Skip to main content
SpringerLink
Log in

Maritime turbulence effect on the axis light intensity of a Bessel higher-order cosh-Gaussian laser beam

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

Abstract

In this study, the axial propagation properties of the Bessel higher-cosh-Gaussian (BHChG) beam in maritime atmospheric turbulence are reported. Based on the extended Huygens-Fresnel principal, we extracted the analytical expression of the BHChG beam spreading in the considered medium. Additionally, under suitable conditions various particular cases of the axial intensity of the BHChG beam have been derived from the derived result. The numerical results show that when the on-axis intensity of the BHChG beam reaches a particular limit value at a certain propagation distance zmax, the beam loses its dark central spot and returns to its original hollow shape. For small constant strength turbulence, low value of the initial beam waist size, large Bessel order, small value the parameter associated with the cosh function and weak parameter. The study also highlights specific cases of the considered beam, providing valuable insights for information coding and transmission applications. The outputs of this study have potential applications in laser designators, optical communication systems and remote sensing.

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

Similar content being viewed by others

Availability of data and materials

No datasets is used in the present study.

References

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

  • Andrews, L.C.: An analytical model for the refractive index power spectrum and its application to optical scintillations in the atmosphere. J. Mod. Opt. 39, 1849–1853 (1992)

    Article  ADS  Google Scholar 

  • Andrews, L.C., Phillips, R.L.: Laser Beam Propagation Through Random Medium Bellingham. SPIE Press, Bellingham (1998)

    Google Scholar 

  • Baykal, Y.: Higher-order laser beam scintillation in weakly turbulent marine atmospheric medium. J. Opt. Soc. Am. A Opt. Image Sci. vis. 33, 758–763 (2016)

    Article  ADS  PubMed  Google Scholar 

  • Belafhal, A., Hennani, S., Ez-zariy, L., Chafq, A., Khouilid, M.: Propagation of truncated Bessel-modulated Gaussian beams in turbulent atmosphere. Phys. Chem. News 62, 36–43 (2011)

    Google Scholar 

  • Belafhal, A., Chib, S., Khannous, F., Usman, T.: Evaluation of integral transforms using special functions with applications to biological tissues. Comput. Appl. Math. 40, 156–178 (2021)

    Article  MathSciNet  Google Scholar 

  • Benzehoua, H., Belafhal, A.: Analysis of the behavior of pulsed vortex beams in oceanic turbulence. Opt. Quant. Electron. 55, 684–701 (2023a)

    Article  Google Scholar 

  • Benzehoua, H., Belafhal, A.: Analyzing the spectral characteristics of a pulsed Laguerre higher-order cosh-Gaussian beam propagating through a paraxial ABCD optical system. Opt. Quant. Electron. 55, 663–681 (2023b)

    Article  Google Scholar 

  • Benzehoua, H., Belafhal, A.: Spectral properties of pulsed Laguerre higher-order cosh-Gaussian beam propagating through the turbulent atmosphere. Opt. Commun. 541, 129492–129501 (2023c)

    Article  CAS  Google Scholar 

  • Born, M., Wolf, E.: Principles of Optics, seventh (Expanded). Cambridge University Press, Cambridge (1999)

    Book  Google Scholar 

  • Boufalah, F., Dalil-Essakali, L., Ez-zariy, L., Belafhal, A.: Introduction of generalized Bessel–Laguerre–Gaussian beams and its central intensity travelling a turbulent atmosphere. Opt. Quant. Electron. 50, 305–324 (2018)

    Article  Google Scholar 

  • Chang, M.P., Font, C.O., Gilbreath, G.C., Oh, E.: Humidity’s influence on visible region refractive index structure parameter. Appl. Opt. 4613, 2453–2459 (2007)

    Article  ADS  Google Scholar 

  • Cheng, M., Guo, L., Zhang, Y.: Scintillation and aperture averaging for Gaussian beams through non-Kolmogorov maritime atmospheric turbulence channels. Opt. Express 23, 32606–32621 (2015)

