Abstract
We apply the generalized Huygens-Fresnel diffraction integral to investigate propagation of Circular Lorentz-Gaussian beams (referred as CLGBs) through an ABCD optical system and a Spiral Phase Plate (SPP). The conversion of these beams by the considered optical elements permit us the generation of the Superposition of Humbert-Gaussian beams (SHGBs). This beams family created by the SPP is doughnut with a dark spot at the centre. The generated waves can be applied in trapping neutral atoms, in atmospheric and oceanic turbulent studies and in other scientific fields.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
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., Nossir, N., Dalil-Essakali, L., Usman, T.: Integral transforms involving the product of Humbert and Bessel functions and its application. AIMS Mathematics 5(2), 1260–1274 (2020)
Belafhal, A., El Halba, E.M., Usman, T.: An integral transform and its application in the propagation of Lorentz-Gaussian beams. Commu. Math. 29, 483–491 (2021)
Belafhal A, Saad F. Conversion of Circular Beams by a Spiral Phase Plate: Generation of Generalized Humbert beams, Optik 1–16 (2017).
Collins, S.A.: Lens-system diffraction integral written in terms of matrix optics. J. Opt. Soc. Am. 60, 1168–1177 (1970)
Ebrahim AAA, Yahya NAA, Swillam A. M, Belafhal A.: Introduction and Propagation Properties of Circular Lorentz-Bessel-Gaussian Beams. Optical and Quantum Electronics (2022), preprint.
Gradshteyn I.S., Ryzhik I.M.: Table of Integrals, Series, and Products (Academic, 1994).
Guoquan, Z.: Fractional Fourier transform of Lorentz-Gauss beams. J. Opt. Soc. Am. a. 26(2), 350–355 (2009)
Keshavarz, A., Honarasa, G.: Propagation of Lorentz-Gaussian beams in strongly nonlocal nonlinear media. Commun. Theor. Phys. 61, 241–245 (2014)
Khan, N.U., Usman, T., Ghayasuddin, M.: A note on integral transforms associated with Humbert’s confluent hypergeometric function. Electron. J. Math. Anal. Appl. 4(2), 259–265 (2016)
Klar, T.A., Hell, S.: Subdifraction resolution in far-feld fuorescence 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)
Li, J., Sang, P., Shi, P., Gao, X., Wang, X.: Focusing properties of Lorentz-Gaussian beam with azimuthally-variant phase filters. Optik 144, 459–466 (2017)
Li, X., Zhou, Y.M., Xu, Y.Q., Zhou, G.Q.: Airy transformation of Lorentz-Gauss beams. Results in Physics 19, 103643–103710 (2020)
Nossir, N., Dalil-Essakali, L., Belafhal, A.: Propagation analysis of some doughnut lasers beams through a paraxial ABCD optical system. Opt. Quant. Electron. 52, 329–330 (2020)
Nossir, N., Dalil-Essakali, L., Belafhal, A.: Difraction of generalized Humbert-Gaussian beams by a helical axicon. Opt. Quant. Electron. 53, 94–107 (2021b)
Nossir N, Dalil-Essakali L, Belafhal A.: Behavior of the central intensity of generalized Humbert-Gaussian beams against the atmospheric turbulence,” - Optical and Quantum Electronics, 2021a, preprint.
Schmidt, P.P.: A method for the convolution of line shapes which involve the Lorentz distribution. J. Phys. 9, 2331–2339 (1976)
Srivastava, H., Karlsson, P.W.: Multiple Gaussian Hypergeometric Series. Halsted Press, New York (1985)
Sun, F., Li, Y., Wang, G., Li, Y., Dong, X., Gao, X.: Linearly polarized Airy–Lorentz–Gaussian beam modulated by a triangular phase function. Optik 219, 165302 (2020)
Tang, B., Bian, L.: Finite-energy Airy–Lorentz–Gaussian beam and its paraxial propagation. Optical Society of America A 36(10), 1624–1630 (2019)
Xu, Y., Zhou, G.: Circular Lorentz-Gauss beams. J. Opt. Soc. Am. A 36, 179–185 (2019)
Xu, Y., Zhou, Y., Chen, R., Zhou, G.: Circular Lorentz-Gauss beams with the power-exponent-phase vortex. Laser Phys. 30, 025002–025009 (2020)
Yin J., Gao W., Zhu Y.: Generation of dark hollow beams and their applications. Progress in Optics, Vol. 44, E. Wolf, ed., North-Holland, Amsterdam (2003).
Zhou, G.: Focal shift of focused truncated Lorentz-Gauss beam. J. Opt. Soc. Am. a. 25(10), 2594–2599 (2008)
Zhou, G.: Fractional Fourier transform of Lorentz-Gauss beams. J. Opt. Soc. Am. A 26, 350–355 (2009)
Zhou, G.: Beam propagation factors and kurtosis parameters of a Lorentz-Gauss vortex beam. J. Opt. Soc. Am. A 31, 1239–1246 (2014)
Zhou, G., Chu, X.: Average intensity and spreading of a Lorentz-Gauss beam in turbulent atmosphere. Opt. Express 18(2), 731–735 (2010)
Zhou, G.Q., Wang, X.G., Chu, X.X.: Fractional Fourier transform of Lorentz-Gauss vortex beams. Sci. China Phys. Mechanics and Astro. 56(8), 1487–1494 (2013)
Zhou, G., Xu, Y., Zhou, Y.: Non-paraxial propagation of a circular Lorentz-Gauss vortex beam. Opt Soc Am a. 36(7), 1221–1228 (2019)
Acknowledgements
The first auteur was supported by Scholar Rescue Fund Institute of International Education (IIE-SRF), One World Trade Center, 36th Floor New York, NY 10007, USA. Also, thanks to the American University in Cairo and Ministry of Education of Yemen for their financial support and moral encouragement.
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
Ebrahim, A.A.A., Swillam, M.A. & Belafhal, A. Generation and Propagation Analysis of the Superposition of Humbert-Gaussian Beams. Opt Quant Electron 54, 519 (2022). https://doi.org/10.1007/s11082-022-03901-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-022-03901-7