nonlinear coefficient increases. The intensity of AAAB is altered due to the B-integral, and the effect of the B-integral on the transmission of the AAAB cannot be ignored. The research results will be a great boost to the application of the AAAB in biomedicine, particle manipulation, and various other fields. [ABSTRACT FROM AUTHOR]

Aiming at the propagation of asymmetric vortex beam, we investigate the spreading and wander characteristics of asymmetric Bessel-Gaussian beam in oceanic turbulence. Based on the cross-spectral density and Wigner distribution function of beam field, the theoretical expressions of spreading factor and beam center displacement are established to evaluate spreading and wander. The anisotropic turbulent condition is adopted to analyze turbulence impacts with more generality. The turbulence dominated by salinity fluctuation with lower anisotropy, larger temperature dissipation and smaller kinetic energy dissipation induces more beam spreading and wander. As for asymmetric Bessel-Gaussian beam, the increment of asymmetry can improve beam directionality. Besides, smaller beam scale but larger Gaussian waist radius, vortex order and beam wavelength also mitigate spreading and wander. The investigations are instructive for the underwater applications of asymmetric vortex beams.

We present the twisted electromagnetic sinc-correlation Schell-model (EM TSSM) beam as an extension of the cylindrical sinc Schell-model beam and analyze the necessary source parameter conditions to generate a physically viable beam. Furthermore, we thoroughly investigate the propagation properties of the EM TSSM beam in atmospheric turbulence using the extended Huygens-Fresnel integral, explicitly focusing on spectral intensity, degree of polarization (DOP), and degree of coherence (DOC). It shows that the twisted phase has a noticeable impact on the intensity profiles of these beams, causing them to exhibit rotation and self-splitting while still maintaining their shape in free space. Moreover, during propagation through a turbulent atmosphere, it exhibits self-combining properties over a long range and recovers the plat-topped distribution. Compared with the sinc Schell-model beam without the twisted phase, the DOP distribution of such a beam can rotate around its distribution center. As these beams propagate through turbulent atmospheres, they can self-heal their DOP distribution within specific ranges affected by atmospheric turbulence. A twist factor causes non-unidirectional rotation of the DOC distribution in free space. The DOC gradually transforms from multi-strip profiles into a Gaussian-like distribution. Furthermore, the beam parameters play a crucial role in shaping the DOC. The results will be useful in optical trapping and optical communication. [ABSTRACT FROM AUTHOR]

One possible way to generalize scalar to wave optics, thus including polarization in the treatment consistent with the Maxwell equations was shown by Mukunda, Simon and Sudarshan (MSS) for paraxial systems, based on a group theoretical analysis. Later, the MSS theory for the passage from the Helmholtz scalar wave optics to the Maxwell vector wave optics was derived by casting the basic formalism in a framework very similar to the Dirac electron theory. Here, we show that the elegant MSS substitution rule is equivalent to a second-order 6 × 6 matrix differential operator for passage from scalar to vector wave optics. We explicitly obtained this matrix differential operator in a series and exponential forms respectively. Expressions for the electromagnetic field components are derived without making any assumptions on the form of the transverse beam profile. It is observed that all types of beams have certain characteristic relations among their field components. The power of the formalism is demonstrated by considering five specific beams.

The connections between Laguerre–Gauss and Bessel–Gauss beams, and between Hermite–Gauss and cosine-Gauss beams are investigated. We review different asymptotic expressions for generalized Laguerre and Hermite polynomials of large radial/transverse order. The amplitude variations of generalized Laguerre–Gauss beams, including standard and elegant Laguerre–Gauss beams as special cases, are compared with Bessel–Gauss beams. Bessel–Gauss beams can be well-approximated by elegant Laguerre–Gauss beams. For non-integral values of the Laguerre function radial order, a generalized Laguerre–Gauss beam with integer order matches the width of the central lobe well, even for low radial orders. Previous approximations are found to be inaccurate for large azimuthal mode number (topolgical charge), and an improved approximation for this case is also introduced. [ABSTRACT FROM AUTHOR]

In this paper, diffraction of scalar waves by a screen with a circular aperture is explored, considering the incidence of either a collimated beam or a focused wave, a historical review of the development of the theory is presented, and the introduction of the Fresnel approximation is described. For diffraction by a focused wave, the general case is considered for both high numerical aperture and for finite values of the Fresnel number. One aim is to develop a theory based on the use of dimensionless optical coordinates that can help to determined the general behaviour and trends of different system parameters. An important phenomenon, the focal shift effect, is discussed as well. Explicit expressions are provided for focal shift and the peak intensity for different numerical apertures and Fresnel numbers. This is one application where the Rayleigh–Sommerfeld diffraction integrals provide inaccurate results.

