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 profil...
The various forms of Airy’s differential equation are discussed in this work, together with the special functions that arise in the processes of their solutions. Further properties of the arising integral functions are discussed, and their conn...
Airy beams represent an important type of non-diffracting beams—they are the only non-diffracting wave in one dimension, and thus they can be produced with a cylindrical geometry that modifies a wavefront in one dimension. In this paper, we show the...
In order to study the transmission characteristics of Airy beams in the plasma sheath, the flow field around a hypersonic vehicle was numerically simulated and analyzed based on the Navier–Stokes (N-S) equation and a turbulence model. Then, acc...
Owing to their nondiffracting, self-accelerating, and self-healing properties, Airy beams of different nature have become a subject of immense interest in the past decade. Their interesting properties have opened doors to many diverse applications. C...
In recent years, structured light with novel propagation properties has attracted great attention. Among these structured beams, the Airy beam is one of the most representative and widely used beams. In this paper, we propose a kind of quadruple Gaus...
The propagation characteristics of a single Airy beam in nonlinear Kerr media were numerically investigated by utilizing the split-step Fourier transform method. We show that in addition to normal breathing solitons, the anomalous bound states of Air...
We report a deep penetration microscopic imaging method with a non-diffracting Airy beam. The direct mapping of volume imaging in free space shows that the axial imaging range of the Airy beam is approximately 4 times that of the traditional Gaussian...
In this paper, we generated polarization-independent ring-Airy beams by designing metasurfaces that can realize modulations of both phase and amplitude. In numerical simulation, such metasurfaces are designed by placing subwavelength rectangular slit...
A family of 2D light fields consisting of the product of three Airy functions with linear arguments has been studied theoretically and experimentally. These fields, called three-Airy beams, feature a parameter shift and have a cubic phase and a super...
Orbital angular momentum (OAM) carried by bi-photon entangled Airy beams in unstable oceanic turbulence is theoretically investigated. The analytical expression of the spatial coherence radius of a spherical wave in the unstable stratification oceani...
A new power-exponent-phase vortex beam with nonlinear phase winding has shown flexible control freedom compared with conventional vortex beams. In order to further enrich the modulation freedom and expand the ability of self-healing to meet current a...
Airy beams exhibit enormous application potential in the field of optics and microwave owing to their unique self-bending, self-accelerating, and non-diffracting characteristics. In this paper, the Airy beams are dynamically generated and manipulated...
The paper concerns the solution of the ordinary differential equation
We generate an ultrafast Airy beam with a mode-locked fiber laser. A diffractive optical element is placed inside the laser cavity and applies phase modulation on the pulses propagating in the cavity. The pulsed Airy beam is then obtained by Fourier...
The propagation characteristics of Airy beams in an inhomogeneous medium with periodic potential are studied theoretically and numerically. The Gross–Pitaevskii equation was solved with periodic potential using the separating variables method,...
Based on the second-order moments, the analytical expression of the beam propagation factor of a cosh-Airy beam has been derived. The beam propagation factor was determined by the decay factor and the cosh parameter. Because the beam propagation fact...
Airy beams are an intriguing type of non-diffraction wave packet that can exist in one-dimensional (1D) curved orbital plane systems. These beams have gained significant attention due to their unique properties, including non-diffraction, self-healin...
Theoretical predictions of laser beam interactions with jet-engine-exhaust-induced turbulence are of importance for optimization of various optical systems, including LIDARs and airborne laser measurement systems. This paper is based on the extended...
We investigate the interactions of in-phase Airy beams modulated by a fundamental Gaussian beam and fourth-order diffraction in Kerr nonlinear media. Directly numerical simulations show that normal (anomalous) fourth-order diffraction and an in-phase...
We construct the Green functions (or Feynman’s propagators) for the Schrödinger equations of the form
Airy beams showing curved paths have found extensive applications in fields such as optical trapping, biomedical analysis, and material processing. Despite their utility, dynamic control of Airy beams poses a significant challenge. This work investig...
We investigate a lensless Airy-type optical beam generated by direct Fresnel propagation of a Gaussian apodized real space cubic phase. Starting from the scalar Fresnel diffraction integral, we derive a closed-form expression showing that the propaga...
In this work, our primary focus is on the numerical computation of highly oscillatory integrals involving the Airy function. Specifically, we address integrals of the form
A question of physical importance is whether finite-energy spatiotemporally localized (i.e., pulsed) generalizations of monochromatic accelerating Airy beams are feasible. For luminal solutions, this question has been answered within the framework of...
The orbital angular momentum (OAM) holography has been marked a path to achieving ultrahigh capacity holographic information systems. However, the practical applicability of the OAM holography is limited by the complicated optical setup and unadjusta...
