scispace - formally typeset
Search or ask a question
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.
Abstract: A 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.
Citations
More filters
Journal ArticleDOI
01 Sep 2021-Optik
TL;DR: In this article, the model of controllable anomalous hollow beam (CAHB) is proposed and the analytical expression of CAHB propagating in A B C D paraxial optical systems is derived.

5 citations

Journal ArticleDOI
TL;DR: In this article, an analytical expression of an elliptical Bessel beam (EBB) is deduced on the basis of the angular spectrum decomposition (ASD) method, starting from an ellipsis Bessel-like profile in the initial transverse plane.
Abstract: An analytical expression of an elliptical Bessel beam (EBB) is deduced on the basis of the angular spectrum decomposition (ASD) method, starting from an elliptical Bessel-like profile in the initial transverse plane. The angular spectrum representation is also obtained for another approximate EBB that is produced by the refraction of a circular Bessel beam at an interface in oblique incidence. The expressions are further expanded into a series of vector spherical harmonic functions for describing the scattering of the beams by a spherical particle. Numerical calculations are implemented with different parameters and the results are discussed. A length parameter is obtained for evaluating the variation of the EBB along the propagation. It is confirmed that the refracted CBB at small incident angle behaves in a similar way to the EBB. When the incident angle increases, the asymmetry of the transverse beam profile becomes serious and the propagation of the beam deviates gradually from the predicted direction.

2 citations

Proceedings ArticleDOI
01 Dec 2008
TL;DR: In this paper, the authors reported the experimental generation of a high-quality partially coherent dark hollow beam (DHB) by coupling a partially coherent beam into a multimode fiber with a suitable incidence angle.
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 multimode fiber, the quality and the coherence of the generated partially coherent DHB are closely controlled by the coherence of the input beam A partially coherent elliptical DHB is generated through focusing the generated partially coherent DHB with a cylindrical lens

1 citations

Journal ArticleDOI
TL;DR: In this paper, a technique for generating a structurally stable hyperbolic beam using Fourier transform holography is reported, and the resulting beam keeps its shape unchanged up to ~45 cm.
Abstract: A technique for generation of a structurally stable hyperbolic beam using Fourier transform holography is reported. Bessel function with their arguments having hyperbolic locus is used for generating a diffractive optical element (DOE). For the introduction of optical vortex a circular vortex term is used. However, it is also possible to generate such beams without any optical vortex term. Both the techniques have their own advantages. The resultant DOE is illuminated with a collimated beam and proper filtering of its Fourier transform generates the expected hyperbolic beam. The resultant beam keeps its shape unchanged up to ~45 cm.

1 citations

References
More filters
Book
01 Jan 1966
TL;DR: In this article, the authors present a model for vector analysis based on the Calculus of Variations and the Sturm-Liouville theory, which includes the following: Curved Coordinates, Tensors.
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.

7,811 citations

Journal ArticleDOI
TL;DR: In this paper, exact nonsingular solutions of the scalar-wave equation for beams that are non-diffracting were presented, which means that the intensity pattern in a transverse plane is unaltered by propagating in free space.
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.

2,283 citations

Book
01 Jan 1964

2,100 citations