Abstract
The so-called Generalized Bessel–Laguerre–Gaussian (GBLG) beam is introduced, in this paper, and an approximate formula of the average axial intensity of its propagation through a turbulent atmosphere is investigated using the extended Huygens–Fresnel diffraction integral in the paraxial approximation and on the Rytov theory. The analytical expression elaborated is regarded as the main result of this work. Several above studies are derived here as special cases from our research. The impact of some parameters, including incident beam parameters and turbulence strength, on the distribution of the axial intensity of the GBLG beam and on the profiles of some particular beams through a turbulent atmosphere are carried out numerically in the paper. From our numerical results-, the propagation of Gaussian beams, Laguerre–Gaussian beams and Bessel–Gaussian beams through the considered medium are deduced as particular cases.
Similar content being viewed by others
References
Andrews, L.C., Philips, R.L.: Laser Beam Propagation Through Random Media. SPIE, Bellingham (1998)
Andrews, L.C., Phillips, R.L., Hopen, C.Y.: Laser Beam Scintillation with Applications, p. 99. SPIE Press, Washington (2001)
Ata, Y., Baykal, Y.: Flat-topped beam transmittance in anisotropic non-Kolmogorov turbulent marine atmosphere. Opt. Eng. 56, 104107–104110 (2017)
Belafhal, A., Hennani, S., Ez-zariy, L., Chafiq, A., Khouilid, M.: Propagation of truncated Bessel-modulated Gaussian beams in turbulent atmosphere. Phys. Chem. News 62, 36–43 (2011)
Boufalah, F., Dalil-Essakali, L., Nebdi, H., Belafhal, A.: Effect of turbulent atmosphere on the on-axis average intensity of Pearcey-Gaussian beam. Chin. Phys. B. (2016). https://doi.org/10.1088/1674-1056/25/6/064208
Cang, J., Zhang, Y.: Axial intensity distribution of truncated Bessel-Gauss beams in a turbulent atmosphere. Optik 121, 239–245 (2010)
Eyyuboglu, H.T., Hardalaç, F.: Opt. Laser Technol. 40, 343–351 (2008)
Ez-zariy, L., Ebrahim, A.A.A., Belafhal, A.: Behavior of the central intensity of a Hollow-Gaussian beam against the turbulence. Optik 127, 11522–11528 (2016)
Gradshteyn, I.S., Ryzhik, I.M.: Tables of Integrals, Series and Products. Academic Press, New York (1994)
Khannous, F., Belafhal, A.: A new study of turbulence effects in the marine environment on the intensity distributions of flat-topped Gaussian beams. Optik 127, 8194–8202 (2016)
Khannous, F., Boustimi, M., Nebdi, H., Belafhal, A.: Li’s flattened Gaussian beams propagation in maritime atmospheric turbulence. Phys. Chem. News 73, 73–82 (2014)
Kinani, A., Ez-zariy, L., Chafiq, A., Nebdi, H., Belafhal, A.: Effects of atmospheric turbulence on the propagation of Li’s flat-topped optical beams. Phys. Chem. News 61, 24–33 (2011)
Korotkova, O., Gbur, G.: Propagation of beams with any spectral, coherence, and polarization properties in turbulent atmosphere. Proc-SPIE. (2007). https://doi.org/10.1117/12.700465
Li, Y., Lee, H., Emil, W.: New generalized Bessel–Gaussian beams. Opt. Soc. Am. A 21, 640–646 (2004)
Liu, X., Liang, C., Yuan, Y., Cai, Y., Eyyuboglu, H.T.: Scintillation properties of a truncated flat-topped beam in a weakly turbulent atmosphere. Opt. Laser Technol. 45, 587–592 (2013)
Mei, Z., Zhao, D.: Nonparaxial analysis of vectorial Laguerre–Bessel–Gaussian beams. Opt. Express 15, 11942–11951 (2007)
Nie, Z., Shi, G., Li, D., Zhang, X., Wang, Y., Song, Y.: Tight focusing of a radially polarized Laguerre–Bessel–Gaussian beam and its application to manipulation of two types of particle. Phys. Lett. A 379, 857–863 (2015)
Noriega-Manez, R.J., Gutiérrez-Vega, J.C.: Rytov theory for Helmholtz-Gauss beams in turbulent atmosphere. Opt. Express 15, 16328–16341 (2007)
Saad, F., Hricha, Z., Khouilid, M., Belafhal, A.: A theoretical study of the Fresnel diffraction of Laguerre–Bessel–Gaussian beam by a helical axicon. Optik 149, 416–422 (2017)
Tovar, A.A.: Propagation of Laguerre–Bessel–Gaussian beams. J. Opt. Soc. Am. A 17, 2010–2018 (2000)
Wang, L.G., Zheng, W.W.: The effect of atmospheric turbulence on the propagation properties of optical vortices formed by using coherent laser beam arrays. J. Opt. A. (2009). https://doi.org/10.1088/1464-4258/11/6/065703
Wang, F., Cai, Y., Eyyuboglu, H.T., Baykal, Y.: Average intensity and spreading of partially coherent standard and Elegant Laguerre-Gaussian beam in turbulent atmosphere. Prog. Electrom. Res. 103, 33–56 (2010)
Wen, J.J., Breazeale, M.A.: A diffraction beam field expressed as the superposition of Gaussian beams. J. Acoust. Soc. Am. 83, 1752–1756 (1988)
Wen, W., Chu, X., Ma, H.: The propagation of a combining Airy beam in turbulence. Opt. Commun. 336, 326–329 (2015)
**u-bo, M.A., En-bang, L.I.: Opto- Elect. Eng. 6, 011 (2009)
Ya-Qing, L., Zhen-Sen, W., Ming-Jun, W.: Partially coherent Gaussian—Schell model pulse beam propagation in slant atmospheric turbulence. Chin. Phys. B. (2014). https://doi.org/10.1088/1674-1056/23/6/064216
Zhou, P., Liu, Z., Xu, X., Chu, X.: Propagation of coherently combined flattened laser beam array in turbulent atmosphere. Opt. Laser Technol. 41, 403–407 (2009)
Zhu, K.C., Zhou, G.Q., Li, X.G., Li, X.G., Zheng, X.J., Tang, H.Q.: Opt. Express 16, 9897–9905 (2012)
Zhu, Z., Liu, L., Wang, F., Cai, Y.: Evolution properties of a Laguerre-Gaussian correlated Schell-model beam propagating in uniaxial crystals orthogonal to the optical axis. J. Opt. Soc. Am. A 32, 374–380 (2015)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Boufalah, F., Dalil-Essakali, L., Ez-zariy, L. et al. Introduction of generalized Bessel–Laguerre–Gaussian beams and its central intensity travelling a turbulent atmosphere. Opt Quant Electron 50, 305 (2018). https://doi.org/10.1007/s11082-018-1573-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-018-1573-2