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Degree of polarization of a tightly focused partially coherent dark hollow beam

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Abstract

Propagation of a linearly polarized partially coherent dark hollow beam (DHB) through a high numerical aperture (NA) thin lens is formulated. The tight focusing properties, such as the degree of polarization, the intensity distribution, and the degree of coherence, of a partially coherent DHB are investigated in detail. It is found that the focusing properties of a partially coherent DHB are closely determined by the initial coherence, beam order, and the NA of the thin lens.

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References

  1. H.T. Eyyuboğlu, A. Arpali, Y. Baykal, Opt. Express 14, 4196 (2006)

    Article  ADS  Google Scholar 

  2. N. Nishi, T. Jitsuno, K. Tsubakimoto, S. Matsuoka, N. Miyanaga, M. Nakatsuka, Opt. Rev. 7, 216 (2000)

    Article  Google Scholar 

  3. C. Zhao, Y. Cai, X. Lu, Eyyuboğlu, Opt. Express 17, 1753 (2009)

    Article  ADS  Google Scholar 

  4. Y. Cai, J. Opt. A, Pure Appl. Opt. 8, 537 (2006)

    Article  ADS  Google Scholar 

  5. J. Yin, W. Gao, Y. Zhu, in Progress in Optics, ed. by E. Wolf, vol. 44 (North-Holland, Amsterdam, 2003), p. 119

    Google Scholar 

  6. T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, H. Sasada, Phys. Rev. Lett. 78, 4713 (1997)

    Article  ADS  Google Scholar 

  7. F. Gori, G. Guattari, C. Padovani, Opt. Commun. 64, 491 (1987)

    Article  ADS  Google Scholar 

  8. J.C. Gutierrez-Vega, M.D. Iturbe-Castillo, S. Chavez-Cerda, Opt. Lett. 25, 1493 (2000)

    Article  ADS  Google Scholar 

  9. Y. Cai, X. Lu, Q. Lin, Opt. Lett. 28, 1084 (2003)

    Article  ADS  Google Scholar 

  10. Y. Cai, C. Chen, F. Wang, Opt. Commun. 278, 34 (2007)

    Article  ADS  Google Scholar 

  11. Y. Cai, S. He, Opt. Express 14, 1353 (2006)

    Article  ADS  Google Scholar 

  12. Y. Cai, Opt. Lett. 32, 3179 (2007)

    Article  ADS  Google Scholar 

  13. Y. Cai, Z. Wang, Q. Lin, Opt. Express 16, 15254 (2008)

    Article  ADS  Google Scholar 

  14. H. Ito, T. Nakata, K. Sakaki, M. Ohtsu, K.I. Lee, W. Jhe, Phys. Rev. Lett. 76, 4500 (1996)

    Article  ADS  Google Scholar 

  15. X. Wang, M.G. Littman, Opt. Lett. 18, 767 (1993)

    Article  ADS  Google Scholar 

  16. H.S. Lee, B.W. Atewart, K. Choi, H. Fenichel, Phys. Rev. A 49, 4922 (1994)

    Article  ADS  Google Scholar 

  17. J. Yin, H. Noh, K. Lee, K. Kim, Y. Wang, W. Jhe, Opt. Commun. 138, 287 (1997)

    Article  ADS  Google Scholar 

  18. N.R. Heckenberg, R. McDuff, C.P. Smith, A.G. White, Opt. Lett. 17, 221 (1992)

    Article  ADS  Google Scholar 

  19. Z. Liu, H. Zhao, J. Liu, J. Lin, M.A. Ahmad, S. Liu, Opt. Lett. 32, 2076 (2007)

    Article  ADS  Google Scholar 

  20. Y. Zhang, Opt. Commun. 281, 508 (2008)

    Article  ADS  Google Scholar 

  21. H. Ma, P. Zhou, X. Wang, Y. Ma, F. Xi, X. Xu, Z. Liu, Opt. Express 18, 8251 (2010)

    Article  ADS  Google Scholar 

  22. Y. Cai, Q. Lin, J. Opt. Soc. Am. A 21, 1058 (2004)

    Article  ADS  Google Scholar 

  23. Y. Cai, D. Ge, Phys. Lett. A 357, 72 (2006)

    Article  ADS  MATH  Google Scholar 

  24. Y. Chen, Y. Cai, H.T. Eyyuboğlu, Y. Baykal, Appl. Phys. B 90, 87 (2008)

    Article  ADS  Google Scholar 

  25. Y. Cai, S. He, J. Opt. Soc. Am. A 23, 1410 (2006)

    Article  ADS  Google Scholar 

  26. Y. Cai, H.T. Eyyuboğlu, Y. Baykal, J. Opt. Soc. Am. A 25, 1497 (2008)

    Article  ADS  Google Scholar 

  27. Y. Cai, H.T. Eyyuboğlu, Y. Baykal, Opt. Commun. 281, 5291 (2008)

    Article  ADS  Google Scholar 

  28. D. Deng, Q. Guo, J. Opt. Soc. Am. B 26, 2044 (2009)

    Article  ADS  Google Scholar 

  29. D. Liu, Z. Zhou, J. Opt. A, Pure Appl. Opt. 10, 095005 (2008)

    Article  ADS  Google Scholar 

