Skip to main content

Optical trapping of particles by radiation forces of doughnut laser beams in the Rayleigh regime


In the present paper, we will investigate the radiation forces produced by Generalized Humbert-Gaussian beams (GHGBs), after propagating through a thin lens optical system, exerted on a dielectric sphere in the Rayleigh scattering approximation. The impact of the optical parameters of the beams on radiation forces is studied in detail. The numerical results reveal that the Generalized Humbert-Gaussian beams can be used to trap the particle with higher refractive index. Finally, the conditions of trapping stability are also discussed.

This is a preview of subscription content, access via your institution.

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


  • Ashkin, A.: Acceleration and Trapping of Particles by Radiation Pressure. Phys. Rev. Lett. 24, 156–159 (1970)

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    Google Scholar 

  • Belafhal, A., Nossir, N., Dalil-Essakali, L., Usman, T.: Integral transforms involving the product of Humbert and Bessel functions and its application. AIMS Math. 5, 1260–1274 (2020)

    MathSciNet  Article  Google Scholar 

  • Calander, N., Willander, M.: Optical trapping of single fluorescent molecules at the Detection Spots of Nanoprobes. Phys. Rev. Lett. 89, 143603-1-143603–4 (2002)

    ADS  Article  Google Scholar 

  • Day, C.: Optical trap Resolves the Stepwise Transfer of Genetic Information from DNA to RNA. Phys. To-day 59, 26–27 (2006)

    ADS  Google Scholar 

  • Hennani, S., Ez-zariy, L., Belafhal, A.: Radiation Forces on a Dielectric Sphere Produced by Finite Olver-Gaussian Beams. Opt. Photonics J. 5, 344–353 (2015)

    ADS  Article  Google Scholar 

  • Jiang, Y., Huang, K., Lu, X.: Radiation force of abruptly autofocusing Airy beams on a Rayleigh particle. Opt. Express. 21, 24413–24421 (2013)

    ADS  Article  Google Scholar 

  • Liu, Z., Zhao, D.: Radiation forces acting on a Rayleigh dielectric sphere produced by highly focused elegant Hermite-cosine-Gaussian beams. Opt. Express. 20, 2895–2904 (2012)

    ADS  Article  Google Scholar 

  • Liu, Z., Wang, X., Hang, K.: Enhancement of trapping efficiency by utilizing a hollow sinh-Gaussian beam. Sci. Rep. 9, 1–8 (2019)

    ADS  Article  Google Scholar 

  • Mao, F., Xing, Q., Wang, K., Lang, L., Wang, Z., Chai, L., Wang, Q.: Optical trapping of red blood cells and two-photon excitation-based photodynamic study using a femtosecond laser. Opt. Commun. 256, 358–363 (2005)

    ADS  Article  Google Scholar 

  • Mitri, F.G.: Acoustic radiation force on a sphere in standing and quasi-standing zero-order Bessel beam tweezers. Ann. Phys. 323, 1604–1620 (2008)

    ADS  Article  Google Scholar 

  • Nie, Z., Shi, G., Li, D., Zhang, X., Wang, Y., Song, Y.: Tight focusing of a radially polarized Laguerre-Bessel–Gaussian beam and its application to manipulation of two types of particles. Phys. Lett. A. 379, 857–863 (2015)

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Okamoto, K., Kawata, S.: Radiation Force Exerted on Subwavelength Particles near a Nanoaperture. Phys. Rev. Lett. 83, 4534–4537 (1999)

    ADS  Article  Google Scholar 

  • Svoboda, K., Block, S.M.: Biological Applications of Optical Forces. Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994)

    Article  Google Scholar 

  • Taguchi, K., Ueno, H., Hiramatsu, T., Ikeda, M.: Optical trapping of dielectric particle and biological cell using optical fibre. Electron. Lett. 33, 413–414 (1997)

    ADS  Article  Google Scholar 

  • Tang, B., Chen, K., Huang, L., Zhou, X., Lang, X.: Radiation force acting on a Rayleigh dielectric sphere produced by Whittaker-Gaussian beams. Opt. Laser Technol. 107, 239–243 (2018)

    ADS  Article  Google Scholar 

  • Wang, L.G., Zhao, C.L.: Dynamic radiation force of a pulsed Gaussian beam acting on rayleigh dielectric sphere. Opt. Express 15, 10615–10621 (2007)

    ADS  Article  Google Scholar 

  • Xie, C., Li, Y.Q.: Confocal micro-raman spectroscopy of single biological cells using optical trapping and shifted excitation difference techniques. J. Appl. Phys. 93, 2982–2986 (2003)

    ADS  Article  Google Scholar 

  • Yavuz, D.D., Kulatunga, P.B., Urban, E., Johnson, T.A., Proite, N., Henage, T., Walker, T.G., Saffman, M.: Fast ground state manipulation of neutral atoms in microscopic optical traps. Phys. Rev. Lett. 96, 063001–063004 (2006)

    ADS  Article  Google Scholar 

  • Zemánek, P., Jonás, A., Srámek, L., Liska, M.: Optical trapping of rayleigh particles using a Gaussian standing wave. Opt. Commun. 151, 273–285 (1998)

    ADS  Article  Google Scholar 

  • Zhao, C.L., Wang, L.G., Lu, X.H.: Radiation forces on a dielectric sphere produced by highly focused hollow Gaussian beams. Phys. Lett. A. 363, 502–506 (2007)

    ADS  Article  Google Scholar 

  • Zhao, C., Cai, Y., Lu, X., Eyyuboğlu, H.T.: Radiation force of coherent and partially coherent flat-topped beams on a Rayleigh particle. Opt. Express. 17, 1753–1765 (2009)

    ADS  Article  Google Scholar 

  • Zhou, Y., Xu, H.-F., Yuan, Y., Peng, J., Qu, J., Huang, W.: Trapping Two Types of Particles Using a Laguerre-Gaussian Correlated Schell-Model Beam. IEEE Photonics J. 8, 1–10 (2016)

    Google Scholar 

Download references

Author information

Authors and Affiliations


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

Verify currency and authenticity via CrossMark

Cite this article

Nossir, N., Dalil-Essakali, L. & Belafhal, A. Optical trapping of particles by radiation forces of doughnut laser beams in the Rayleigh regime. Opt Quant Electron 53, 100 (2021).

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI:


  • Radiation forces
  • Generalized humbert-gaussian beams
  • Dielectric sphere
  • Rayleigh scattering approximation