In this manuscript, we put forward two new types of structured light beams, the vortex Pearcey–Gauss (VPeG) beam, with a homogeneous polarisation distribution, and the vector VPeG (VVPeG) beam, with a non-homogeneous polarisation distribution. The latter is generated as a non-separable superposition of the spatial and polarisation degrees of freedom of light. We achieve their experimental realization through the combination of a spatial light modulator, which creates a scalar Pearcey–Gauss beam, and a q -plate which transforms it into a vortex or a vortex vector beam, depending on its input polarisation state. Their intensity and polarisation distributions along the propagation direction were determined through Stokes polarimetry, which was compared with numerical simulations. As demonstrated, the VVPeG beam evolves from an all-linear polarisation distribution to an approximately full Poincaré beam. The proposed vector beams add to the extensive family of non-separable states of light. We anticipate that both types of beams will find applications in fields as diverse as optical metrology and tweezers, amongst others.

The electrical field of hollow vortex Gaussian beam (HVGB) with an arbitrary combination of the beam order and topological charge is formulated by using the cylindrical wave spectrum representation (CWSR), which satisfies Maxwell’s equations rigorously and allows to study analytically and numerically the evolution of the beam along its propagation in the source region and the near/far- field regions. It is found that in the source region there exists a sharp and very narrow peak, due to the contribution of evanescent waves when the beam order and the topological charge satisfy specific relations. The effect of the spiral phase plate (SPP) in generating a non-vortex Gaussian beam to a vortex one is explained. Besides, it is found that the divergence of the beam is mainly determined by the topological charge and the hollow structure is mainly determined by the beam order.

We have designed an arrangement of 19 high-power fiber laser collimators on an aluminum step bulk, theoretically to coherently combine and use in directed energy applications. The propagation conditions for high-power laser beam have been investigated in this work. Laser beam propagating undergoes unavoidable spreading and wondering because of laser beam’s inherent and environmental conditions which affect power density and propagation efficiency on target. We have used the beam spreading factors classification to diffraction limited, beam quality, and atmosphere turbulence to calculate the related effects. Diffraction-limited beam spreading is dependent with initial beam radius where it is degraded by growing it up. The second affecting parameter is beam quality factor where it will be ignored for single-mode laser beam (M2 = 1). The most important one is atmosphere turbulence and defined as the refractive index structure constant, Cn2 and based on, it would be categorized as weak, moderate, and strong turbulences. On the other hand, the deep turbulences make more spreading and wondering of long distance laser beam propagation where it concludes to low power density on target. Although adaptive optics could be used to adjust and moderate the atmosphere perturbation effect, it has no impact to low-quality laser beam. [ABSTRACT FROM AUTHOR]

We investigate the interference of high-order perfect optical vortex (POV) beams with different topological charges. Through numerical simulations, we reveal a remarkable phenomenon: keeping the beam width, and beam radius fixed while changing the topological charge, the splitting of the composite POV beam into two distinct individual perfect vortices occurs exactly at the same inter-axial separation. The observed interference pattern exhibits pronounced sensitivity to factors such as axial separation, phase shift, beam radius, and topological charges of the constituent beams. Notably, our findings are contrasted with the interference of high-order Laguerre-Gauss (LG) beams, highlighting that the splitting of composite vortices into their individual components is more rapid in the case of LG beams. We also investigate the evolution of the interference pattern for both POV, and LG beams along the propagation direction in free-space. Our research provides significant insights into the distinct interference properties of high-order POV beams, presenting potential applications in the fields of optical manipulation and communication systems. • Remarkable interference phenomenon. • Composite vortex splitting. • Pronounced pattern sensitivity. [ABSTRACT FROM AUTHOR]

