OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 15 — Jul. 16, 2012
  • pp: 16421–16435

Calculation of radiation force and torque exerted on a uniaxial anisotropic sphere by an incident Gaussian beam with arbitrary propagation and polarization directions

Zheng-Jun Li, Zhen-Sen Wu, Qing-Chao Shang, Lu Bai, and Chun-Hui Cao  »View Author Affiliations

Optics Express, Vol. 20, Issue 15, pp. 16421-16435 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (1237 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



On the basis of spherical vector wave functions and coordinate rotation theory, the expansion of the fields of an incident Gaussian beam with arbitrary propagation and polarization directions in terms of spherical vector wave functions is investigated, and beam shape coefficients are derived. Using the results of electromagnetic scattering by a uniaxial anisotropic sphere, the analytical expressions of the radiation force and torque exerted on a homogeneous absorbing uniaxial anisotropic sphere by the arbitrary incident Gaussian beam. We numerically analyze and discuss the following: the effects of an anisotropic absorbing dielectric on the axial and transverse radiation forces exerted by an off-axis Gaussian beam on a uniaxial anisotropic sphere; the variations in the axial, transverse, and resultant radiation forces (with incident angle β and polarization angle α) imposed by an obliquely Gaussian beam on a uniaxial anisotropic sphere; and the results on the characteristics of the three components of the radiation forces versus the center-to-center distance between the sphere and beam. Selected numerically results on the radiation torque exerted on a stationary uniaxial anisotropic transparent or absorbing sphere by a linearly polarized Gaussian beam are shown, and the results are compared with those exerted an isotropic sphere. The accuracy of the theory and code is confirmed by comparing the axial radiation forces with the results obtained from references.

© 2012 OSA

OCIS Codes
(140.0140) Lasers and laser optics : Lasers and laser optics
(160.1190) Materials : Anisotropic optical materials
(290.5850) Scattering : Scattering, particles

ToC Category:
Optical Trapping and Manipulation

Original Manuscript: April 18, 2012
Revised Manuscript: June 8, 2012
Manuscript Accepted: June 22, 2012
Published: July 5, 2012

