Abstract
Based on the Huygens–Fresnel diffraction integral, the analytical expression for a vortex Hermite-cosh-Gaussian beam (vHChGB) propagating in a gradient-index medium (GIM) is derived. From the obtained expression, the evolution of the intensity and the phase distributions of the vHChGB through GIM are analyzed numerically as a function of the gradient-index parameter \(\beta\) and under the change of the incident beam parameters. The results show that the output beam evolves periodically versus the propagation distance, and the period of the self-repetition slows down as the parameter \(\beta\) is increased. It is found that the self-repetition of the intensity and phase distributions of the field in GIM is altered by the incident beam parameters. The results obtained may be beneficial for applications in fiber communications and beam shaping.
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References
Belafhal, A., Hricha, Z., Dalil-Essakali, L., Usman, T.: A note on some integrals involving Hermite polynomials and their applications. Adv. Math. Mod. and Appl. 5(3), 313–319 (2020)
Collins, S.A.: Lens-system diffraction integral written in terms of matrix optics. J. Opt. Soc. Am 60, 1168–1177 (1970)
Feng, L., Zhang, J., Pang, Z., Wang, L., Zhong, T., Yang, X., Deng, D.: Propagation properties of the chirped Airy beams through the gradient-index medium. Opt. Commun. 402, 60–65 (2017)
Gomez-Reino, C., Perez, M.V., Bao, C.: Gradient-Index Optics. Fundamentals and Applications. Springer, Berlin (2002)
Gradshteyn, I.S., Ryzhik, I.M.: Tables of Integrals Series, and Products, 5th edn. Academic Press, New York (1994)
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 (2020)
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, 80–87 (2021a)
Hricha, Z., Yaalou, M., Belafhal, A.: Propagation properties of vortex cosine-hyperbolic-Gaussian beams in strongly nonlocal nonlinear media. J. Quant. Spectrosc. Radiat. Transf. 5, 107554–107561 (2021b)
Hricha, Z., El Halba, E.M., Lazrek, M., Belafhal, A.: Focusing properties and focal shift of a vortex cosine-hyperbolic Gaussian beam. Opt. Quant. Elect. 53(8), 449–465 (2021c)
Hricha, Z., Lazrek, M., El Halba, E., Belafhal, A.: Parametric characterization of vortex cosine-hyperbolic-Gaussian beams. Resuls in Optics 5, 100120–100127 (2021d)
Hricha, Z., Lazrek, M., Yaalou, M., Belafhal, A.: Propagation of vortex cosine-hyperbolic-Gaussian beams in atmospheric turbulence. Opt. Quant. Elect 53(7), 383–398 (2021e)
Hricha, Z., Lazrek, M., Yaalou, M., Belafhal, A.: Propagation of vortex Hermite-cosine-hyperbolic-Gaussian beams in turbulent atmosphere. Opt. Quant. Elect. 53(11), 624–638 (2021f)
Hricha, Z., El Halba, E.M, Belafhal, A.: Focusing properties and focal shift of vortex Hermite-cosh- Gaussian beams. Submitted to Opt. Quant. Elect. (2021g)
Kotlyar, V.V., Kovalev, A.A., Porfirev, A.P.: Vortex Hermite-Gaussian laser beams’. Opt. Lett. 40(5), 701–704 (2015)
Leger, J.R., Kunkel, W.M.: Gradient-index design for mode conversion of diffracting beams. Opt. Express 24, 13480–13488 (2016)
McMullin, J.N.: The abcd matrix in arbitrarily tapered quadratic-index waveguides. Appl. Opt. 25(13), 2184–2187 (1986)
Moore, D.T.: Gradient-index optics: a review. Appl. Opt. 19, 1035–1038 (1980)
Saad, F., Belafhal, A.: Propagation properties of Hollow higher-order cosh-Gaussian beams in quadratic index medium and Fractional Fourier transform. Opt. Quant. Elect. 53(1), 28–43 (2021)
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, 52–54 (1997)
Song, S.H., Park, S., Oh, C.H., Kim, P.S., Cho, M.H., Kim, Y.S.: Gradient-index planar optics for optical interconnections. Opt. Lett. 23, 1025–1027 (1998)
Song, H.Y., Song, T.R., Chen, S.H., Huang, Y.C., Li, Y.T., Zhang, W.L.: Propagation properties of cosine-Gaussian beams in gradient-index medium. High Power Laser Part. Beams 23, 890–894 (2011)
Uchida, T., Furukawa, M., Kitano, I., Koizumi, K., Matsumura, H.: Optical characteristics of a light-focusing fiber guide and its applications. IEEE J. Quant. Elect. 6, 606–612 (1970)
Yang, S., Wang, J., Guo, M., Qin, Z., Li, J.: Propagation properties of Gaussian vortex beams through the gradient-index medium. Opt. Commun. 465, 125559–125563 (2020)
Zhao, R., Deng, F., Yu, W., Huang, J., Deng, D.: Propagation properties of Airy-Gaussian vortex beams through the gradient-index medium. J. Opt. Soc. Am. A 33, 1025–1031 (2016)
Zhou, G.: Propagation of a Lorentz-Gauss beam in gradient-index medium. High Power Laser Part. Beams 25(1), 42–46 (2013)
Zhou, G.Q., Cai, Y., Dai, C.Q.: Hollow vortex Gaussian beams. Sci. in Chin. 56(5), 896–903 (2013)
Zou, D., Li, X., Pang, X., Zheng, H., Ge, Y.: Propagation properties of hollow sinh-Gaussian beams in quadratic-index medium. Opt. Commun. 401, 54–58 (2017)
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Lazrek, M., Hricha, Z. & Belafhal, A. Propagation of vortex Hermite-cosh-Gaussian beams in a gradient-index medium. Opt Quant Electron 54, 67 (2022). https://doi.org/10.1007/s11082-021-03427-4
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DOI: https://doi.org/10.1007/s11082-021-03427-4