Skip to main content
SpringerLink
Log in

Propagation of the Laguerre-Gaussian correlated Shell-model beams through a turbulent jet engine exhaust

  • Published:
Optical and Quantum Electronics Aims and scope Submit manuscript

Abstract

In this paper, we investigated the influence of a turbulence jet engine exhaust on Laguerre-Gaussian correlated shell-model beams (LGSMBs). The analytical formulae of the cross-spectral density function as well as the beam width are derived based on the Huygens–Fresnel diffraction principle and the second-order moments of the Wigner distribution function, respectively. From our main results, the spectral density, the degree of coherence and the beam width of a LGSMB are analyzed numerically. It is found that for high source coherence width, the spectral density changes gradually its profiles from circular to elliptical shape at short propagation distance, then the beam transforms into a well like Gaussian at long propagation distance. Although, at very short propagation distance, the beam becomes an elliptical dark hollow if the source coherence is very lower. Also, the numerical results show that the LGSMB spreads more rapidly than the Gaussian Schell-model beam (GSMB) in the same conditions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Abramowitz, M., Stegun, I.: Handbook of Mathematical Functions with Formulas, Graphs. and Mathematical Tables. U. S. Department of Commerce. (1970)

  • Andrews, L.C., Phillips, R.L.: Laser Beam Propagation Through Random Media, 2nd edn. SPIE Publications, Bellingham, Washington (2005)

    Book  Google Scholar 

  • Beason, M., Smith, C., Coffaro, J., Belichki, S., Spychalsky, J., Titus, F., Crabbs, R., Andrews, L., Phillips, R.: Near ground measure and theoretical model of plane wave covariance of intensity in anisotropic turbulence. Opt. Lett. 43(11), 2607–2610 (2018)

    Article  ADS  Google Scholar 

  • Boufalah, F., Dalil-Essakali, L., Ez-zariy, L., Belafhal, A.: Introduction of generalized Bessel–Laguerre–Gaussian beams and its central intensity traveling a turbulent atmosphere. Opt. Quant. Electron. 50, 305–325 (2018)

    Article  Google Scholar 

  • Cang, J., Xiu, P., Liu, X.: Propagation of Laguerre-Gaussian and Bessel-Gaussian Schell-model beams through paraxial optical systems in turbulent atmosphere. Opt. and Laser Technol. 54, 35–41 (2013)

    Article  ADS  Google Scholar 

  • Chen, R., Liu, L., Zhu, S.J., Wu, G.F., Wang, F., Cai, Y.J.: Statistical properties of a Laguerre-Gaussian Schell-model beam in turbulent atmosphere. Opt. Express. 22(2), 1871–1883 (2014)

    Article  ADS  Google Scholar 

  • Chib, S., Essakali, L.D., Belafhal, A.: Evolution of the partially coherent Generalized Flattened Hermite-Cosh-Gaussian beam through a turbulent atmosphere. Opt. Quant. Electron. 52, 484–500 (2020)

    Article  Google Scholar 

  • Consortini, A., Ronchi, L., Stefanutti, L.: Investigation of atmospheric turbulence by narrow laser beams. Appl. Opt. 9(11), 2543–2547 (1970)

    Article  ADS  Google Scholar 

  • Dan, Y., Zhang, B.: Beam propagation factor of partially coherent flat-topped beams in a turbulent atmosphere. Opt. Express. 16(20), 15563–15575 (2008)

    Article  ADS  Google Scholar 

  • Dijk, T.V., Fischer, D.G., Visser, T.D., Wolf, E.: Effects of spatial coherence on the angular distribution of radiant intensity generated by scattering on a sphere. Phys. Rev. Lett. 104, 173902–173905 (2010)

    Article  ADS  Google Scholar 

  • Ding, C., Korotkova, O., Li, D., Zhao, D., Pan, L.: Propagation of Gaussian Schell-model beams through a jet engine exhaust. Opt. Express. 28(2), 1037–1050 (2020)

    Article  ADS  Google Scholar 

  • Dogariu, A., Amarande, S.: Propagation of partially coherent beams: turbulence-induced degradation. Opt. Lett. 28(1), 10–12 (2003)

    Article  ADS  Google Scholar 

  • Erdelyi, A., Magnus, W., Oberhettinger, F.: Tables of Integral Transforms. McGraw-Hill (1954)

    MATH  Google Scholar 

  • Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products. Academic Press, New York (1994)

    MATH  Google Scholar 

  • Hogge, C.B., Visinsky, W.L.: Laser beam probing of jet exhaust turbulence. Appl. Opt. 10(4), 889–892 (1971)

    Article  ADS  Google Scholar 

  • Hricha, Z., Yaalou, M., Belafhal, A.: Intensity characteristics of double-half inverse Gaussian hollow beams through turbulent atmosphere. Opt. Quant. Electron. 52, 201–208 (2020)

    Article  Google Scholar 

  • Huang, Y.P., Zeng, A.P.: Effect of anisotropic non-Kolmogorov turbulence on the evolution behavior of Gaussian Schell-model vortex beams. Opt. Commun. 436, 63–68 (2019)

