Airy-Gauss beams and their transformation by paraxial optical systems

Bandres, Miguel A.; Gutiérrez-Vega, Julio C.

doi:10.1364/oe.15.016719

Cited by 251 publications

(153 citation statements)

References 9 publications

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“…Airy beams which are regarded as the zeroth-order Olver beams attract the attention of a lot of scientists of the laser community [24]- [30]. These zeroth-order Olver (Airy) beams have been the subject of many other studies in various optical systems, be it aligned, misaligned, turbulence, crystal, Kerr media [31]- [36] or others. More recently, Liu et al [37] have obtained an approximate analytical expression for the propagation of an Airy-Gaussian beams passing through an ABCD optical system with a rectangular annular aperture.…”

Section: Introductionmentioning

confidence: 99%

Propagation Properties of Finite Olver-Gaussian Beams Passing through a Paraxial ABCD Optical System

Hennani¹,

Ez-zariy²,

Belafhal³

2015

OPJ

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In this paper, an exact analytical propagation formula of Finite Olver-Gaussian Beams (FOGBs) passing through a paraxial ABCD optical system is developed and some numerical examples are performed. The propagation properties of the FOGBs through general optical systems characterized by given ABCD matrix are studied on the basis of the generalized Huygens-Fresnel diffraction integral, which permits to show the behavior of this laser beams family and its properties depending of the laser parameters. This research is of interest to prove some investigations done in the past by other researchers.

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Section: Introductionmentioning

confidence: 99%

Propagation Properties of Finite Olver-Gaussian Beams Passing through a Paraxial ABCD Optical System

Hennani¹,

Ez-zariy²,

Belafhal³

2015

OPJ

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“…To have a quasi-diffractive behavior we want to avoid this as much as possible; therefore, the finite accelerating parabolic beams However the expected value of u (i.e., the centroid of the beam), ͗u͑s͒͘ = ͐͐u͉ n ͉ 2 dudv / ͉͐͐ n ͉ 2 dudv, of a finite-energy accelerating parabolic beam can be defined, and it is given by ͗u͑s͒͘ = ͗u͑0͒͘ + 2Im͑a͒s, where ͗u͑0͒͘ is the centroid at s = 0, and ͗v͑s͒͘ =0 by parity. Therefore, as for the finite-energy Airy beam [3,8,9], the propagation of the accelerating parabolic beam's centroid follows exactly the expected geometrical path. Also, the accelerating parabolic beams follow the same transformation laws as the Airy beams while propagating through ABCD optical systems [9].…”

Section: ͑9͒mentioning

confidence: 73%

“…Therefore, as for the finite-energy Airy beam [3,8,9], the propagation of the accelerating parabolic beam's centroid follows exactly the expected geometrical path. Also, the accelerating parabolic beams follow the same transformation laws as the Airy beams while propagating through ABCD optical systems [9].…”

Section: ͑9͒mentioning

confidence: 73%

Accelerating parabolic beams

Bandres

2008

Opt. Lett.

Self Cite

130

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We demonstrate the existence of accelerating parabolic beams that constitute, together with the Airy beams, the only orthogonal and complete families of solutions of the two-dimensional paraxial wave equation that exhibit the unusual ability to remain diffraction-free and freely accelerate during propagation. Since the accelerating parabolic beams, like the Airy beams, carry infinite energy, we present exact finite-energy accelerating parabolic beams that still retain their unusual features over several diffraction lengths. © 2008 Optical Society of America OCIS codes: 050.1940, 260.1960.5500.Recently Siviloglou et al. [1][2][3] called the attention of the optics community by demostrating the existence of the accelerating Airy beams. These beams are finite-energy solutions of the paraxial wave equation that have the unusual ability to remain diffraction free while having a quadratic transverse shift during propagation over long distances. The pure Airy beams are perfectly diffractionless and have a quadratic transverse shift during propagation but cannot be physically realizable, because they have infinite energy. However, the Airy beams have finite energy and retain these unusual properties over long distances.In this Letter, we introduce the accelerating parabolic beams and prove that they are, together with the two-dimensional Airy beams, the only orthogonal and complete family of explicit solutions of the twodimensional paraxial wave equation that remain diffraction free and freely accelerate during propagation. We also introduce a finite-energy version of the accelerating parabolic beams that can be physically realizable and exhibit the unusual properties of the ideal accelerating parabolic beams over a finite propagation distance.We begin our analysis by considering the normalized paraxial wave equation ٌ 2 + i‫ץ‬ s = 0, where ٌ 2 = ‫ץ‬ uu + ‫ץ‬ vv , ͑u , v͒ = ͑x , y͒ / represents the dimensionless transverse coordinates, is an arbitrary transverse scale, s = z /2k 2 is the normalized propagation distance, and k is the wave number.We know that the desired properties of the beam, that is, to remain diffraction free and to exhibit a transverse translation during propagation, can be expressed by ͉͑u,v,s͉͒ = ͉͑u + ⌬͑s͒,v,0͉͒, ͑1͒

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“…The field distribution ( ) 0 , 0 E x z = of finite Airy-Gaussian beam at plane source in the rectangular coordinate system is expressed as follows [13] [31] ( ) a . Furthermore, it should be noted that the intensity maximum decreases with the increasing of 0 a , in the both cases: finite Airy and finite Airy-Gaussian beams.…”

Section: Theorymentioning

confidence: 99%

Propagation Characteristics of Airy-Gaussian Beams Passing through a Misaligned Optical System with Finite Aperture

Ez-zariy¹,

Hennani²,

Nebdi³

et al. 2014

OPJ

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Propagation characteristics of finite Airy-Gaussian beams through an apertured misaligned firstorder ABCD optical system are studied. In this work, the generalized Huygens-Fresnel diffraction integral and the expansion of the hard aperture function into a finite sum of complex Gaussian functions are used. The propagation of Airy-Gaussian beam passing through: an unapertured misaligned optical system, an apertured aligned ABCD optical system and an unapertured aligned ABCD optical system are derived here as particular cases of the main finding. Some numerical simulations are performed in the paper.

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Airy-Gauss beams and their transformation by paraxial optical systems

Cited by 251 publications

References 9 publications

Propagation Properties of Finite Olver-Gaussian Beams Passing through a Paraxial ABCD Optical System

Propagation Properties of Finite Olver-Gaussian Beams Passing through a Paraxial ABCD Optical System

Accelerating parabolic beams

Propagation Characteristics of Airy-Gaussian Beams Passing through a Misaligned Optical System with Finite Aperture

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