## Radiation force of scalar and electromagnetic twisted Gaussian Schell-model beams

Optics Express, Vol. 17, Issue 24, pp. 21472-21487 (2009)

http://dx.doi.org/10.1364/OE.17.021472

Acrobat PDF (448 KB)

### Abstract

Radiation force of a focused scalar twisted Gaussian Schell-model (TGSM) beam on a Rayleigh dielectric sphere is investigated. It is found that the twist phase affects the radiation force and by raising the absolute value of the twist factor it is possible to increase both transverse and longitudinal trapping ranges at the real focus where the maximum on-axis intensity is located. Numerical calculations of radiation forces induced by a focused electromagnetic TGSM beam on a Rayleigh dielectric sphere are carried out. It is found that radiation force is closely related to the twist phase, degree of polarization and correlation factors of the initial beam. The trapping stability is also discussed.

© 2009 OSA

## 1. Introduction

1. E. Wolf and E. Collett, “Partially coherent sources which produce same far-field intensity distribution as a laser,” Opt. Commun. **25**(3), 293–296 (
1978). [CrossRef]

6. Q. S. He, J. Turunen, and A. T. Friberg, “Propagation and imaging experiments with Gaussian Schell-model beams,” Opt. Commun. **67**(4), 245–250 (
1988). [CrossRef]

2. F. Gori, “Collet-Wolf sources and multimode lasers,” Opt. Commun. **34**(3), 301–305 (
1978). [CrossRef]

4. F. Wang and Y. Cai, “Experimental observation of fractional Fourier transform for a partially coherent optical beam with Gaussian statistics,” J. Opt. Soc. Am. A **24**(7), 1937–1944 (
2007). [CrossRef]

5. A. T. Friberg and R. J. Sudol, “Propagation parameters of Gaussian Schell-model beams,” Opt. Commun. **41**(6), 383–387 (
1982). [CrossRef]

6. Q. S. He, J. Turunen, and A. T. Friberg, “Propagation and imaging experiments with Gaussian Schell-model beams,” Opt. Commun. **67**(4), 245–250 (
1988). [CrossRef]

7. Y. Cai and S. Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **71**(5), 056607 (
2005). [CrossRef] [PubMed]

8. J. C. Ricklin and F. M. Davidson, “Atmospheric turbulence effects on a partially coherent Gaussian beam: implications for free-space laser communication,” J. Opt. Soc. Am. A **19**(9), 1794–1802 (
2002). [CrossRef]

9. N. A. Ansari and M. S. Zubairy, “Second-harmonic generation by a Gaussian Schell-model source,” Opt. Commun. **59**(5-6), 385–390 (
1986). [CrossRef]

11. R. Simon and N. Mukunda, “Twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A **10**(1), 95–109 (
1993). [CrossRef]

11. R. Simon and N. Mukunda, “Twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A **10**(1), 95–109 (
1993). [CrossRef]

15. A. T. Friberg, E. Tervonen, and J. Turunen, “Interpretation and experimental demonstration of twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A **11**(6), 1818–1826 (
1994). [CrossRef]

15. A. T. Friberg, E. Tervonen, and J. Turunen, “Interpretation and experimental demonstration of twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A **11**(6), 1818–1826 (
1994). [CrossRef]

16. D. Ambrosini, V. Bagini, F. Gori, and M. Santarsiero, “Twisted Gaussian Schell-model beams: a superposition model,” J. Mod. Opt. **41**(7), 1391–1399 (
1994). [CrossRef]

30. Y. Cai, Q. Lin, and O. Korotkova, “Ghost imaging with twisted Gaussian Schell-model beam,” Opt. Express **17**(4), 2453–2464 (
2009). [CrossRef] [PubMed]

22. M. J. Bastiaans, “Wigner-distribution function applied to twisted Gaussian light propagating in first-order optical systems,” J. Opt. Soc. Am. A **17**(12), 2475–2480 (
2000). [CrossRef]

