Abstract
In this paper, circular Lorentz–Bessel–Gaussian beams (CLBGBs) are introduced as a novel member of the Lorentz-Gaussian beams family. The analytical expression of the propagation of these beams passing through a paraxial optical ABCD system is derived. The generalized Huygens-Fresnel diffraction integral of the form Collins’s formula and the expansion of the Lorentz distribution in terms of the complete orthonormal basis set of the Hermite-Gauss modes are used. The influences of the beam-order and Bessel part β, Gaussian and Lorentzian waists, and propagation distance z on the propagation of CLBGBs are investigated. Some numerical simulation results are done. The beams family in this work may be useful to the practical applications in free-space optical communications because they have vortex properties with their being experimentally realizable.
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References
Belafhal, A., El Halba, E.M., Usman, T.: An integral transform involving the product of bessel functions and whittaker function and Its application. mathematics subject classification. Int. J. Appl. Comput. Math. 6, 177–188 (2020)
Collins, S.A.: Lens-system diffraction integral written in terms of matrix optics. J. Opt. Soc. Am. 60, 1168–1177 (1970)
Du, W., Zhao, C., Cai, Y.: Propagation of Lorentz and Lorentz-Gauss beams through an apertured fractional Fourier transform optical system. Optics Lasers Eng 49, 25–31 (2011)
Dumke, W.P.: The angular beam divergence in double-heterojunction lasers with very thin active regions. IEEE J. Quantum Electron. 11(7), 400–402 (1975)
Duocastella, M., Arnold, C.B.: Bessel and annular beams for materials processing. Laser Photon. Rev. 6, 607–621 (2012)
Erdelyi A., W. Magnus, F. Oberhettinger: Tables of integral transforms (McGraw-Hill, 1954).
Fahrbach, F.O., Simon, P., Rohrbach, A.: Microscopy with self-reconstructing beams. Nat. Photonics 4, 780–785 (2010)
Garcés-Chávez, V., McGloin, D., Melville, H., Sibbett, W., Dholakia, K.: Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam. Nature 419, 145–147 (2002)
Gawhary, O.E., Severini, S.: Lorentz beams and symmetry properties in paraxial optics. J. Opt. A 8, 409–414 (2006)
Gawhary, O.E., Severini, S.: Lorentz beams as a basis for a new class of rectangular symmetric optical fields. Opt. Commun. 269(2), 274–284 (2007)
Li, D., Imasaki, K.: Vacuum laser-driven acceleration by two slits-truncated Bessel beams. Appl. Phys. Lett. 87, 0911061-1–911063 (2005)
Muhsin, C.G., Eyyuboğlu, H.T.: Irradiance fluctuations of partially coherent super Lorentz Gaussian beams. Optics Commun. 284, 4857–4861 (2011)
Naqwi, A., Durst, F.: Focus of diode laser beams: a simple mathematical model. Appl. Opt. 29(12), 1780–1785 (1990)
Planchon, T.A., Gao, L., Milkie, D.E., Davidson, M.W., Galbraith, J.A., Galbraith, C.G., Betzig, E.: Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination. Nat. Methods 8, 417–423 (2011)
Rui, F., Zhang, D., Ting, M., Gao, X., Zhuang, S.: Focusing of linearly polarized Lorentz-Gauss beam with one optical vortex. Optik 124, 2969–2973 (2013)
Schimpf, D.N., Schulte, J., Putnam, W.P., Kartner, F.X.: Generalizing higher-order Bessel-Gauss beams: analytical description and demonstration. Opt. Express 20(24), 26852–26867 (2012)
Schmidt, P.P.: A method for the convolution of line shapes which involve the Lorentz distribution. J. Phys. 9, 2331–2339 (1976)
Xu, Y., Zhou, G.: Circular Lorentz-Gauss beams. J. Opt. Soc. Am. A 36, 179–185 (2019)
Yang J., Chen T., Ding G., Yuan X.: Focusing of diode laser beams: a partially coherent Lorentz model. Proceedings. SPIE 6824, 68240A (1–8) (2008).
Zhao, C., Cai, Y.: Paraxial propagation of Lorentz and Lorentz-Gauss beams in uniaxial crystals orthogonal to the optical axis. J. Mod. Opt. 57(5), 375–384 (2010)
Zhou, G.: Fractional Fourier transform of Lorentz-Gauss beams. J. Opt. Soc. Am. A 26, 350–355 (2009a)
Zhou, G.: Beam propagation factors of a Lorentz-Gauss beam. Appl. Phys. B 96, 149–153 (2009b)
Zhou, G.: The beam propagation factors and the kurtosis parameters of a Lorentz beam. Opt. Laser Technol. 41, 953–955 (2009c)
Zhou, G.: Propagation of a partially coherent Lorentz-Gauss beam through a paraxial ABCD optical. Opt. Express 18(5), 4637–4643 (2010a)
Zhou, G.: Propagation of a Lorentz-Gauss beam through a misaligned optical system. Optics Commun. 283, 1236–1243 (2010b)
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Ahmed Abdulrab Ali Ebrahim and Nabil A. A. Yahya wish to thank the Scholar Rescue Fund, Institute of International Education (IIE-SRF), New York, USA, for the support.
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Ebrahim, A.A.A., Yahya, N.A.A., Swillam, M.A. et al. Introduction and propagation properties of circular lorentz-bessel-gaussian beams. Opt Quant Electron 54, 434 (2022). https://doi.org/10.1007/s11082-022-03868-5
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DOI: https://doi.org/10.1007/s11082-022-03868-5