Abstract

Partially coherent beams with nonconventional correlation functions have displayed many extraordinary properties, such as self-focusing and self-splitting, which are totally different from those of partially coherent beams with conventional Gaussian correlated Schell-model functions and are useful in many applications, such as optical trapping, free-space optical communications, and material thermal processing. In this paper, we present a review of recent developments on generation and propagation of partially coherent beams with nonconventional correlation functions.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  2. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).
  3. Y. Cai and F. Wang, “Tensor method for treating the propagation of scalar and electromagnetic Gaussian Schell-model beams: a review,” Open Opt. J. 4, 1–20 (2010).
  4. Y. Cai, “Generation of various partially coherent beams and their propagation properties in turbulent atmosphere: a review,” Proc. SPIE 7924, 792402 (2011).
    [CrossRef]
  5. Y. Cai, F. Wang, C. Zhao, S. Zhu, G. Wu, and Y. Dong, “Partially coherent vector beams: from theory to experiment,” in Vectorial Optical Fields: Fundamentals and Applications, Q. Zhen, ed. (World Scientific, 2013), Chap. 7, pp. 221–273.
  6. X. Liu, F. Wang, C. Wei, and Y. Cai, “Experimental study of turbulence-induced beam wander and deformation of a partially coherent beam,” Opt. Lett. 39, 3336–3339 (2014).
    [CrossRef]
  7. X. Liu, Y. Shen, L. Liu, F. Wang, and Y. Cai, “Experimental demonstration of vortex phase-induced reduction in scintillation of a partially coherent beam,” Opt. Lett. 38, 5323–5326 (2013).
    [CrossRef]
  8. F. Wang, X. Liu, L. Liu, Y. Yuan, and Y. Cai, “Experimental study of the scintillation index of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 103, 091102 (2013).
    [CrossRef]
  9. Y. Dong, F. Wang, C. Zhao, and Y. Cai, “Effect of spatial coherence on propagation, tight focusing and radiation forces of an azimuthally polarized beam,” Phys. Rev. A 86, 013840 (2012).
    [CrossRef]
  10. C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, “Effect of spatial coherence on determining the topological charge of a vortex beam,” Appl. Phys. Lett. 101, 261104 (2012).
    [CrossRef]
  11. F. Wang, Y. Cai, Y. Dong, and O. Korotkova, “Experimental generation of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 100, 051108 (2012).
    [CrossRef]
  12. F. Wang, G. Wu, X. Liu, S. Zhu, and Y. Cai, “Experimental measurement of the beam parameters of an electromagnetic Gaussian Schell-model source,” Opt. Lett. 36, 2722–2724 (2011).
    [CrossRef]
  13. C. Zhao, Y. Cai, F. Wang, X. Lu, and Y. Wang, “Generation of a high-quality partially coherent dark hollow beam with a multimode fiber,” Opt. Lett. 33, 1389–1391 (2008).
    [CrossRef]
  14. F. Wang and Y. Cai, “Experimental generation of a partially coherent flat-topped beam,” Opt. Lett. 33, 1795–1797 (2008).
    [CrossRef]
  15. 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, 1937–1944 (2007).
    [CrossRef]
  16. Y. Cai and S. He, “Propagation of a partially coherent twisted anisotropic Gaussian Schell-model beam in a turbulent atmosphere,” Appl. Phys. Lett. 89, 041117 (2006).
    [CrossRef]
  17. 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, 1794–1802 (2002).
    [CrossRef]
  18. C. 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, 1753–1765 (2009).
    [CrossRef]
  19. C. Zhao, Y. Cai, and O. Korotkova, “Radiation force of scalar and electromagnetic twisted Gaussian Schell-model beams,” Opt. Express 17, 21472–21487 (2009).
    [CrossRef]
  20. C. Zhao and Y. Cai, “Trapping two types of particles using a focused partially coherent elegant Laguerre–Gaussian beam,” Opt. Lett. 36, 2251–2253 (2011).
    [CrossRef]
  21. J. Zhang, Z. Wang, B. Cheng, Q. Wang, B. Wu, X. Shen, L. Zheng, Y. Xu, and Q. Lin, “Atom cooling by partially spatially coherent lasers,” Phys. Rev. A 88, 023416 (2013).
    [CrossRef]
  22. G. R. M. Robb and W. J. Firth, “Collective atomic recoil lasing with a partially coherent pump,” Phys. Rev. Lett. 99, 253601 (2007).
    [CrossRef]
  23. Y. Cai and S. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E 71, 056607 (2005).
    [CrossRef]
  24. T. E. Gureyev, D. M. Paganin, A. W. Stevenson, S. C. Mayo, and S. W. Wilkins, “Generalized eikonal of partially coherent beams and its use in quantitative imaging,” Phys. Rev. Lett. 93, 068103 (2004).
    [CrossRef]
  25. D. Kermisch, “Partially coherent image processing by laser scanning,” J. Opt. Soc. Am. 65, 887–891 (1975).
    [CrossRef]
  26. Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
    [CrossRef]
  27. A. Belendez, L. Carretero, and A. Fimia, “The use of partially coherent light to reduce the efficiency of silver halide noise gratings,” Opt. Commun. 98, 236–240 (1993).
    [CrossRef]
  28. M. S. Zubairy and J. K. McIver, “Second-harmonic generation by a partially coherent beam,” Phys. Rev. A 36, 202–206 (1987).
