Automatic Fourier transform and self-Fourier beams due to parabolic potential

Zhang, Yiqi; Liu, Xing; Belić, Milivoj R.; Zhong, Wei‐Ping; Petrović, Milan S.

doi:10.1016/j.aop.2015.10.006

Cited by 47 publications

(22 citation statements)

References 46 publications

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“…Clearly, if α = 1, Equations (14) and (15) have the same form, so that both equations have the same solutions but expressed in real (x) and inverse (k) spaces [63], respectively. As before, we are interested in the behavior of Airy beams.…”

Section: One-dimensional Airy Beamsmentioning

confidence: 99%

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Guided Self-Accelerating Airy Beams—A Mini-Review

et al. 2017

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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.

show abstract

Section: One-dimensional Airy Beamsmentioning

confidence: 99%

“…In the one-dimensional (1D) case, the paraxial propagation of a beam in a linear medium with an external harmonic potential is described by the following equation [63,64]:…”

Section: One-dimensional Airy Beamsmentioning

confidence: 99%

Guided Self-Accelerating Airy Beams—A Mini-Review

et al. 2017

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“…(14) leads to the corresponding equation in the inverse space: Clearly, if α = 1, Eqs. (14) and (15) have the same form, so that both equations have the same solutions but expressed in real (x) and inverse (k) spaces [58], respectively. As before, we are interested in the behavior of Airy beams.…”

Section: One-dimensional Airy Beamsmentioning

confidence: 99%

“…In the one-dimensional (1D) case, the paraxial propagation of a beam in a linear medium with an external harmonic potential is described by the following equation [58,59]:…”

Section: One-dimensional Airy Beamsmentioning

confidence: 99%

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Guided Self-Accelerating Airy Beams—A Mini-Review

Zhang¹,

Zhong²,

Belić³

et al. 2017

Preprint

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Owing to the 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 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 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.

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Manipulation of Airy Beams in Dynamic Parabolic Potentials

et al. 2020

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The propagation of finite energy Airy beams in dynamic parabolic potentials, including uniformly moving, accelerating, and oscillating potentials, is investigated. The propagation trajectories of Airy beams are strongly affected by the dynamic potentials, but the periodic inversion of the beam remains invariant. The results may broaden the potential applications of Airy beams, and also enlighten ideas on Airy beam manipulation in nonlinear regimes.

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Automatic Fourier transform and self-Fourier beams due to parabolic potential

Cited by 47 publications

References 46 publications

Guided Self-Accelerating Airy Beams—A Mini-Review

Guided Self-Accelerating Airy Beams—A Mini-Review

Guided Self-Accelerating Airy Beams—A Mini-Review

Manipulation of Airy Beams in Dynamic Parabolic Potentials

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Automatic Fourier transform and self-Fourier beams due to parabolic potential

Cited by 47 publications

References 46 publications

Guided Self-Accelerating Airy Beams—A Mini-Review

Guided Self-Accelerating Airy Beams—A Mini-Review

Guided Self-Accelerating Airy Beams&mdash;A Mini-Review

Manipulation of Airy Beams in Dynamic Parabolic Potentials

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Guided Self-Accelerating Airy Beams—A Mini-Review