We theoretically analyze the methodology for obtaining vectorial three-dimensional bullets, concretely Airy–Gauss bullets. To do this, binary micro zonal plates (BZP) were designed in order to obtain different Airy–Gauss bullets with sub-...
Almost all of the beams under propagation are believed to suffer severe distortion when the source coherence deteriorates, due to the optical diffraction. This implies that low-coherence beams have poor self-healing ability, but were found to be robu...
The supercontinuum generation and manipulation of Airy-Gaussian pulses in a photonic crystal fiber with three zero-dispersion points are studied using the split-step Fourier method. Firstly, the spectral evolution of Airy-Gaussian pulses in four phot...
The remarkable properties of magnetic nanostructures have sparked considerable interest within the biomedical domain, owing to their potential for diverse applications. In targeted drug delivery systems, therapeutic molecules can be loaded onto magne...
Focal depth tuning provides an effective way to enhance the longitudinal flexibility of circular Airy beams (CABs). In this work, we investigate the control of focal depth in CABs by introducing an adjustable amplitude coefficient and varying the ape...
Integrating multiple independent functions into a single optical component is one of the most important topics in research on photoelectric systems. In this paper, we propose a multifunctional all-dielectric metasurface that can achieve a variety of...
This paper presents a stress-function-based finite element formulation for two-dimensional elastoplastic plane-stress problems with holes. The Airy stress function is used as the primary global unknown, and the resulting non-homogeneous biharmonic eq...
The notion of k-symbol special functions has recently been introduced. This new concept offers many interesting geometric properties for these special functions including logarithmic convexity. The aim of the present paper is to exploit essentially t...
Based on the angular spectrum expansion, the spatial Goos–Hänchen (GH) shift of an Airy vortex beam reflected from the graphene/hexagonal boron nitride (hBN) heterostructure is investigated analytically. The influences of graphene/hBN hete...
A universal formula of the beam quality factor for a partially coherent Airy (PCA) beam in non-Kolmogorov turbulence has been investigated. Results of numerical simulation display that expanding the internal scales of non-Kolmogorov turbulence is goo...
The propagation dynamics of two-dimensional (2D) ring-Airy beams is studied in the framework of the fractional Schrödinger equation, which includes saturable or cubic self-focusing or defocusing nonlinearity and Lévy index ((LI) alias for...
The propagation of many kinds of structured light beams in uniaxial crystal has been investigated. However, the investigation of the evolution of these structured light beams after the uniaxial crystal is lacking. In this paper, an evolution formula...
The tight focusing properties of circular partially coherent radially polarized circular Airy vortex beams (CPCRPCAVBs) are theoretically studied in this paper. After deriving the cross-spectral density matrix of CPCRPCAVBs in the focal region of a h...
We investigate the propagation properties of circular Airy beams (CABs) with propagational fractional-order optical vortices (OVs). The superposition of the phase singularity and polarization singularity from a vortex vector beam (VVB) plays a signif...
Circular airy beam (CAB) is a kind of new structured light with non-diffracting, self-focusing, and self-healing properties. Due to its wide applications, recently, numerous researchers have used various methods to modulate this kind of beam. We theo...
The match between the orbital angular momentum (OAM) transmission and receipt is a prerequisite for vortex beams as a carrier of the wireless optical communication system in free space. However, the vortex splitting induced by atmospheric turbulence...
This paper presents a rapid approach for the dynamic separation of radial polarization (R-pol) and azimuthal polarization (A-pol) components in circular Airy vortex beams (CAVBs) by utilizing the linear electro-optic (EO) effect in uniaxial crystals....
This report bridges fundamental ideas from introductory calculus to advanced concepts in quantum mechanics and nonlinear dynamics. Beginning with the behavior of second derivatives in oscillatory and exponential functions, it introduces the Airy equa...
We study the quantum radiation of particle production by vacuum from an ultra-relativistic moving mirror (dynamical Casimir effect) solution that allows (possibly for the first time) analytically calculable time evolution of particle creation and an...
In their treatment of the Airy-Laguerre-Gaussian equation, Zhong, Belic and Zhang constructed an alternative solution for the azimuthal case [...]
Circular airy vortex beams (CAVBs) have attracted much attention due to their “abruptly autofocusing” effect, phase singularity, and their potential applications in optical micromanipulation, communication, etc. In this paper, we numerica...
The use of potential fields in fluid dynamics is retraced, ranging from classical potential theory to recent developments in this evergreen research field. The focus is centred on two major approaches and their advancements: (i) the Clebsch transform...
A generalized model of the variable permeability in the transition layer is introduced in this work. This model can handle flows with a small Darcy number and might be useful in controlling permeability amplifications. A solution method for the resul...
The optical tweezer is one of the important techniques for contactless manipulation in biological research to control the motion of tiny objects. For three-dimensional (3D) optical manipulation, shaped light beams have been widely used. Typically, sp...
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