Nonparaxial Mathieu and Weber accelerating beams

Symmetry in optics and photonics: a group theory approach

Group theory (GT) provides a rigorous framework for studying symmetries in various disciplines in physics ranging from quantum field theories and the standard model to fluid mechanics and chaos theory. To date, the application of such a powerful tool in optical physics remains limited. Over the past few years however, several quantum-inspired symmetry principles (such as parity-time invariance and supersymmetry) have been introduced in optics and photonics for the first time. Despite the intense activities in these new research directions, only few works utilized the power of group theory. Motivated by this status quo, here we present a brief overview of the application of GT in optics, deliberately choosing examples that illustrate the power of this tool in both continuous and discrete setups. We hope that this review will stimulate further research that exploits the full potential of GT for investigating various symmetry paradigms in optics, eventually leading to new photonic devices.

Non-diffracting beams for label-free imaging through turbid media

We propose a new method to image through dynamically changing turbid media based on the scanning of non-diffractive laser beams. We use computer-generated holograms to create Airy beams and compare quantitatively the characteristics of their propagation in clear and turbid media. Imaging contrast is achieved by relative reflection of the scanned beams from the imaged surface. We implement our method to demonstrate experimentally our ability to image a chromium surface on a glass slide through 270 μm of highly scattering milk/water mixtures with a resolution of several microns.

An absorption-free and Doppler-improved optical waveguide for diffractionless light propagation

We propose a novel scheme to realize an optical waveguide induced by an active Raman gain (ARG) process in a four-level N-type atomic system. Because of the nature of the ARG, there are two distinct features related to the waveguide: i) It is not absorptive, on the contrary, weak gain is presented; ii) It can be improved by the Doppler effect in the sense that the dispersion is enhanced while the gain is further reduced. This is in sharp contrast to the previously considered schemes where usually the optical induced waveguide is passive and is severely attenuated by the Doppler effect. We then study the paraxial light propagation in the waveguide which shows that the propagation dynamics is lossless and diffractionless.

Particle manipulation beyond the diffraction limit using structured super-oscillating light beams

The diffraction-limited resolution of light focused by a lens was derived in 1873 by Ernst Abbe. Later in 1952, a method to reach sub-diffraction light spots was proposed by modulating the wavefront of the focused beam. In a related development, super-oscillating functions, that is, band-limited functions that locally oscillate faster than their highest Fourier component, were introduced and experimentally applied for super-resolution microscopy. Up till now, only simple Gaussian-like sub-diffraction spots were used. Here we show that the amplitude and phase profile of these sub-diffraction spots can be arbitrarily controlled. In particular, we utilize Hermite-Gauss, Laguerre-Gauss and Airy functions to structure super-oscillating beams with sub-diffraction lobes. These structured beams are then used for high-resolution trapping and manipulation of nanometer-sized particles. The trapping potential provides unprecedented localization accuracy and stiffness, significantly exceeding those provided by standard diffraction-limited beams.

Real and virtual propagation dynamics of angular accelerating white light beams

Accelerating waves have received significant attention of late, first in the optical domain and later in the form of electron matter waves, and have found numerous applications in non-linear optics, material processing, microscopy, particle manipulation and laser plasma interactions. Here we create angular accelerating light beams with a potentially unlimited acceleration rate. By employing wavelength independent digital holograms for the creation and propagation of white light beams, we are able to study the resulting propagation in real and virtual space. We find that dephasing occurs for real propagation and that this can be compensated for in a virtual propagation scheme when single plane dynamics are important. Our work offers new insights into the propagation dynamics of such beams and provides a versatile tool for further investigations into propagating structured light fields.

Unraveling beam self-healing

We show that, contrary to popular belief, diffraction-free beams may not only reconstruct themselves after hitting an opaque obstacle but also, for example, Gaussian beams. We unravel the mathematics and the physics underlying the self-reconstruction mechanism and we provide for a novel definition for the minimum reconstruction distance beyond geometric optics, which is in principle applicable to any optical beam that admits an angular spectrum representation. Moreover, we propose to quantify the self-reconstruction ability of a beam via a newly established degree of self-healing. This is defined via a comparison between the amplitudes, as opposite to intensities, of the original beam and the obstructed one. Such comparison is experimentally accomplished by tailoring an innovative experimental technique based upon Shack-Hartmann wave front reconstruction. We believe that these results can open new avenues in this field.