• Quasi-Bessel beam generation by an axicon with an exponential phase function. • Theoretical calculation of quasi-Bessel beam propagation by a phase-modified axicon. • Phase parameter optimization for a uniform axial-intensity-profile Bessel beam. • Experimental demonstration of a quasi-Bessel beam by a phase-modified axicon. A simple phase function for a diffractive axicon to allow generation of a quasi-Bessel beam with a uniform axial intensity profile is reported. By adding the new exponential phase function for the diffractive axicon, we theoretically show that a quasi-Bessel beam with a uniform axial intensity profile can be generated without amplitude oscillation or energy loss. We apply this spatial phase function to a spatial light modulator, illuminated by a fundamental Gaussian laser beam, and produce a quasi-Bessel beam with a long, uniform axial intensity profile, which is in very good agreement with theoretical calculation. Dependence of the phase parameters on the axial intensity profile and their optimization are discussed. [ABSTRACT FROM AUTHOR]

• This work demonstrates how to synthesize a highly air-filled (∼33%), tellurite glass-air Transversely Disordered Optical Fiber (TDOF). • 1.55µm laser light was guided through the 15cm length of the fiber. The beam is localized at specific parts of the TDOF. • Simulations were made using the cross-section image of the fiber to understand the difference in localization of the beam. Tellurite glasses, known for their high viscosity changes in a narrow temperature range, make fiber drawing of tellurite glass-air difficult. This work demonstrates how to synthesize a highly air-filled (∼33%), with controlled air-hole sizes, tellurite glass-air Transversely Disordered Optical Fiber (TDOF). 1.55 µm laser light was guided through 15 cm length of the obtained TDOF, and the obtained beam pattern showed a high localization at a specific part of the TDOF while not being localized at another part of the same fiber. Beam propagation simulations were made using the cross-section image of the obtained fiber as the waveguide media. The results highlighted that the beam stays localized when the surroundings are highly air-hole filled and even more so when the surrounding air-hole size is larger. [ABSTRACT FROM AUTHOR]

The connections between Laguerre–Gauss and Bessel–Gauss beams, and between Hermite–Gauss and cosine-Gauss beams are investigated. We review different asymptotic expressions for generalized Laguerre and Hermite polynomials of large radial/transverse order. The amplitude variations of generalized Laguerre–Gauss beams, including standard and elegant Laguerre–Gauss beams as special cases, are compared with Bessel–Gauss beams. Bessel–Gauss beams can be well-approximated by elegant Laguerre–Gauss beams. For non-integral values of the Laguerre function radial order, a generalized Laguerre–Gauss beam with integer order matches the width of the central lobe well, even for low radial orders. Previous approximations are found to be inaccurate for large azimuthal mode number (topolgical charge), and an improved approximation for this case is also introduced.

The incoherent combined beam of lasers has many important applications due to its simple technology and excellent expansibility. Thermal blooming is one factor that will seriously affect the propagation of the combined beam in the atmosphere. Based on the analytical expression of thermal blooming for a Gaussian beam, the thermal blooming of the incoherent combined beam with a basic arrangement was studied and analyzed. From the evolution of thermal blooming for the incoherent combined beam with a basic arrangement, the thermal blooming for the incoherent combined beam with a complex arrangement can be predicted. As an example, incoherent beams with seven channels were studied. Results show that the thermal lens effect will split the beam located at the central path of heat into two parts. [ABSTRACT FROM AUTHOR]

The effects of transverse displacement parameter d and topological charge (TC) m on the beam spreading (BS) of Airy vortex beam array (AVBA) and Airy Gaussian vortex beam array (AGVBA) propagating in a moderate turbulent atmosphere are analysed and studied numerically. Due to the Gaussian function truncation and optical vortex modulation, the behaviours of the BSs of AVBA and AGVBA in turbulent atmosphere are anomalous. Compared with the AVBA, the BS of lower order AGVBA is less affected by atmospheric turbulence when d is small but more affected when d is large. With the increase of m, the BSs of two vortex beam arrays decrease nonlinearly and AVBA is broadened more seriously by atmospheric turbulence than that of AGVBA as d is set to be zero. Compared with AGVBA, the BS of AVBA with lower TC is less affected by atmospheric turbulence but more seriously affected with higher TC. [ABSTRACT FROM AUTHOR]

