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Hypergeometric-Gaussian Modes

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 Added by Ebrahim Karimi
 Publication date 2007
  fields Physics
and research's language is English




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We studied a novel family of paraxial laser beams forming an overcomplete yet nonorthogonal set of modes. These modes have a singular phase profile and are eigenfunctions of the photon orbital angular momentum. The intensity profile is characterized by a single brilliant ring with the singularity at its center, where the field amplitude vanishes. The complex amplitude is proportional to the degenerate (confluent) hypergeometric function, and therefore we term such beams hypergeometric gaussian (HyGG) modes. Unlike the recently introduced hypergeometric modes (Opt. Lett. {textbf 32}, 742 (2007)), the HyGG modes carry a finite power and have been generated in this work with a liquid-crystal spatial light modulator. We briefly consider some sub-families of the HyGG modes as the modified Bessel Gaussian modes, the modified exponential Gaussian modes and the modified Laguerre-Gaussian modes.



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We present a novel family of paraxial optical beams having a confluent hypergeometric transverse profile, which we name hypergeometric Gauss modes of type-II (HyGG-II). These modes are eigenmodes of the photon orbital angular momentum and they have the lowest beam divergence at waist of HyGG-II among all known finite power families of paraxial modes. We propose to exploit this feature of HyGG-II modes for generating, after suitable focusing, a light needle having record properties in terms of size and aspect ratio, possibly useful for near-field optics applications.
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