The topological charge TC of an electromagnetic wave is relate with their wavefront spatial distribution. Electromagnetic waves with factor azimuthal exp(ilθ) in its phase, have TC integer (l=m) or non-integer (l=M). These electromagnetic waves with a well-defined of TC can be produced in the visible regime by computer generated holographic masks with fork shaped. In this paper, we study the formed triangle lattice distribution in the intensity Fraunhofer regime using numerical simulations of the Bessel-Gauss beams with integer and non-integer TC. The beam is diffracted by equilateral triangular aperture to measure both their sign and magnitude. In addition, we showed the experimental results of the intensity in far field regime product of diffraction of Bessel-Gauss beams with integer and noninteger TC by the equilateral triangular aperture. Partial and qualitative explanations have been proposed for the diffraction of electromagnetic beams with topological charge. This paper presents a complete analysis for qualitative and quantitative explanation of diffraction of a beam with topological charge by a triangular aperture. The results of such diffraction are obtained by numerical simulation or experimentally.
This work develops a brief proposal to achieve the superposition of two opposite vortex beams, both with integer or non-integer mean value of the orbital angular momentum. The first part is about the generation of this kind of spatial light distributions through a modified Brown and Lohmann's hologram. The inclusion of a simple mathematical expression into the pixelated grid's transmittance function, based in Fourier domain properties, shifts the diffraction orders counterclockwise and clockwise to the same point and allows the addition of different modes. The strategy is theoretically and experimentally validated for the case of two opposite rotation helical wavefronts.
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