Abstract
A new method of the generation of superposition of Kummer beam is introduced by the illumination of a fractional radial Hilbert transform (FRHT) system with an apertured spiral phase plate (SPP) instrument by a Li’s flattened Gaussian (LFTG) beam. To study the propagation properties of the produced beam, two main approximate analytical expressions are developed. The first one concerns the SPP integer topological charges and the second one is about the non-integer ones. From the both principle formulas devoted, some studies about the generation of the Kummer beam, with integer and non-integer topological charges, by the conversion of a fundamental Gaussian beam and the propagation of the LFTG beams through a FRHT system without apertured SPP are deduced in this work as special investigations of the main studies. For reason to determine the effects of the incident beam parameters and the optical system coefficients on the propagation characteristics of the created beam, several numerical calculations are carried out, analyzed and discussed in the work. Simples concluding remarks are outlined in the end of the paper.
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Ez-zariy, L., Belafhal, A. The conversion of a Li’s flat-topped-Gaussian beam to a superposition of Kummer dark hollow beam by the illumination of a fractional radial Hilbert transform system. Opt Quant Electron 48, 331 (2016). https://doi.org/10.1007/s11082-016-0599-6
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DOI: https://doi.org/10.1007/s11082-016-0599-6