31. M. J. Bastiaans, “Application of the Wigner distribution function to partially coherent light,” J. Opt. Soc. Am. A **3**(8), 1227–1238 (
1986). [CrossRef]

24. Q. Lin and Y. Cai, “Tensor *ABCD* law for partially coherent twisted anisotropic Gaussian-Schell model beams,” Opt. Lett. **27**(4), 216–218 (
2002). [CrossRef] [PubMed]

4. F. Wang and Y. Cai, “Experimental observation of fractional Fourier transform for a partially coherent optical beam with Gaussian statistics,” J. Opt. Soc. Am. A **24**(7), 1937–1944 (
2007). [CrossRef]

25. Q. Lin and Y. Cai, “Fractional Fourier transform for partially coherent Gaussian-Schell model beams,” Opt. Lett. **27**(19), 1672–1674 (
2002). [CrossRef] [PubMed]

28. Y. Cai and S. He, “Propagation of a partially coherent twisted anisotropic Gaussian Schell-model beam in a turbulent atmosphere,” Appl. Phys. Lett. **89**(4), 041117 (
2006). [CrossRef]

29. Y. Cai and U. Peschel, “Second-harmonic generation by an astigmatic partially coherent beam,” Opt. Express **15**(23), 15480–15492 (
2007). [CrossRef] [PubMed]

30. Y. Cai, Q. Lin, and O. Korotkova, “Ghost imaging with twisted Gaussian Schell-model beam,” Opt. Express **17**(4), 2453–2464 (
2009). [CrossRef] [PubMed]

33. D. F. V. James, “Changes of polarization of light beams on propagation in free space,” J. Opt. Soc. Am. A **11**(5), 1641–1643 (
1994). [CrossRef]

34. F. Gori, “Matrix treatment for partially polarized, partially coherent beams,” Opt. Lett. **23**(4), 241–243 (
1998). [CrossRef] [PubMed]

46. B. Kanseri and H. C. Kandpal, “Experimental determination of electric cross-spectral density matrix and generalized Stokes parameters for a laser beam,” Opt. Lett. **33**(20), 2410–2412 (
2008). [CrossRef] [PubMed]

36. F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian schell-model beams,” J. Opt. A, Pure Appl. Opt. **3**(1), 301 (
2001). [CrossRef]

47. M. Yao, Y. Cai, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “The evolution of the degree of polarization of an electromagnetic Gaussian Schell-model beam in a Gaussian cavity,” Opt. Lett. **33**(19), 2266–2268 (
2008). [CrossRef] [PubMed]

49. Y. Cai, O. Korotkova, H. T. Eyyuboğlu, and Y. Baykal, “Active laser radar systems with stochastic electromagnetic beams in turbulent atmosphere,” Opt. Express **16**(20), 15834 (
2008). [CrossRef] [PubMed]

50. Y. Cai and O. Korotkova, “Twist phase-induced polarization changes in electromagnetic Gaussian Schell-model beams,” Appl. Phys. B **96**(2-3), 499–507 (
2009). [CrossRef]

## 2. Focusing properties of scalar and electromagnetic twisted Gaussian Schell-model beams

33. D. F. V. James, “Changes of polarization of light beams on propagation in free space,” J. Opt. Soc. Am. A **11**(5), 1641–1643 (
1994). [CrossRef]

50. Y. Cai and O. Korotkova, “Twist phase-induced polarization changes in electromagnetic Gaussian Schell-model beams,” Appl. Phys. B **96**(2-3), 499–507 (
2009). [CrossRef]

50. Y. Cai and O. Korotkova, “Twist phase-induced polarization changes in electromagnetic Gaussian Schell-model beams,” Appl. Phys. B **96**(2-3), 499–507 (
2009). [CrossRef]

*α*=

*β*due to the non-negativity requirement of the cross-spectral density [Eq. (7)] [11

