Skip to main content
SpringerLink
Log in

Introduction of Bessel higher-order cosh-Gaussian beam and its propagation through a paraxial ABCD optical system

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

Abstract

In this paper, we introduce a new laser beam called Bessel higher-order cosh-Gaussian (BHChG) beam and analyzed its propagation properties through a paraxial ABCD optical system. The analytical expression of the diffracted beam is derived based on the extended Huygens–Fresnel integral and some numerical examples of BHChG beam propagating in a free space, through a thin lens and a Fractional Fourier transform system are exposed. The results reveal that the behavior of the output BHChG beam is affected by the optical system and the source beam parameters. The propagation of some laser beams through a paraxial ABCD optical system is deduced as particular case from the present study such as the fundamental Gaussian beam, the Bessel-Gaussian beam, the cosh-Gaussian beam, the Bessel-cosh-Gaussian beam and the Higher-order-cosh-Gaussian beam. The outcomes can be helpful for free-space optical communication, remote sensing and optical micromanipulation.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Data availability

No datasets is used in the present study.

References

  • Abramowitz, M., Stegun, I.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. U. S., Department of Commerce (1970)

  • Arlt, J., Garcés-Chávez, V., Sibbett, W., Dholakia, K.: Optical micromanipulation using a Bessel light beam. Opt. Commun. 197, 239–245 (2001)

    Article  ADS  Google Scholar 

  • Ashkin, A., Dziedzic, J.M., Yamane, T.: Optical trapping and manipulation of single cells using infrared laser beams. Nature 330, 769–771 (1987)

    Article  ADS  Google Scholar 

  • Augustyniak, I., Lamperska, W., Masajada, J., Płociniczak, L., Popiołek-Masajada, A.: Off-axis vortex beam propagation through classical optical system in terms of Kummer confluent hypergeometric function. Photonics 7, 1–21 (2020)

    Article  Google Scholar 

  • Belafhal, A., Dalil-Essakali, L.: Collins formula and propagation of Bessel-modulated Gaussian light beams through an ABCD optical system. Opt. Commun. 177, 181–188 (2000)

    Article  ADS  Google Scholar 

  • Benzehoua, H., Belafhal, A.: Effects of Hollow-Gaussian beams on Fresnel diffraction by an opaque disk. Opt. Quantum Electron. 55, 1–16 (2022)

    Google Scholar 

  • Benzehoua, H., Belafhal, A.: Analyzing the spectral characteristics of a pulsed Laguerre higher-order cosh-Gaussian beam propagating through a paraxial ABCD optical system. Opt. Quantum Electron. 55, 7–18 (2023a)

    Article  Google Scholar 

  • Benzehoua, H., Belafhal, A.: Spectral properties of pulsed Laguerre higher-order cosh-Gaussian beam propagating through the turbulent atmosphere. Opt. Commun. 541, 129492–129412 (2023b)

    Article  Google Scholar 

  • Boufalah, F., Essakali, L.D., Belafhal, A.: Transformation of a generalized Bessel Laguerre-Gaussian beam by a paraxial ABCD optical system. Opt. Quantum Electron. 51, 274–288 (2019)

    Article  Google Scholar 

  • Chen, S., Zhang, T., Feng, X.: Propagation properties of cosh-squared-Gaussian beam through fractional Fourier transform systems. Opt. Commun. 282, 1083–1087 (2009)

    Article  ADS  Google Scholar 

  • Chib, S., Hricha, Z., Belafhal, A.: Finite-Wright beams and their paraxial propagation. Opt. Quantum Electron. 54, 1–9 (2022)

    Article  Google Scholar 

  • Collins, S.A.: Lens-system diffraction integral written in terms of matrix optics. J. Opt. Soc. Am. 60, 1168–1177 (1970)

    Article  ADS  Google Scholar 

  • Dickson, L.D.: Characteristics of a propagating Gaussian beam. Appl. Opt. 9, 1854–1861 (1970)

    Article  ADS  Google Scholar 

  • Ditkine, V., Proudnikov, A.: Transformations Integrales et Calcul Operationnel. Moscow (1978)

  • Durnin, J.: Exact solutions for nondiffracting beams. I. The scalar theory. J. Opt. Soc. Am. A 4, 651–654 (1987)

    Article  ADS  Google Scholar 

  • Durnin, J., Miceli, J.J., Everly, J.H.: Diffraction free beams. Phys. Rev. Lett. 58, 1499–1501 (1987)

    Article  ADS  Google Scholar 

  • El Halba, E.M., Hricha, Z., Belafhal, A.: Fractional Fourier transforms of vortex Hermite-cosh-Gaussian beams. Results Opt. 5, 1–9 (2021)

