Coupled Airy breathers

Interactions of Airy beams in nonlinear media with fourth-order diffraction

We investigate to the best of our knowledge the first time the interactions of in-phase and out-of-phase Airy beams in Kerr, saturable and nonlocal nonlinear media with fourth-order diffraction using split-step Fourier transform method. Directly numerical simulations show that normal and anomalous fourth-order diffractions have profound effects on the interactions of the Airy beams in Kerr and saturable nonlinear media. We demonstrate the dynamics of the interactions in detail. In nonlocal media with fourth-order diffraction, nonlocality induces 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 soliton pairs which are always repulsive in local media. Our results have potential applications in all-optical devices for communication and optical interconnects, etc.

Propagation properties of radially and azimuthally polarized chirped Airy-Gaussian vortex beams through slabs of right-handed materials and left-handed materials

By using Huygens-Fresnel diffraction integral formula and the transfer matrix method, the analytical expression of radially and azimuthally polarized chirped Airy-Gaussian vortex beams through left-handed materials and right-handed materials can be obtained. We study the effects of the chirp factor and the distribution factor on the radially and azimuthally polarized chirped Airy-Gaussian vortex beams in the propagation process, including the light intensity, the phase distribution, the propagation path, the peak intensity, and the radiation force. The focal position of the beams can be adjusted by the chirp parameter.

Partially coherent dual and quad airy beams

We investigate the partially coherent dual and quad Airy beams, which are the partially coherent version of multiple Airy beams, in the framework of cross-spectral density functions. They are constructed by the superposition of two and four partially coherent Airy beams without reduced acceleration properties (rate and range). In the case where the interference effect is not considered, the property of lacking side lobes in the partially coherent quad Airy beams leads to the performance of the optical frame during propagation. In the case with constructive interference, we find that the interference pattern produced by the partially coherent dual and quad Airy beams can remain stable and display a spot right in the center of the optical frame. The shape and peak intensity of this interference spot can be controlled by the transverse width of the beams. These results may provide new understanding for the partially coherent field of accelerating beams.

Interactions of solitons with positive and negative masses: Shuttle motion and coacceleration

We consider a possibility to realize self-accelerating motion of interacting states with effective positive and negative masses in the form of pairs of solitons in two-component BEC loaded in an optical-lattice (OL) potential. A crucial role is played by the fact that gap solitons may feature a negative dynamical mass, keeping their mobility in the OL. First, the respective system of coupled Gross-Pitaevskii equations (GPE) is reduced to a system of equations for envelopes of the lattice wave functions. Two generic dynamical regimes are revealed by simulations of the reduced system, viz., shuttle oscillations of pairs of solitons with positive and negative masses, and splitting of the pair. The coaccelerating motion of the interacting solitons, which keeps constant separation between them, occurs at the boundary between the shuttle motion and splitting. The position of the coacceleration regime in the system's parameter space can be adjusted with the help of an additional gravity potential, which induces its own acceleration, that may offset the relative acceleration of the two solitons, while gravity masses of both solitons remain positive. The numerical findings are accurately reproduced by a variational approximation. Collisions between shuttling or coaccelerating soliton pairs do not alter the character of the dynamical regime. Finally, regimes of the shuttle motion, coacceleration, and splitting are corroborated by simulations of the original GPE system, with the explicitly present OL potential.

Three-dimensional localized Airy-Cartesian and Airy-helical-Cartesian wave packets in free space

We have analytically investigated three-dimensional (3D) Airy-Cartesian (AiC) and Airy-helical-Cartesian (AiHC) wave packets by solving the (3+1)-dimensional free space Schrödinger equation. The complex amplitude of the AiC and AiHC wave packets is described by the product of the Hermite polynomials, the Gaussian functions, and the Airy functions. We find that the AiC and AiHC wave packets will gradually spread along the propagation distances, but attenuate along the time domain. The distributions of the radiation force depend on the distribution factor. In addition, the chirp factor has the effect of the energy concentration of the wave packets. The different 3D spatiotemporal profiles, the photoelasticity, and vortex rings can be obtained by choosing different values of the mode number, the distribution factor, the chirp factor, the initial velocity, and the propagation distances.

