Skip to main content
Log in

Propagation properties of general model vortex higher-order Cosh-Gaussian laser beam through uniaxial crystal orthogonal to the optical axis

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

Abstract

Properties of a General Model vortex higher-order Cosh-Gaussian (GMvHchG) beam propagating through uniaxial crystals orthogonal to the optical axis are investigated. Received field formula is derived based on Huygens-Fresnel integral. From the obtained formula, some numerical illustrative examples are plotted to analyze the propagation properties of the considered beam. The results show that the evolutions of the intensity and phase distributions of GMvHchG beam strongly depend on the refractive indices of the uniaxial crystal, the topological charge, the beam order and the decentered parameter of cosh part during propagation distances. The current study may provide a convenient way to produce astigmatic vortex hollow beams with variable profiles.

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
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

  • Bayraktar, M.: Propagation of hyperbolic sinusoidal Gaussian beams in uniaxial crystals orthogonal to the optical axis. Optik 233, 1–11 (2021)

    Article  Google Scholar 

  • Bayraktar, M.: Propagation of cosh-Gaussian beams in uniaxial crystals orthogonal to the optical axis. Indian J. Phys. 96, 2531–2540 (2022)

    Article  ADS  Google Scholar 

  • Bayraktar, M., Chib, S., Belafhal, A.: Propagation of finite-wright and mainardi beams in uniaxial crystals orthogonal to the optical axis. Opt. Quant. Electron. 55, 1–17 (2023)

    Article  Google Scholar 

  • Belafhal, A., Hricha, Z., Dalil-Essakali, L., Usman, T.: A note on some integrals involving Hermite polynomials and their applications. Adv. Math. Mod. Appl. 5, 313–319 (2020)

    Google Scholar 

  • Born, M., Wolf, E.: Principles of Optics, 7th edn. Cambridge University Press, Cambridge (1999)

    Book  Google Scholar 

  • Chib, S., Khannous, F., Belafhal, A.: Propagation of general model vortex higher-order cosh-Gaussian beam in maritime turbulence. Opt. Quant. Electron. 55, 1–12 (2023)

    Article  Google Scholar 

  • Ciattoni, A., Palma, C.: Optical propagation in uniaxial crystals orthogonal to the optical axis: paraxial theory and beyond. J. Opt. Soc. Am. A 20, 2163–2171 (2003)

    Article  ADS  Google Scholar 

  • Ciattoni, A., Crosignani, B., Porto, P.D.: Vectorial theory of propagation in uniaxially anisotropic media. J. Opt. Soc. Am. A 18, 1656–1661 (2001a)

    Article  ADS  Google Scholar 

  • Ciattoni, A., Cincotti, G., Palma, C.: Ordinary and extraordinary beams characterization inuniaxially anisotropic media. Opt. Commun. 195, 55–61 (2001b)

    Article  ADS  Google Scholar 

  • Cincotti, G., Ciattoni, A., Palma, C.: Hermite-Gauss beams in uniaxially anisotropic crystals. IEEE J. Quantum Electron. 37, 1517–1524 (2001)

    Article  ADS  Google Scholar 

  • Cincotti, G., Ciattoni, A., Palma, C.: Laguerre-Gauss and Bessel-Gauss beams in uniaxial crystals. Opt. Commun. 19, 1680–1688 (2002)

    MathSciNet  Google Scholar 

  • Cincotti, G., Ciattoni, A., Sapia, C.: Radially and azimuthally polarized vortices in uniaxial crystals. . 220, 33–40 (2003)

    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 

  • Deng, D., Yu, H., Xu, S., Shao, J., Fan, Z.: Propagation and polarization properties of hollow Gaussian beams in uniaxial crystals. Opt. Commun. 281, 202–209 (2008)

    Article  ADS  Google Scholar 

  • Ebrahim, A.A.A., Swillam, M.A., Belafhal, A.: Atmospheric turbulent effects on the propagation properties of a general model vortex higher-order cosh-Gaussian beam. Opt. Quant. Electron. 55, 1–13 (2023)

    Article  Google Scholar 

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

    Google Scholar 

  • Khonina, S.N., Karpeev, S.V., Alferov, S.V., Soifer, V.A.: Generation of cylindrical vector beams of high orders using uniaxial crystals. J. Opt. 17, 065001–065011 (2015)

    Article  ADS  Google Scholar 

  • Lazrek, M., Hricha, Z., Belafhal, A.: Propagation of vortex cosine hyperbolic Gaussian beams in uniaxial crystals orthogonal to the optical axis. Opt. Quantum. Electron. 54, 1–15 (2022)

    Google Scholar 

  • Li, J., Chen, Y.R.: Propagation of confluent hypergeomtric beam through uniaxial crystals orthogonal to the optical axis. Opt. Laser Technol. 44, 1603–1610 (2012)

    Article  ADS  Google Scholar 

  • Li, J., Xin, Y., Chen, Y.R., Xu, S.X., Wang, Y.Q., Zhou, M.C., Zhao, Q., Chen, F.N.: Diffraction of Gaussian vortex beam in uniaxial crystals orthogonal to the optical axis”. Eur. Phys. J. Appl. Phys. 53, 20701–20706 (2011)

    Article  ADS  Google Scholar 

  • Li, D.D., Peng, X., Peng, Y.L., Zhang, L.P., Deng, D.M.: Nonparaxial evolution of the Airy-Gaussian vortex beam in uniaxial crystal. J. Opt. Soc. Am. B 34, 891–898 (2017)