    Article  Google Scholar 

  • El Halba, E.M., Hricha, Z., Belafhal, A.: Fractional Fourier transforms of circular cosine-hyperbolic Gaussian beams. J. Mod. Opt. 69, 1086–1093 (2022)

    Article  ADS  Google Scholar 

  • Gradshteyn, I.S., Ryzhik, I.M.: Tables of Integrals, Series, and Products, 5th edn. Academic Press, New York (1994)

    MATH  Google Scholar 

  • Ho, Q.Q., Hoang, D.H.: Dynamic of the dielectric nano-particle in optical tweezer using counter-propagating pulsed laser beams. J. Phys. Sci. Appl. 2, 345–351 (2012)

    Google Scholar 

  • Hricha, Z., El Halba, E.M., Belafhal, A.: Circular cosine-hyperbolic-Gaussian beam and its paraxial propagation properties. Opt. Commun. 502, 127400–127406 (2022)

    Article  Google Scholar 

  • Kotlyar, V.V., Abramochkin, E.G., Kovalev, A.A., Savelyeva, A.A.: Product of two Laguerre-Gaussian beams. Photonics 9, 496-1–9 (2022)

    Article  Google Scholar 

  • Mendlovic, D., Ozaktas, H.M.: Fractional Fourier transforms and their optical implementation: I. J. Opt. Soc. Am. 10, 1875–1881 (1993)

    Article  ADS  Google Scholar 

  • Mendoza-Hernández, J., Arroyo-Carrasco, M.L., Iturbe-Castillo, M.D., Chávez-Cerda, S.: Laguerre-Gauss beams versus Bessel beams showdown: peer comparison. Opt. Lett. 40, 3739–3742 (2015)

    Article  ADS  Google Scholar 

  • Monin, E.O., Ustinov, A.V.: The transformation of Hermite-Gauss beams with embedded optical vortex by lens system. J. Phys. Conf. Ser. 1038, 012039–012045 (2018)

    Article  Google Scholar 

  • Namias, V.: The fractional order Fourier transform and its application to quantum mechanics. IMA J. Appl. Math. 25, 241–265 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  • Nossir, N., Dalil-Essakali, L., Belafhal, A.: Propagation analysis of some doughnut lasers beams through a paraxial ABCD optical system. Opt. Quantum Electron. 52, 1–16 (2020)

    Article  MATH  Google Scholar 

  • Ozaktas, H.M., Mendlovic, D.: Fractional Fourier transforms and their optical implementation. J. Opt. Soc. Am. A 10, 2522–2531 (1993)

    Article  ADS  Google Scholar 

  • Saad, F., Belafhal, A.: Propagation properties of Hollow higher-order cosh-Gaussian beams in quadratic index medium and Fractional Fourier transform. Opt. Quantum Electron. 53, 1–16 (2021)

    Article  Google Scholar 

  • Saad, F., Hricha, Z., Khouilid, M., Belafhal, A.: A theoretical study of the Fresnel diffraction of Laguerre-Bessel-Gaussian beam by a helical axicon. Optik 149, 416–422 (2017)

    Article  ADS  Google Scholar 

  • Soskind, M., Soskind, Y.G.: Propagation invariant laser beams for optical metrology applications: In: Modeling Aspects in Optical Metrology. Proceedings of SPIE 9526, pp. 1–7 (2015)

  • Xu, X., Wang, Y., Jhe, W.: Theory of atom guidance in a hollow laser beam: dressed-atom approach. J. Opt. Soc. Am. B 17, 1039–1050 (2000)

    Article  ADS  Google Scholar 

  • Yu, S., Guo, H., Fu, X., Hu, W.: Propagation properties of elegant Hermite-cosh Gaussian laser beams. Opt. Commun. 204, 59–66 (2002)

    Article  ADS  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

Download references

Funding

No funding is received from any organization for this work.

Author information

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

    N. Nossir, L. Dalil-Essakali & A. Belafhal

Authors
  1. N. Nossir
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Dalil-Essakali
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Belafhal
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the study conception and design. All authors performed simulations, data collection and analysis and commented the present version of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to A. Belafhal.

Ethics declarations

Conflict of interest

The authors have no financial or proprietary interests in any material discussed in this article.

Ethical approval

This article does not contain any studies involving animals or human participants performed by any of the authors. We declare this manuscript is original, and is not currently considered for publication elsewhere. We further confirm that the order of authors listed in the manuscript has been approved by all of us.

Consent for publication

The authors confirm that there is informed consent to the publication of the data contained in the article.

Consent to participate

Informed consent was obtained from all authors.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

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. Introduction of Bessel higher-order cosh-Gaussian beam and its propagation through a paraxial ABCD optical system. Opt Quant Electron 55, 1082 (2023). https://doi.org/10.1007/s11082-023-05409-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-023-05409-0

Keywords

Search

Navigation