Abstract
The propagation properties of a vortex Hermite-cosh-Gaussian beam (vHChGB) in atmospheric turbulence are investigated based on the extended Huygens–Fresnel diffraction integral and Rytov method. The analytical formula for the average intensity of a vHChGB propagating in turbulent atmosphere is derived in detail. The influence of the turbulence strength on the intensity distribution under the change of beam parameters conditions is illustrated numerically and discussed. Results show that the profile of the initial vHChGB remains unchanged within small propagation distance range, and at certain propagation distance a central peak intensity appears, and finally the beam evolves into Gaussian profile–like in far-field. The rising speed of the central peak intensity is faster when the turbulence strength is larger or the beam parameters such as the beam order, the vortex charge and the Gaussian waist width are smaller. With a small decentered parameter b, the beam profile changes faster as the wavelength is larger, whereas the reverse behavior occurs when b is large. The obtained results may be useful for the practical applications of vHChGB in optical communications and remote sensing.
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References
Allen, L., Begersbergen, M.W., Spreeuw, R.J.C., Woerdman, J.P.: Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys. Rev. A 45, 8185–8189 (1992)
Andrews, L.C., Philips, R.L.: Laser beam propagation through random media. SPIE Press, Washington (1998)
Baykal, Y.: Correlation and structure functions of Hermite-sinusoidal-Gaussian beams in the turbulent atmosphere. J. Opt. Soc. Am. A Opt. Imag. Sci. Vis. 21, 1290–1299 (2004)
Belafhal, A., Ibnchaikh, M.: Propagation properties of Hermite-cosh-Gaussian laser beams. Opt. Comm. 186, 269–276 (2000)
Belafhal, A., Hricha, Z., Dalil-Essakali, L., Usman, T.: A note on some integrals involving Hermite polynomials and their applications. Adv. Math. Mod. App. 5(3), 313–319 (2020)
Bishop, A.I., Nieminen, T.A., Heckenberg, N.R., Rubinsztein, H.: Optical microrheology using rotating laser-trapped particles. Phys. Rev. Lett. 92(19), 198104–198107 (2004)
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. Elect. 50, 305–325 (2018)
Cai, Y.: Propagation of various flat-topped beams in a turbulent atmosphere. J. Opt. A. Pure Appl. Opt. 8, 537–545 (2006)
Cai, Y., He, S.: Propagation of various dark hollow beams in a turbulent atmosphere. Opt. Exp. 14, 1353–1367 (2006)
Cai, Y., Lu, X., Lin, Q.: Hollow Gaussian beam and its propagation. Opt. Lett. 28, 1084–1086 (2003)
Casperson, L.W., Tovar, A.A.: Hermite-Sinusoidal-Gaussian beams in complex optical systems. J. Opt. Soc. Am. A 15, 954–961 (1998)
Dai, H.T., Liu, Y.J., Luo, D., Sun, X.W.: Propagation properties of an optical vortex carried by an airy beam: experimental implementation’. Opt. Lett. 36(9), 1617–1619 (2011)
Eyyuboglu, H.T.: Propagation of Hermite-cosh-Gaussian laser beams in turbulent atmosphere. Opt. Comm. 245, 37–47 (2005)
Gao, C., Wei, G., Weber, H.: Orbital angular momentum of the laser beam and the second-order intensity moments. Sci. in Chin. A 43(12), 1306–1311 (2000)
Gradshteyn, I.S., Ryzhik, I.M.: Tables of integrals series and products, 5th edn. Academic Press, New York (1994)
Guo, L., Tang, Z., Wan, W.: Propagation of a four-petal Gaussian vortex beam through a paraxial ABCD optical system. Optik 125(19), 5542–5545 (2014)
Hricha, Z., Belafhal, A.: Focusing properties of focal Hermite-cosh-Gaussian beams. Opt. Comm. 253, 242–249 (2005)
Hricha, Z., Yaalou, M., Belafhal, A.: Intensity characteristics of double–half inverse Gaussian hollow beams through turbulent atmosphere. Opt. Quant. Elect. 52, 201–207 (2020a)
Hricha, Z., Yaalou, M., Belafhal, A.: Introduction of a new vortex cosine-hyperbolic-Gaussian beam and the study of its propagation properties in fractional fourier transform optical system. Opt. Quant. Elect. 52, 296–302 (2020b)
Hricha, Z., Lazrek, M., Yaalou, M., Belafhal, A.: Propagation of vortex cosine-hyperbolic-Gaussian beams in atmospheric turbulence. Opt. Quant. Elect. 53(8), 383–398 (2021a)
Hricha, Z., Yaalou, M., Belafhal, A.: Introduction of the vortex Hermite-Cosh-Gaussian beam and the analysis of its intensity pattern upon propagation. Opt. Quant. Elect. 53, 80 (2021b)
Ibnchaikh, M., Dalil-Essakali, L., Hricha, Z., Belafhal, A.: Parametric characterization of truncated Hermite-cosh-Gaussian beams. Opt. Comm. 190, 29–36 (2001)
Korotkova O, Gbur G (2007) “Propagation of beams with any spectral, coherence and polarization properties in turbulent atmosphere”. Proc-SPIE 6457, 64570J1–64570J12.
