## Generation of an elliptic hollow beam using Mathieu and Bessel functions

JOSA A, Vol. 23, Issue 9, pp. 2278-2282 (2006)

http://dx.doi.org/10.1364/JOSAA.23.002278

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### 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.

© 2006 Optical Society of America

**OCIS Codes**

(090.0090) Holography : Holography

(090.1760) Holography : Computer holography

(140.0140) Lasers and laser optics : Lasers and laser optics

(140.3300) Lasers and laser optics : Laser beam shaping

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: January 12, 2006

Revised Manuscript: March 8, 2006

Manuscript Accepted: March 9, 2006

**Citation**

Rijuparna Chakraborty and Ajay Ghosh, "Generation of an elliptic hollow beam using Mathieu and Bessel functions," J. Opt. Soc. Am. A **23**, 2278-2282 (2006)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-9-2278

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