## Calculation of radiation forces exerted on a uniaxial anisotropic sphere by an off-axis incident Gaussian beam |

Optics Express, Vol. 19, Issue 17, pp. 16044-16057 (2011)

http://dx.doi.org/10.1364/OE.19.016044

Acrobat PDF (1144 KB)

### Abstract

Using the theory of electromagnetic scattering of a uniaxial anisotropic sphere, we derive the analytical expressions of the radiation forces exerted on a uniaxial anisotropic sphere by an off-axis incident Gaussian beam. The beam’s propagation direction is parallel to the primary optical axis of the anisotropic sphere. The effects of the permittivity tensor elements

© 2011 OSA

## 1. Introduction

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,” Science **210**(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]

*et al*. [4

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]

*et al*. [5

5. 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,” Cytometry **12**(6), 479–485 (1991). [CrossRef] [PubMed]

*et al*. [6

6. R. C. Gauthier and S. Wallace, “Optical levitation of spheres: analytical development and numerical computations of force equations,” J. Opt. Soc. Am. B **12**(9), 1680–1687 (1995). [CrossRef]

*et al*. [7] researched on the influence of polarization on axial and lateral forces exerted by optical tweezers. Meanwhile, in 1998, Shojiro et al. [8

8. 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]

9. 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. A **5**(9), 1427–1443 (1988). [CrossRef]

11. K. F. Ren, G. Gréhan, 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]

12. 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]

13. 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]

10. 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), 4954–4962 (1989). [CrossRef]

14. 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]

15. 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. J. Euro. Opt. Soc. Part A **4**(5), 571–585 (1995). [CrossRef]

16. 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]

17. 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]

18. F. Xu, K. F. Ren, G. Gouesbet, X. S. Cai, and G. Gréhan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **75**(2), 026613 (2007). [CrossRef] [PubMed]

19. M. Kawano, J. T. Blakely, R. Gordon, and D. Sinton, “Theory of dielectric micro-sphere dynamics in a dual-beam optical trap,” Opt. Express **16**(13), 9306–9317 (2008). [CrossRef] [PubMed]

20. Y. L. Geng, X. B. Wu, and L. W. Li, “Mie scattering by a uniaxial anisotropic sphere,” physical review E **70**, 056609 (2004). [CrossRef]

23. M. Sluijter, D. K. de Boer, and J. J. M. Braat, “General polarized ray-tracing method for inhomogeneous uniaxially anisotropic media,” J. Opt. Soc. Am. A **25**(6), 1260–1273 (2008). [CrossRef] [PubMed]

24. 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. A **26**(8), 1778–1788 (2009). [CrossRef]

25. 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. A **27**(6), 1457–1465 (2010). [CrossRef] [PubMed]

26. Z. J. Li, Z. S. Wu, and H. Y. Li, “Analysis of electromagnetic scattering by uniaxial anisotropic bispheres,” J. Opt. Soc. Am. A **28**(2), 118–125 (2011). [CrossRef] [PubMed]

9. 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. A **5**(9), 1427–1443 (1988). [CrossRef]

24. 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. A **26**(8), 1778–1788 (2009). [CrossRef]

25. 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. A **27**(6), 1457–1465 (2010). [CrossRef] [PubMed]

*ω*is the circular frequency.

## 2. Scattering of a uniaxial anisotropic sphere by an off-axis Gaussian beam

*a*centrally located in a spherical coordinate system. The primary optical axis is coincident with the

*z*-axis. As Fig. 1 illustrates, the particle is illuminated by an

*x*-polarized at the waist Gaussian beam propagating in the

*z-*axis direction, while the center of the beam waist

25. 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. A **27**(6), 1457–1465 (2010). [CrossRef] [PubMed]

*λ*is light wavelength in the surrounding medium,

27. G. Gouesbet, G. Grehan, and B. Maheu, “Computations of the gn coefficients in the geneeralized Lorenz-Mie theory using three different methods,” Appl. Opt. **27**(23), 4874–4883 (1988). [CrossRef] [PubMed]