  30. Y. Cai, H.T. Eyyuboğlu, Y. Baykal, Opt. Lasers Eng. 48, 1019 (2010)

    Article  Google Scholar 

  31. X. Chu, G. Zhou, Opt. Express 15, 7697 (2007)

    Article  ADS  Google Scholar 

  32. H.T. Eyyuboğlu, C.Z. Çil, Appl. Phys. B 93, 595 (2008)

    Article  ADS  Google Scholar 

  33. Y. Cai, L. Zhang, Opt. Commun. 265, 607 (2006)

    Article  ADS  Google Scholar 

  34. Y. Cai, L. Zhang, J. Opt. Soc. Am. B 23, 1398 (2006)

    Article  ADS  Google Scholar 

  35. X. Lu, Y. Cai, Phys. Lett. A 369, 157 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  36. Y. Cai, F. Wang, Phys. Lett. A 372, 4654 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  37. X. Li, F. Wang, Y. Cai, Opt. Laser Technol. 43, 577 (2011)

    Article  ADS  Google Scholar 

  38. H.T. Eyyuboğlu, Opt. Laser Technol. 40, 156 (2008)

    Article  ADS  Google Scholar 

  39. Y. Yuan, Y. Cai, J. Qu, H.T. Eyyuboğlu, Y. Baykal, O. Korotkova, Opt. Express 17, 17344 (2009)

    Article  ADS  Google Scholar 

  40. Y. Qiu, Z. Chen, L. Liu, J. Mod. Opt. 57, 662 (2010)

    Article  ADS  MATH  Google Scholar 

  41. C. Zhao, Y. Cai, F. Wang, X. Lu, Y. Wang, Opt. Lett. 33, 1389 (2008)

    Article  ADS  Google Scholar 

  42. X. Li, Y. Cai, Appl. Phys. B 102, 205 (2011)

    Article  ADS  Google Scholar 

  43. R. Dorn, S. Quabis, G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003)

    Article  ADS  Google Scholar 

  44. K.S. Youngworth, T.G. Brown, Opt. Express 7, 77 (2000)

    Article  ADS  Google Scholar 

  45. Q. Zhan, Opt. Express 12, 3377 (2004)

    Article  ADS  Google Scholar 

  46. E.Y.S. Yew, C.J.R. Sheppard, Opt. Lett. 32, 3417 (2007)

    Article  ADS  Google Scholar 

  47. B. Sick, B. Hecht, L. Novotny, Phys. Rev. Lett. 85, 4482 (2000)

    Article  ADS  Google Scholar 

  48. L. Novotny, M.R. Beversluis, K.S. Youngworth, T.G. Brown, Phys. Rev. Lett. 86, 5251 (2001)

    Article  ADS  Google Scholar 

  49. Q. Zhan, Adv. Opt. Photonics 1, 1 (2009)

    Article  Google Scholar 

  50. Z. Zhang, J. Pu, X. Wang, Opt. Lett. 33, 49 (2008)

    Article  ADS  Google Scholar 

  51. B. Chen, Z. Zhang, J. Pu, J. Opt. Soc. Am. A 26, 862 (2009)

    Article  ADS  Google Scholar 

  52. K. Lindfors, T. Setala, M. Kaivola, A.T. Friberg, J. Opt. Soc. Am. A 22, 561 (2005)

    Article  ADS  Google Scholar 

  53. T. Setala, A. Shevchenko, M. Kaivola, A.T. Friberg, Phys. Rev. E 66, 016615 (2002)

    Article  ADS  Google Scholar 

  54. K. Lindfors, A. Priimagi, T. Setala, A. Shevchenko, A.T. Friberg, Nat. Photonics 1, 228 (2007)

    Article  ADS  Google Scholar 

  55. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995)

    Google Scholar 

  56. Q. Lin, Y. Cai, Opt. Lett. 27, 216 (2002)

    Article  ADS  Google Scholar 

  57. Q. Lin, Y. Cai, Opt. Lett. 27, 1672 (2002)

    Article  ADS  Google Scholar 

  58. Y. Cai, L. Hu, Opt. Lett. 31, 685 (2006)

    Article  ADS  Google Scholar 

  59. Y. Cai, S. He, Appl. Phys. Lett. 89, 041117 (2006)

    Article  ADS  Google Scholar 

  60. F. Wang, Y. Cai, J. Opt. Soc. Am. A 24, 1937 (2007)

    Article  ADS  Google Scholar 

  61. F. Wang, Y. Cai, Q. Lin, J. Opt. Soc. Am. A 25, 2001 (2008)

    Article  ADS  Google Scholar 

  62. B. Richards, E. Wolf, Proc. R. Soc. Lond. Ser. A 253, 358 (1959)

    Article  ADS  MATH  Google Scholar 

  63. M. Gu, Advanced Optical Imaging Theory (Springer, Berlin, 2000)

    Google Scholar 

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Dong, Y., Cai, Y. & Zhao, C. Degree of polarization of a tightly focused partially coherent dark hollow beam. Appl. Phys. B 105, 405–414 (2011). https://doi.org/10.1007/s00340-011-4517-0

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  • DOI: https://doi.org/10.1007/s00340-011-4517-0

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