11. R. Simon and N. Mukunda, “Twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A **10**(1), 95–109 (
1993). [CrossRef]

**96**(2-3), 499–507 (
2009). [CrossRef]

**r**of the source plane is defined by the expression [33

33. D. F. V. James, “Changes of polarization of light beams on propagation in free space,” J. Opt. Soc. Am. A **11**(5), 1641–1643 (
1994). [CrossRef]

**96**(2-3), 499–507 (
2009). [CrossRef]

*Q*, we find that

**r**is defined by the expression [33

**11**(5), 1641–1643 (
1994). [CrossRef]

**96**(2-3), 499–507 (
2009). [CrossRef]

*Q*of all considered beams in this paper at the input plane is set to be 1W and the wavelength is set to be

*f*is located at the input plane (z=0), and the output plane is located at

*z*. Then the transfer matrix between the input and output planes can be expressed as follows

15. A. T. Friberg, E. Tervonen, and J. Turunen, “Interpretation and experimental demonstration of twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A **11**(6), 1818–1826 (
1994). [CrossRef]

*f*), but rather closer to the lens due to the focus shift [see Fig. 2(b)]. The focus shift is dependent on the intensity and coherence widths, as well as on the twist parameter which decreases the effective coherence width (see, for instance, Ref. 6

6. Q. S. He, J. Turunen, and A. T. Friberg, “Propagation and imaging experiments with Gaussian Schell-model beams,” Opt. Commun. **67**(4), 245–250 (
1988). [CrossRef]

*P*

_{0}with

## 3. Radiation force induced by focused scalar and electromagnetic twisted GSM beams on a Rayleigh particle

*a*, (

54. 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]

*nm*,

54. 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]

## 4. Analysis of the trapping stability

66. K. Okamoto and S. Kawata, “Radiation force exerted on subwavelength particles near a nanoaperture,” Phys. Rev. Lett. **83**(22), 4534–4537 (
1999). [CrossRef]

*κ*is the viscosity of the ambient (in our case, for water [67

67. J. Kestin, M. Sokolov, and W. A. Wakeham, “Viscosity of Liquid Water in the Range - 8°C to 150° C,” J. Phys. Chem. Ref. Data **7**, 941–948 (
1978). [CrossRef]

*a*is the radius of the particle and

## 5. Conclusion

## Acknowledgements

## References and links

1. | E. Wolf and E. Collett, “Partially coherent sources which produce same far-field intensity distribution as a laser,” Opt. Commun. |

2. | F. Gori, “Collet-Wolf sources and multimode lasers,” Opt. Commun. |

3. | P. De Santis, F. Gori, G. Guattari, and C. Palma, “An example of a Collett-Wolf source,” Opt. Commun. |

4. | F. Wang and Y. Cai, “Experimental observation of fractional Fourier transform for a partially coherent optical beam with Gaussian statistics,” J. Opt. Soc. Am. A |

5. | A. T. Friberg and R. J. Sudol, “Propagation parameters of Gaussian Schell-model beams,” Opt. Commun. |

6. | Q. S. He, J. Turunen, and A. T. Friberg, “Propagation and imaging experiments with Gaussian Schell-model beams,” Opt. Commun. |

7. | Y. Cai and S. Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

8. | J. C. Ricklin and F. M. Davidson, “Atmospheric turbulence effects on a partially coherent Gaussian beam: implications for free-space laser communication,” J. Opt. Soc. Am. A |

9. | N. A. Ansari and M. S. Zubairy, “Second-harmonic generation by a Gaussian Schell-model source,” Opt. Commun. |

10. | L. Mandel, and E. Wolf, |

11. | R. Simon and N. Mukunda, “Twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A |

12. | R. Simon, K. Sundar, and N. Mukunda, “Twisted Gaussian Schell-model beams. I. Symmetry structure and normal-mode spectrum,” J. Opt. Soc. Am. A |