28. Z. S. Wu, L. X. Guo, K. F. Ren, G. Gouesbet, and G. Gréhan, “Improved algorithm for electromagnetic scattering of plane waves and shaped beams by multilayered spheres,” Appl. Opt. **36**(21), 5188–5198 (1997). [CrossRef] [PubMed]

29. G. Gousbet, “Localized interpretation to compute all the coefficients gmn in the generalized Lorentz-Mie theory,” J. Opt. Soc. Am. A **7**(6), 998–1007 (1990). [CrossRef]

30. J. A. Lock and G. Gouesbet, “Rigorous justification fo the localized approximation to the beam-shape coefficients in generalized Lorenz-Mie theory.I. On-axis beams,” J. Opt. Soc. Am. A **11**(9), 2503–2515 (1994). [CrossRef]

31. 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]

20. Y. L. Geng, X. B. Wu, and L. W. Li, “Mie scattering by a uniaxial anisotropic sphere,” physical review E **70**, 056609 (2004). [CrossRef]

24. 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. A **26**(8), 1778–1788 (2009). [CrossRef]

**27**(6), 1457–1465 (2010). [CrossRef] [PubMed]

20. Y. L. Geng, X. B. Wu, and L. W. Li, “Mie scattering by a uniaxial anisotropic sphere,” physical review E **70**, 056609 (2004). [CrossRef]

**70**, 056609 (2004). [CrossRef]

**26**(8), 1778–1788 (2009). [CrossRef]

**27**(6), 1457–1465 (2010). [CrossRef] [PubMed]

**27**(6), 1457–1465 (2010). [CrossRef] [PubMed]

## 3. Radiation forces exerted on a uniaxial anisotropic sphere

10. 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), 4954–4962 (1989). [CrossRef]

*c*is the speed of light in vacuum,

## 4. Numerical results and discussion

### 3.1 Axial radiation force

*et al.*[5

5. 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,” Cytometry **12**(6), 479–485 (1991). [CrossRef] [PubMed]

5. 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,” Cytometry **12**(6), 479–485 (1991). [CrossRef] [PubMed]

8. 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]

16. 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]

*d*denotes the distance of the sphere center from the beam center. The remaining figures possess similar conditions as well.

*d*for several values of beam waist widths

*w*

_{0}< 0.4μm) the axial radiation force

*F*is negative around

_{z}*d*= 1μm and positive elsewhere, i.e. in a small region after the beam waist, the uniaxial anisotropic sphere is attracted by the beam to the opposite direction of the propagation. This situation may indicate that the uniaxial anisotropic spherical particle can also be captured by a focus Gaussian beam, which is similar to the capture trait for isotropic sphere [5

**12**(6), 479–485 (1991). [CrossRef] [PubMed]

8. 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]

12. 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]

*F*take maximal value shift slightly to the beam waist center and the minimum of

_{z}*F*decreases, however, the form of the curves exhibits little change.

_{z}*d*for several values of sphere radius

*a*. The negative axial radiation forces appear as the sphere radius increases when the beam waist width is stated. More calculations and simulations indicate that the negative axial radiation forces appear at several positions and the values of

**37**(27), 6386–6394 (1998). [CrossRef] [PubMed]

*d*for several values of

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]

6. R. C. Gauthier and S. Wallace, “Optical levitation of spheres: analytical development and numerical computations of force equations,” J. Opt. Soc. Am. B **12**(9), 1680–1687 (1995). [CrossRef]

**37**(27), 6386–6394 (1998). [CrossRef] [PubMed]

12. 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]

32. H. Polaert, G. Gréhan, and G. Gouesbet, “Improved standard beams with application to reverse radiation pressure,” Appl. Opt. **37**(12), 2435–2440 (1998). [CrossRef] [PubMed]