Observation of linear plasmonic breathers and adiabatic elimination in a plasmonic multi-level coupled system

We provide experimental and numerical demonstrations of plasmonic propagation dynamics in a multi-level coupled system, and present the first observation of plasmonic breathers propagating in such systems. The effect is observed both for the simplest symmetric case of a thin metal layer surrounded by two identical dielectrics, and also for a more complex system that includes five and more layers. By a careful choice of the permittivities and thicknesses of the intermediate layers, we can adiabatically eliminate the plasmonic waves in all the intermediate interfaces, thus enabling efficient vertical delivery and extraction of plasmonic signals between the top layer and deeply buried layers. The observation relies on controlling the excited mode by breaking the symmetry of excitation, which is crucial for obtaining the results experimentally. We also observe this breathing effect for transversely shaped plasmonic beams, with Hermite-Gauss, Airy and Weber wavefronts, that despite the oscillatory nature of propagation in such systems, still preserve all their unique wavefront properties. Finally, we show that such approaches can be extended to plasmonic propagation in a general multi-layered system, opening a path for efficient three-dimensional integrated plasmonic circuitry.

Interactions between self-accelerating beams in photorefractive media

We investigate interactions between in-phase or out-of-phase Airy beams and nonlinear accelerating beams in photorefractive crystals by means of direct numerical simulations. Since self-accelerating beams possess infinite energy, we evaluated the propagation of two shifted counter beams by truncating the oscillating tails. The numerical results show that the external bias electric field has a profound effect on the propagation dynamics and the solitons shed from the Airy beam. We also found that during interactions between two nonlinear accelerating beams, single solitons, soliton pairs, and bound breathing solitons were produced. When the nonlinear accelerating beam collides with a soliton beam, the main lobe continues accelerating while the soliton intensity fluctuates with the lobes.

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.

Suppression of collapse for two-dimensional Airy beam in nonlocal nonlinear media

Dynamics and collapse of two-dimensional Airy beams are investigated numerically in nonlocal nonlinear media with split step Fourier transform method. In particular, the stability and self-healing properties of the Airy beams depend crucially on the location and topological charge of the vortex when the beams carry angular momentum. The propagation of abruptly autofocusing Airy beams is also demonstrated in local and nonlocal media. In strongly self-focusing regime, with the help of nonlocality, stationary propagation of two-dimensional Airy beams can be obtained, which always collapse in local nonlinear media.

Propagation properties and radiation forces of the Airy Gaussian vortex beams in a harmonic potential

We investigate the propagation properties and the radiation forces of Airy Gaussian vortex (AiGV) beams in a harmonic potential analytically and numerically in this paper. Obtaining the propagation expression of AiGV beams by solving the dimensionless linear (2+1) D Schrödinger equation in a harmonic potential, we perform the track, the intensity and phase distributions, the propagation shapes, the energy flow and the angular momentum of AiGV beams in a harmonic potential with the method of numerical simulations. The trajectory acting like a cosine curve is shown. Periodic inversion and phase oscillation are demonstrated during propagation. The influence of the distribution factor and the vortex factor on the propagation of AiGV beams in a harmonic potential are discussed. Likewise, the motion of the Poynting vector and the angular momentum is elucidated respectively. As for the radiation forces, we explore the gradient and scattering forces on Rayleigh dielectric particles induced by AiGV beams. In particular, it's found that the value of the scattering force is approximately seven orders of magnitude larger than that of the gradient force during the propagation in a harmonic potential.

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.

Airy-type solitary wave in highly noninstantaneous Kerr media

We investigate the dynamics of a decelerating Airy pulse in the highly noninstantaneous Kerr media. It is found that the deceleration of the Airy pulse can be counteracted by the highly noninstantaneous nonlinearity. When the power of the pulse is specifically chosen, the deceleration of the Airy pulse can be totally restrained, and an Airy-type solitary wave is observed within several dispersion lengths.

Two-dimensional χ2 solitons generated by the downconversion of Airy waves

Conversion of truncated Airy waves (AWs) carried by the second-harmonic (SH) component into axisymmetric χ² solitons is considered in a 2D system with quadratic nonlinearity. The spontaneous conversion is driven by the parametric instability of the SH wave. The input in the form of the AW vortex is also considered. As a result, one, two, or three stable solitons emerge in a well-defined form, unlike the recently studied 1D setting, where the picture is obscured by radiation jets. Shares of the total power captured by the emerging solitons and conversion efficiency are found as functions of parameters of the AW input.

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.

Three-dimensional localized Airy-Hermite-Gaussian and Airy-Helical-Hermite-Gaussian wave packets in free space

We have investigated the 3D Airy-Hermite-Gaussian and Airy-Helical-Hermite-Gaussian wave packets by solving the (3+1)D free-space Schrödinger equation in Cartesian coordinates analytically. The complex amplitudes of these wave packets are described by the product of the superposition of two Airy functions, the Hermite-Gaussian functions and the helical Hermite-Gaussian functions. The different 3D spatiotemporal profiles, the photoelastics and vortex rings can be obtained by selecting different values of the following parameters: the mode number, the decay factor and the propagation distance.