13. | K. Sundar, R. Simon, and N. Mukunda, “Twisted Gaussian Schell-model beams. II. Spectrum analysis and propagation characteristics,” J. Opt. Soc. Am. A |

14. | R. Simon and N. Mukunda, “Twist phase in Gaussian-beam optics,” J. Opt. Soc. Am. A |

15. | A. T. Friberg, E. Tervonen, and J. Turunen, “Interpretation and experimental demonstration of twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A |

16. | D. Ambrosini, V. Bagini, F. Gori, and M. Santarsiero, “Twisted Gaussian Schell-model beams: a superposition model,” J. Mod. Opt. |

17. | K. Sundar, N. Mukunda, and R. Simon, “Coherent-mode decomposition of general anisotropic Gaussian Schell-model beams,” J. Opt. Soc. Am. A |

18. | R. Simon, A. T. Friberg, and E. Wolf, “Transfer of radiance by twisted Gaussian Schell-model beams in paraxial systems,” Pure Appl. Opt. |

19. | R. Simon and N. Mukunda, “Gaussian Schell-model beams and general shape invariance,” J. Opt. Soc. Am. A |

20. | S. A. Ponomarenko, “Twisted Gaussian Schell-model solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

21. | J. Serna and J. M. Movilla, “Orbital angular momentum of partially coherent beams,” Opt. Lett. |

22. | M. J. Bastiaans, “Wigner-distribution function applied to twisted Gaussian light propagating in first-order optical systems,” J. Opt. Soc. Am. A |

23. | P. Östlund and A. T. Friberg, “Radiometry and Radiation Efficiency of Twisted Gaussian Schell-Model Sources,” Opt. Rev. |

24. | Q. Lin and Y. Cai, “Tensor |

25. | Q. Lin and Y. Cai, “Fractional Fourier transform for partially coherent Gaussian-Schell model beams,” Opt. Lett. |

26. | Y. Cai, Q. Lin, and D. Ge, “Propagation of partially coherent twisted anisotropic Gaussian Schell-model beams in dispersive and absorbing media,” J. Opt. Soc. Am. A |

27. | Y. Cai and L. Hu, “Propagation of partially coherent twisted anisotropic Gaussian Schell-model beams through an apertured astigmatic optical system,” Opt. Lett. |

28. | Y. Cai and S. He, “Propagation of a partially coherent twisted anisotropic Gaussian Schell-model beam in a turbulent atmosphere,” Appl. Phys. Lett. |

29. | Y. Cai and U. Peschel, “Second-harmonic generation by an astigmatic partially coherent beam,” Opt. Express |

30. | Y. Cai, Q. Lin, and O. Korotkova, “Ghost imaging with twisted Gaussian Schell-model beam,” Opt. Express |

31. | M. J. Bastiaans, “Application of the Wigner distribution function to partially coherent light,” J. Opt. Soc. Am. A |

32. | C. Brosseau, |

33. | D. F. V. James, “Changes of polarization of light beams on propagation in free space,” J. Opt. Soc. Am. A |

34. | F. Gori, “Matrix treatment for partially polarized, partially coherent beams,” Opt. Lett. |

35. | G. P. Agrawal and E. Wolf, “Propagation-induced polarization changes in partially coherent optical beams,” J. Opt. Soc. Am. A |

36. | F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian schell-model beams,” J. Opt. A, Pure Appl. Opt. |

37. | G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. |

38. | E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A |

39. | Y. Cai, D. Ge, and Q. Lin, “Fractional Fourier transform for partially coherent and partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. |

40. | O. Korotkova, M. Salem, and E. Wolf, “Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source,” Opt. Lett. |

41. | E. Wolf, Introduction to the theory of coherence and polarization of light (Cambridge U. Press, 2007). |

42. | O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. |

43. | T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. |

44. | H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. |

45. | F. Gori, M. Santarsiero, R. Borghi, and V. Ramírez-Sánchez, “Realizability condition for electromagnetic Schell-model sources,” J. Opt. Soc. Am. A |

46. | B. Kanseri and H. C. Kandpal, “Experimental determination of electric cross-spectral density matrix and generalized Stokes parameters for a laser beam,” Opt. Lett. |

47. | M. Yao, Y. Cai, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “The evolution of the degree of polarization of an electromagnetic Gaussian Schell-model beam in a Gaussian cavity,” Opt. Lett. |

48. | O. Korotkova, M. Yao, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “The state of polarization of a stochastic electromagnetic beam in an optical resonator,” J. Opt. Soc. Am. A |

49. | Y. Cai, O. Korotkova, H. T. Eyyuboğlu, and Y. Baykal, “Active laser radar systems with stochastic electromagnetic beams in turbulent atmosphere,” Opt. Express |

50. | Y. Cai and O. Korotkova, “Twist phase-induced polarization changes in electromagnetic Gaussian Schell-model beams,” Appl. Phys. B |

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

52. | A. Ashkin, “Trapping of atoms by resonance radiation pressure,” Phys. Rev. Lett. |

53. | 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. |

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

55. | S. M. Block, L. S. Goldstein, and B. J. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature |

56. | C. Day, “Optical trap resolves the stepwise transfer of genetic information from DNA to RNA,” Phys. Today |

57. | C. H. Chen, P. T. Tai, and W. F. Hsieh, “Bottle beam from a bare laser for single-beam trapping,” Appl. Phys. Lett. |

58. | J. Y. Ye, G. Chang, T. B. Norris, C. Tse, M. J. Zohdy, K. W. Hollman, M. O’Donnell, and J. R. Baker Jr., “Trapping cavitation bubbles with a self-focused laser beam,” Opt. Lett. |

59. | Q. Lin, Z. Wang, and Z. Liu, “Radiation forces produced by standing wave trapping of non-paraxial Gaussian beams,” Opt. Commun. |

60. | Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express |

61. | L. G. Wang, C. L. Zhao, L. Q. Wang, X. H. Lu, and S. Y. Zhu, “Effect of spatial coherence on radiation forces acting on a Rayleigh dielectric sphere,” Opt. Lett. |

62. | C. L. Zhao, Y. Cai, X. Lu, and H. T. Eyyuboğlu, “Radiation force of coherent and partially coherent flat-topped beams on a Rayleigh particle,” Opt. Express |

63. | E. Wolf, “Coherence and polarization properties of electromagnetic laser modes,” Opt. Commun. |

64. | M. Salem and E. Wolf, “Coherence-induced polarization changes in light beams,” Opt. Lett. |

65. | T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. |

66. | K. Okamoto and S. Kawata, “Radiation force exerted on subwavelength particles near a nanoaperture,” Phys. Rev. Lett. |

67. | J. Kestin, M. Sokolov, and W. A. Wakeham, “Viscosity of Liquid Water in the Range - 8°C to 150° C,” J. Phys. Chem. Ref. Data |

**OCIS Codes**

(030.1640) Coherence and statistical optics : Coherence

(030.1670) Coherence and statistical optics : Coherent optical effects

(140.7010) Lasers and laser optics : Laser trapping

(260.5430) Physical optics : Polarization

**ToC Category:**

Optical Trapping and Manipulation

**History**

Original Manuscript: August 10, 2009

Revised Manuscript: October 7, 2009

Manuscript Accepted: October 28, 2009

Published: November 10, 2009

**Citation**

Chengliang Zhao, Yangjian Cai, and Olga Korotkova, "Radiation force of scalar and electromagnetic twisted Gaussian Schell-model beams," Opt. Express **17**, 21472-21487 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-24-21472