*d*increases; as the value of

### 4.2 Transverse radiation forces

*x*-axis and

*y*-axis. The variations of

*x*-polarization incident field and the two eigen waves in the uniaxial anisotropic sphere. It is different from the properties of isotropic sphere; the variations of

*x*

_{0}and

*w*

_{0}increases, the secondary extremum of

## 5. Conclusion

## Appendix

## Acknowledgments

## References and links

1. | A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. |

2. | A. Ashkin, “Applications of laser radiation pressure,” Science |

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. |

4. | Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. |

5. | 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,” Cytometry |

6. | R. C. Gauthier and S. Wallace, “Optical levitation of spheres: analytical development and numerical computations of force equations,” J. Opt. Soc. Am. B |

7. | 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.) |

8. | S. Nemoto and H. Togo, “Axial force acting on a dielectric sphere in a focused laser beam,” Appl. Opt. |

9. | 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. A |

10. | 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. |

11. | K. F. Ren, G. Gréhan, 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. |

12. | K. F. Ren, G. Gréhan, and G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz-Mie theory,” Appl. Opt. |

13. | 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. |

14. | Y. K. Nahmias and D. J. Odde, “Analysis of Radiation Forces in Laser Trapping and Laser-Guided Direct Writing Applications,” IEEE J. Quantum Electron. |

15. | 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. J. Euro. Opt. Soc. Part A |

16. | Y. K. Nahmias, B. Z. Gao, and D. J. Odde, “Dimensionless parameters for the design of optical traps and laser guidance systems,” Appl. Opt. |

17. | 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. |

18. | F. Xu, K. F. Ren, G. Gouesbet, X. S. Cai, and G. Gréhan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

19. | M. Kawano, J. T. Blakely, R. Gordon, and D. Sinton, “Theory of dielectric micro-sphere dynamics in a dual-beam optical trap,” Opt. Express |

20. | Y. L. Geng, X. B. Wu, and L. W. Li, “Mie scattering by a uniaxial anisotropic sphere,” physical review E |

21. | B. Stout, M. Nevière, and E. Popov, “Mie scattering by an anisotropic object. Part I. Homogeneous sphere,” J. Opt. Soc. Am. A |

22. | 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. |

23. | M. Sluijter, D. K. de Boer, and J. J. M. Braat, “General polarized ray-tracing method for inhomogeneous uniaxially anisotropic media,” J. Opt. Soc. Am. A |

24. | 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. A |

25. | 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. A |

26. | Z. J. Li, Z. S. Wu, and H. Y. Li, “Analysis of electromagnetic scattering by uniaxial anisotropic bispheres,” J. Opt. Soc. Am. A |

27. | G. Gouesbet, G. Grehan, and B. Maheu, “Computations of the gn coefficients in the geneeralized Lorenz-Mie theory using three different methods,” Appl. Opt. |

28. | Z. S. Wu, L. X. Guo, K. F. Ren, G. Gouesbet, and G. Gréhan, “Improved algorithm for electromagnetic scattering of plane waves and shaped beams by multilayered spheres,” Appl. Opt. |

29. | G. Gousbet, “Localized interpretation to compute all the coefficients gmn in the generalized Lorentz-Mie theory,” J. Opt. Soc. Am. A |

30. | J. A. Lock and G. Gouesbet, “Rigorous justification fo the localized approximation to the beam-shape coefficients in generalized Lorenz-Mie theory.I. On-axis beams,” J. Opt. Soc. Am. A |

31. | 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. |

32. | H. Polaert, G. Gréhan, and G. Gouesbet, “Improved standard beams with application to reverse radiation pressure,” Appl. Opt. |

**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

**History**

Original Manuscript: June 21, 2011

Revised Manuscript: July 20, 2011

Manuscript Accepted: July 20, 2011

Published: August 8, 2011

**Virtual Issues**

Vol. 6, Iss. 9 *Virtual Journal for Biomedical Optics*

**Citation**

Zheng-Jun Li, Zhen-Sen Wu, and Qing-Chao Shang, "Calculation of radiation forces exerted on a uniaxial anisotropic sphere by an off-axis incident Gaussian beam," Opt. Express **19**, 16044-16057 (2011)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-19-17-16044

