Airy Wave Packets Research Articles

Highly efficient Airy beam generator with high polarization purity by a receiving-transmitting metasurface

This paper presents a highly efficient Airy beam generator at microwave frequency using a transparent metasurface with a receiving-transmitting scheme. The amplitude and phase of the transmitted orthogonal polarization wave can be flexibly controlled by orientation angles of receiving and transmitting patches of the proposed meta-atom. Utilizing this property to reshape the field of transmitted waves following the desired phase and amplitude profile of the Airy wave packet, an Airy beam generator is designed and experimentally demonstrated. Simulation and measurement results both show a self-healing Airy beam with an efficiency of 23.5% and polarization purity above 20 dB, which approaches the theoretical limitation of the designed Airy beam. Due to the well-performed beam efficiency and polarization purity resulting from the receiving-transmitting metasurface, our design holds great promise for efficient wavefront shaping and facilitates the use of high-purity Airy beams for practical applications.

Exact and Paraxial Broadband Airy Wave Packets in Free Space and a Temporally Dispersive Medium

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 paraxial geometry. The time-diffraction technique that has been motivated by the Lorentz invariance of the equation governing the narrow angular spectrum and narrowband temporal spectrum paraxial approximation has been used to derive finite-energy spatiotemporally confined subluminal, luminal, and superluminal Airy wave packets. The goal in this article is to provide novel exact finite-energy broadband spatio-temporally localized Airy solutions (a) to the scalar wave equation in free space; (b) in a dielectric medium moving at its phase velocity; and (c) in a lossless second-order temporally dispersive medium. Such solutions can be useful in practical applications involving broadband (few-cycle) wave packets.

Energy densities in quantum mechanics

Quantum mechanics does not provide any ready recipe for defining energy density in space, since the energy and coordinate do not commute. To find a well-motivated energy density, we start from a possibly fundamental, relativistic description for a spin-12 particle: Dirac's equation. Employing its energy-momentum tensor and going to the non-relativistic limit we find a locally conserved non-relativistic energy density that is defined via the Terletsky-Margenau-Hill quasiprobability (which is hence selected among other options). It coincides with the weak value of energy, and also with the hydrodynamic energy in the Madelung representation of quantum dynamics, which includes the quantum potential. Moreover, we find a new form of spin-related energy that is finite in the non-relativistic limit, emerges from the rest energy, and is (separately) locally conserved, though it does not contribute to the global energy budget. This form of energy has a holographic character, i.e., its value for a given volume is expressed via the surface of this volume. Our results apply to situations where local energy representation is essential; e.g. we show that the energy transfer velocity for a large class of free wave-packets (including Gaussian and Airy wave-packets) is larger than its group (i.e. coordinate-transfer) velocity.

Airy-type bichromatic wave pulses on the sea surface and generation of rogue waves

We present a theoretical study of bichromatic weakly non-collinear Airy-type waves propagating with various amplitudes in water of infinite depth. The coupled nonlinear Schrödinger equations are invoked to study the behavior of self- and cross-interacting Airy wave packets. We demonstrate that bichromatic pulses possess the main properties of single Airy wave packets—shape invariance and self-acceleration or self-deceleration—when propagating in a dispersive medium. Accounting for nonlinearity leads to a strong dependence of the structure, stability, and propagation velocity of wave pulses on their amplitude. We show that interacting pulses of Airy-type waves can form giant accelerating and decelerating waves.

Exact and paraxial Airy propagation of relativistic electron plasma wavepackets

The different forms of propagation of relativistic electron plasma wavepackets in terms of Airy functions are studied. It is shown that exact solutions can be constructed showing accelerated propagations along coordinates transverse to the thermal speed cone coordinate. Similarly, Airy propagation is a solution for relativistic electron plasma waves in the paraxial approximation. This regime is considered in time domain, when paraxial approximation is considered for frequency, and in space domain, when paraxial approximation is considered for wavelength. In both different cases, the wavepackets remain structured in the transverse plane. Using these solutions we are able to define generalized and arbitrary Airy wavepackets for electron plasma waves, depending on arbitrary spectral functions. Examples of this construction are presented. These electron plasma Airy wavepackets are the most general solutions of this kind.

Observation of Bohm trajectories and quantum potentials of classical waves

In 1952 David Bohm proposed an interpretation of quantum mechanics, in which the evolution of states results from trajectories governed by classical equations of motion but with an additional potential determined by the wave function. There exist only a few experiments that test this concept and they employed weak measurement of non-classical light. In contrast, we reconstruct the Bohm trajectories in a classical hydrodynamic system of surface gravity water waves, by a direct measurement of the wave packet. Our system is governed by a wave equation that is analogous to the Schrödinger equation which enables us to transfer the Bohm formalism to classical waves. In contrast to a quantum system, we can measure simultaneously their amplitude and phase. In our experiments, we employ three characteristic types of surface gravity water wave packets: two and three Gaussian temporal slits and temporal Airy wave packets. The Bohm trajectories and their energy flows follow the valleys and bounce off the hills in the corresponding quantum potential landscapes.

Trajectory analysis of phase effects associated with truncated Airy beams

Airy wave packets constitute a very peculiar type of structured light: during their propagation, their transverse profile undergoes a self-accelerating displacement while it remains shape invariant. They are thus the only non-dispersive beam-type solution to the Helmholtz paraxial equation in free space. Such properties are possible by virtue of their infinite power content. However, experimentally, Airy beams can only be reproduced in an approximate manner, with a limited extension and hence a finite power content. To this end, differentcutoffprocedures have been reported in the literature, based on a convenient tuning of the transmission properties of aperture functions. In this Communication, we present and discuss our latest advances in the analysis of the effects that convolving an Airy beam with different aperture functions have on their propagation properties. More specifically, we make use of a trajectory-based methodology, which allows us to analyze and explain the beam propagation in terms of trajectories directly connected with the beam local phase variations.

Partially coherent Airy beams: A cross-spectral-density approach

Airy beams are known for displaying shape invariance and self-acceleration along the transverse direction while they propagate forwards. Although these properties could be associated with the beam coherence, it has been revealed that they also manifest in the case of partially coherent Airy-type. Here, these properties are further investigated by introducing and analyzing a class of partially coherent Airy beams under both infinite and finite energy conditions. The key element within the present approach is the so-called cross-spectral density, which enables a direct connection with the quantum density matrix, making the analysis exportable to the quantum realm to study the dynamics of Airy wave packets acted by both incoherence and decoherence. As it is shown, in the case of infinite energy beams both properties are preserved even under the circumstance of total incoherence provided the underlying structure of the beam remains equal to that of an Airy beam. In the case of finite energy beams, a situation closer to a realistic scenario, as experimental beams cannot have an infinite extension, it is shown that a propagation range along which both properties are preserved can be warranted. This is controlled by a critical distance, which depends on the spread range determined by the parameters ruling the extension of random field spatial fluctuations. Such a distance is determined by defining a position-dependent parameter that quantifies the degree of overlapping between the propagated beam and the input one displaced by an amount equivalent to the propagation distance.

Mutual manipulation between a dark soliton and an Airy pulse at the optical event horizon

A fiber-optical analog of the event horizon is proposed via the collision dynamics between a dark soliton and an Airy pulse for the first time, under the effect of soliton-induced Kerr nonlinear effect. An Airy wave packet is more effective in manipulating the properties of a dark soliton than a Gaussian-like pulse in the regime of the optical event horizon since the Airy-soliton horizon can be regarded as the successively isolated horizon processes. Besides, the initial chirp and attenuation factor are two key regulators of the Airy pulse, which can not only adjust the flatness and width of the output spectrum during the collision process but also modify the properties of the output dark soliton. The interesting dynamic investigated in this work as a process of mutual manipulation can be considered as a promising candidate for frequency conversion and broadband supercontinuum generation, which proves the theory basis for further understanding of the light-by-light controlling in a more controllable manner.

Terahertz emission from curved plasma filaments induced by two-color 2D Airy wave packets.

We experimentally demonstrate that 2D Airy wave packets can produce intense curved two-color filaments that emit terahertz (THz) radiation with unique characteristics. Due to the curvature of the plasma channel, THz waves, emitted from different longitudinal regions of the plasma, propagate in different directions resulting in non-concentric THz cones in the far-field. These cones have different cone angles and polarization which we attribute to the way the two-color 2D Airy driving fields are produced in the nonlinear crystal and then propagate to form the curved plasma filament.

Arbitrarily accelerating space-time wave packets.

All known realizations of optical wave packets that accelerate along their propagation axis, such as Airy wave packets in dispersive media or wave-front-modulated X-waves, exhibit a constant acceleration; that is, the group velocity varies linearly with propagation. Here we synthesize space-time wave packets that travel in free space with arbitrary axial acceleration profiles, including group velocities that change with integer or fractional exponents of the distance. Furthermore, we realize a composite acceleration profile: the wave packet accelerates from an initial to a terminal group velocity, before decelerating back to the initial value. These never-before-seen optical-acceleration phenomena are produced using the same experimental arrangement that precisely sculpts the wave packet's spatio-temporal spectral structure.

Fractionality-induced deformation in Airy and Hermit-Gaussian wavepackets traveling through the Gaussian wells

In this study, we investigate the transport properties of Airy and Hermit-Gaussian wavepackets traveling through a Gaussian potential well in the standard and fractional media. We use a split step Fourier method to solve the corresponding two-dimensional fractional nonlinear linear Schrodinger equation. We study the interference phenomenon, Huygens principle and trapping properties of the system in different situations. For this purpose, the position of the system has also selected inside the potential well to consider the wavepacket evolution. Then, the effect of the well and incident wavepackets parameters on the evolution the transport properties of employed wavepackets have properly been considered.