Zheng-Jun Li, Zhen-Sen Wu, Qing-Chao Shang, Lu Bai, and Chun-Hui Cao, "Calculation of radiation force and torque exerted on a uniaxial anisotropic sphere by an incident Gaussian beam with arbitrary propagation and polarization directions," Opt. Express 20, 16421-16435 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett.24(4), 156–159 (1970). [CrossRef]
  2. A. Ashkin, “Applications of laser radiation pressure,” Science210(4474), 1081–1088 (1980). [CrossRef] [PubMed]
  3. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett.11(5), 288–290 (1986). [CrossRef] [PubMed]
  4. Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun.124(5-6), 529–541 (1996). [CrossRef]
  5. P. C. Chaumet and M. Nieto-Vesperinas, “Time-averaged total force on a dipolar sphere in an electromagnetic field,” Opt. Lett.25(15), 1065–1067 (2000). [CrossRef] [PubMed]
  6. A. Rohrbach and E. H. K. Stelzer, “Optical trapping of dielectric particle in arbitrary fields,” J. Opt. Soc. Am. A18(4), 839–853 (2001). [CrossRef]
  7. T. C. B. Schut, G. Hesselink, B. G. de Grooth, and J. Greve, “Experimental and theoretical investigations on the validity of the geometrical optics model for calculating the stability of optical traps,” Cytometry12(6), 479–485 (1991). [CrossRef] [PubMed]
  8. A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J.61(2), 569–582 (1992). [CrossRef] [PubMed]
  9. R. Gussgard, T. Lindmo, and I. Brevik, “Calculation of the trapping force in a strongly focused laser beam,” J. Opt. Soc. Am. B9(10), 1922–1930 (1992). [CrossRef]
  10. R. C. Gauthier and S. Wallace, “Optical levitation of spheres: analytical development and numerical computations of force equations,” J. Opt. Soc. Am. B12(9), 1680–1687 (1995). [CrossRef]
  11. T. Wohland, A. Rosin, and E. H. K. Stelzer, “Theoretical determination of the influence of the polarization on forces exerted by optical tweezers,” Optik (Stuttg.)102(4), 181–190 (1996).
  12. S. Nemoto and H. Togo, “Axial force acting on a dielectric sphere in a focused laser beam,” Appl. Opt.37(27), 6386–6394 (1998). [CrossRef] [PubMed]
  13. J. S. Kim and S. S. Lee, “Scattering of laser beams and the optical potential well for a homogeneous sphere,” J. Opt. Soc. Am.73(3), 303–312 (1983). [CrossRef]
  14. J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys.64(4), 1632–1639 (1988). [CrossRef]
  15. J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys.66(10), 4594–4962 (1989). [CrossRef]
  16. G. Gouesbet, B. Maheu, and G. Grehan, “Light Scattering from a sphere arbitrarily located in a Gaussian beam,using a Bromwich formulation,” J. Opt. Soc. Am. A5(9), 1427–1443 (1988). [CrossRef]
  17. G. Gouesbet, G. Gréhan, and B. Maheu, “Localized interpretation to compute all the coefficients gmn in the generalized Lorentz-Mie theory,” J. Opt. Soc. Am. A7(6), 998–1007 (1990). [CrossRef]
  18. K. F. Ren, G. Gréha, and G. Gouesbet, “Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian beam by using the generalized Lorenz-Mie theory and associated resonance effects,” Opt. Commun.108(4-6), 343–354 (1994). [CrossRef]
  19. K. F. Ren, G. Gréhan, and G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz-Mie theory,” Appl. Opt.35(15), 2702–2710 (1996). [CrossRef] [PubMed]
  20. J. A. Lock, “Calculation of the radiation trapping force for laser tweezers by use of generalized Lorenz-Mie theory. I. Localized model description of an on-axis tightly focused laser beam with spherical aberration,” Appl. Opt.43(12), 2532–2544 (2004). [CrossRef] [PubMed]
  21. Y. K. Nahmias and D. J. Odde, “Analysis of Radiation Forces in Laser Trapping and Laser-Guided Direct Writing Applications,” IEEE J. Quantum Electron.38(2), 131–141 (2002). [CrossRef]
  22. G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Grehan, and G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centred Gaussian beams. II. GLMT analysis,” Pure Appl. Opt.4(5), 571–585 (1995). [CrossRef]
  23. Y. K. Nahmias, B. Z. Gao, and D. J. Odde, “Dimensionless parameters for the design of optical traps and laser guidance systems,” Appl. Opt.43(20), 3999–4006 (2004). [CrossRef] [PubMed]