In this work, we investigate and compare propagation of Laguerreâ€"Gaussian (LG) and the recently introduced radial carpet (RC) beams through an indoor convective air turbulence under weak to strong turbulence conditions. By determining the radial displacement of the intensity maxima over the donut ring of the LG beam, and tracing the radial coordinates of the main intensity spots of the RC beam, when the beams are propagating through the turbulence, we estimate the variance of the local displacements for both of the beams in the radial direction. It is shown that, under the same turbulence conditions, the RC beam experiences less disturbance and is more resilient to turbulence, especially when it has a complicated structure. The measured values of the image displacement variance for the RC beam are almost one order of magnitude smaller than the same parameter for the LG beam. In addition, for the LG beam, the symmetry of the beam is broken and in many places the intensity ring is even cut off. Although there are slight changes in the RC beams transverse intensity distribution, the number of the main intensity spots rarely changes. This feature makes the RC beam a good candidate for the transmission of information. We also show that a set of RC beams having different values of the main intensity spots (generated with different radial gratings having different spoke numbers) can be used as an orthogonal bases for free-space optical communication. [ABSTRACT FROM AUTHOR]

The evolution characteristics of Hermite-cosine-Gaussian beams in optical nonlinear medium with spatial nonlocality are investigated theoretically in detail. We obtain a series of analytical expressions to describe the evolution characteristics of Hermite-cosine-Gaussian beams in nonlocal medium, such as the expressions of the evolutionary propagation, the beam spot size, the statistical wavefront curvature, the critical energy etc. The results show that the statistical spot size of Hermite-cosine-Gaussian beam can remain unchanged or change periodically according to different initial incident energy. However, the transverse intensity mode of Hermite-cosine-Gaussian beam always presents periodic transformation. This is consistent with high-order temporal solitons, so the evolution of Hermite-cosine-Gaussian beams can also be called generalized solitons or breathers. The influences of initial incident energy and cosine parameters on the evolution characteristics of Hermite-cosine-Gaussian beams are analyzed in detail. Through numerical simulation, some typical evolution characteristics are shown graphically.

We investigate the propagation characteristics of Cauchy–Riemann beams in gradient-index media. Our study reveals two key findings: first, the preservation of their form during propagation; and second, the surprising feasibility of obtaining the two-dimensional fractional Fourier transform for any arbitrary entire function. We elucidate an explicit and straightforward expression for this transform. Additionally, our results contribute to a deeper understanding of the behavior of Cauchy–Riemann beams in inhomogeneous media, offering insights that may have implications for various applications in optics and wave propagation. [ABSTRACT FROM AUTHOR]

Using the extended Huygens-Fresnel principle, the expressions for the cross-spectral density function of both the circular and square multi-sinc Schell-model (MSSM) beams propagating in an anisotropic oceanic turbulent medium have been derived respectively. Based on the expression, the effects of the oceanic turbulence parameters and the anisotropic factor on the intensity and coherence properties of such beams are explored explicitly. By comparative analysis with the case in free space, it is shown that the adjustable multi-ring and square lattice intensity structures of the MSSM beam in ocean are shaped to be circular flat-topped, square flat-topped or Gaussian-like due to different strength of turbulence. The unique intensity patterns can be maintained for a relatively long propagation distance as the anisotropic factor increases. Furthermore, it is found that the turbulent parameters including the salinity and temperature contribution factor, rate of dissipation of turbulent kinetic energy and rate of dissipation of the mean squared temperature have less impacts on the propagation behaviors of the MSSM beam in anisotropic oceanic turbulence in comparison to the corresponding isotropic case. The results presented here have potential applications in oceanic optical telecommunication links.

An effective method capable of measuring the topological charges of optical vortex beams by using a generalized ring Pearcey (GRP) phase is proposed theoretically and demonstrated experimentally in this paper. The number and orientation of fringes in the diffraction patterns respectively reveal the modulus and sign of topological charges. One can also tell the sign by observing the rotation of fringes during propagation. Moreover, the measurement of high‐order topological charges is shown to be significantly affected by the elliptical parameter in the GRP phase. Finally, the physical principle of these measurements is unveiled by applying the stationary phase approach. This work offers an alternative way of evaluating the photonic topological charges in vortex beams. [ABSTRACT FROM AUTHOR]

