Hypergeometric laser beams in a parabolic waveguide
V.V. Kotlyar, A.A. Kovalev, A.G. Nalimov

Full text of article: Russian language.

Abstract:
Expression for a complex amplitude of paraxial hypergeometric laser beams, propagated in a gradient parabolic waveguide is obtained. Wide class of mode solves of Helmholtz equation in cylindrical coordinates for a gradient parabolic medium is received. This solves are proportion to Kummer functions, but only those have limited energy (physical able), which is equal to Laguerre-Gauss modes. A part of gradient parabolic fiber is considered as a parabolic micro lens, equations for numerical aperture and focal spot full width half maximum are obtained for it. Focal spot diameter can be less then a diffraction limit in a medium with a refraction number is equal to the diffraction number of the lens optical axis. Strict formulation for rings radii of a binar lens, which approximates gradient parabolic lens is obtained.

Key words:
hypergeometric beams, gradient lens, binar lens, waveguide modes, parabolic lens.

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