  24. F. L. Mao, Q. R. Xing, K. Wang, L. Y. Lang, L. Chai, and Q. Y. Wang, “Calculation of axial optical forces exerted on medium-sized particles by optical trap,” Opt. Laser Technol.39(1), 34–39 (2007). [CrossRef]
  25. R. D. Graglia and P. L. E. Uslenghi, “Electromagnetic Scattering from Anisotropic Materials, Part I: General Theory,” IEEE Trans. Antenn. Propag.32(8), 867–869 (1984). [CrossRef]
  26. S. N. Papadakis, N. K. Uzunoglu, and C. N. Capsalis, “Scattering of a plane wave by a general anisotropic dielectric ellipsoid,” J. Opt. Soc. Am. A7(6), 991–997 (1990). [CrossRef]
  27. W. Ren, “Contributions to the electromagnetic wave theory of bounded homogeneous anisotropic media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics47(1), 664–673 (1993). [CrossRef] [PubMed]
  28. J. A. Pereda, L. A. Vielva, A. Vegas, and A. Prieto, “FDTD Analysis of Magnetized Ferrites: Application to the Calculation of Dispersion Characteristics of Ferrite-Loaded Waveguides,” IEEE Trans. Antenn. Propag.43(2), 350–357 (1995).
  29. S. C. Mao, Z. S. Wu, and H.-Y. Li, “Three-dimensional scattering by an infinite homogeneous anisotropic elliptic cylinder in terms of Mathieu functions,” J. Opt. Soc. Am. A26(11), 2282–2291 (2009). [CrossRef] [PubMed]
  30. Y. L. Geng, X. B. Wu, L. W. Li, and B. R. Guan, “Mie scattering by a uniaxial anisotropic sphere,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70(5), 056609 (2004). [CrossRef] [PubMed]
  31. B. Stout, M. Nevière, and E. Popov, “Mie scattering by an anisotropic object. Part I. Homogeneous sphere,” J. Opt. Soc. Am. A23(5), 1111–1123 (2006). [CrossRef] [PubMed]
  32. C. W. Qiu, S. Zouhdi, and A. Razek, “Modified Spherical Wave Functions With Anisotropy Ratio: Application to the Analysis of Scattering by Multilayered Anisotropic Shells,” IEEE Trans. Antenn. Propag.55(12), 3515–3523 (2007). [CrossRef]
  33. M. Sluijter, D. K. G. de Boer, and J. J. M. Braat, “General polarized ray-tracing method for inhomogeneous uniaxially anisotropic media,” J. Opt. Soc. Am. A25(6), 1260–1273 (2008). [CrossRef] [PubMed]
  34. Z. S. Wu, Q. K. Yuan, Y. Peng, and Z. J. Li, “Internal and external electromagnetic fields for on-axis Gaussian beam scattering from a uniaxial anisotropic sphere,” J. Opt. Soc. Am. A26(8), 1778–1788 (2009). [CrossRef]
  35. Q. K. Yuan, Z. S. Wu, and Z. J. Li, “Electromagnetic scattering for a uniaxial anisotropic sphere in an off-axis obliquely incident Gaussian beam,” J. Opt. Soc. Am. A27(6), 1457–1465 (2010). [CrossRef] [PubMed]
  36. Z. J. Li, Z. S. Wu, and Q. C. Shang, “Calculation of radiation forces exerted on a uniaxial anisotropic sphere by an off-axis incident Gaussian beam,” Opt. Express19(17), 16044–16057 (2011). [CrossRef] [PubMed]
  37. S. Chang and S. S. Lee, “Optical torque exerted on a homogeneous sphere levitated in the circularly polarized fundamental-mode laser beam,” J. Opt. Soc. Am. B2(11), 1853–1860 (1985). [CrossRef]
  38. F. Xu, J. Lock, G. Gouesbet, and C. Tropea, “Radiation torque exerted on a spheroid: Analytical solution,” Phys. Rev. A78(1), 013843 (2008). [CrossRef]
  39. G. Gouesbet, “T-matrix formulation and generalized lozrenz-Mie theories in spherical coordinates,” Opt. Commun.283(4), 517–521 (2010). [CrossRef]
  40. G. Gouesbet and J. A. Lock, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz-Mie theory. II. off-axis beams,” J. Opt. Soc. Am. A11(9), 2516–2525 (1994). [CrossRef]
  41. A. Doicu and T. Wriedt, “Computation of the beam-shape coefficients in the generalized Lorenz-Mie theory by using the translational addition theorem for spherical vector wave functions,” Appl. Opt.36(13), 2971–2978 (1997). [CrossRef] [PubMed]
  42. Y. P. Han, H. Y. Zhang, and G. X. Han, “The expansion coefficients of arbitrary shaped beam in oblique illumination,” Opt. Express15(2), 735–746 (2007). [CrossRef] [PubMed]
  43. G. Gouesbet, J. J. Wang, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz-Mie theories through rotations of coordinate systems,” Opt. Commun.283(17), 3218–3225 (2010). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited