Finite Energy Airy Beams Research Articles

Virtual source for an Airy beam

We identify a virtual source for generating an Airy wave. A spectral integral expression is derived to describe the Airy wave, which, in the paraxial limit, yields the freely accelerating, nondiffracting, and finite energy Airy beam. From the spectral representation of the Airy wave, the first two orders of nonparaxial corrections to the paraxial Airy beam are determined. Also, a connection between the obtained Airy wave and the well-known complex source point spherical wave is given.

Negative propagation effect in nonparaxial Airy beams

Negative propagation is an unusual effect concerning the local sign change in the Poynting vector components of an optical beam under free propagation. We report this effect for finite-energy Airy beams in a subwavelength nonparaxial regime. This effect is due to a coupling process between propagating and evanescent plane waves forming the beam in the spectral domain and it is demonstrated for a single TE or TM mode. This is contrary to what happens for vector Bessel beams and vector X-waves, for which a complex superposition of TE and TM modes is mandatory. We also show that evanescent waves cannot contribute to the energy flux density by themselves such that a pure evanescent Airy beam is not physically realizable. The break of the shape-preserving and diffraction-free properties of Airy beams in a nonparaxial regime is exclusively caused by the propagating waves. The negative propagation effect in subwavelength nonparaxial Airy beams opens new capabilities in optical traps and tweezers, optical detection of invisibility cloacks and selective on-chip manipulation of nanoparticles.

An “Airy gun”: Self-accelerating solutions of the time-dependent Schrödinger equation in vacuum

We consider generalizations of the Berry and Balazs nonspreading and accelerating solution of the time-dependent Schrödinger equation in empty space, which has been experimentally demonstrated in paraxial optics. In particular, we show that the original nonspreading wave packet is unstable. An explicit variation of the initial Airy-state evolves into the self-accelerating and self-compressing solution presented here. Quasi-diffraction-free finite energy Airy beams that are more realistic for experimental study are obtained by analytic continuation and their Wigner function is evaluated. Nonlinear generalizations related to second Painlevé transcendents are briefly discussed.

The optical Airy transform and its application in generating and controlling the Airy beam

We propose an optical Airy transform in this paper, and obtain the analytical expressions for the Airy transform of fundamental Gaussian beams and finite energy Airy beams. The setup for performing the optical Airy transform is presented. The Airy transform for Gaussian beams and finite energy Airy beams are theoretically calculated and analyzed. Our results show that the Airy beam can be conveniently generated and controlled through the optical Airy transform of the Gaussian beam. The optical Airy transform also can be used to directly modulate the beam parameters of the incident Airy beam, and it can transform the incident Airy beam into the Gaussian beam.

Reduced side-lobe Airy beams

The primary interest in the finite-energy Airy beam derives from the special properties possessed by the maximum intensity at its central lobe. However, the defining spatial dependence, the Airy function, is an oscillatory function that consists of decaying side lobes. For some applications these side lobes may create deleterious effects. Fortunately, a nonsymmetric apodization of the beam in Fourier space is shown to enhance the central lobe as the side lobes are reduced and clipped. The properties of the central lobe are unaffected over a large proportion of the propagation path.

Propagation of Airy-related beams

New types of finite energy Airy beams are proposed. We consider two different types of beams, namely, beams that are obtained as blocked and exponentially attenuated versions of Airy functions Ai and Bi, and beams of finite width but having the Airy functions typical phase. All of them show very interesting properties, such as parabolic trajectories for longer propagation distances, profile evolution exhibiting less diffraction, or better definiteness of the main peak, when compared with other finite energy Airy beams studied before.

Contribution of the internal topological structure of optical Airy beams to opticalbehaviors

The influence of the internal topological structure of optical Airy beams on the opticalbehavior is numerically analyzed and experimentally verified. The Airy beams can bedivided into several different parts, and the isolated and the interactional topologicalstructures are investigated in detail. The results show that each topological structure bearsdifferent functions and the optical properties are attributed to the topological structure ofAiry beams. A new method is presented to generate the finite-energy Airy beams based ontopological structure. It is believed that this study will provide useful information forfurther applications and production of Airy beams in various optical systems.

Electrically switchable finite energy Airy beams generated by a liquid crystal cell with patterned electrode

A pair of electrically switchable finite energy Airy beams is generated by a liquid crystal (LC) cell, where one electrode is patterned by a photomask with a binary-phase pattern. Applying voltage across the LC cell, an index modulation is produced due to the liquid crystal molecules realignment, and the finite energy Airy beams can be generated or erased corresponding to the phase difference between the regions with and without electrode. The diffraction-free and transverse acceleration dynamics of this binary-phase element based finite energy Airy beams were experimentally verified, exhibiting excellent agreement with the theory.

A note on an accelerating finite energy Airy beam

A recently derived Airy beam solution to the (1+1)D paraxial equation is shown to obey two salient properties characterizing arbitrary finite energy solutions associated with second-order diffraction; the centroid of the beam is a linear function of the range and its variance varies quadratically in range. Some insight is provided regarding the local acceleration dynamics of the beam. It is shown, specifically, that the interpretation of this beam as accelerating, i.e., one characterized by a nonlinear lateral shift, depends significantly on the parameter a entering into the solution.