A model of the generalized dark hollow sine-Gaussian beam (GDHsGB) is proposed to uniformly describe both conventional dark hollow beams (DHBs) and anomalous dark hollow beams (ADHBs) with circular or elliptic geometrical patterns. Using the Collins formula, we derive the analytical expression for GDHsGBs propagating in ABCD paraxial optical systems. We analyze the evolution of the intensity pattern and beam width of circular ADHBs, as well as the ellipticity of elliptic ADHBs, providing mathematical expressions for these physical quantities. The results reveal various evolution forms based on beam parameters, with elliptic ADHBs exhibiting more intricate propagation behavior compared to circular ADHBs. By controlling parameters, the intensity pattern of elliptic ADHBs undergoes a transformation into a petal-like distribution in the near field, later reverting to its original elliptic configuration but rotated 90° from its initial orientation on the source plane in the far field., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2024 The Authors.)

The incoherent combined beam of lasers has many important applications due to its simple technology and excellent expansibility. Thermal blooming is one factor that will seriously affect the propagation of the combined beam in the atmosphere. Based on the analytical expression of thermal blooming for a Gaussian beam, the thermal blooming of the incoherent combined beam with a basic arrangement was studied and analyzed. From the evolution of thermal blooming for the incoherent combined beam with a basic arrangement, the thermal blooming for the incoherent combined beam with a complex arrangement can be predicted. As an example, incoherent beams with seven channels were studied. Results show that the thermal lens effect will split the beam located at the central path of heat into two parts.

Scattering and turbulence are the main factors affecting imaging in natural water environment. A new model for underwater turbulent degradation is obtained by calculating the scattering transfer factors including the intensity distribution of beam propagation, turbulent fluid medium and suspended particle. In order to verify the proposed model, a controlled laboratory simulation system of turbulent water is established, from which the degradation transfer factor is measured and compared by image restoration and reconstruction. The new model is also applied for field tests in natural ocean water. Experimental results show that based on the proposed model, effect of image restoration and reconstruction can be substantially improved, which proves the correctness and validity of the model.

Modern optical technology has greatly facilitated the implementation of free-space quantum key distribution. However, the influence of atmosphere on the beam propagation is always unpredictable and could impair the system performance to some extent. It is necessary to develop an efficient model that could describe the beam propagation and receiving. In this paper, a single-photon receiving efficiency model is proposed incorporating the single-photon acquisition probability and channel transmittance based on the Gaussian beam propagation. We also present simulation and experiment of beam-spot size widening through a 0.5 km free-space channel to verify the proposed model. The results show that with the increase of turbulence strengths, the single-photon acquisition probability will degrade more sharply. The single-photon receiving efficiency will decrease with the increment of the ratio between beam centroid deflection and the receiving aperture radius r / a. [ABSTRACT FROM AUTHOR]

We investigate the propagation and evolution of multiple modified hollow Gaussian beams (MHGBs) for the off-axis incident case in highly nonlocal nonlinear media. The propagation expression of the off-axis MHGB is obtained, the evolution characteristics, such as the optical field distribution, the motion track, the off-axis distance, the rotating angle, and the rotating speed of multiple MHGBs have been discussed analytically and graphically. The results of this paper may have potential applications in related research fields such as exploring the control of multi-beam motion track and designing novel high-order beam forms.

Needle beams are highly attractive for applications which take advantage from a spatial and temporal localization of photons. High intensities, high resolution and extended depth of focus lead to fundamental advances in the optical system performance. Ultrashort, fringe-free, self-reconstructing nondiffracting pulses with undistorted temporal transfer are obtained by generating truncated Bessel beams under self-apodization conditions. Nondiffracting Talbot self-imaging of needle beam arrays enables to transfer near field information to the Fraunhofer zone. With addressable arrays of needle beams, reconfigurable time-wavefront sensors are built up. Moreover, spatial light modulators and flexible axicons are used to realize structured, highly localized wavepackets, accelerating beams and nondiffracting images.

We propose and experimentally demonstrate an optical bottle beam (BB) and an abruptly autofocusing beam (AB), which were generated using a ring-Airy beam array. The method can form BB arrays with varying sizes during propagation; consequently, it can produce multiple optical traps. Additionally, the BB size and the AB focal position can be controlled by varying the array radius. The intensity of the resulting beams improved significantly with increasing array number, and the value abruptly increased 800 times at the focal position when array radius and number were 2 mm and 64, respectively. It is the lateral acceleration of Airy beams that causes this abrupt increase in intensity. Numerical simulations were consistent with experimental results. These advantages could be beneficial for potential applications, such as optical traps, laser ablation, and the ignition of nonlinear effect. (The caption of Graphic Abstract is generation of high-power BBs and ABs using a ring-Airy beam array.)

