Realizing a Gauss hypergeometric beam described as ₂F₁ (a, b, c; x²) by Bessel spiral zone plate

Abstract

The apodizing spiral zone plate with Bessel functions shows interesting focusing behavior in the generation of a variety of uni- and multiannular (specially biannular) azimuthal and annular vortex beams carrying screw and annular phase dislocation. Theoretically, studies utilizing scalar diffraction integrals show generation of hypergeometric ${{}_{2}F}_1(a,b,c;x^2)$ beams. Then, considering two important parameters, the order of the Bessel functions and topological charge, their impacts and roles in the features of the generated focused beams are examined. Simulation and experimental results are in very good agreement with each other.

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