Skip to main content
Log in

Diffraction of generalized Humbert–Gaussian beams by a helical axicon

  • Published:
Optical and Quantum Electronics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

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)

    Article  ADS  Google Scholar 

  • Bandres, M.A., Gutierrez-Vega, J.C.: Circular beams. Opt. Lett. 33, 177–179 (2008)

    Article  ADS  Google Scholar 

  • 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)

    Google Scholar 

  • Belafhal, A., Saad, F.: Conversion of circular beams by a spiral phase plate: Generation of Generalized Humbert beams. Optik 138, 516–528 (2017)

    Article  ADS  Google Scholar 

  • Born, M., Wolf, E.: Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th edn. Cambridge University Press, Cambridge (1999)

    Book  Google Scholar 

  • 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)

    Article  ADS  Google Scholar 

  • 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)

    Article  ADS  Google Scholar 

  • Dang, X., Geng, T., Zhuang, S.: Focusing properties of hyperbolic-cosine-Gaussian beams combining a helical axicon. Optik 124, 3422–3426 (2013)

    Article  ADS  Google Scholar 

  • Davidson, N., Friesem, A.A., Hasman, E.: Optical coordinate transformations. Appl. Opt. 31, 1067–1073 (1992)

    Article  ADS  Google Scholar 

  • 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)

    Article  ADS  Google Scholar 

  • Deng, D., Guo, Q.: Propagation of self-trapped circular beams in strongly nonlocal nonlinear media. Optics commun. 283, 3777–3783 (2010)

    Article  ADS  Google Scholar 

  • Felsen, L.B., Marcuvitz, N.: Radiation and scattering of waves. IEEE Press, New York (1994)

    Book  Google Scholar 

  • Gahagan, K.T., Swartzlander, G.A.: Optical vortex trapping of particles. Opt. Lett. 21, 827–829 (1996)

    Article  ADS  Google Scholar 

  • 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)

    Article  ADS  Google Scholar 

  • Gradshteyn, I.S., Ryzhik, I.M., Jeffrey, A.: Table of integrals, series and products, 6th edn. Academic Press, Amsterdam (2000)

    MATH  Google Scholar 

  • 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)

    Article  ADS  Google Scholar 

  • Indebetouw, G.: Optical vortices and their propagation. J. Mod. Opt. 40, 73–87 (1993)

    Article  ADS  Google Scholar 

  • 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)

    Article  ADS  Google Scholar 

  • 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)

    Article  ADS  MathSciNet  Google Scholar 

  • McGloin, D., Spalding, G., Melville, H., Sibbett, W., Dholakia, K.: Applications of spatial light modulators in atom optics. Opt. Express. 11, 158–166 (2003)

    Article  ADS  Google Scholar 

  • Molloy, E.J., Dholakia, K., Padgett, M.J.: Optical tweezers in a new light. J. Mod. Opt. 50, 1501–1507 (2003)

    ADS  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Prudnikov, A.P., Brichkov, Y.A., Marichev, O.I.: Integrals and Series. Special Functions, Nauka, Moskva (1983)

    Google Scholar 

  • 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)

    Google Scholar 

  • Ramachandran, S., Kristensen, P., Yan, M.F.: Generation and propagation of radially polarized beams in optical fibers. Opt. Lett. 34, 2525–2527 (2009)

    Article  ADS  Google Scholar 

  • 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)

    Article  ADS  Google Scholar 

  • 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)

    Article  ADS  Google Scholar 

  • 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)

    Google Scholar 

  • Topuzoski, S.: Fraunhofer diffraction of Laguerre-Gaussian laser. Opt. Commun. 330, 184–190 (2014)

    Article  ADS  Google Scholar 

  • Topuzoski, S., Janicijevic, L.: Diffraction of Laguerre-Gaussian beam by a helical. Acta Phys. Pol. A. 116, 557–559 (2009)

    Article  ADS  Google Scholar 

  • 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)

    Article  ADS  Google Scholar 

  • Vallone, G.: On the properties of circular beams: normalization, Laguerre–Gauss expansion and free-space divergence. Opt. lett. 40, 1717–1720 (2015)

    Article  ADS  Google Scholar 

  • Vasara, A., Turunen, J., Friberg, A.T.: Realization of general nondiffracting beams with computer-generated holograms. JOSA A. 6, 1748–1754 (1989)

    Article  ADS  Google Scholar 

  • 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)

    Article  ADS  Google Scholar 

  • Wei, L., Gao, Y., Wen, X., Zhao, Z., Cao, L., Gu, Y.: Fractional spiral zone plates. JOSA A. 30, 233–237 (2013)

    Article  ADS  Google Scholar 

  • 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)

    Article  ADS  Google Scholar 

  • 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)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. Belafhal.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-020-02662-5

Keywords

Navigation