Practical algorithm for custom-made caustic beams

We present a practical algorithm for designing an aperture field (source) that propagates along a predefined generic beam trajectory that consists of both convex and concave sections. We employ here the mechanism that forms the well-known Airy beam in which the beam trajectory follows a smooth convex caustic of the geometric optics rays and generalize it for a class of beams that are referred to as "caustic beams" (CBs). The implementation is based on "back-tracing" rays from the predefined beam trajectory to the source's aperture to form its phase distribution. The amplitude is set in order to form a uniform smooth amplitude of the CBs along their trajectories. Several numerical examples are included.

Laser filamentation in air via Mathieu modulation: ranging from trajectory-predesigned curved filament to quasi-soliton and ring light bullet

We propose theoretically various kinds of filaments via the Mathieu modulation. Our results indicate curved filaments, in-phase and out-of-phase quasi-solitons and nonlinear light bullets can be formed successfully in air. Through calculated initial Mathieu accelerating beam (MAB), curved filament is able to propagate along a predesigned elliptical trajectory. By transforming the MAB into an axial symmetrical structure with in-phase and out-of-phase modulations, we obtain two kinds of quasi-solitons in air, respectively. The latter case can even propagate in a breathing fashion. With a ring structure of MAB, we successfully form a light bullet in air that generates a chain of intensity peaks over extended distances. These unique filaments can offer significant advantages for numerous applications, such as micro engineering of materials, THz radiation generation and attosecond physics.

Engineering and Optimization of Quasi-Nondiffracting Helicon-Like Beams With an Evolutionary Algorithm

Nondiffracting beams maintain their intensity profiles over a large propagation distance without substantial diffraction and exhibit unique propagation trajectories, leading to scientific impacts in various fields. However, the nonlocalized intensity distribution of non-diffracting beams is restrictive for many practical applications. Thus, strategies to optimize the beam profiles remain much in demand. In this report, we demonstrate an evolutionary algorithmic framework for optical beam engineering and optimization and experimentally validate it by realizing quasi-nondiffracting radially self-accelerating (or self-rotating) beams in a high-resolution imaging system. The work reports a tightly confined side-lobe-suppressed helicon-like beam that largely maintains its properties of radial self-acceleration and non-diffraction in the 3-D space. The optimization method represents a new methodological avenue that can be extended to a broad range of beam engineering problems.

Interaction of Airy-Gaussian beams in photonic lattices with defects

We investigate numerically the interaction between two finite Airy-Gaussian (AiG) beams in different media with the defected photonic lattices in one transverse dimension. We discuss that the beams with different intensities and phases launch into the different lattice structures but accelerate in opposite directions. During interactions, the interference fringe, breathers, and soliton pairs are observed. In the linear media, the initial deflection direction of the accelerated beams is changed by adjusting the phase shift and the beam interval. For a certain lattice period, the periodic interference fringe can form. A constructive or destructive interference can vary with the defect depth and phase shift. While the nonlinearity is introduced, the breathers is generated. Especially in the self-defocusing media, the appropriate AiG beam amplitude and lattice depth may lead to the formation of soliton pairs, On the contrary, the interaction of two Gaussian beams is diffraction.

Non-diffracting optical Bloch oscillations in hexagonal photonic lattices

Light beams undergoing optical Bloch oscillations (OBOs) in two-dimensional (2D) photonic lattices suffer from severe diffraction along the perpendicular direction to the oscillation plane. In this paper, we propose and demonstrate that such diffraction could be suppressed in hexagonal photonic lattices via sophisticated managements of the discrete diffraction. By positioning the Fourier spectrum of the beam to a special region in the Brillouin zone, the light driven by the OBO experiences normal and anomalous diffractions alternatively, leading to a non-diffracting propagation for a long distance. We show that non-diffracting OBOs can be implemented not only for Gaussian beam but also for other complex 2D beams including self-accelerating Airy beams and vortex beams. Our results provide novel insights into the diffraction or dispersion engineering of waves in periodic structures.