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### References

- E. Wolf and E. Collett, “Partially coherent sources which produce same far-field intensity distribution as a laser,” Opt. Commun. 25(3), 293–296 (1978). [CrossRef]
- F. Gori, “Collet-Wolf sources and multimode lasers,” Opt. Commun. 34(3), 301–305 (1978). [CrossRef]
- P. De Santis, F. Gori, G. Guattari, and C. Palma, “An example of a Collett-Wolf source,” Opt. Commun. 29(3), 256–260 (1979). [CrossRef]
- F. Wang and Y. Cai, “Experimental observation of fractional Fourier transform for a partially coherent optical beam with Gaussian statistics,” J. Opt. Soc. Am. A 24(7), 1937–1944 (2007). [CrossRef]
- A. T. Friberg and R. J. Sudol, “Propagation parameters of Gaussian Schell-model beams,” Opt. Commun. 41(6), 383–387 (1982). [CrossRef]
- Q. S. He, J. Turunen, and A. T. Friberg, “Propagation and imaging experiments with Gaussian Schell-model beams,” Opt. Commun. 67(4), 245–250 (1988). [CrossRef]
- Y. Cai and S. Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(5), 056607 (2005). [CrossRef] [PubMed]
- J. C. Ricklin and F. M. Davidson, “Atmospheric turbulence effects on a partially coherent Gaussian beam: implications for free-space laser communication,” J. Opt. Soc. Am. A 19(9), 1794–1802 (2002). [CrossRef]
- N. A. Ansari and M. S. Zubairy, “Second-harmonic generation by a Gaussian Schell-model source,” Opt. Commun. 59(5-6), 385–390 (1986). [CrossRef]
- L. Mandel, and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
- R. Simon and N. Mukunda, “Twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A 10(1), 95–109 (1993). [CrossRef]
- R. Simon, K. Sundar, and N. Mukunda, “Twisted Gaussian Schell-model beams. I. Symmetry structure and normal-mode spectrum,” J. Opt. Soc. Am. A 10(9), 2008–2016 (1993). [CrossRef]
- K. Sundar, R. Simon, and N. Mukunda, “Twisted Gaussian Schell-model beams. II. Spectrum analysis and propagation characteristics,” J. Opt. Soc. Am. A 10(9), 2017–2023 (1993). [CrossRef]
- R. Simon and N. Mukunda, “Twist phase in Gaussian-beam optics,” J. Opt. Soc. Am. A 15(9), 2373–2382 (1998). [CrossRef]
- A. T. Friberg, E. Tervonen, and J. Turunen, “Interpretation and experimental demonstration of twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A 11(6), 1818–1826 (1994). [CrossRef]
- D. Ambrosini, V. Bagini, F. Gori, and M. Santarsiero, “Twisted Gaussian Schell-model beams: a superposition model,” J. Mod. Opt. 41(7), 1391–1399 (1994). [CrossRef]
- K. Sundar, N. Mukunda, and R. Simon, “Coherent-mode decomposition of general anisotropic Gaussian Schell-model beams,” J. Opt. Soc. Am. A 12(3), 560–569 (1995). [CrossRef]
- R. Simon, A. T. Friberg, and E. Wolf, “Transfer of radiance by twisted Gaussian Schell-model beams in paraxial systems,” Pure Appl. Opt. 5(3), 331–343 (1996). [CrossRef]
- R. Simon and N. Mukunda, “Gaussian Schell-model beams and general shape invariance,” J. Opt. Soc. Am. A 16(10), 2465–2475 (1999). [CrossRef]
- S. A. Ponomarenko, “Twisted Gaussian Schell-model solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(3), 036618 (2001). [CrossRef] [PubMed]
- J. Serna and J. M. Movilla, “Orbital angular momentum of partially coherent beams,” Opt. Lett. 26(7), 405–407 (2001). [CrossRef] [PubMed]
- M. J. Bastiaans, “Wigner-distribution function applied to twisted Gaussian light propagating in first-order optical systems,” J. Opt. Soc. Am. A 17(12), 2475–2480 (2000). [CrossRef]
