Paraxial hypergeometric laser beams with singularity in the center of the waist
A.A. Kovalev, V.V. Kotlyar, S.N. Khonina, V.A. Soifer

Image Processing Systems Institute оf the RAS,
Samara State Aerospace University (SSAU)

Full text of article: Russian language.

Abstract:
We study a new two-parameter family of paraxial laser beams generated by initial complex amplitude consisting of four cofactors: Gaussian beam, logarithmic axicon, spiral phase plate (or angular harmonic), and the amplitude reciprocal function with a singularity at the origin. In the near field, complex amplitude of these beams is proportional to the degenerate hypergeometric function, and thus the beams are called hypergeometric. If the Gaussian beam is replaced by a plane wave, these beams change into hypergeometric modes preserving their shape up to scale on propagation in space. The cross-section intensity distribution of these beams is similar to that of the Bessel modes and consists of a set of concentric alternating light and dark rings.

Key words:
paraxial laser beams, hypergeometric function, Bessel modes.

Citation: Kovalev AA, Kotlyar VV, Khonina SN, Soifer VA. Paraxial hypergeometric laser beams with singularity in the center of the waist [In Russian]. Computer Optics 2007; 31(1): 9-13.

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