Radially dependent angular acceleration of twisted light

While photons travel in a straight line at constant velocity in free space, the intensity profile of structured light may be tailored for acceleration in any degree of freedom. Here we propose a simple approach to control the angular acceleration of light. Using Laguerre-Gaussian modes as our twisted beams carrying orbital angular momentum, we show that superpositions of opposite handedness result in a radially dependent angular acceleration as they pass through a focus (waist plane). Due to conservation of orbital angular momentum, we find that propagation dynamics are complex despite the free-space medium: the outer part of the beam (rings) rotates in an opposite direction to the inner part (petals), and while the outer part accelerates, the inner part decelerates. We outline the concepts theoretically and confirm them experimentally. Such exotic structured light beams are topical due to their many applications, for instance in optical trapping and tweezing, metrology, and fundamental studies in optics.

Nonparaxial self-accelerating beams in an atomic vapor with electromagnetically induced transparency

We theoretically and numerically investigate the nonparaxial self-accelerating beams in a Λ-type three-level energy system of rubidium atomic vapor in the electromagnetically induced transparency (EIT) window. In the EIT window, the absorption of the atomic vapor is small, and robust nonparaxial self-accelerating beams can be generated. The reason is that the energy of the tail transfers to the main lobe, which then maintains its shape, owing to the self-healing effect. Media with large absorption would demand large energy to compensate, and the tail would be lifted too high to maintain the profile of an accelerating beam, so that self-accelerating beams cannot be obtained any longer. An atomic vapor with small absorption is the ideal medium to produce such self-accelerating beams and, in return, self-accelerating beams may inspire new ideas in the research associated with atomic vapors and atomic-like ensembles.

Dynamics of accelerating Bessel solutions of Maxwell's equations

We investigate the propagation dynamics of accelerating beams that are shape-preserving solutions of the Maxwell equations, and explore the contribution of their evanescent field components in detail. Both apodized and nonapodized Bessel beam configurations are considered. We show that, in spite of the fact that their evanescent tails do not propagate, these nonparaxial beams can still accelerate along circular trajectories and can exhibit large deflections. Subsequently, our formulation is extended in other two-dimensional vectorial arrangements. The reported results can be useful in plasmonic and other subwavelength and near-field settings.

Fractional nonparaxial accelerating Talbot effect

We demonstrate the fractional Talbot effect of nonparaxial accelerating beams, theoretically and numerically. It is based on the interference of nonparaxial accelerating solutions of the Helmholtz equation in two dimensions. The effect originates from the interfering lobes of a superposition of the solutions that accelerate along concentric semicircular trajectories with different radii. Talbot images form along certain central angles, which are referred to as Talbot angles. The fractional nonparaxial Talbot effect is obtained by choosing the coefficients of beam components properly. A single nonparaxial accelerating beam possesses duality-it can be viewed as a Talbot effect of itself with an infinite or zero Talbot angle. These results improve the understanding of the nonparaxial accelerating beams and of the Talbot effect among them.

Indefinite Plasmonic Beam Engineering by In-plane Holography

Recent advances in controlling the optical phase at the sub-wavelength scale by meta-structures offer unprecedented possibilities in the beam engineering, holograms, and even invisible cloaks. In despite of developments of plasmonic beam engineering for definite beams, here, we proposed a new holographic strategy by in-plane diffraction process to access indefinite plasmonic beams, where a counterintuitive oscillating beam was achieved at a free metal surface that is against the common recognition of light traveling. Beyond the conventional hologram, our approach emphasizes on the phase correlation on the target, and casts an in-depth insight into the beam formation as a kind of long depth-of-field object. Moreover, in contrast to previous plasmonic holography with space light as references, our approach is totally fulfilled in a planar dimension that offers a thoroughly compact manipulation of the plasmonic near-field and suggests new possibilities in nanophotonic designs.

Diffraction-free beams in fractional Schrödinger equation

We investigate the propagation of one-dimensional and two-dimensional (1D, 2D) Gaussian beams in the fractional Schrödinger equation (FSE) without a potential, analytically and numerically. Without chirp, a 1D Gaussian beam splits into two nondiffracting Gaussian beams during propagation, while a 2D Gaussian beam undergoes conical diffraction. When a Gaussian beam carries linear chirp, the 1D beam deflects along the trajectories z = ±2(x - x0), which are independent of the chirp. In the case of 2D Gaussian beam, the propagation is also deflected, but the trajectories align along the diffraction cone z = 2√(x(2) + y(2)) and the direction is determined by the chirp. Both 1D and 2D Gaussian beams are diffractionless and display uniform propagation. The nondiffracting property discovered in this model applies to other beams as well. Based on the nondiffracting and splitting properties, we introduce the Talbot effect of diffractionless beams in FSE.