Self-healing of a heralded single-photon Airy beam.

Self-healing of an Airy beam during propagation is of fundamental interest and also promises important applications. Despite many studies of Airy beams in the quantum regime, it is unclear whether an Airy beam only including a single photon can heal after passing an obstacle because the photon may be blocked. Here we experimentally observe self-healing of a heralded single-photon Airy beam. Our observation implies that an Airy wave packet is robust against obstacle caused distortion and can restore even at the single-photon level.

Superoscillations in Finite-Energy Airy Beams

Superoscillations naturally arise in optical fields with dense packing of nodal points of amplitude. Airy wave packets are highly oscillatory and rich of phase singularities. We study to the best of our knowledge, for the first time, the superoscillatory behavior in a band-limited Airy beam whose spectrum is sharply truncated. Our results show that not as expected, the superoscillations occur outside of the Airy-like region, but in regions above a defining line where the beam stops being Airy-like. The degree of superoscillation can be very high there.

Nondiffracting gravitational waves

It is proved that accelerating nondiffracting gravitational Airy wave-packets are solutions of linearized gravity. It is also showed that Airy functions are exact solutions to Einstein equations for non-accelerating nondiffracting gravitational wave-packets.

Classical analog to the Airy wave packet

The solution of the Liouville equation for the ensemble of free particles is presented and the classical analog to the quantum accelerating Airy wave packet is constructed and discussed. Considering the motion of various classical packets – with an infinite and restricted distribution of velocities of particles – and also the motion of their fronts, we demonstrate in the simplest and most definite way why the packet can display a more sophisticated behaviour (even acceleration) as compared with a free individual particle that moves at a fixed velocity. A comparison of this classical solution with the quantum one in the Wigner representation of quantum mechanics, which provides the closest analogy, is also presented.

Quantum Mechanical and Optical Analogies in Surface Gravity Water Waves

We present the theoretical models and review the most recent results of a class of experiments in the field of surface gravity waves. These experiments serve as demonstration of an analogy to a broad variety of phenomena in optics and quantum mechanics. In particular, experiments involving Airy water-wave packets were carried out. The Airy wave packets have attracted tremendous attention in optics and quantum mechanics owing to their unique properties, spanning from an ability to propagate along parabolic trajectories without spreading, and to accumulating a phase that scales with the cubic power of time. Non-dispersive Cosine-Gauss wave packets and self-similar Hermite-Gauss wave packets, also well known in the field of optics and quantum mechanics, were recently studied using surface gravity waves as well. These wave packets demonstrated self-healing properties in water wave pulses as well, preserving their width despite being dispersive. Finally, this new approach also allows to observe diffractive focusing from a temporal slit with finite width.

Recovery time of matter Airy beams using the path integral quantum trajectory model

Abstract Following their discovery in the late 1970s, optical Airy beams have found numerous applications in technologies such as microscopy and optical trapping, many of which are based on the wave packets’ unique features such as zero or minimal diffraction, self-acceleration, and self-healing. Recent advancements have shown that Airy beams can also be produced using matter waves with many of the same unique characteristics of their optical counterparts. We present here a study of the recovery time of damaged matter Airy wave packets in free space and a nonlinear Kerr-type medium. We show that in free space the recovery time increases approximately linearly with mass and is independent of other kinematical parameters such as momentum, velocity, and spatial width. In the Kerr-type medium, recovery time is decreased compared to free space and does not scale linearly with mass. In order to study matter Airy beams, we introduce the Path Integral Quantum Trajectory model as a new computational tool for the study of non-relativistic, quantum mechanical wave packets and demonstrate its effectiveness in dealing with heavy particle dynamics.

The control of intensity peak dynamics for paraxial waves

Since the theoretical discovery of Airy wave packet and its experimental confirmation, numerous attempts of manipulating the intensity peak dynamics have been made using the Airy function as the starting point of the analysis. In this paper, we propose a methodology of identifying local properties of the initial condition for the propagation equation that influence the dynamics. Based on this approach, one can construct numerical initial conditions that satisfy a desired dynamic by making use of the above-mentioned local properties.

Storage of Airy wavepackets based on electromagnetically induced transparency.

The research of Airy beams has attained much attention due to their unique characteristics. Coherent control of Airy beams is important for further light beam manipulation and information processing. In this paper, we experimentally investigate the storage and retrieval of 2D Airy wavepackets in a solid-state medium driven by electromagnetically induced transparency (EIT). The transverse profile of the weak probe pulse is modulated by Airy wavepackets. Under EIT condition, the probe Airy wavepackets are stored into the experimental medium by manipulating the intensity of the control field, and later retrieved by the opposite process. The retrieved Airy wavepackets keep a high similarity compared with those before the storage. Furthermore, the self-healing property of the retrieved Airy wavepackets is investigated. This storage of Airy wavepackets develops the control method of Airy beams, which will be useful in further applications.