    Article  ADS  PubMed  Google Scholar 

  • Chib, S., Bayraktar, M., Belafhal, A.: Theoretical and computational study of a partially coherent laser beam in a marine environment. Phys. Scr. 98, 015513–015526 (2023a)

    Article  ADS  Google Scholar 

  • Chib, S., Khannous, F., Belafhal, A.: Propagation of general model vortex higher-order cosh-Gaussian beam in maritime turbulence. Opt. Quant. Electron. 55, 971–983 (2023b)

    Article  Google Scholar 

  • Cui, X., Yin, X., Chang, H., Sun, Z., Wang, Y., Tian, Q., Wu, G., Xin, X.: Analysis of the orbital angular momentum spectrum for Laguerre-Gaussian beams under moderate-to-strong marine-atmospheric turbulent channels. Opt. Commun. 426, 471–476 (2018)

    Article  ADS  CAS  Google Scholar 

  • Dalil-Essakali, L., Nossir, N., Belafhal, A.: Axial intensity of Bessel higher-order cosh-Gaussian beam propagating in a turbulent atmosphere. Opt. Quant. Electron. 56, 184 (2023)

    Article  Google Scholar 

  • Eckart, C., Ferris, H.G.: Equations of motion of the ocean and atmosphere. Rev. Mod. Phys. 28, 48–52 (1956)

    Article  ADS  MathSciNet  Google Scholar 

  • Elmabruk, K., Eyyuboğlu, H.T.: Analysis of flat-topped Gaussian vortex beam scintillation properties in atmospheric turbulence. Opt. Eng. 58, 066115–066115 (2019)

    Article  ADS  Google Scholar 

  • Friehe, C.A., La Rue, J.C., Champagne, F.H., Gibson, C.H., Dreyer, G.F.: Effects of temperature and humidity fluctuations on the optical refractive index in the marine boundary layer. J. Opt. Soc. Am. 65, 1502–1511 (1975)

    Article  ADS  Google Scholar 

  • Gradshteyn, I.S., Ryzhik, I.M.: Tables of Integrals, Series, and Product, 5th edn. Academic Press, New York (1994)

    Google Scholar 

  • Grayshan, K.J., Vetelino, F.S., Young, C.Y.: A marine atmospheric spectrum for laser propagation. Waves Random Complex Media 18, 173–184 (2008)

    Article  ADS  Google Scholar 

  • Jellen, C., Nelson, C., Brownell, C., Burkhardt, J., Oakley, M.: Measurement and analysis of atmospheric optical turbulence in a near-maritime environment. IOP SciNotes 1, 1–7 (2020)

    Article  Google Scholar 

  • Khannous, F., Belafhal, A.: new study of turbulence effects in the marine environment on the intensity distributions of flat-topped Gaussian beams. Optik 127, 8194–8202 (2016)

    Article  ADS  CAS  Google Scholar 

  • Khannous, F., Belafhal, A.: A new atmospheric spectral model for the marine environment. Optik 153, 86–94 (2018)

    Article  ADS  CAS  Google Scholar 

  • Khannous, F., Boustimi, M., Nebdi, N., Belafhal, A.: Li’s flattened Gaussian beams propagation in maritime atmospheric turbulence. Phys. Chem. Ews. 73, 73–82 (2014)

    Google Scholar 

  • Khannous, F., Chib, S., Belafhal, A.: Intensity characteristics of hypergeometric-gaussian type II beams in maritime turbulence. Opt. Quant. Electron. 55, 1108–1108 (2023)

    Article  Google Scholar 

  • Korotkova, O., Avramov-Zamurovic, S., Malek-Madani, R., Nelson, C.: Probability density function of the intensity of a laser beam propagating in the maritime environment. Opt. Express 19, 20322–20331 (2011)

    Article  ADS  PubMed  Google Scholar 

  • Maiman, T.H.: Optical and microwave-optical experiments in ruby. Phys. Rev. Lett. 4, 564–566 (1960)

