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Propagation behavior of a generalized Hermite cosh-gaussian laser beam through marine environment

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Abstract

Based on the extended Huygens-Fresnel principal, we investigate the propagation behavior of a Generalized a Hermite cosh-Gaussian (GHCG) beam through random medium namely maritime atmospheric turbulence. The analytical formula for the GHCG beam propagating in the considered medium is derived. The influences of the maritime turbulence parameters and the source beam parameters on the propagation characteristics of the GHCG beam are illustrated using numerical calculations. The results show that the evolution behavior of average intensity for a GHCG beam through maritime turbulence will gradually lose its properties and its resistance to fluctuations and then evolve faster into Gaussian distribution in the far field as the turbulent constant structure increases and as the inner scale size of the turbulence decreases. The propagation of optical radiation across this medium has differing impacts compared to the atmosphere above land. The obtained results can be significantly contributed to the practical application for free-space optical communication and remote sensing.

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References

  • Aggarwal, M., Vij, S., Kant, N.: Propagation of cosh Gaussian laser beam in plasma with density ripple in relativistic-ponderomotive regime. Optik 125, 5081–5084 (2014)

    ADS  Google Scholar 

  • Andrews, L.C., Phillips, R.L.: Laser Beam Propagation through Random Media. SPIE Press, Bellingham, Washington, DC, USA (2005)

    Google Scholar 

  • Belafhal, A., Hricha, Z., Dalil-Essakali, L., Usman, T.: A note on some integrals involving Hermite polynomials encountered in caustic optics. Adv. Math. Models App. 5, 313–319 (2020)

    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)

    MathSciNet  Google Scholar 

  • Benzehoua, H., Belafhal, A.: Analysis of the behavior of pulsed vortex beams in oceanic turbulence. Opt. Quant. Electron. 55, 1–14 (2023a)

    Google Scholar 

  • Benzehoua, H., Belafhal, A.: The effects of atmospheric turbulence on the spectral changes of diffracted pulsed hollow higher-order cosh-Gaussian beam. Opt. Quant. Electron. 55, 1–20 (2023)

    Google Scholar 

  • Benzehoua, H., Belafhal, A.: Spectral properties of pulsed Laguerre higher-order cosh-gaussian beam propagating through the turbulent atmosphere. Opt. Commun. 15, 129492–1294101 (2023c)

    Google Scholar 

  • Born, M., Wolf, E.: Principles of Optics, 7th edn. Cambridge University Press, Cambridge, UK (1999)

    Google Scholar 

  • Cai, Y., Lin, Q.: The elliptical Hermite-gaussian beam and its propagation through paraxial systems. Opt. Commun. 207, 139–147 (2002)

    CAS  ADS  Google Scholar 

  • Cao, P.: Effect of anisotropy on the M2-factor and angular spreading of partially coherent Hermite-gaussian beam propagating in anisotropic oceanic turbulence. Optik 178, 1145–1153 (2019)

    ADS  Google Scholar 

  • Casperson, L.W., Tovar, A.A.: Hermite-sinusoidal-Gaussian beams in complex optical systems. J. Opt. Soc. Am. A 15, 954–961 (1998)

    ADS  Google Scholar 

  • Casperson, L.W., Hall, D.G., Tovar, A.A.: Sinusoidal-Gaussian beams in complex optical systems. J. Opt. Soc. Am. A 14, 3341–3348 (1997)

    MathSciNet  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, 1–12 (2023)

    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 (2023)

    ADS  Google Scholar 

  • Chu, X.: Propagation of a cosh-gaussian beam through an optical system in turbulent atmosphere. Opt. Express 15, 17613–17618 (2007)

    PubMed  ADS  Google Scholar 

  • Chu, X., Ni, Y., Zhou, G.: Propagation of cosh-gaussian beams diffracted by a circular aperture in turbulent atmosphere. Appl. Phys. B 87, 547–552 (2007)

    CAS  ADS  Google Scholar 

  • Ebrahim, A.A.A., Saad, F., Swillam, M.A., Belafhal, A.: Propagation of the kurtosis parameter of hollow higher-order cosh gaussian beams through paraxial optical ABCD system. Opt. Quant. Electron. 54, 1–12 (2022)

    Google Scholar 

  • Elmabruk, K., Bayraktar, M.: Propagation of hollow higher-order cosh-gaussian beam in oceanic turbulence. Phys. Scr. 98, 035519–035529 (2023)

