Accelerating and abruptly autofocusing matter waves

Efremidis, Nikolaos K.; Paltoglou, Vassilis; Klitzing, Wolf von

doi:10.1103/physreva.87.043637

Cited by 91 publications

(60 citation statements)

References 33 publications

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“…In addition, light can follow curved trajectories in periodic array configurations by utilizing the Floquet structure of the system [24][25][26][27]. Besides optics, curved and accelerated waves have been considered in different settings such as in electron beams [28], in matter waves [29], and in antenna arrays [30]. * nefrem@tem.uoc.gr Up to now most of the studies on Airy wave have been limited to uniform media.…”

Section: Introductionmentioning

confidence: 99%

Accelerating beam propagation in refractive-index potentials

Efremidis

2014

Phys. Rev. A

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We study the dynamics of spatially accelerating beams impinging on refractive-index potentials. We concentrate our attention to the particular case of Airy-type optical waves that are reflected and transmitted by two generic classes of potentials. These are (a) localized potentials whose index contrast reduces to zero outside a specific region and (b) smooth-interface sigmoid-type potentials that take different constant values outside a bounded region. We find analytic expressions for the beam dynamics for particular types of potentials which are in excellent agreement with the numerical simulations. Our results show that, in general, the parabolic trajectory of the Airy wave is not maintained by the transmitted and reflected waves. An exception is made in the case of reflection from piecewise linear potentials, where the reflected wave follows a parabolic trajectory that is, in general, different from the incident.

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Section: Introductionmentioning

confidence: 99%

Accelerating beam propagation in refractive-index potentials

Efremidis

2014

Phys. Rev. A

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“…Bose-Einstein condensates [16], the surface of a metal [17][18][19][20][21], atomic vapors with electromagnetically induced transparency [22], chiral media [23], photonic crystals [24], and so on. All along, special attention has been focused on Airy [1,2] and Bessel beams [25].…”

mentioning

confidence: 99%

“…Compared to that, interactions between Airy beams have attracted little attention. Although radially symmetric Airy beams display self-focusing in a nonlinear (NL) medium [7,16,28], the interaction between two Airy beams with varying distance between them has not been studied much. Until now, the experimental observation of Airy beams [2], Airy beams in NL materials [5,14], and accelerating nonlinear beams [26,29,30] in NL materials has been reported.…”

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confidence: 99%

Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear media

et al. 2014

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Abstract:We investigate numerically interactions between two in-phase or out-of-phase Airy beams and nonlinear accelerating beams in Kerr and saturable nonlinear media in one transverse dimension. We discuss different cases in which the beams with different intensities are launched into the medium, but accelerate in opposite directions. Since both the Airy beams and nonlinear accelerating beams possess infinite oscillating tails, we discuss interactions between truncated beams, with finite energies. During interactions we see solitons and soliton pairs generated that are not accelerating. In general, the higher the intensities of interacting beams, the easier to form solitons; when the intensities are small enough, no solitons are generated. Upon adjusting the interval between the launched beams, their interaction exhibits different properties. If the interval is large relative to the width of the first lobes, the generated soliton pairs just propagate individually and do not interact much. However, if the interval is comparable to the widths of the maximum lobes, the pairs strongly interact and display varied behavior.

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“…It has to be mentioned that, vice versa, programming in the Fourier domain is used to generate the angular components for Airy beams with spatial light modulators [55]. A link between the Fourier transform and the ray concept can be constructed on the basis of the spatial transfer function (STF) which adds a certain angular spread to the geometrical rays in the far field.…”

Section: Optical Information In the Fourier Plane In Classical Framementioning

confidence: 99%

Propagation and wavefront ambiguity of linear nondiffracting beams

Grünwald

Böck

2014

SPIE Proceedings

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Ultrashort-pulsed Bessel and Airy beams in free space are often interpreted as "linear light bullets". Usually, interconnected intensity profiles are considered a "propagation" along arbitrary pathways which can even follow curved trajectories. A more detailed analysis, however, shows that this picture gives an adequate description only in situations which do not require to consider the transport of optical signals or causality. To also cover these special cases, a generalization of the terms "beam" and "propagation" is necessary. The problem becomes clearer by representing the angular spectra of the propagating wave fields by rays or Poynting vectors. It is known that quasi-nondiffracting beams can be described as caustics of ray bundles. Their decomposition into Poynting vectors by Shack-Hartmann sensors indicates that, in the frame of their classical definition, the corresponding local wavefronts are ambiguous and concepts based on energy density are not appropriate to describe the propagation completely. For this reason, quantitative parameters like the beam propagation factor have to be treated with caution as well. For applications like communication or optical computing, alternative descriptions are required. A heuristic approach based on vector field based information transport and Fourier analysis is proposed here. Continuity and discontinuity of far field distributions in space and time are discussed. Quantum aspects of propagation are briefly addressed.

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Accelerating and abruptly autofocusing matter waves

Cited by 91 publications

References 33 publications

Accelerating beam propagation in refractive-index potentials

Accelerating beam propagation in refractive-index potentials

Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear media

Propagation and wavefront ambiguity of linear nondiffracting beams

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