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Transformation of higher-order cosh-Gaussian beams into an Airy-related beams by an optical airy transform system

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Abstract

In this paper, we investigate the transformation of a higher-order cosh-Gaussian beam into an Airy-related beam by an Airy transform optical system. Based on the Huygens-Fresnel integral diffraction, the analytical expression of the generated curved beam is derived. The effects of the decentered parameter b, the beam orders, and the phase constants (α and β) on the generated beam are discussed numerically. It is shown that the number and the intensity distributions of side lobes of the generated beam pattern depend on the parameter b and the beam orders. Peak band structures are observed for higher-orders and large b. Furthermore, the localization of the beam pattern in the plane depends on the relative signs of α and β. The obtained results may be useful in practical applications dealing with Airy beams.

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References

  • Baumgartl, J., Mazilu, M., Dholakia, K.: Optically mediated particle clearing using Airy wavepackets. Nat. Photo. 2(11), 675–678 (2008)

    ADS  Google Scholar 

  • Berry, M.V., Balazs, N.L.: Nonspreading wave packets. Am. J. Phys. 47(3), 264–267 (1979)

    ADS  Google Scholar 

  • Casperson, L.W., Tovar, A.A.: Hermite-sinusoidal-Gaussian beams in complex optical systems. J. Opt. 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)

    ADS  MathSciNet  Google Scholar 

  • Chremmos, I.D., Efremidis, N.K.: Reflection and refraction of an Airy beam at a dielectric interface. J. Opt. Soc. Am. A 29, 861–868 (2012)

    ADS  Google Scholar 

  • Cottrell, D.M., Davis, J.A., Hazard, T.M.: Direct generation of accelerating Airy beams using a 3/2 phase-only pattern. Opt. Lett. 34(17), 2634–2636 (2009)

    ADS  Google Scholar 

  • Dai, H.T., Sun, X.W., Luo, D., Liu, Y.J.: Airy beams generated by binary phase element made of polymer dispersed liquid crystals. Opt. Exp. 17, 19365–19370 (2009)

    ADS  Google Scholar 

  • Davis, J.A., McNamara, D.E., Cottrell, D.M.: Analysis of the fractional Hilbert transform. App. Opt. 37(29), 6911–6913 (1998)

    ADS  Google Scholar 

  • Davis, J.A., McNamara, D.E., Cottrell, D.M., Campos, J.: Image processing with the radial Hilbert transform: theory and experiments. Opt. Lett. 25(2), 99–101 (2000)

    ADS  Google Scholar 

  • Dolev, I., Ellenbogen, T., Voloch-Bloch, N., Arie, A.: Control of free space propagation of Airy beams generated by quadratic nonlinear photonic crystals. Appl. Phys. Lett. 95(20), 201112–201112 (2009)

    ADS  Google Scholar 

  • Duan, K., Lü, B.: Four-petal Gaussian beams and their propagation. Opt. Commun. 261, 27–331 (2006)

    Google Scholar 

  • Ellenbogen, T., Voloch-Bloch, N., Ganany-Padowicz, A., Arie, A.: Nonlinear generation and manipulation of Airy beams. Nat. Photo. 3(7), 395–398 (2009)

    ADS  Google Scholar 

  • Ez-zariy, L., Hricha, Z., Belafhal, A.: Novel finite airy array beams generated from Gaussian array beams illuminating an optical airy transform system. Prog. in Electro. Res. M 49, 41–50 (2016)

    Google Scholar 

  • Ez-zariy, L., Boufalah, F., Dalil-Essakali, L.: Belafhal, “a conversion of the hyperbolic-cosine Gaussian beam to a novel Finite Airy-related beam using an optical Airy transform system.” Optik 171, 501–506 (2018)

    ADS  Google Scholar 

  • Goodman, J.W.: Introduction to fourier optics. Roberts and Company Publishers, US (2005)

    Google Scholar 

  • Gradshteyn, I.S., Ryzhik, I.M.: Tables of integrals series and products, 5th edn. Academic Press, New York (1994)

    MATH  Google Scholar 

  • Hu, Y., Zhang, P., Lou, C., Huang, S., Xu, J., Chen, Z.: Optimal control of the ballistic motion of Airy beams. Opt. Let. 35(13), 2260–2262 (2010)

    ADS  Google Scholar 

  • Jia, S., Lee, J., Fleischer, J.W., Siviloglou, G.A., Christodoulides, D.N.: Diffusion-trapped Airy beams in photorefractive media. Phys. Rev. Lett. 104(25), 253904–253907 (2010)