Control on the anomalous interactions of Airy beams in nematic liquid crystals

We reveal a controllable manipulation of anomalous interactions between Airy beams in nonlocal nematic liquid crystals numerically. With the help of an in-phase fundamental Gaussian beam, attraction between in-phase Airy beams can be suppressed or become a repulsive one to each other; whereas the attraction can be strengthened when the Gaussian beam is out-of-phase. In contrast to the repulsive interaction in local media, stationary bound states of breathing Airy soliton pairs are found in nematic liquid crystals.

Experimental demonstration of 3D accelerating beam arrays

Accelerating beams have attracted much attention in the frontiers of optical physics and technology owing to their unique propagation dynamics of nondiffracting, self-healing, and freely accelerating along curved trajectories. Such behaviors essentially arise from the particular phase factor occurring in their spatial frequency spectrum, e.g., the cubic phase associated to the spectrum of Airy beam. In this paper, we theoretically and experimentally demonstrate a sort of accelerating beam arrays, which are composed of spatially separated accelerating beams. By superimposing kinoforms of multifocal patterns into the spatial frequency spectrum of accelerating beams, different types of beam arrays, e.g., Airy beam arrays and two-main-lobe accelerating beam arrays, are generated and measured by scanning a reflection mirror near the focal region along the optical axis. The 3D intensity patterns reconstructed from the experimental data present good agreement with the theoretical counterparts. The combination of accelerating beams with optical beam arrays proposed here may find potential applications in various fields such as optical microscopes, optical micromachining, optical trapping, and so on.

Nonparaxial abruptly autofocusing beams

We study nonparaxial autofocusing beams with pre-engineered trajectories. We consider the case of linearly polarized electric optical beams and examine their focusing properties, such as contrast, beam width, and numerical aperture. Such beams are associated with larger intensity contrasts, can focus at smaller distances, and have smaller spot sizes as compared to the paraxial regime.

Wavefront shaping through emulated curved space in waveguide settings

The past decade has witnessed remarkable progress in wavefront shaping, including shaping of beams in free space, of plasmonic wavepackets and of electronic wavefunctions. In all of these, the wavefront shaping was achieved by external means such as masks, gratings and reflection from metasurfaces. Here, we propose wavefront shaping by exploiting general relativity (GR) effects in waveguide settings. We demonstrate beam shaping within dielectric slab samples with predesigned refractive index varying so as to create curved space environment for light. We use this technique to construct very narrow non-diffracting beams and shape-invariant beams accelerating on arbitrary trajectories. Importantly, the beam transformations occur within a mere distance of 40 wavelengths, suggesting that GR can inspire any wavefront shaping in highly tight waveguide settings. In such settings, we demonstrate Einstein's Rings: a phenomenon dating back to 1936.

Lossless Airy Surface Polaritons in a Metamaterial via Active Raman Gain

We propose a scheme to realize a lossless propagation of linear and nonlinear Airy surface polaritons (SPs) via active Raman gain (ARG). The system we suggest is a planar interface superposed by a negative index metamaterial (NIMM) and a dielectric, where three-level quantum emitters are doped. By using the ARG from the quantum emitters and the destructive interference effect between the electric and magnetic responses from the NIMM, we show that not only the Ohmic loss of the NIMM but also the light absorption of the quantum emitters can be completely eliminated. As a result, non-diffractive Airy SPs may propagate for very long distance without attenuation. We also show that the Kerr nonlinearity of the system can be largely enhanced due to the introduction of the quantum emitters and hence lossless Airy surface polaritonic solitons with very low power can be generated in the system.

Correlation-induced changes of the degree of paraxiality of a partially coherent beam

The degree of paraxiality (DOP) is a quantification of how paraxial (or nonparaxial) a light field is. In this article, we study the DOP of a partially coherent beam with a nonconventional spatial correlation function and explore the correlation-induced changes of the DOP. Analytical expressions for the DOP and the far-field divergence angle of a generalized multi-Gaussian correlated Schell-model (MGCSM) beam are derived. The properties of the DOP and the far-field divergence angle for the first type and the second type of generalized MGCSM beams without and with truncation in free space are illustrated numerically, and we find that the DOP and far-field divergence angle are closely related with the distribution of the correlation function. Modulation of the correlation function provides a novel way for modulating the nonparaxial properties of a partially coherent beam.

