Abstract
In this paper, we have introduced a general formula of a new laser beam with a nearly Flattened-top profile. The propagation properties of this beam, called Generalized Flattened Hermite-cosh-Gaussian (GFHChG) beam are studied in detail. Based on the Huygens–Fresnel integral, an analytical expression of the intensity distribution for GFHChG passing through a paraxial ABCD optical system is developed. Several particular cases such as the propagation of the flattened Gaussian beam, the cosh-Gaussian beam, the higher and squared cosh-Gaussian beam and the Hermite-cosh-Gaussian beam are deduced from our result. Numerical simulations are also given in free space and through a circular thin lens in a free space to study the comportment of this beam during propagation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Belafhal, A., Hricha, Z., Dalil-Essakali, L., Usman T. A note on some integrals involving Hermite polynomials encountered in caustic optics, Submitted (2019)
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., Ibnchaikh, M.: Propagation properties of Hermite-cosh-Gaussian laser beams. Opt. Commun. 186, 269–276 (2000)
Boufalah, F., Dalil-Essakali, L., Belafhal, A.: Transformation of a generalized Bessel–Laguerre–Gaussian beam by a paraxial ABCD optical system. Opt. Quantum Electron. 51, 274–288 (2019)
Cai, Y., Lu, X., Lin, Q.: Hollow Gaussian beams and their propagation properties. Chin. Phys. Lett. 20, 2155–2157 (2003)
Casperson, L.W., Tovar, A.A.: Hermite–sinusoidal-Gaussian beams in complex optical systems. J. Opt. Soc. Am. A 15, 954–961 (1998)
Chen, S., Zhang, T., Feng, X.: Propagation properties of cosh-squared-Gaussian beam through fractional Fourier transform systems. Opt. Commun. 282, 1083–1087 (2009)
Collins, S.A.: Lens-system diffraction integral written in terms of matrix optics. J. Opt. Soc. Am. 60, 1168–1177 (1970)
Deng, D.: Propagation of elegant hermite cosine Gaussian laser beams. Opt. Commun. 259, 409–414 (2006)
Ebrahim, A.A.A., Ez-zariy, L., Belafhal, A.: Propagation of finite airy hermite hollow Gaussian beams through a paraxial ABCD optical system. IJAEE S 3, 11–20 (2015)
El Halba, E.M., Boustimi, M., Ez-zariy, L., Hennani, S., Belafhal, A.: Propagation characteristics of Bessel-like beams through ABCD optical system. Opt. Quantum Electron. 49, 269–279 (2017)
Gradshteyn, I.S., Ryzhik, I.M., Jeffrey, A.: Table of Integrals, Series, and Products. Academic Press, Amsterdam (2007)
Hashemi, S.S., Sabouri, S.G., Soltanolkotabi, M.: A study of propagation of cosh-squared-Gaussian beam through fractional Fourier transform systems. Opt. Appl. 41, 898–909 (2011)
Hennani, S., Ez-Zariy, L., Belafhal, A.: Propagation properties of finite Olver-Gaussian beams passing through a paraxial ABCD optical system. Opt. Photonics J 05, 273–294 (2015)
Kaplan, A., Friedman, N., Davidson, N.: Optimized single-beam dark optical trap. J. Opt. Soc. Am. B 19, 1233–1238 (2002)
Klar, T.A., Hell, S.W.: Subdiffraction resolution in far-field fluorescence microscopy. Opt. Lett. 24, 954–956 (1999)
Kuga, T., Torii, Y., Shiokawa, N., Hirano, T., Shimizu, Y., Sasada, H.: Novel optical trap of atoms with a doughnut beam. Phys. Rev. Lett. 78, 4713–4716 (1997)
Lü, B., Ma, H., Zhang, B.: Propagation properties of cosh-Gaussian beams. Opt. Commun. 164, 165–170 (1999)
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)
Tovar, A.A., Casperson, L.W.: Production and propagation of Hermite–sinusoidal-Gaussian laser beams. J. Opt. Soc. Am. A 15, 2425–2432 (1998)
Xu, P., He, X., Wang, J., Zhan, M.: Trapping a single atom in a blue detuned optical bottle beam trap. Opt. Lett. 35, 2164–2166 (2010)
Xuan-Hui, L., Xu-Min, C., Lei, Z., Da-Jian, X.: High-order Bessel-Gaussian beam and its propagation properties. Chin. Phys. Lett. 20, 2155–2157 (2003)
Yu, S., Guo, H., Fu, X., Hu, W.: Propagation properties of elegant Hermite-cosh-Gaussian laser beams. Opt. Commun. 204, 59–66 (2002)
Zhou, G.: Fractional Fourier transform of a higher-order cosh–Gaussian beam. J. Mod. Opt. 56, 886–892 (2009)
Zhou, G., Zheng, J.: Beam propagation of a higher-order cosh-Gaussian beam. Opt. Laser Technol. 41, 202–208 (2009)
Zhu, K., Tang, H., Wang, X., Liu, T.: Flattened light beams with an axial shadow generated through superposing cosh-Gaussian beams. Optik 113, 222–226 (2002)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Chib, S., Dalil-Essakali, L. & Belafhal, A. Propagation propertiesof a novel generalized flattened Hermite-cosh-Gaussian light beam. Opt Quant Electron 52, 277 (2020). https://doi.org/10.1007/s11082-020-02406-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-020-02406-5