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Journal ArticleDOI

Generation of an elliptic hollow beam using Mathieu and Bessel functions

01 Sep 2006-Journal of The Optical Society of America A-optics Image Science and Vision (Optical Society of America)-Vol. 23, Iss: 9, pp 2278-2282

TL;DR: A new (to the authors' knowledge) technique for the generation of a propagation-invariant elliptic hollow beam is reported, which avoids the use of the radial Mathieu function and hence is mathematically simpler.

AbstractA new (to our knowledge) technique for the generation of a propagation-invariant elliptic hollow beam is reported. It avoids the use of the radial Mathieu function and hence is mathematically simpler. Bessel functions with their arguments having elliptic locus are used to generate the mask, which is then recorded using holographic technique. To generate such an elliptic beam, both the angular Mathieu function, i.e., elliptic vortex term, and the expression for the circular vortex are used separately. The resultant mask is illuminated with a plane beam, and the proper filtering of its Fourier transform generates the expected elliptic beam. Results with both vortex terms are satisfactory. It has been observed that even for higher ellipticity the vortices do not separate.

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Citations
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Journal Article
Abstract: We report the first experimental generation of high-order Mathieu beams and confirm their propagation invariance over a limited range. In our experiment we use a computer-generated phase hologram. The peculiar behaviour of the vortices in Mathieu beams gives rise to questions about their orbital-angular-momentum content, which we calculate by performing a decomposition in terms of Bessel beams.

102 citations

Journal ArticleDOI
TL;DR: The experimental generation of a high-quality partially coherent dark hollow beam (DHB) is reported by coupling a partially coherent beam into a multimode fiber (MMF) with a suitable incidence angle by closely controlled coherence of the input beam.
Abstract: We report the experimental generation of a high-quality partially coherent dark hollow beam (DHB) by coupling a partially coherent beam into a multimode fiber (MMF) with a suitable incidence angle. The interference experiment of the generated partially coherent DHB passing through double slits is demonstrated. It is found that the coupling efficiency of the MMF, the quality, and the coherence of the generated partially coherent DHB are closely controlled by the coherence of the input beam.

84 citations


Cites background from "Generation of an elliptic hollow be..."

  • ...Over the past several years, dark-hollow beams (DHBs) with zero central intensity have been widely investigated both theoretically and experimentally due to their wide applications in atomic optics, free space optical communications, optical trapping of particles and life sciences [1-14]....

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Journal ArticleDOI
Abstract: The on-axis scintillation index for a circular dark hollow beam (DHB) propagating in a weak turbulent atmosphere is formulated, and the scintillation properties of a DHB are investigated in detail. The scintillation index for a DHB reduces to the scintillation index for a Gaussian beam, an annular beam and a flat-topped beam under certain conditions. It is found that the scintillation index of a DHB is closely related to the beam parameters and can be lower than that of a Gaussian beam, an annular beam and a flat-topped beam in a weak turbulent atmosphere at smaller waist sizes and longer propagation lengths.

77 citations

Journal ArticleDOI
TL;DR: The scintillation properties of astigmatic dark hollow beams (DHBs) in weak atmospheric turbulence were investigated and it was found that dark size, beam waist size, and wavelength can be smaller than that of a stigmatic DHB and that of stigmatic and astigmatic flat-topped, annular, and Gaussian beams inWeak atmospheric turbulence particularly at long propagation ranges.
Abstract: The scintillation properties of astigmatic dark hollow beams (DHBs) in weak atmospheric turbulence were investigated in detail. An explicit expression for the on-axis scintillation index of an astigmatic DHB propagating in weak atmospheric turbulence was derived. It was found that the scintillation index value of an astigmatic DHB with suitable astigmatism (i.e., ratio of the beam waist size in the x direction to that in the y direction), dark size, beam waist size, and wavelength can be smaller than that of a stigmatic DHB and that of stigmatic and astigmatic flat-topped, annular, and Gaussian beams in weak atmospheric turbulence particularly at long propagation ranges. Our results will be useful in long-distance free-space optical communications.

59 citations

Journal ArticleDOI
Yahong Chen1, Lin Liu1, Fei Wang1, Chengliang Zhao1, Yangjian Cai1 
TL;DR: Analytical propagation formula for an elliptical LGCSM beam passing through a stigmatic ABCD optical system is derived and the experimental results are consistent with the theoretical predictions.
Abstract: A new kind of partially coherent beam with non-conventional correlation function named elliptical Laguerre-Gaussian correlated Schell-model (LGCSM) beam is introduced. Analytical propagation formula for an elliptical LGCSM beam passing through a stigmatic ABCD optical system is derived. The elliptical LGCSM beam exhibits unique features on propagation, e.g., its intensity in the far field (or in the focal plane) displays an elliptical ring-shaped beam profile, being qualitatively different from the circular ring-shaped beam profile of the circular LGCSM beam. Furthermore, we carry out experimental generation of an elliptical LGCSM beam with controllable ellipticity, and measure its focusing properties. Our experimental results are consistent with the theoretical predictions. The elliptical LGCSM beam will be useful in atomic optics.

55 citations


References
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Book
01 Jan 1966
Abstract: Vector Analysis. Curved Coordinates, Tensors. Determinants and Matrices. Group Theory. Infinite Series. Functions of a Complex Variable I. Functions of a Complex Variable II. Differential Equations. Sturm-Liouville Theory. Gamma-Factrial Function. Bessel Functions. Legendre Functions. Special Functions. Fourier Series. Integral Transforms. Integral Equations. Calculus of Variations. Nonlinear Methods and Chaos.

7,810 citations

01 Jan 1970

4,231 citations

Book
01 Jan 1964

2,077 citations

Journal ArticleDOI
Abstract: We present exact, nonsingular solutions of the scalar-wave equation for beams that are nondiffracting. This means that the intensity pattern in a transverse plane is unaltered by propagating in free space. These beams can have extremely narrow intensity profiles with effective widths as small as several wavelengths and yet possess an infinite depth of field. We further show (by using numerical simulations based on scalar diffraction theory) that physically realizable finite-aperture approximations to the exact solutions can also possess an extremely large depth of field.

2,074 citations