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.
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TL;DR: In this article, the superposition of the Bessel and Mirrored Bessel beams and their self-healing characteristics using the defined similarity function have been investigated, quantitatively, using the Huygens convolution method.
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TL;DR: In this paper, the propagation properties of partially coherent anomalous hollow beams in uniaxial crystals and in free space are studied numerically and comparatively, and it is found that the propagation property of partially coherence anomalous beams in the free space behaves very differently from those in the non-free space.
Abstract: Analytical propagation formulae for partially coherent anomalous hollow beams in uniaxial crystals are derived. Paraxial propagation of partially coherent anomalous hollow beams in uniaxial crystals orthogonal to the optical axis is investigated based on the beam propagation equations. The propagation properties of partially coherent anomalous hollow beams in uniaxial crystals and in free space are studied numerically and comparatively. It is found that the propagation properties of partially coherent anomalous hollow beams in uniaxial crystals behave very differently from those in free space and are closely determined by the parameters of the uniaxial crystals and the initial coherence width. The uniaxial crystals provide an effective way for generating astigmatic beams.
11 citations
TL;DR: Based on the generalized Huygens-Fresnel diffraction integral, a closed-form propagation equation related to sine-Gaussian beams through a cylindrical lens and a focusing lens is derived and illustrated with numerical methods as mentioned in this paper.
Abstract: Based on the generalized Huygens–Fresnel diffraction integral, a closed-form propagation equation related to sine-Gaussian beams through a cylindrical lens and a focusing lens is derived and illustrated with numerical methods. It is found that a sine-Gaussian beam through such a system may be converted into a dark hollow beam (DHB) with topological charge index one and its bright enclosure is approximately an elongated ellipse with very high ellipticity. Moreover, the parameter values at which the DHBs have perfect intensity patterns are designed. The optimal relative orientation between the dislocation line of the input sine-Gaussian beam and the axial orientation of the cylindrical lens is specified. And the ellipticity of the elliptical DHBs is mainly defined by the focal length of the cylindrical lens and the Fresnel number of the optical system.
10 citations
TL;DR: In this paper, the authors derived the source field expressions of different Mathieu beams, including infinite summations of J-type Bessel functions and their Gaussian counterparts, by plotting the source intensities of such beams, the variations of the related profiles are examined against the changes in the source parameters.
Abstract: We derive the source field expressions of different Mathieu beams. In particular, Mathieu beams consisting of the infinite summations of J-type Bessel functions and their Gaussian counterparts are studied. Mathieu beams based on the summation of I-type Bessel functions are introduced as well. By plotting the source intensities of such beams, the variations of the related profiles are examined against the changes in the source parameters. It is found that, via the adjustment of these parameters, it is possible to obtain completely new beam configurations and also those similar to the existing beams of the present literature.
5 citations
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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.
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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.
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