Self-Interfering Wave Packets

We study the propagation of noninteracting polariton wave packets. We show how two qualitatively different concepts of mass that arise from the peculiar polariton dispersion lead to a new type of particlelike object from noninteracting fields-much like self-accelerating beams-shaped by the Rabi coupling out of Gaussian initial states. A divergence and change of sign of the diffusive mass results in a "mass wall" on which polariton wave packets bounce back. Together with the Rabi dynamics, this yields propagation of ultrafast subpackets and ordering of a spacetime crystal.

Spinning of a submicron sphere by Airy beams

We show that by employing two incoherent counter-propagating Airy beams, we can manipulate a submicron sphere to spin around a transverse axis. We can control not only the spinning speed, but also the direction of the spinning axis by changing the polarization directions of Airy beams.

Generating a Bessel-Gaussian beam for the application in optical engineering

Bessel beam is the important member of the family of non-diffracting beams and has many novel properties which can be used in many areas. However, the source of Bessel beam generated by the existing methods can be used only in a short distance due to its low power. In this paper, based on the coherent combining technology, we have proposed a method which can be used to generate a high-power Bessel beam. Even more, we give an innovative idea to form vortex phase by using discontinuous piston phase. To confirm the validity of this method, the intensity evolution of the combined beam and the Bessel-Gaussian beam at different propagation distance have been studied and compared. Meanwhile, the experimental realization has been discussed from the existing experimental result related to the coherent combining technology.

Three-dimensional collimated self-accelerating beam through acoustic metascreen

We report the generation of three-dimensional acoustic collimated self-accelerating beam in non-paraxial region with sourceless metascreen. Acoustic metascreen with deep subwavelength spatial resolution, composed of hybrid structures combining four Helmholtz resonators and a straight pipe, transmitting sound efficiently and shifting fully the local phase is evidenced. With an extra phase profile provided by the metascreen, the transmitted sound can be tuned to propagate along arbitrary caustic curvatures to form a focused spot. Due to the caustic nature, the formed beam possesses the capacities of bypassing obstacles and holding the self-healing feature, paving then a new way for wave manipulations and indicating various potential applications, especially in the fields of ultrasonic imaging, diagnosis and treatment.

Measurement of acceleration and orbital angular momentum of Airy beam and Airy-vortex beam by astigmatic transformation

Special beams, including the Airy beam and the vortex-embedded Airy beam, draw much attention due to their unique features and promising applications. Therefore, it is necessary to devise a straightforward method for measuring these peculiar features of the beams with ease. Hence we present the astigmatic transformation of Airy and Airy-vortex beam. The "acceleration" coefficient of the Airy beam is directly determined from a single image by fitting the astigmatically transformed beam to an analytic expression. In addition, the orbital angular momentum of optical vortex in Airy-vortex beam is measured directly using a single image.

Theoretical Study of Large-Angle Bending Transport of Microparticles by 2D Acoustic Half-Bessel Beams

Conventional microparticle transports by light or sound are realized along a straight line. Recently, this limit has been overcome in optics as the growing up of the self-accelerating Airy beams, which are featured by many peculiar properties, e.g., bending propagation, diffraction-free and self-healing. However, the bending angles of Airy beams are rather small since they are only paraxial solutions of the two-dimensional (2D) Helmholtz equation. Here we propose a novel micromanipulation by using acoustic Half-Bessel beams, which are strict solutions of the 2D Helmholtz equation. Compared with that achieved by Airy beams, the bending angle of the particle trajectory attained here is much steeper (exceeding 90^o). The large-angle bending transport of microparticles, which is robust to complex scattering environment, enables a wide range of applications from the colloidal to biological sciences.