    Article  ADS  Google Scholar 

  • Li, L., Huan, Y., Wang, Y., Hua, D., Yang, X., Liu, D., Wang, Y.: The effects of uniaxial crystal on off-axis hollow vortex Gaussian beams. Optik 194, 163133–163141 (2019)

    Article  ADS  Google Scholar 

  • Lia, 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, 419–425 (2010)

    Article  ADS  Google Scholar 

  • Lin, R., Sun, H., Zhang, H., Liu, Y., Wu, J., Yu, J., Cai, Y., Zhu, X.: The Evolution in Characteristics of Twisted Hermite-Gaussian Schell-Model Beams Propagating in a Uniaxial Crystal. Photonics 10, 1–14 (2023)

    Article  Google Scholar 

  • Liu, D., Zhou, Z.: Various dark hollow beams propagating in uniaxial crystals orthogonal to the optical axis. J. Optics a-Pure Appl. Opt. 10, 095005–095013 (2008)

    Article  ADS  Google Scholar 

  • Liu, D.J., Zhou, Z.: Propagation properties of anomalous hollow beam in uniaxial crystals orthogonal to the optical axis. Opt. Laser Technol. 41, 877–884 (2009)

    Article  ADS  Google Scholar 

  • Liu, D., Zhou, Z.: Propagation and the kurtosis parameter of Gaussian flat-topped beams in uniaxial crystals orthogonal to the optical axis. Opt. Laser Eng. 48, 58–63 (2010)

    Article  Google Scholar 

  • Liu, D., He, W., Wang, Y., Yin, H.: Evolution properties of four-petal Gaussian vortex beam propagating in uniaxial crystals orthogonal to the optical axis. Eur. Phys. J. D 69, 218–223 (2015a)

    Article  ADS  Google Scholar 

  • Liu, D., Wang, H., Wang, Y., Yin, H.: Propagation properties of elliptical Gaussian beam in uniaxial crystals along the optical axis. Opt. Laser Technol. 73, 12–18 (2015b)

    Article  ADS  Google Scholar 

  • Liu, L.J., Khan, H.A., Li, J.J., Hillier, A.C., Lu, M.: A strain-tunable nanoimprint lithography for linear variable photonic crystal 0filters. Nanotechnol. 7, 295301–295306 (2016a)

    Article  Google Scholar 

  • Liu, D., Wang, Y., Wang, G., Yin, H.: Propagation properties of flat-topped vortex hollow beam in uniaxial crystals orthogonal to the optical axis. Optik 127, 7842–7851 (2016b)

    Article  ADS  Google Scholar 

  • Liu, D., Wang, Y., Wang, G., Yin, H.: Propagation properties of a partially coherent anomalous hollow vortex beam in uniaxial crystal orthogonal to the optical axis. J. Mod. Opt. 65, 1442–1449 (2018)

    Article  ADS  Google Scholar 

  • Liu, D.J., Wang, G.Q., Zhong, H.Y., Yin, H.M., Dong, A.Y., Wang, Y.C.: Properties of a four-petal Lorentz-Gauss beam propagating in uniaxial crystal orthogonal to the optical axis. Optik 183, 257–265 (2019)

    Article  ADS  Google Scholar 

  • Lu, B.D., Luo, S.R.: Propagation properties of three-dimensional flattened Gaussian beams in uniaxially anisotropic crystals. Opt. Laser Technol. 36, 51–56 (2004)

    Article  ADS  Google Scholar 

  • Ma, X., Wang, G., Zhong, H., Wang, Y., Liu, D.: Propagation of a rectangular multi-Gaussian Schell-model vortex beam in uniaxial crystal. Optik 221, 165318–165327 (2020)

    Article  ADS  Google Scholar 

  • Saad, F., Belafhal, A.: A detailed investigation of a Generalized Hermite cosh-Gaussian beam propagating in uniaxial crystals orthogonal to the optical axis. Opt. Quant. Electron. 55, 1–12 (2023)

    Google Scholar 

  • Tang, B.: Hermite-cosine-Gaussian beams propagating in uniaxial crystals orthogonal to the optical axis. J. Opt. Soc. Am. A 26, 2480–2487 (2009)

    Article  ADS  Google Scholar 

  • Wang, X., Liu, Z., Zhao, D.: Nonparaxial propagation of elliptical Gaussian vortex beams in uniaxial crystal orthogonal to the optical axis. J. Opt. Soc. Am. A 31, 2268–2274 (2014)

    Article  ADS  Google Scholar 

  • Xu, Y., Zhou, G., Wang, X.: Nonparaxial propagation of Hermite-Laguerre Gaussian beams in uniaxial crystal orthogonal to the optical axis. Chin. Phys. B 22, 064101–064108 (2013)

    Article  ADS  Google Scholar 

  • Ye, J., Zhang, J., Ye, F., Xie, J., Deng, D.: Propagation properties of the rotating elliptical chirped Gaussian beam in uniaxial crystals orthogonal to the optical axis. Waves Random Complex Media 32, 1758–1772 (2022)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Funding

No funding is received from any organization for this work.

Author information

Authors and Affiliations

Authors

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 Faroq Saad.

Ethics declarations

Competing interests

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 to participate

Informed consent was obtained from all authors.

Consent for publication

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

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

Saad, F. Propagation properties of general model vortex higher-order Cosh-Gaussian laser beam through uniaxial crystal orthogonal to the optical axis. Opt Quant Electron 56, 790 (2024). https://doi.org/10.1007/s11082-024-06423-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-024-06423-6

Keywords

Navigation