Phase singularities in beams

Brand, G. F.

doi:10.1119/1.19191

Cited by 30 publications

(10 citation statements)

References 21 publications

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“…The situation is similar with the results in [9], where the Fraunhofer diffraction of a plane wave by forked gratings is treated. The authors solved the problem in cylindrical coordinates, performing the integration over the azimuthal variable only.…”

Section: Introductionsupporting

confidence: 80%

“…Optical vortices have attracted an increased interest and have become very important in optical trapping and manipulation of small particles. Among the optical elements which generate optical vortex beams are phase spiral plate [1,2,3], helical axicon [4,5,6], forked grating [7,8,9,10], spiral zone plates [11]. It was recognized by Allen et al [12] for the first time that a beam with helical wavefront characterized by azimuthal phase ( ) ϕ il exp , where ϕ is the azimuthal coordinate, l is an integer, posses an orbital angular momentum per photon, in its propagation direction.…”

Section: Introductionmentioning

confidence: 99%

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Fresnel and Fraunhofer diffraction of a Gaussian laser beam by fork-shaped gratings

Janicijevic

Topuzoski

2008

J. Opt. Soc. Am. A

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Expressions describing the vortex beams that are generated by the process of Fresnel diffraction of a Gaussian beam incident out of waist on fork-shaped gratings of arbitrary integer charge p, and vortex spots in the case of Fraunhofer diffraction by these gratings, are deduced. The common general transmission function of the gratings is defined and specialized for the cases of amplitude holograms, binary amplitude gratings, and their phase versions. Optical vortex beams, or carriers of phase singularity with charges mp and -mp, are the higher negative and positive diffraction-order beams. The radial part of their wave amplitudes is described by the product of the mpth-order Gauss-doughnut function and a Kummer function, or by the first-order Gauss-doughnut function and the difference of two modified Bessel functions whose orders do not match the singularity charge value. The wave amplitude and the intensity distributions are discussed for the near and far fields in the focal plane of a convergent lens, as well as the specialization of the results when the grating charge p=0; i.e., the grating turns from forked into rectilinear. The analytical expressions for the vortex radii are also discussed.

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Section: Introductionsupporting

confidence: 80%

Section: Introductionmentioning

confidence: 99%

Fresnel and Fraunhofer diffraction of a Gaussian laser beam by fork-shaped gratings

Janicijevic

Topuzoski

2008

J. Opt. Soc. Am. A

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“…4). The forked patterns are usually calculated by computer and then made as Computer Generated Holograms (CGHs) with either transmittance modulation 18,19 or blazed phase modulation. 20…”

Section: Forked Conventional (Isotropic) Gratingsmentioning

confidence: 99%

Controlling orbital angular momentum using forked polarization gratings

2010

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We examine a novel method to control the orbital angular momentum (OAM) of lightwaves using forked polarization gratings (FPGs). We significantly improve the fabrication of FPGs and achieve substantially higher quality and efficiency than prior work. This is obtained by recording the hologram of two orthogonally polarized beams with phase singularities introduced by q-plates. As a single compact thin-film optical element, an FPG can control the OAM state of light with higher efficiency and better flexibility than current methods, which usually involve many bulky optical elements and are limited to lower OAM states. Our simulations confirm that FPGs work as polarization-controlled OAM state ladder operators that raise or lower the OAM states (charge l) of incident lightwaves, by the topological charge (l g ) on the FPGs, to new OAM states (charge l ± l g ). This feature allows us to generate, detect, and modify the OAM state with an arbitrary and controllable charge. An important application of FPGs are the essential state controlling elements in quantum systems based on OAM eigenstates, which may enable extreme high capacity quantum computation and communication.

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“…rich technology is available for generation [18][19][20][21]23], transformation [22] and measurement [23][24][25] of beams carrying OAM, as well as for the transfer of quantum information between polarization and spatial degrees of freedom [26][27][28].…”

mentioning

confidence: 99%

Arbitrary orbital angular momentum addition in second harmonic generation

et al. 2014

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We demonstrate second harmonic generation performed with optical vortices with different topological charges imprinted on orthogonal polarizations. Besides the intuitive charge doubling, we implement arbitrary topological charge addition on the second harmonic field using polarization as an auxiliary parameter.Besides their intrinsic beauty, optical beams carrying orbital angular momentum (OAM) have proved to be a powerful tool for encoding and processing quantum information. First order Laguerre-Gaussian and Hermite-Gaussian (HG) modes carry the mathematical structure of a qubit [1] and allow for a two-qubit encoding when combined with polarization of a single photon. The interplay between the two degrees of freedom leads to interesting applications, including topological phases [2,3], quantum cryptography [4][5][6], Bell inequalities [7-9], quantum logic gates [10][11][12], and quantum teleportation [13][14][15]. Polarization controlled spatial correlations between entangled photon pairs were first demonstrated in [16,17]. Nowadays, a

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Phase singularities in beams

Cited by 30 publications

References 21 publications

Fresnel and Fraunhofer diffraction of a Gaussian laser beam by fork-shaped gratings

Fresnel and Fraunhofer diffraction of a Gaussian laser beam by fork-shaped gratings

Controlling orbital angular momentum using forked polarization gratings

Arbitrary orbital angular momentum addition in second harmonic generation

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