Laser-assisted guiding of electric discharges around objects

Electric breakdown in air occurs for electric fields exceeding 34 kV/cm and results in a large current surge that propagates along unpredictable trajectories. Guiding such currents across specific paths in a controllable manner could allow protection against lightning strikes and high-voltage capacitor discharges. Such capabilities can be used for delivering charge to specific targets, for electronic jamming, or for applications associated with electric welding and machining. We show that judiciously shaped laser radiation can be effectively used to manipulate the discharge along a complex path and to produce electric discharges that unfold along a predefined trajectory. Remarkably, such laser-induced arcing can even circumvent an object that completely occludes the line of sight.

Solitons shedding from Airy beams and bound states of breathing Airy solitons in nonlocal nonlinear media

We investigate the spatially optical solitons shedding from Airy beams and anomalous interactions of Airy beams in nonlocal nonlinear media by means of direct numerical simulations. Numerical results show that nonlocality has profound effects on the propagation dynamics of the solitons shedding from the Airy beam. It is also shown that the strong nonlocality can support periodic intensity distribution of Airy beams with opposite bending directions. Nonlocality also provides a long-range attractive force between Airy beams, leading to the formation of stable bound states of both in-phase and out-of-phase breathing Airy solitons which always repel in local media.

Closed-form expressions for nonparaxial accelerating beams with pre-engineered trajectories

In this Letter, we propose a general real-space method for the generation of nonparaxial accelerating beams with arbitrary predefined convex trajectories. Our results lead to closed-form expressions for the required phase at the input plane. We present such closed-form results for a variety of caustic curves: beside circular, elliptic, and parabolic, we find for the first time general power-law and exponential trajectories. Furthermore, by changing the initial amplitude, we can design different intensity profiles along the caustic.

Improved nonparaxial accelerating beams due to additional off-axis spiral phases

An accelerating beam with a Gaussian transverse profile can preserve its shape while propagating along a quarter of a circle. When an off-axis spiral phase is imposed, however, the beam will have an additional acceleration perpendicular to the circle. A two-dimensional accelerating beam is constructed and is found to accelerate along both the x and the y directions, but its transverse intensity profile cannot be maintained well due to the interaction of accelerations along different directions. The intensity profile can be improved by imposing two off-axis spiral phases onto the input beam.

Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles' trajectories

Self-accelerating beams--shape-preserving bending beams--are attracting great interest, offering applications in many areas such as particle micromanipulation, microscopy, induction of plasma channels, surface plasmons, laser machining, nonlinear frequency conversion and electron beams. Most of these applications involve light-matter interactions, hence their propagation range is limited by absorption. We propose loss-proof accelerating beams that overcome linear and nonlinear losses. These beams, as analytic solutions of Maxwell's equations with losses, propagate in absorbing media while maintaining their peak intensity. While the power such beams carry decays during propagation, the peak intensity and the structure of their main lobe region are maintained over large distances. We use these beams for manipulation of particles in fluids, steering the particles to steeper angles than ever demonstrated. Such beams offer many additional applications, such as loss-proof self-bending plasmons. In transparent media these beams show exponential intensity growth, which facilitates other novel applications in micromanipulation and ignition of nonlinear processes.

Nonlinear volume holography for wave-front engineering

The concept of volume holography is applied to the design of an optical superlattice for the nonlinear harmonic generation. The generated harmonic wave can be considered as a holographic image caused by the incident fundamental wave. Compared with the conventional quasi-phase-matching method, this new method has significant advantages when applied to complicated nonlinear processes such as the nonlinear generation of special beams. As an example, we experimentally realized a second-harmonic Airy beam, and the results are found to agree well with numerical simulations.

Delivering sound energy along an arbitrary convex trajectory

Accelerating beams have attracted considerable research interest due to their peculiar properties and various applications. Although there have been numerous research on the generation and application of accelerating light beams, few results have been published on the generation of accelerating acoustic beams. Here we report on the experimental observation of accelerating acoustic beams along arbitrary convex trajectories. The desired trajectory is projected to the spatial phase profile on the boundary which is discretized and sampled spatially. The sound field distribution is formulated with the Green function and the integral equation method. Both the paraxial and the non-paraxial regimes are examined and observed in the experiments. The effect of obstacle scattering in the sound field is also investigated and the results demonstrate that the approach is robust against obstacle scattering. The realization of accelerating acoustic beams will have an impact on various applications where acoustic information and energy are required to be delivered along an arbitrary convex trajectory.

