Focusing properties and focal shift in hyperbolic-cosine-Gaussian beams

2005 ◽  
Vol 253 (4-6) ◽  
pp. 242-249 ◽  
Author(s):  
Z. Hricha ◽  
A. Belafhal
Keyword(s):  
Gaussian Beams ◽  
Hyperbolic Cosine ◽  
Focal Shift ◽  
Focusing Properties

Focusing properties of hyperbolic-cosine-Gaussian beams combining a helical axicon

Optik ◽  
2013 ◽  
Vol 124 (18) ◽  
pp. 3422-3426 ◽  
Author(s):  
Xiangmei Dong ◽  
Tao Geng ◽  
Songlin Zhuang
Keyword(s):  
Gaussian Beams ◽  
Hyperbolic Cosine ◽  
Focusing Properties

Focusing properties and focal shift of a vortex cosine-hyperbolic Gaussian beam

2021 ◽  
Author(s):  
Zoubir Hricha ◽  
El Mostapha El Halba ◽  
Mohammed Lazrek ◽  
Abdelmajid Belafhal
Keyword(s):  
Incident Beam ◽  
Beam Width ◽  
Spot Size ◽  
Fresnel Number ◽  
Beam Focusing ◽  
Diffraction Integral ◽  
Focal Shift ◽  
Beam Parameters ◽  
Focus Plane ◽  
Focusing Properties

Abstract In this paper, we investigate the focusing properties of a vortex-cosh-Gaussian (vChG) beam passing through a converging thin lens. Based on the Huygens-Fresnel diffraction integral, we derived the analytical propagation equation as well as the beam width expression of a focused vChGB. It is shown that the focusing properties including the focal shift of the focused vChGB are crucially dependent on the incident beam parameters namely the decentered parameter and the topological charge in addition to the Gaussian Fresnel number\({N_F}\). From typical numerical examples, it is found that the focused vChGB is transformed into a multi-lobes structure shape at the real focus plane, and the principal maximum intensity of the beam is located away from the axis. The amount of focal shift, which is determined from the minimum spot size criterion, is strongly dependent on the Fresnel number, the decentered parameter and the vortex charge m. The obtained results may be useful for the applications of the vChGBs in beam shaping and beam focusing.

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