    Article  ADS  Google Scholar 

  • Nelson, C., Avramov-Zamurovic, S., Korotkova, O., Malek-Madani, R., Sova, R., Davidson, F.: Measurements of partially spatially coherent laser beam intensity fluctuations propagating through a hot-air turbulence emulator and comparison with both terrestrial and maritime environments. In Free-Space Laser Communication and Atmospheric Propagation XX 8610, pp. 185–196 (2013)

  • Nossir, N., Dalil-Essakali, L., Belafhal, A.: Behavior of the central intensity of generalized Humbert-Gaussian beams against the atmospheric turbulence. Opt. Quant. Electron. 53, 1–3 (2021)

    Article  Google Scholar 

  • Nossir, N., Dalil-Essakali, L., Belafhal, A.: Introduction of Bessel higher-order cosh-Gaussian beam and its propagation through a paraxial ABCD optical system. Opt. Quant. Electron. 55, 1–16 (2023b)

    Article  Google Scholar 

  • Nossir, N., Dalil-Essakali, L., Belafhal, A.: Effects of moderate to weak atmospheric turbulence on the propagation properties of the Whittaker-Gaussian laser beam. Opt. Quant. Electron. (2023a).

  • Peixoto, J.P., Oort, A.H.: Physics of climate. Rev. Mod. Phys. 56, 365–429 (1984)

    Article  ADS  Google Scholar 

  • Saad, F., Benzehoua, H., Belafhal, A.: Propagation behavior of a new generalized laser beam through marine environment. Opt. Quant. Electron. (2023).

  • Toselli, I., Agrawal, B., Restaino, S.: Gaussian beam propagation in maritime atmospheric turbulence: long term beam spread and beam wander analysis. Proc. SPIE: Free-Space Laser Commun. X 7814, 207–216 (2010)

    Google Scholar 

  • Vetelino, F.S., Grayshan, K., Young, C.Y.: Inferring path average Cn2 values in the marine environment. J. Opt. Soc. Am. A 24, 3198–3206 (2007)

    Article  ADS  Google Scholar 

  • Zhang, Y., Shan, L., Li, Y., Yu, L.: Effects of moderate to strong turbulence on the Hankel Bessel-Gaussian pulse beam with orbital angular momentum in the marine-atmosphere. Opt. Express 25, 33469–33479 (2017)

    Article  ADS  Google Scholar 

  • Zhu, Y., Chen, M., Zhang, Y., Li, Y.: Propagation of the OAM mode carried by partially coherent modified Bessel-Gaussian beams in an anisotropic non-Kolmogorov marine atmosphere. J. Opt. Soc. Am. A Opt. Image Sci. vis. 33, 2277–2283 (2016a)

    Article  ADS  PubMed  Google Scholar 

  • Zhu, Y., Zhang, Y., Hu, Z.: Spiral spectrum of Airy beams propagation through moderate-to-strong turbulence of maritime atmosphere. Opt. Express 24, 10847–10857 (2016b)

    Article  ADS  PubMed  Google Scholar 

Download references

Funding

No funding is received from any organization for this work.

Author information

Authors and Affiliations

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

    N. Nossir, L. Dalil-Essakali & A. Belafhal

Authors
  1. N. Nossir
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Dalil-Essakali
    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

Contributions

All authors contributed to the study conception and design. All authors performed simulations, data collection and analysis and commented the present version of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to A. Belafhal.

Ethics declarations

Conflict of interest

The authors have no financial or proprietary interests in any material discussed in this article.

Ethical approval

This article does not contain any studies involving animals or human participants performed by any of the authors. We declare this manuscript is original, and is not currently considered for publication elsewhere. We further confirm that the order of authors listed in the manuscript has been approved by all of us.

Consent for publication

The authors confirm that there is informed consent to the publication of the data contained in the article.

Consent to participate

Informed consent was obtained from all authors.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nossir, N., Dalil-Essakali, L. & Belafhal, A. Maritime turbulence effect on the axis light intensity of a Bessel higher-order cosh-Gaussian laser beam. Opt Quant Electron 56, 364 (2024). https://doi.org/10.1007/s11082-023-06052-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-023-06052-5

Keywords

Search

Navigation