    ADS  Google Scholar 

  • Eyyuboğlu, H.T.: Propagation of Hermite-cosh-Gaussian laser beams in turbulent atmosphere. Opt. Commun. 245, 37–47 (2005)

    ADS  Google Scholar 

  • Eyyuboğlu, H.T., Baykal, Y.: Analysis of reciprocity of cos-gaussian and cosh- gaussian laser beams in a turbulent atmosphere. Opt. Express 12, 4659–4674 (2004)

    PubMed  ADS  Google Scholar 

  • Eyyuboğlu, H.T., Baykal, Y.: Average intensity and spreading of cosh-gaussian laser beams in the turbulent atmosphere. Appl. Opt. 44, 976–983 (2005)

    PubMed  ADS  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • Friehe, C.A., La, J.C., Rue, F.H., Champagne-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)

    ADS  Google Scholar 

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

    Google Scholar 

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

    ADS  Google Scholar 

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

    CAS  ADS  Google Scholar 

  • Miks, A., Novak, J.: Propagation of Gaussian beam in optical system with aberrations. Optik 114, 437–440 (2003)

    ADS  Google Scholar 

  • Mikš, A., Novák, P.: Paraxial properties of two-element zoom systems for Gaussian beam transformation. Optik 126, 4249–4253 (2015)

    ADS  Google Scholar 

  • Moshkelgosha, M.: Controlling the relativistic self-focusing of Hermite-cosh-gaussian beams in plasma. Optik 182, 80–87 (2019)

    ADS  Google Scholar 

  • Qiu, Y., Guo, H., Chen, Z.: Paraxial propagation of partially coherent Hermite-Gauss beams. Opt. Commun. 245, 21–26 (2005)

    CAS  ADS  Google Scholar 

  • Saad, F., Belafhal, A.: Investigation on propagation properties of a new optical vortex beam: generalized Hermite cosh-Gaussian beam. Opt. Quant. Electron. 55, 1–16 (2022)

    Google Scholar 

  • Saad, F., Belafhal, A.: A comprehensive investigation on the propagation properties of a generalized Hermite cosh-Gaussian beam through atmospheric turbulence. Opt. Quant. Electron. 55, 1–12 (2023)

    Google Scholar 

  • Saad, F., Ebrahim, A.A.A., Belafhal, A.: Beam propagation factor of hollow higher-order cosh-Gaussian beams. Opt. Quant. Electron. 54, 1–10 (2022)

    Google Scholar 

  • Tovar, A.A., Casperson, L.W.: Production and propagation of Hermite-sinusoidal-gaussian laser beams. J. Opt. Soc. Am. A 15, 2425–2432 (1998)

    CAS  ADS  Google Scholar 

  • Wang, F., Liu, X., Cai, Y.: Propagation of partially coherent beam in turbulent atmosphere: a review. Prog. Electromagn. Res. 150, 123–143 (2015)

    Google Scholar 

  • Wang, Y., Liang, Y., Yao, J., Yuan, C., Zhou, Z.: Nonlinear propagation characteristics and ring structure of a Gaussian beam in collisionless plasmas with high order paraxial ray theory. Optik 179, 744–749 (2019)

    ADS  Google Scholar 

  • Wu, Y., Zhang, Y., Li, Y., Hu, Z.: Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence. Opt. Commun. 371, 59–66 (2016)

    CAS  ADS  Google Scholar 

  • Ye, F., Zhang, J., Xie, J., Deng, D.: Propagation properties of the rotating elliptical chirped Gaussian vortex beam in the oceanic turbulence. Opt. Commun. 426, 456–462 (2018)

    CAS  ADS  Google Scholar 

  • Zhou, G.: Propagation of higher-order cosh-Gaussian beams in turbulent atmosphere. Opt. Express 19, 3945–3951 (2011)

    PubMed  ADS  Google Scholar 

  • Zhou, G., Liu, F.: Far field structural characteristics of cosh-Gaussian beam. Opt. Laser Technol. 40, 302–308 (2008)

    ADS  Google Scholar 

  • Zhou, G., Zheng, J.: Beam propagation of a higher-order cosh-Gaussian beam. Opt. Laser Technol. 41, 202–208 (2009)

    ADS  Google Scholar 

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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.

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Correspondence to Abdelmajid Belafhal.

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Saad, F., Benzehoua, H. & Belafhal, A. Propagation behavior of a generalized Hermite cosh-gaussian laser beam through marine environment. Opt Quant Electron 56, 130 (2024). https://doi.org/10.1007/s11082-023-05711-x

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