Symmetry breaking bifurcations of solitons are investigated in framework of a nonlinear fractional Schrödinger equation (NLFSE) with competing cubic‐quintic nonlinearity. Some prototypical characteristics of the symmetry breaking, featured by transformations of symmetric and antisymmetric soliton families into asymmetric ones, are found. Stable asymmetric solitons emerge from unstable symmetric and antisymmetric ones by way of two different symmetry breaking scenarios. A twisting branch, featured with double loops bifurcation, bifurcates off from the base branch of symmetric soliton solutions and crosses it, then merges into the base branch driven by the competitive nonlinear effect. A supercritical pitchfork bifurcation is bifurcated from the branch of antisymmetric soliton solutions and gives rise to a supercritical pitchfork bifurcation. Stability of the soliton families is explored by linear stability analysis. With the increase of the Lévy index, stability region induced by the twisting loops bifurcation is expanded. However, stability region of the pitchfork bifurcation is shrunk on the parameter plane of the Lévy index and the soliton power. [ABSTRACT FROM AUTHOR]

We derive the analytical expression of the probability density of orbital angular momentum modes for elegant and standard Laguerre–Gaussian beams in turbulence. The results show that we can increase the initial topological charge of the beams to reduce the detrimental mode crosstalk induced by the turbulence. We also discuss the influence of the beam parameters on the probability of signal and the variances of crosstalk probability. The results obtained show that the beams with smaller beam width and longer wavelength have higher detection probabilities of signal and are less affected by turbulence. Comparing with the results of elegant and standard Laguerre–Gaussian beams, we find that elegant Laguerre–Gaussian beams display stronger turbulence resistance. Our results will be useful in free-space optical communications. [ABSTRACT FROM AUTHOR]

An updated fast solution in modeling quasi-optical beam waveguides is reported, where several mirror reflectors are utilized for the beam transformation. The fast Fourier transform Poynting vector ray tracing between virtual apertures (FFT-PVVAs) algorithm has been introduced and applied in modeling the reflected beam, based on the FFT-accelerated beam propagator between parallel apertures, and the Poynting vector ray tracing for the mirror reflection. However, for designing and optimizing a beam path with multireflectors, it is desired that the accumulated precision loss due to the Poynting vector ray tracing can be further reduced. As a modification, angular spectrum transform-based beam propagator between oblique apertures is introduced, so as to reduce the ray tracing path length. The improved method is named as FFT-PVVA-tilted propagation (FFT-PVVA-TP). As validation, beam propagation in a four-mirror beam waveguide is simulated by FFT-PVVA, FFT-PVVA-TP, and physical optics integration. Numerical results suggest that FFT-PVVA-TP provides clearly better accuracy after four times of beam reflection. [ABSTRACT FROM AUTHOR]

The analytical expressions of one-dimensional cosh-Airy and cos-Airy beams in the parabolic potential are derived in the general and the phase transition points. The expression in the phase transition point shows a symmetric Gaussian intensity profile and is independent of any Airy features, which is completely different from that in the general point. The intensity, the center of gravity, and the effective beam size of the cosh-Airy and cos-Airy beams in the parabolic potential are periodic and have the same period. The effects of the transverse displacement, the cosh factor, and the cosine factor on these periodic behaviors are also investigated. The direction of self-acceleration reverses every half-period. The phase transition point is also the inversion point of the intensity distribution, which indicates that the intensity distributions before and after the phase transition point are mirror symmetrical. The periodic behaviors of the normalized intensity, the center of gravity, and the effective beam size of the cosh-Airy and cos-Airy beams in the parabolic potential are attractive and well displayed. The results obtained here may have potential applications in particle manipulation, signal processing, and so on. [ABSTRACT FROM AUTHOR]