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### References

- A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970). [CrossRef]
- A. Ashkin, “Applications of laser radiation pressure,” Science 210(4474), 1081–1088 (1980). [CrossRef] [PubMed]
- 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]
- 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]
- 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,” Cytometry 12(6), 479–485 (1991). [CrossRef] [PubMed]
- R. C. Gauthier and S. Wallace, “Optical levitation of spheres: analytical development and numerical computations of force equations,” J. Opt. Soc. Am. B 12(9), 1680–1687 (1995). [CrossRef]
- 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, 181–190 (1996).
- 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]
- 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. A 5(9), 1427–1443 (1988). [CrossRef]
- 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), 4954–4962 (1989). [CrossRef]
- K. F. Ren, G. Gréhan, 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]
- 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]
- 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]
- 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]
- 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. J. Euro. Opt. Soc. Part A 4(5), 571–585 (1995). [CrossRef]
- 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]
- 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]
- F. Xu, K. F. Ren, G. Gouesbet, X. S. Cai, and G. Gréhan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2), 026613 (2007). [CrossRef] [PubMed]
- M. Kawano, J. T. Blakely, R. Gordon, and D. Sinton, “Theory of dielectric micro-sphere dynamics in a dual-beam optical trap,” Opt. Express 16(13), 9306–9317 (2008). [CrossRef] [PubMed]
- Y. L. Geng, X. B. Wu, and L. W. Li, “Mie scattering by a uniaxial anisotropic sphere,” physical review E 70, 056609 (2004). [CrossRef]
- B. Stout, M. Nevière, and E. Popov, “Mie scattering by an anisotropic object. Part I. Homogeneous sphere,” J. Opt. Soc. Am. A 23(5), 1111–1123 (2006). [CrossRef] [PubMed]
- 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]
- M. Sluijter, D. K. de Boer, and J. J. M. Braat, “General polarized ray-tracing method for inhomogeneous uniaxially anisotropic media,” J. Opt. Soc. Am. A 25(6), 1260–1273 (2008). [CrossRef] [PubMed]
- 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. A 26(8), 1778–1788 (2009). [CrossRef]
- 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. A 27(6), 1457–1465 (2010). [CrossRef] [PubMed]
- Z. J. Li, Z. S. Wu, and H. Y. Li, “Analysis of electromagnetic scattering by uniaxial anisotropic bispheres,” J. Opt. Soc. Am. A 28(2), 118–125 (2011). [CrossRef] [PubMed]
- G. Gouesbet, G. Grehan, and B. Maheu, “Computations of the gn coefficients in the geneeralized Lorenz-Mie theory using three different methods,” Appl. Opt. 27(23), 4874–4883 (1988). [CrossRef] [PubMed]
- Z. S. Wu, L. X. Guo, K. F. Ren, G. Gouesbet, and G. Gréhan, “Improved algorithm for electromagnetic scattering of plane waves and shaped beams by multilayered spheres,” Appl. Opt. 36(21), 5188–5198 (1997). [CrossRef] [PubMed]
- G. Gousbet, “Localized interpretation to compute all the coefficients gmn in the generalized Lorentz-Mie theory,” J. Opt. Soc. Am. A 7(6), 998–1007 (1990). [CrossRef]
- J. A. Lock and G. Gouesbet, “Rigorous justification fo the localized approximation to the beam-shape coefficients in generalized Lorenz-Mie theory.I. On-axis beams,” J. Opt. Soc. Am. A 11(9), 2503–2515 (1994). [CrossRef]
- 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]
- H. Polaert, G. Gréhan, and G. Gouesbet, “Improved standard beams with application to reverse radiation pressure,” Appl. Opt. 37(12), 2435–2440 (1998). [CrossRef] [PubMed]

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