Coupled Airy breathers

The dynamics of two component-coupled vectorial Airy beams is investigated. In the linear propagation regime, a complete analytic solution describes the breather-like propagation of two components that feature nondiffracting self-accelerating Airy behavior. The superposition of two beams with different input properties opens the possibility of designing more complex nondiffracting propagation scenarios. In the strongly nonlinear regime, the dynamics remain qualitatively robust as is revealed by direct numerical simulations. Because of the Kerr effect, the two beams emit solitonic breathers whose coupling period is compatible with the remaining Airy-like beams. The results of this study are relevant for the description of photonic and plasmonic beams that propagate in coupled planar waveguides, as well as for birefrigent or multiwavelength beams.

Rapidly accelerating Mathieu and Weber surface plasmon beams

We report the generation of two types of self-accelerating surface plasmon beams which are solutions of the nonparaxial Helmholtz equation in two dimensions. These beams preserve their shape while propagating along either elliptic (Mathieu beam) or parabolic (Weber beam) trajectories. We show that owing to the nonparaxial nature of the Weber beam, it maintains its shape over a much larger distance along the parabolic trajectory, with respect to the corresponding solution of the paraxial equation-the Airy beam. Dynamic control of the trajectory is realized by translating the position of the illuminating free-space beam. Finally, the ability of these beams to self-heal after blocking obstacles is demonstrated as well.

Dynamical deformed Airy beams with arbitrary angles between two wings

We study both numerically and experimentally the acceleration and propagation dynamics of 2D Airy beams with arbitrary initial angles between their "two wings." Our results show that the acceleration of these generalized 2D Airy beams strongly depends on the initial angles and cannot be simply described by the vector superposition principle (except for the normal case of a 90° angle). However, as a result of the "Hyperbolic umbilic" catastrophe (a two-layer caustic), the main lobes of these 2D Airy beams still propagate along parabolic trajectories even though they become highly deformed. Under such conditions, the peak intensity (leading energy flow) of the 2D Airy beams cannot be confined along the main lobe, in contrast to the normal 90° case. Instead, it is found that there are two parabolic trajectories describing the beam propagation: one for the main lobe, and the other for the peak intensity. Both trajectories can be readily controlled by varying the initial wing angle. Due to their self-healing property, these beams tend to evolve into the well-known 1D or 2D Airy patterns after a certain propagation distance. The theoretical analysis corroborates our experimental observations, and explains clearly why the acceleration of deformed Airy beams increases with the opening of the initial wing angle.

Production of accelerating quad Airy beams and their optical characteristics

Based on a geometric caustic argument and diffraction catastrophe theory, we generate a novel form of accelerating beams using a symmetric 3/2 phase-only pattern. Such beams can be called accelerating quad Airy beams (AQABs) because they look very much like four face-to-face combined Airy beams. Optical characteristics of AQABs are subsequently investigated. The research results show that the beams have axial-symmetrical and centrosymmetrical transverse intensity patterns and quasi-diffraction-free propagation features for their four main lobes while undergoing transverse shift along parabolic trajectories. Moreover, we also demonstrate that AQABs possess self-construction ability when local areas are blocked. The unique optical properties of these beams will make them useful tools for future scientific applications.

Dynamic generation of plasmonic bottle-beams with controlled shape

We demonstrate the generation of plasmonic bottle-beams based on self-accelerating surface plasmons. These beams are excited from free-space beams through a special binary phase mask. The mask generates two mirror-imaged self-accelerating surface plasmons, which form the plasmonic bottle-beam and a hot-spot at the point of convergence. The shape and area of the bottle-beams, together with the location of the hot-spot, are statically controlled by designing arbitrary convex trajectories for the two counter-accelerating beams and also are dynamically controlled by the illumination beam.

Efficient light bending with isotropic metamaterial Huygens' surfaces

Metamaterial Huygens' surfaces manipulate electromagnetic wavefronts without reflection. A broadband Huygens' surface that efficiently refracts normally incident light at the telecommunication wavelength of 1.5 μm is reported. The electric and magnetic responses of the surface are independently controlled by cascading three patterned, metallic sheets with a subwavelength overall thickness of 430 nm. The peak efficiency of the device is significantly enhanced by reducing the polarization and reflection losses that are inherent to earlier single-layer designs.