- P. Östlund and A. T. Friberg, “Radiometry and Radiation Efficiency of Twisted Gaussian Schell-Model Sources,” Opt. Rev. 8(1), 1–8 (2001). [CrossRef]
- Q. Lin and Y. Cai, “Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams,” Opt. Lett. 27(4), 216–218 (2002). [CrossRef] [PubMed]
- Q. Lin and Y. Cai, “Fractional Fourier transform for partially coherent Gaussian-Schell model beams,” Opt. Lett. 27(19), 1672–1674 (2002). [CrossRef] [PubMed]
- Y. Cai, Q. Lin, and D. Ge, “Propagation of partially coherent twisted anisotropic Gaussian Schell-model beams in dispersive and absorbing media,” J. Opt. Soc. Am. A 19(10), 2036–2042 (2002). [CrossRef]
- Y. Cai and L. Hu, “Propagation of partially coherent twisted anisotropic Gaussian Schell-model beams through an apertured astigmatic optical system,” Opt. Lett. 31(6), 685–687 (2006). [CrossRef] [PubMed]
- Y. Cai and S. He, “Propagation of a partially coherent twisted anisotropic Gaussian Schell-model beam in a turbulent atmosphere,” Appl. Phys. Lett. 89(4), 041117 (2006). [CrossRef]
- Y. Cai and U. Peschel, “Second-harmonic generation by an astigmatic partially coherent beam,” Opt. Express 15(23), 15480–15492 (2007). [CrossRef] [PubMed]
- Y. Cai, Q. Lin, and O. Korotkova, “Ghost imaging with twisted Gaussian Schell-model beam,” Opt. Express 17(4), 2453–2464 (2009). [CrossRef] [PubMed]
- M. J. Bastiaans, “Application of the Wigner distribution function to partially coherent light,” J. Opt. Soc. Am. A 3(8), 1227–1238 (1986). [CrossRef]
- C. Brosseau, Fundamentals of polarized light-a statistical approach (Wiley, New York, 1998).
- D. F. V. James, “Changes of polarization of light beams on propagation in free space,” J. Opt. Soc. Am. A 11(5), 1641–1643 (1994). [CrossRef]
- F. Gori, “Matrix treatment for partially polarized, partially coherent beams,” Opt. Lett. 23(4), 241–243 (1998). [CrossRef] [PubMed]
- G. P. Agrawal and E. Wolf, “Propagation-induced polarization changes in partially coherent optical beams,” J. Opt. Soc. Am. A 17(11), 2019–2023 (2000). [CrossRef]
- F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian schell-model beams,” J. Opt. A, Pure Appl. Opt. 3(1), 301 (2001). [CrossRef]
- G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208(1-3), 9–16 (2002). [CrossRef]
- E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312(5-6), 263–267 (2003). [CrossRef]
- Y. Cai, D. Ge, and Q. Lin, “Fractional Fourier transform for partially coherent and partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 5(5), 453–459 (2003). [CrossRef]
- O. Korotkova, M. Salem, and E. Wolf, “Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source,” Opt. Lett. 29(11), 1173–1175 (2004). [CrossRef] [PubMed]
- E. Wolf, Introduction to the theory of coherence and polarization of light (Cambridge U. Press, 2007).
- O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233(4-6), 225–230 (2004). [CrossRef]
- T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7(5), 232–237 (2005). [CrossRef]
- H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249(4-6), 379–385 (2005). [CrossRef]
- F. Gori, M. Santarsiero, R. Borghi, and V. Ramírez-Sánchez, “Realizability condition for electromagnetic Schell-model sources,” J. Opt. Soc. Am. A 25(5), 1016–1021 (2008). [CrossRef]