    Article  ADS  Google Scholar 

  • Jian, W.: Propagation of a Gaussian-Schell beam through turbulent media. J. Mod. Opt. 37, 671–684 (1990)

    Article  ADS  Google Scholar 

  • Khannous, F., Boustimi, M., Nebdi, H., Belafhal, A.: Theoretical investigation on the Hollow Gaussian beams propagating in atmospheric turbulent. Chin. J. Phys. 54, 194–204 (2016)

    Article  MathSciNet  Google Scholar 

  • Korotkova, O., Andrews, L.C., Phillips, R.L.: Model for a partially coherent Gaussian beam in atmospheric turbulence with application in Lasercom. Opt. Eng. 43, 330–341 (2004)

    Article  ADS  Google Scholar 

  • Mei, Z., Korotkova, O.: Random sources generating ring-shaped beams. Opt. Lett. 38(2), 91–93 (2013)

    Article  ADS  Google Scholar 

  • Mei, Z.R., Shchepakina, E., Korotkova, O.: Propagation of cosine-Gaussian-correlated Schell-model beams in atmospheric turbulence. Opt. Express. 21(15), 17512–17519 (2013)

    Article  ADS  Google Scholar 

  • Saad, F., El Halba, E.M., Belafhal, A.: A theoretical study of the on-axis average intensity of Generalized spiraling Bessel beams in a turbulent atmosphere. Opt. Quant. Electron. 49, 94–105 (2017)

    Article  Google Scholar 

  • Sirazetdinov, V.S.: Experimental study and numerical simulation of laser beams propagation through the turbulent aerojet. Appl. Opt. 47(7), 975–985 (2008)

    Article  ADS  Google Scholar 

  • Sjöqvist, L.: Laser beam propagation in jet engine plume environments: a review, Proc. SPIE, vol. 7115, pp. 71150C (1–15). (2008)

  • Wang, F., Korotkova, O.: Random optical beam propagation in anisotropic turbulence along horizontal links. Opt. Express. 24(21), 24422–24434 (2016)

    Article  ADS  Google Scholar 

  • Wang, F., Liu, X., Yuan, Y., Cai, Y.: Experimental generation of partially coherent beams with different complex degrees of coherence. Opt. Lett. 38(11), 1814–1816 (2013)

    Article  ADS  Google Scholar 

  • Wang, F., Toselli, I., Li, J., Korotkova, O.: Measuring anisotropy ellipse of atmospheric turbulence by intensity correlations of laser light. Opt. Lett. 42(6), 1129–1132 (2017)

    Article  ADS  Google Scholar 

  • Wu, G., Cai, Y.: Detection of a semirough target in turbulent atmosphere by a partially coherent beam. Opt. Lett. 36, 1939–1941 (2011)

    Article  ADS  Google Scholar 

  • Wu, Y., Zhang, Y., Wang, Q., Hu, Z.: Average intensity and spreading of partially coherent model beams propagating in a turbulent biological tissue. J. Quant. Spectrosc. Radiat. Transf. 184, 308–315 (2016)

    Article  ADS  Google Scholar 

  • Yaalou, M., El Halba, E.M., Hricha, Z., Belafhal, A.: Propagation characteristics of Dark and Antidark Gaussian beams in a turbulent atmosphere. Opt. Quant. Electron. 51, 255–266 (2019)

    Article  Google Scholar 

  • Yao, M., Toselli, I., Korotkova, O.: Propagation of electromagnetic stochastic beams in anisotropic turbulence. Opt. Express. 22(26), 31608–31619 (2014)

    Article  ADS  Google Scholar 

  • Yura, H.T.: Mutual coherence function of a finite cross section optical beam propagating in a turbulent medium. Appl. Opt. 11(6), 1399–1406 (1972)

    Article  ADS  Google Scholar 

  • Zhao, L., Xu, Y., Yang, S.: Statistical properties of partially coherent vector beams propagating through anisotropic atmospheric turbulence. J. Light. Elect. Opt. 227, 166115 (2021)

    Article  Google Scholar 

Download references

Funding

The authors have not disclosed any funding.

Author information

Authors and Affiliations

  1. LISA, Hassan First University of Settat, École Nationale Des Sciences Appliquées, 26100, Berrechid, Morocco

    H. Nabil & A. Balhamri

  2. Laboratory LPNAMME, Laser Physics Group, Departments of Physics, Faculty of Sciences, Chouaïb Doukkali University, P.B 20, 24000, El Jadida, Morocco

    H. Nabil & A. Belafhal

Authors
  1. H. Nabil
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Balhamri
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Belafhal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Belafhal.

Ethics declarations

Conflict of interest

The authors have not disclosed any competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nabil, H., Balhamri, A. & Belafhal, A. Propagation of the Laguerre-Gaussian correlated Shell-model beams through a turbulent jet engine exhaust. Opt Quant Electron 54, 231 (2022). https://doi.org/10.1007/s11082-022-03623-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-022-03623-w

Keywords

Search

Navigation