Abstract
We present in this work the propagation properties of Generalized Humbert-Gaussian beams (GHGBs) passing through a paraxial ABCD optical system. Based on the extended Huygens-Fresnel integral, the analytical expression of the intensity distribution for GHGBs is derived and some numerical simulations are performed for particular cases in free space, thin lens in a free space and graded refractive index system. Our results show that the comportment of several particular cases of these beams during the propagation is influenced by the beam orders and the characteristic parameters of the system.
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References
Bandres, M.A., Gutierrez-Vega, J.C.: Circular beams. Opt. Lett. 33, 177–179 (2008)
Beijersbergen, M.W., Allen, L., van der Veen, H.E.L.O., Woerdman, J.P.: Astigmatic laser mode converters and transfer of orbital angular momentum. Opt. Commun. 96, 123–132 (1993)
Belafhal, A., Dalil-Essakali, L.: Collins formula and propagation of Bessel-modulated Gaussian light beams through an ABCD optical system. Opt. Commun. 177, 181–188 (2000)
Belafhal, A., Nebdi, H.: Generation and propagation of novel donut beams by a spiral phase plate: Humbert beams. Opt. Quant. Electron. 46, 201–208 (2014)
Belafhal, A., Saad, F.: Conversion of circular beams by a spiral phase plate: generation of generalized Humbert beams. Optik 138, 516–528 (2017)
Boufalah, F., Dalil-Essakali, L., Belafhal, A.: Transformation of a generalized Bessel-Laguerre-Gaussian beam by a paraxial ABCD optical system. Opt. Quant. Electron. 51, 1–15 (2019)
Chafiq, A., Hricha, Z., Belafhal, A.: Paraxial propagation of Mathieu beams through an apertured ABCD optical system. Opt. Commun. 253, 223–230 (2005)
Chafiq, A., Hricha, Z., Belafhal, A.: Flat-topped Mathieu-Gaussian beam and its transformation by paraxial optical systems. Opt. Commun. 278, 142–146 (2007)
Collins, S.A.: Lens-system diffraction integral written in terms of matrix optics. J. Opt. Soc. Am. 60, 1168–1177 (1970)
Curtis, J.E., Grier, D.G.: Modulated optical vortices. Opt. Lett. 28, 872–874 (2003)
Ebrahim, A.A.A., Ez-zariy, L., Belafhal, A.: Propagation of modified Bessel Gaussian beams through an annular apertured paraxial ABCD optical system. Phys. Chem. News 61, 52–58 (2011)
Ebrahim, A.A.A., Khannous, F., Chafiq, A., Belafhal, A.: Theoretical investigation of propagation characteristics of Hypergeometric-Gaussian beams type-II through an ABCD optical system with an annular aperture. Int. J. Photon. Opt. Technol. 2, 18–24 (2016)
Erdélyi, A.: Tables of integral transforms. McGraw-Hill Book Company, INC, vol. I. (1954).
Gradshteyn, I.S., Ryzhik, I.M.: Tables of Integrals, Series, and Products, 5th edn. Academic Press, New York (1994)
Heckenberg, N.R., McDuff, R., Smith, C.P., White, A.G.: Generation of optical phase singularities by computer generated holograms. Opt. Lett. 17, 221–223 (1992)
Kaplan, A., Friedman, N., Davidson, N.: Optimized single-beam dark optical trap. J. Opt. Soc. Am. 19, 1233–1238 (2002)
Klar, T.A., Hell, S.: Subdiffraction resolution in far-field fluorescence microscopy. Opt. Lett. 24, 954–956 (1999)
Kuga, T., Torii, Y., Shiokawa, N., Hirano, T.: Novel optical trap of atoms with a doughnut beam. Phys. Rev. J. 78, 4713–4716 (1997)
Lopez-Mago, D., Miguel Bandres, A., Julio Gutiérrez-Vega, C.: Propagation of Whittaker Gaussian Beams. The International Society for Optical Engineering, 7430, 743013 (1–8) (2009).
Mei, Z., Zhao, D., Gu, J.: Propagation of Elegant Laguerre-Gaussian beams through an annular aperture paraxial ABCD optical system. Opt. Commun. 240, 337–343 (2004)
Mei, Z., Zhao, D., Wei, X., Jing, F., Zhu, Q.: Propagation of Bessel-modulated Gaussian beams through a paraxial ABCD optical system with an annular aperture. Optik 116, 521–526 (2005)
Tang, B., Jiang, C., Zhu, H., Zhou, X., Wang, S.: The propagation of Hypergeometric beams through an annular apertured paraxial ABCD optical system. Laser Phys. 24, 125002–125008 (2014)
Wei, S., Bu, J., Zhu, S., Yuan, X.: Image edge-enhancement in optical microscopy with a phase mismatched spiral phase plate. Chin. Opt. Lett. 9(1-4), 031001 (2009).
Xu, P., He, X., Wang, J., Zhan, M.: Trapping a single atom in a blue detuned optical bottle beam traps. Opt. Lett. 35, 2164–2166 (2010)
Yang, C., Lai, Y.: Apodised fiber Bragg gratings fabricated with a uniform phase mask using Gaussian beam laser. Opt. Laser Technol. 32, 307–310 (2000)
Zhao, D., Mei, Z., Gu, J., Mao, H., Chen, L., Wang, S.: Propagation characteristics of truncated standard and elegant Laguerre-Gaussian beams. Adapt. Opt. Appl. III(5639), 149–158 (2004)
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Nossir, N., Dalil-Essakali, L. & Belafhal, A. Propagation analysis of some doughnut lasers beams through a paraxial ABCD optical system. Opt Quant Electron 52, 330 (2020). https://doi.org/10.1007/s11082-020-02444-z
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DOI: https://doi.org/10.1007/s11082-020-02444-z