- B. Kanseri and H. C. Kandpal, “Experimental determination of electric cross-spectral density matrix and generalized Stokes parameters for a laser beam,” Opt. Lett. 33(20), 2410–2412 (2008). [CrossRef] [PubMed]
- M. Yao, Y. Cai, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “The evolution of the degree of polarization of an electromagnetic Gaussian Schell-model beam in a Gaussian cavity,” Opt. Lett. 33(19), 2266–2268 (2008). [CrossRef] [PubMed]
- O. Korotkova, M. Yao, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “The state of polarization of a stochastic electromagnetic beam in an optical resonator,” J. Opt. Soc. Am. A 25(11), 2710–2720 (2008). [CrossRef]
- Y. Cai, O. Korotkova, H. T. Eyyuboğlu, and Y. Baykal, “Active laser radar systems with stochastic electromagnetic beams in turbulent atmosphere,” Opt. Express 16(20), 15834 (2008). [CrossRef] [PubMed]
- Y. Cai and O. Korotkova, “Twist phase-induced polarization changes in electromagnetic Gaussian Schell-model beams,” Appl. Phys. B 96(2-3), 499–507 (2009). [CrossRef]
- A. Ashkin, “Acceleration and trapping of particles by radiation forces,” Phys. Rev. Lett. 24(4), 156–159 (1970). [CrossRef]
- A. Ashkin, “Trapping of atoms by resonance radiation pressure,” Phys. Rev. Lett. 40(12), 729–732 (1978). [CrossRef]
- 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]
- S. M. Block, L. S. Goldstein, and B. J. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature 348(6299), 348–352 (1990). [CrossRef] [PubMed]
- C. Day, “Optical trap resolves the stepwise transfer of genetic information from DNA to RNA,” Phys. Today 59(1), 26–27 (2006). [CrossRef]
- C. H. Chen, P. T. Tai, and W. F. Hsieh, “Bottle beam from a bare laser for single-beam trapping,” Appl. Phys. Lett. 43, 6001–6006 (2004).
- J. Y. Ye, G. Chang, T. B. Norris, C. Tse, M. J. Zohdy, K. W. Hollman, M. O’Donnell, and J. R. Baker., “Trapping cavitation bubbles with a self-focused laser beam,” Opt. Lett. 29(18), 2136–2138 (2004). [CrossRef] [PubMed]
- Q. Lin, Z. Wang, and Z. Liu, “Radiation forces produced by standing wave trapping of non-paraxial Gaussian beams,” Opt. Commun. 198(1-3), 95–100 (2001). [CrossRef]
- Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12(15), 3377–3382 (2004). [CrossRef] [PubMed]
- L. G. Wang, C. L. Zhao, L. Q. Wang, X. H. Lu, and S. Y. Zhu, “Effect of spatial coherence on radiation forces acting on a Rayleigh dielectric sphere,” Opt. Lett. 32(11), 1393–1395 (2007). [CrossRef] [PubMed]
- C. L. Zhao, Y. Cai, X. Lu, and H. T. Eyyuboğlu, “Radiation force of coherent and partially coherent flat-topped beams on a Rayleigh particle,” Opt. Express 17(3), 1753–1765 (2009). [CrossRef] [PubMed]
- E. Wolf, “Coherence and polarization properties of electromagnetic laser modes,” Opt. Commun. 265(1), 60–62 (2006). [CrossRef]
- M. Salem and E. Wolf, “Coherence-induced polarization changes in light beams,” Opt. Lett. 33(11), 1180–1182 (2008). [CrossRef] [PubMed]
- T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78(25), 4713–4716 (1997). [CrossRef]
- K. Okamoto and S. Kawata, “Radiation force exerted on subwavelength particles near a nanoaperture,” Phys. Rev. Lett. 83(22), 4534–4537 (1999). [CrossRef]
- J. Kestin, M. Sokolov, and W. A. Wakeham, “Viscosity of Liquid Water in the Range - 8°C to 150° C,” J. Phys. Chem. Ref. Data 7, 941–948 (1978). [CrossRef]

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