Dual accelerating Airy-Talbot recurrence effect

We demonstrate the dual accelerating Airy-Talbot recurrence effect, i.e., the self-imaging of accelerating optical beams, by propagating a superposition of Airy beams with successively changing transverse displacements. The dual Airy-Talbot effect is a spontaneous recurring imaging of the input and of the input with alternating component signs. It results from the constructive interference of Airy wave functions, which is also responsible for other kinds of Airy beams, for example, Airy breathers. An input composed of finite-energy Airy beams also displays the dual Airy-Talbot effect, but it demands a large transverse displacement and diminishes fast along the propagation direction.

Generation of χ(2) solitons from the Airy wave through the parametric instability

Spontaneous creation of solitons in quadratic media by the downconversion (i.e., parametric instability against the generation of fundamental-frequency excitations) from the truncated Airy-wave (AW) mode in the second-harmonic component is studied. Parameter regions are identified for the generation of one, two, and three solitons, with additional small-amplitude "jets." Shares of the total power carried by individual solitons are found. Also considered are soliton patterns generated by the downconversion from a pair of AWs bending in opposite directions.

Soliton formation by decelerating interacting Airy beams

We demonstrate a new type of soliton formation arising from the interaction of multiple two-dimensional Airy beams in a nonlinear medium. While in linear regime, interference effects of two or four spatially displaced Airy beams lead to accelerated intensity structures that can be used for optical induction of novel light guiding refractive index structures, the nonlinear cross-interaction between the Airy beams decelerates their bending and enables the formation of straight propagating solitary states. Our experimental results represent an intriguing combination of two fundamental effects, accelerated optical beams and nonlinearity, together enable novel mechanisms of soliton formation that will find applications in all-optical light localization and switching architectures. Our experimental results are supported by corresponding numerical simulations.

Spatiotemporal dynamics of counterpropagating Airy beams

We analyse theoretically the spatiotemporal dynamics of two incoherent counterpropagating Airy beams interacting in a photorefractive crystal under focusing conditions. For a large enough nonlinearity strength the interaction between the two Airy beams leads to light-induced waveguiding. The stability of the waveguide is determined by the crystal length, the nonlinearity strength and the beam’s intensities and is improved when comparing to the situation using Gaussian beams. We further identify the threshold above which the waveguide is no longer static but evolves dynamically either time-periodically or even chaotically. Above the stability threshold, each Airy-soliton moves erratically between privileged output positions that correspond to the spatial positions of the lobes of the counterpropagating Airy beam. These results suggest new ways of creating dynamically varying waveguides, optical logic gates and chaos-based computing.

Anharmonic propagation of two-dimensional beams carrying orbital angular momentum in a harmonic potential

We analytically and numerically investigate an anharmonic propagation of two-dimensional beams in a harmonic potential. We pick noncentrosymmetric beams of common interest that carry orbital angular momentum. The examples studied include superposed Bessel-Gauss (BG), Laguerre-Gauss (LG), and circular Airy (CA) beams. For the BG beams, periodic inversion, phase transition, and rotation with periodic angular velocity are demonstrated during propagation. For the LG and CA beams, periodic inversion and variable rotation are still there but not the phase transition. On the whole, the "center of mass" and the orbital angular momentum of a beam exhibit harmonic motion, but the motion of the beam intensity distribution in detail is subject to external and internal torques and forces, causing it to be anharmonic. Our results are applicable to other superpositions of finite circularly asymmetric beams.

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.

Periodic inversion and phase transition of finite energy Airy beams in a medium with parabolic potential

We study periodic inversion and phase transition of normal, displaced, and chirped finite energy Airy beams propagating in a parabolic potential. This propagation leads to an unusual oscillation: for half of the oscillation period the Airy beam accelerates in one transverse direction, with the main Airy beam lobe leading the train of pulses, whereas in the other half of the period it accelerates in the opposite direction, with the main lobe still leading - but now the whole beam is inverted. The inversion happens at a critical point, at which the beam profile changes from an Airy profile to a Gaussian one. Thus, there are two distinct phases in the propagation of an Airy beam in the parabolic potential - the normal Airy and the single-peak Gaussian phase. The length of the single-peak phase is determined by the size of the decay parameter: the smaller the decay, the smaller the length. A linear chirp introduces a transverse displacement of the beam at the phase transition point, but does not change the location of the point. A quadratic chirp moves the phase transition point, but does not affect the beam profile. The two-dimensional case is discussed briefly, being equivalent to a product of two one-dimensional cases.

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.