We numerically and experimentally study the autofocusing and self-healing of partially blocked circular Airy derivative beams (CADBs). The CADB consists of multiple rings, and partial blocking of CADB with different kinds is achieved by using symmetric and asymmetric binary amplitude apertures, enabling blocking of inner/outer rings and sectorially. The CADB blocked with different types possesses the ability to autofocus, however, the abruptness in the autofocusing varies with the amount in certain types of blocking. The abrupt autofocusing is quantified by a maximum k-value, and how fast it changes around the autofocusing distance (z a f). In particular, CADB blocked with inner rings (first/two/three) exhibits an abrupt autofocusing, as the k-value sharply increases [decreases] just before [after] z a f. The maximum k-value always occurs at z a f , which decreases as the number of blocked inner rings increases. For CADB blocked with outer rings, the k-value gradually changes around z a f , indicating a lack of abrupt autofocusing. The value of z a f increases with the number of blocked outer rings. This suggests that although outer rings contain low intensities, these play an important role in abrupt autofocusing. A sectorially blocked CADB possesses an abrupt autofocusing, and maximum k-value depends on the amount of blocking. The CADB blocked with different types possesses good self-healing abilities, where blocked parts reappear as a result of redistribution of intensity. The maximum self-healing occurs at z a f , where an overlap integral approaches a maximum value. Finally, we have compared ideal CADB and partially blocked CADB having the same radii of central dark region, and found that an ideal CADB possesses better abrupt autofocusing. We have found a good agreement between the numerical simulations and experimental results. • Autofocusing and self-healing of partially blocked CADBs are investigated. • CADBs blocked with different amounts and types possess the ability to autofocus. • Irrespective of blocking, maximum self-healing always occurs at autofocusing distance. • In contrary to the CABs, maximum k-value decreases with the blocking of CADBs. • Abruptness in the autofocusing can be controlled by precise blocking of the CADBs. [ABSTRACT FROM AUTHOR]

We present a simple and highly efficient approach to directly generate tunable Airy beams, which can propagate along arbitrary monotonic curves. Such beams are generated by modulating a Gaussian beam imposed by tunable phase-only patterns. The analytic relationship between phase and propagation trajectory is derived by applying caustic theory. In addition, by utilizing symmetry of phase, we also generate tunable quadrate Airy beams that are composed of four independent Airy beams. As opposed to conventional Airy beams, quadrate Airy beams exhibit distinctly symmetric intensity profiles, autofocusing, and tunable trajectories. Moreover, such beams present a thin needle-like structure in the focus region along longitudinal directions. Despite differences in propagation trajectories, such accelerating beams also show nondiffracting and self-healing characteristics. Experimental results agreed well with theoretical predictions. The tunability of such beams may provide further possibilities for applications such as flexible optical manipulation. (The caption of Graphic Abstract is geometrical model of the tunable Airy beams).

We analytically and numerically investigate the dynamic propagation of the quadratically chirped Airy beams in right-handed material (RHM) and left-handed material (LHM) slabs. Based on the analytical expressions and numerical calculations, we find that through choosing the appropriate value of the quadratic chirp, one can modify the diffraction, the intensity distribution, the propagation path, and acceleration and deceleration of the quadratically chirped Airy beams to meet the actual usage accordingly. In addition, we also demonstrate the effect of the quadratic chirp on the Poynting vector and the angular momentum of the quadratically chirped Airy beams, respectively. Furthermore, we explore the gradient and scattering forces on a Rayleigh dielectric particles induced by the quadratically chirped Airy beams.

Here, we introduce a compact way of studying coherence properties of a classical field using techniques in Matrix Algebra. We then apply it to the extended sources case to find out the maximum possible polarization obtainable through the propagation of a partially coherent beam. [ABSTRACT FROM AUTHOR]

We study the propagation properties of optical bottle beams in turbulent atmosphere. By allowing the mathematical expression of source plane to cover both the symmetric and asymmetric forms, the beam is propagated through turbulence using random phase screens. On the source plane, the intensity profile of the bottle beam resembles a dark hollow beam with an outside ring for symmetric cases, whereas it becomes divided into two or more separate lobes for the asymmetric cases. During propagation, both symmetric and asymmetric beams concentrate the intensity toward the center, eventually assuming a Gaussian shape, where this process seems to be more rapid for the former beam types. The rising trend of the kurtosis parameter of bottle beams changes to a falling trend when the refractive index structure constant is reduced from 10-14 to 10-13 m-2/3. [ABSTRACT FROM AUTHOR]