    ADS  Google Scholar 

  • Jiang, Y., Huang, K., Lu, X.: The optical Airy transform and its application in generating and controlling the Airy beam. Opt. Commun. 285, 4840–4843 (2012a)

    ADS  Google Scholar 

  • Jiang, Y., Huang, K., Lu, X.: Airy related beam generated from flat-topped Gaussian beams. J. Opt. Soc. Am. A. 29(7), 1412–1416 (2012b)

    ADS  Google Scholar 

  • Li, J., Chen, Y., Xin, Y., Xu, S.: Propagation of higher-order cosh-Gaussian beams in uniaxial crystals orthogonal to the optical axis. Eur. Phys. J. D 57(3), 419–425 (2010)

    ADS  Google Scholar 

  • Li, J., Chen, Y., Xu, S., Wang, Y., Zhou, M., Zhao, Q., Xin, Y., Chen, F.: Far-field vectorial structure of a higher-order cosh-Gaussian beam. J. Mod. Opt. 57(20), 2039–2047 (2010)

    ADS  MATH  Google Scholar 

  • Ozaktas, H.M., Zalevsky, Z., Kutay, M.A.: The fractional fourier transform with applications in optics and signal processing. Wiley, New York (2001)

    Google Scholar 

  • Polynkin, P., Kolesik, M., Moloney, J.V., Siviloglou, G.A., Christodoulides, D.N.: Curved plasma channel generation using ultraintense Airy beams. Scien. 324(5924), 229–232 (2009)

    ADS  Google Scholar 

  • Polynkin, P., Kolesik, M., Moloney, J., Siviloglou, G., Christodoulides, D.N.: Extreme nonlinear optics with ultra-intense self-bending Airy beams. Opt. and Photo. News 21(9), 38–43 (2010)

    Google Scholar 

  • Rose, P., Diebel, F., Boguslawski, M., Denz, C.: Airy beam induced optical routing. Appl. Phys. Lett. 102, 101101–101103 (2013)

    ADS  Google Scholar 

  • Siviloglou, G.A., Christodoulide, D.N.: Accelerating finite energy Airy beams. Opt. Lett. 32, 979–981 (2007)

    ADS  Google Scholar 

  • Siviloglou, G.A., Broky, J., Dogariu, A., Christodoulides, D.N.: Observation of accelerating Airy beams. Phys. Rev. Lett. 99, 213901–213904 (2007)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  • Vallée, O., Soares, M.: Airy functions and their applications to physics. Imperial College Press, London (2004)

    MATH  Google Scholar 

  • Widder, D.V.: The Airy transform. Am. Math. Month. 86, 271–277 (1979)

    MathSciNet  MATH  Google Scholar 

  • Yaalou, M., El Halba, E.M., Hricha, Z., Belafhal, A.: Transformation of double half inverse Gaussian hollow beams into superposition of finite Airy beams using an optical Airy transform. Opt. Quant. Electron. 51, 64–75 (2019)

    Google Scholar 

  • Yaalou, M., Hricha, Z., Halba, E.M., ELBelafhal, A.: Production of Airy-related beams by an Airy transform optical system. Opt. Quant. Electron. 51, 308–317 (2019)

    Google Scholar 

  • Yaalou, M., Hricha, Z., Belafhal, A.: Propagation properties of Cosh-Airy beams by through an Airy transform optical system. Opt. Quant. Electron. 51, 356–368 (2019)

    Google Scholar 

  • Yaalou, M., Hricha, Z., Belafhal, A.: Investigation on Airy transform of Four Petal Gaussian beams. Opt. Quant. Electron. 52, 165–178 (2020)

    Google Scholar 

  • Zhou, G.: Fractional Fourier transform of a higher-order cosh-Gaussian beam. J. Mod. Opt. 56(7), 886–892 (2009)

    ADS  MATH  Google Scholar 

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

    ADS  Google Scholar 

  • Zhou, G., Zheng, J.: Beam propagation of a higher-order cosh-Gaussian beams. Opt. Laser Techno. 41(2), 202–208 (2009)

    ADS  Google Scholar 

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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

    M. Yaalou, Z. Hricha & A. Belafhal

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  1. M. Yaalou
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  2. Z. Hricha
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  3. A. Belafhal
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Correspondence to Z. Hricha or A. Belafhal.

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Yaalou, M., Hricha, Z. & Belafhal, A. Transformation of higher-order cosh-Gaussian beams into an Airy-related beams by an optical airy transform system. Opt Quant Electron 52, 461 (2020). https://doi.org/10.1007/s11082-020-02594-0

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