Virtual source of a Pearcey beam

A virtual source that yields a family of a Pearcey wave is demonstrated. A closed-form expression is derived for the Pearcey wave that simplifies to the paraxial Pearcey beam (PB) in the appropriate limit. From the perturbative series representation of a complex-source-point spherical wave, an infinite series nonparaxial correction expression for a PB is obtained. The infinite series expression of a PB can give accuracy up to any order of the diffraction angle. By applying the integral representation of the Pearcey wave, the first three terms in the nonparaxial correction series to the paraxial PB are provided.

Nonparaxial shape-preserving Airy beams with Bessel signature

Spatially accelerating beams that are solutions to Maxwell equations may propagate along incomplete circular trajectories. Taking these truncated Bessel fields to the paraxial limit, some authors have sustained that it has recovered the known Airy beams (AiBs). Based on the angular spectrum representation of optical fields, we demonstrated that the paraxial approximation rigorously leads to off-axis focused beams instead of finite-energy AiBs. The latter will arise under the umbrella of a nonparaxial approach following elliptical trajectories in place of parabolas. The analytical expression of such a shape-preserving wave field under Gaussian apodization is disclosed by using third-order nonparaxial coefficients. Deviations from full-wave simulations appear more severely in beam positioning rather than its local profile.

Dynamics of three-Airy beams carrying optical vortices

We study numerically and demonstrate experimentally a novel type of singular optical beams formed by the phase imprinting of an optical vortex into the structure of the three-Airy beams. In contrast to a vortex-free product of three Airy beams, in this type of singular-Airy beam, the vortex in the beam axis causes a twist in the beam transverse intensity profile with propagation. Such a new type of singular beams appears especially attractive for applications in optical micromanipulation.

Conical light sword optical beam and its healing property

A new diffractive optical element, named as a conical light sword optical element, is presented. In the focal volume, this element produces a helical amplitude profile that can be used as an optical twister. We have experimentally demonstrated the optical healing property of the conical light sword optical beam (CLSOB). This healing property comes from the transverse helical energy flow, due to the evolution of multiple unipolar vortices in the propagation of CLSOB. We envisage that this spiral intensity profile and optical healing property of the beam find potential applications in propagation through a scattering and turbulent media, imaging with extended depth of field, and in optical tweezers.

Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear media

We investigate numerically interactions between two in-phase or out-of-phase Airy beams and nonlinear accelerating beams in Kerr and saturable nonlinear media in one transverse dimension. We discuss different cases in which the beams with different intensities are launched into the medium, but accelerate in opposite directions. Since both the Airy beams and nonlinear accelerating beams possess infinite oscillating tails, we discuss interactions between truncated beams, with finite energies. During interactions we see solitons and soliton pairs generated that are not accelerating. In general, the higher the intensities of interacting beams, the easier to form solitons; when the intensities are small enough, no solitons are generated. Upon adjusting the interval between the launched beams, their interaction exhibits different properties. If the interval is large relative to the width of the first lobes, the generated soliton pairs just propagate individually and do not interact much. However, if the interval is comparable to the widths of the maximum lobes, the pairs strongly interact and display varied behavior.

Generation of nonparaxial accelerating fields through mirrors. I: two dimensions

Accelerating beams are wave packets that preserve their shape while propagating along curved trajectories. Recent constructions of nonparaxial accelerating beams cannot span more than a semicircle. Here, we present a ray based analysis for nonparaxial accelerating fields and pulses in two dimensions. We also develop a simple geometric procedure for finding mirror shapes that convert collimated fields or fields emanating from a point source into accelerating fields tracing circular caustics that extend well beyond a semicircle.

Accelerating light beams with arbitrarily transverse shapes

Accelerating beams are wave packets that preserve their shape while propagating along curved trajectories. Their unique characteristics have opened the door to applications that range from optical micromanipulation and plasma-channel generation to laser micromachining. Here, we demonstrate, theoretically and experimentally, that accelerating beams can be generated with a variety of arbitrarily chosen transverse shapes. We present a general method to construct such beams in the paraxial and nonparaxial regime and demonstrate experimentally their propagation in the paraxial case. The key ingredient of our method is the use of the spectral representation of the accelerating beams, which offers a unique and compact description of these beams. The on-demand accelerating light patterns described here are likely to give rise to new applications and add versatility to the current ones.