Abstract
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. Consequently, the questions of how to properly design the spatial manipulation of Airy beams or how to implement them in different setups have become important and timely in the development of various optical devices. Here, based on our previous work, we present a short review on the spatial control of Airy beams, including the interactions of Airy beams in nonlinear media, beam propagation in harmonic potential, and the dynamics of abruptly autofocusing Airy beams in the presence of a dynamic linear potential. We demonstrate that, under the guidance of nonlinearity and an external potential, the trajectory, acceleration, structure, and even the basic properties of Airy beams can be adjusted to suit specific needs. We describe other fascinating phenomena observed with Airy beams, such as self-Fourier transformation, periodic inversion of Airy beams, and the appearance of spatial solitons in the presence of nonlinearity. These results have promoted the development of Airy beams, and have been utilized in various applications, including particle manipulation, self-trapping, and electronic matter waves.
Highlights
Diffraction is a fundamental phenomenon in physical optics, due to which beams bend and spread, and the peak intensity of the beam decreases upon propagation
The Schrödinger equation (SE) for a quantum particle moving in free space is written as:
∂ψ h2 ∂2 ψ ih where his the reduced Planck’s constant and m is the particle mass. This equation describes the development of the wave function ψ of the particle, but in appropriate units it could describe the development of an Airy wave packet
Summary
Diffraction is a fundamental phenomenon in physical optics, due to which beams bend and spread, and the peak intensity of the beam decreases upon propagation. In 2009, Ellenbogen et al produced an Airy beam in an asymmetrically modulated quadratic optical NL medium by the three-wave mixing process [30] This novel nonlinear generation method produced an Airy beam at a new wavelength and a higher energy, and provided new possibilities for manipulating the dynamics of Airy beams in NL media [31,32,33,34,35]. Immense research work has been devoted to Airy beams, from theoretical predications to experimental verifications, from fundamental research to potential applications Without doubt, it has become one of the hottest developing fields in linear and nonlinear optics [47,48,49,50].
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