Kotlyar, V.V., Kovalev, A.A., Porfirev, A.P.: Vortex Hermite-Gaussian laser beams’. Opt. Lett. 40(5), 701–704 (2015)
Kuga, T., Torii, Y., Shiokawa, N., Hirano, T., Shimizu, Y., Sasada, H.: Novel optical trap of atoms with a doughnut beam. Phys. Rev. Lett. 78, 4713–4716 (1997)
Liu, H., Lü, Y., Xia, J., Pu, X., Zhang, L.: Flat-topped vortex hollow beam and its propagation properties’. J. Opt. 17, 075606 (2015)
Lukin, V.P., Konyaev, P.A., Sennikov, V.A.: Beam spreading of vortex beams propagating in turbulent atmosphere. App. Opt. 51(10), 84–87 (2012)
Mei, Q.X., Yue, Z.W., Zhong, R.R.: Intensity distribution properties of Gaussian vortex beam propagation in atmospheric turbulence. Chin. Phys. B 24(4), 044201–044205 (2015)
Ni, Y., Zhou, G.: Propagation of a Lorentz-Gauss vortex beam through a paraxial ABCD optical system. Opt. Comm. 291, 19–25 (2013)
Noriega-Manez, R.J., Gutiérrez-Vega, J.C.: Rytov theory for Helmholtz-Gauss beams in turbulent atmosphere. Opt. Exp. 15, 16328–16341 (2007)
Paterson, L., MacDonald, M.P., Arlt, J., Sibbett, W., Bryant, P.E., Dholakia, K.: Controlled rotation of optically trapped microscopic particles. Science 292(5518), 912–914 (2001)
Ponomarenko, S.A.: A class of partially coherent beams carrying optical vortices. J. Opt. Soc. Am. A 18, 150–156 (2001)
Rubinsztein-Dunlop, H., Forbes, A., Berry, M.V., Dennis, M.R., Andrews, D.L., Mansuripur, M., Denz, C., Alpmann, C., Banzer, P., Bauer, T., Karimi, E., Marrucci, L., Padgett, M., Ritsch-Marte, M., Litchinitser, N.M., Bigelow, N.P., Rosales-Guzmán, C., Belmonte, A., Torres, J.P., Neely, T.W., Baker, M., Gordon, R., Stilgoe, A.B., Romero, J., White, A.G., Fickler, R., Willner, A.E., Xie, G., McMorran, B., Weiner, A.M.: “Roadmap on structured light”. J. Opt. 19(1), 013001 (2017)
Simpson, N.B., Dholakia, K., Allen, L., Padgett, M.J.: Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner. Opt. Lett. 22(1), 52–54 (1997)
Tovar, A.A., Casperson, L.W.: Production and propagation of Hermite-sinusoidal-Gaussian laser beams. J. Opt. Soc. Am. A 15, 2425–2432 (1998)
Wang, Z., Lin, Q., Wang, Y.: Control of atomic rotation by elliptical hollow beam carrying zero angular momentum. Opt. Comm. 240, 357–362 (2004)
Wang, F., Liu, X., Cai, Y.: Propagation of partially coherent beam in turbulent atmosphere: a review. Prog. Elec. Res. 150, 123–143 (2015)
Wang, J., Yang, J.Y., Fazal, I.M., Ahmed, N., Yan, Y., Huang, H., Ren, Y., Yue, Y., Dolinar, S., Tur, M., Willner, A.E.: Terabit free-space data transmission employing orbital angular momentum multiplexing. Nat. phot. 6(7), 488–496 (2012)
Yaalou, M., El Halba, E.M., Hricha, Z., Belafhal, A.: Propagation characteristics of Dark and Antidark Gaussian beams in a turbulent atmosphere. Opt. Quant. Elect. 51, 255–266 (2019)
Zhou, G.Q., Cai, Y., Dai, C.Q.: Hollow vortex Gaussian beams. Sci. Chin. Phys. Mech. Astron. 56(5), 896–903 (2013)
Zhou, Y., Zhou, G.: Orbital angular momentum density of a hollow vortex-Gausssian beam’. Prog. In. Elect. Res. M 38, 15–24 (2014)
Zhu, X., Wu, G., Luo, B.: Propagation of elegant vortex Hermite-Gaussian beams in turbulent atmosphere. Proc. SPIE 10158, 101580F-F101581 (2016)
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Hricha, Z., Lazrek, M., Yaalou, M. et al. Effects of turbulent atmosphere on the propagation properties of vortex Hermite-cosine-hyperbolic-Gaussian beams. Opt Quant Electron 53, 624 (2021). https://doi.org/10.1007/s11082-021-03255-6
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DOI: https://doi.org/10.1007/s11082-021-03255-6