Abstract
In the present paper, the diffraction of the Generalized Humbert–Gaussian beams by a helical axicon based on the process of the Fresnel diffraction is investigated. We have derived an analytical expression of the intensity distribution for the diffracted beams and compared it to that obtained by the stationary phase method. Numerical simulations are performed to analyze the comportment of the diffracted beams by controlling the parameters of the input beams and the topological charge of the helical axicon.
Similar content being viewed by others
References
Arlt, J., Dholakia, K.: Generation of high-order Bessel beams by use of an axicon. Opt. Commun. 177, 297–301 (2000)
Bandres, M.A., Gutierrez-Vega, J.C.: Circular beams. Opt. Lett. 33, 177–179 (2008)
Bandres, M.A., Lopez-Mago, D., Gutierrez-Vega, J.C.: Higher-order moments and overlaps of rotationally symmetric beams. J. Opt. 12, 1–10 (2010)
Belafhal, A., Saad, F.: Conversion of circular beams by a spiral phase plate: Generation of Generalized Humbert beams. Optik 138, 516–528 (2017)
Born, M., Wolf, E.: Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th edn. Cambridge University Press, Cambridge (1999)
Bozinovic, N., Yue, Y., Ren, Y., Tur, M., Kristensen, P., Huang, H., Willner, A.E., Ramachandran, S.: Terabit-scale orbital angular momentum mode division multiplexing in fibers. Science 340, 1545–1548 (2013)
Čižmár, T., Kollárová, V., Tsampoula, X., Gunn-Moore, F., Sibbett, W., Bouchal, Z., Dholakia, K.: Generation of multiple Bessel beams for a biophotonics workstation. Opt. Express. 16, 14024–14035 (2008)
Dang, X., Geng, T., Zhuang, S.: Focusing properties of hyperbolic-cosine-Gaussian beams combining a helical axicon. Optik 124, 3422–3426 (2013)
Davidson, N., Friesem, A.A., Hasman, E.: Optical coordinate transformations. Appl. Opt. 31, 1067–1073 (1992)
Davis, J.A., Carcole, E., Cottrell, D.M.: Intensity and phase measurements of nondiffracting beams generated with a magneto-optic spatial light modulator. Appl. Opt. 35, 593–598 (1996)
Deng, D., Guo, Q.: Propagation of self-trapped circular beams in strongly nonlocal nonlinear media. Optics commun. 283, 3777–3783 (2010)
Felsen, L.B., Marcuvitz, N.: Radiation and scattering of waves. IEEE Press, New York (1994)
Gahagan, K.T., Swartzlander, G.A.: Optical vortex trapping of particles. Opt. Lett. 21, 827–829 (1996)
Garcés-Chávez, V., McGloin, D., Melville, H., Sibbett, W., Dholakia, K.: Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam. Nature 419, 145–147 (2002)
Gradshteyn, I.S., Ryzhik, I.M., Jeffrey, A.: Table of integrals, series and products, 6th edn. Academic Press, Amsterdam (2000)
Heckenberg, N.R., McDuff, R., Smith, C.P., White, A.G.: Generation of optical phase singularities by computer-generated holograms. Opt. Lett. 17, 221–223 (1992)
Indebetouw, G.: Optical vortices and their propagation. J. Mod. Opt. 40, 73–87 (1993)
Khonina, S.N., Kotlyar, V.V., Shinkaryev, M.V., Soifer, V.A., Uspleniev, G.V.: The phase rotor filter. J. Mod. Opt. 39, 1147–1154 (1992)
Kotlyar, V.V., Kovalev, A.A., Skidanov, R.V., Moiseev, OYu., Soifer, V.A.: Diffraction of a finite-radius plane wave and a Gaussian beam by a helical axicon and a spiral phase plate. J. Opt. Soc. Am. A 24, 1955–1964 (2007)
McGloin, D., Spalding, G., Melville, H., Sibbett, W., Dholakia, K.: Applications of spatial light modulators in atom optics. Opt. Express. 11, 158–166 (2003)
Molloy, E.J., Dholakia, K., Padgett, M.J.: Optical tweezers in a new light. J. Mod. Opt. 50, 1501–1507 (2003)
Nossir, N., Dalil-Essakali, L., Belafhal, A.: Propagation analysis of some doughnut lasers beams through a paraxial ABCD optical system. Opt. Quan. Elec. 52, 1–16 (2020)
Prudnikov, A.P., Brichkov, Y.A., Marichev, O.I.: Integrals and Series. Special Functions, Nauka, Moskva (1983)
Qiong-Ge, S., Ke-Ya, Z., Guang-Yu, F., Zheng-Jun, L., Shu-Tian, L.: Generalization and propagation of spiraling Bessel beams with a helical axicon. Chin. Phys. B 21, 1–10 (2012)
Ramachandran, S., Kristensen, P., Yan, M.F.: Generation and propagation of radially polarized beams in optical fibers. Opt. Lett. 34, 2525–2527 (2009)
Ren, Z., Hu, H., Peng, B.: Generation of Mathieu beams using the method of combined axicon and amplitude modulation. Opt. Commun. 426, 226–230 (2018)
Saad, F., Hricha, Z., Khouilid, M., Belafhal, A.: A theoretical study of the Fresnel diffraction of Laguerre–Bessel–Gaussian beam bya helical axicon. Optik 149, 416–422 (2017)
Tamburini, F., Mari, E., Sponselli, A., Thidé, B., Bianchini, A., Romanato, F.: Encoding many channels on the same frequency through radio vorticity: first experimental test. New J. Phys. 14, 1–17 (2012)
Topuzoski, S.: Fraunhofer diffraction of Laguerre-Gaussian laser. Opt. Commun. 330, 184–190 (2014)
Topuzoski, S., Janicijevic, L.: Diffraction of Laguerre-Gaussian beam by a helical. Acta Phys. Pol. A. 116, 557–559 (2009)
Topuzoski, S., Janicijevic, L.J.: Conversion of high-order Laguerre-Gaussian beams into Bessel beams of increased, reduced or zeroth order by use of a helical axicon. Opt. Commun. 282, 3426–3432 (2009)
Vallone, G.: On the properties of circular beams: normalization, Laguerre–Gauss expansion and free-space divergence. Opt. lett. 40, 1717–1720 (2015)
Vasara, A., Turunen, J., Friberg, A.T.: Realization of general nondiffracting beams with computer-generated holograms. JOSA A. 6, 1748–1754 (1989)
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. Photonics 6, 488–496 (2012)
Wei, L., Gao, Y., Wen, X., Zhao, Z., Cao, L., Gu, Y.: Fractional spiral zone plates. JOSA A. 30, 233–237 (2013)
Yan, Y., Xie, G., Lavery, M.P.J., Huang, H., Ahmed, N., Bao, C., Ren, Y., Cao, Y., Li, L., Zhao, Z., Molisch, A.F., Tur, M., Padgett, M.J., Willner, A.E.: High-capacity millimetre-wave communications with orbital angular momentum multiplexing. Nat. Commun. 5, 4876–4884 (2014)
Zhang, P., Goodwin, P.M., Werner, J.H.: Fast, super resolution imaging via Bessel-beam stimulated emission depletion microscopy. Opt. Express. 22, 12398–12409 (2014)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Nossir, N., Dalil-Essakali, L. & Belafhal, A. Diffraction of generalized Humbert–Gaussian beams by a helical axicon. Opt Quant Electron 53, 94 (2021). https://doi.org/10.1007/s11082-020-02662-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-020-02662-5