    [CrossRef]
  29. Y. Cai and U. Peschel, “Second-harmonic generation by an astigmatic partially coherent beam,” Opt. Express 15, 15480–15492 (2007).
    [CrossRef]
  30. T. van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, “Effects of spatial coherence on the angular distribution of radiant intensity generated by scattering on a sphere,” Phys. Rev. Lett. 104, 173902 (2010).
    [CrossRef]
  31. C. Ding, Y. Cai, O. Korotkova, Y. Zhang, and L. Pan, “Scattering-induced changes in the temporal coherence length and the pulse duration of a partially coherent plane-wave pulse,” Opt. Lett. 36, 517–519 (2011).
    [CrossRef]
  32. E. Wolf and E. Collett, “Partially coherent sources which produce the same far-field intensity distribution as a laser,” Opt. Commun. 25, 293–296 (1978).
    [CrossRef]
  33. F. Gori, “Collet–Wolf sources and multimode lasers,” Opt. Commun. 34, 301–305 (1980).
    [CrossRef]
  34. P. de Santis, F. Gori, G. Guattari, and C. Palma, “An example of a Collett–Wolf source,” Opt. Commun. 29, 256–260 (1979).
    [CrossRef]
  35. A. T. Friberg and R. J. Sudol, “Propagation parameters of Gaussian Schell-model beams,” Opt. Commun 41, 383–387 (1982).
    [CrossRef]
  36. E. Tervonen, A. T. Friberg, and J. Turunen, “Gaussian Schell-model beams generated with synthetic acousto-optic holograms,” J. Opt. Soc. Am. A 9, 796–803 (1992).
    [CrossRef]
  37. Q. Lin and Y. Cai, “Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams,” Opt. Lett. 27, 216–218 (2002).
    [CrossRef]
  38. F. Gori and G. Guattari, “Modal expansion for J0-correlated Schell-model sources,” Opt. Commun. 64, 311–316 (1987).
    [CrossRef]
  39. C. Palma, R. Borghi, and G. Cincotti, “Beams originated by J0-correlated Schell-model planar sources,” Opt. Commun. 125, 113–121 (1996).
    [CrossRef]
  40. G. Gbur and T. D. Visse, “Can spatial coherence effects produce a local minimum of intensity at focus?” Opt. Lett. 28, 1627–1629 (2003).
    [CrossRef]
  41. T. van Dijk, G. Gbur, and T. D. Visser, “Shaping the focal intensity distribution using spatial coherence,” J. Opt. Soc. Am. A 25, 575–581 (2008).
    [CrossRef]
  42. S. B. Raghunathan, T. van Dijk, E. J. G. Peterman, and T. D. Visser, “Experimental demonstration of an intensity minimum at the focus of a laser beam created by spatial coherence: application to the optical trapping of dielectric particles,” Opt. Lett. 35, 4166–4168 (2010).
    [CrossRef]
  43. F. Gori, M. Santarsiero, and R. Borghi, “Modal expansion for J0-correlated electromagnetic sources,” Opt. Lett. 33, 1857–1859 (2008).
    [CrossRef]
  44. Y. Gu and G. Gbur, “Scintillation of pseudo-Bessel correlated beams in atmospheric turbulence,” J. Opt. Soc. Am. A 27, 2621–2629 (2010).
    [CrossRef]
  45. F. Gori and M. Santarsiero, “Devising genuine spatial correlation functions,” Opt. Lett. 32, 3531–3533 (2007).
    [CrossRef]
  46. F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A 11, 085706 (2009).
    [CrossRef]
  47. R. Martínez-Herrero, P. M. Mejías, and F. Gori, “Genuine cross-spectral densities and pseudo-modal expansions,” Opt. Lett. 34, 1399–1401 (2009).
    [CrossRef]
  48. R. Martínez-Herrero and P. M. Mejías, “Elementary-field expansions of genuine cross-spectral density matrices,” Opt. Lett. 34, 2303–2305 (2009).
    [CrossRef]
  49. L. Waller, G. Situ, and J. W. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nat. Photonics 6, 474–479 (2012).
    [CrossRef]
  50. H. Lajunen and T. Saastamoinen, “Propagation characteristics of partially coherent beams with spatially varying correlations,” Opt. Lett. 36, 4104–4106 (2011).
    [CrossRef]
  51. Z. Tong and O. Korotkova, “Electromagnetic nonuniformly correlated beam,” J. Opt. Soc. Am. A 29, 2154–2158 (2012).
    [CrossRef]
  52. H. Lajunen and T. Saastamoinen, “Non-uniformly correlated partially coherent pulses,” Opt. Lett. 21, 190–195 (2013).
  53. C. Ding, Y. Cai, Y. Zhang, H. Wang, Z. Zhao, and L. Pan, “Stochastic electromagnetic plane-wave pulse with non-uniform correlation distribution,” Phys. Lett. A 377, 1563–1565 (2013).
    [CrossRef]
  54. S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. 37, 2970–2972 (2012).
    [CrossRef]
  55. O. Korotkova, S. Sahin, and E. Shchepakina, “Multi-Gaussian Schell-model beams,” J. Opt. Soc. Am. A 29, 2159–2164 (2012).
    [CrossRef]
  56. Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. 15, 025705 (2013).
    [CrossRef]
  57. O. Korotkova, “Random sources for rectangularly-shaped far fields,” Opt. Lett. 39, 64–67 (2014).
    [CrossRef]
  58. Y. Zhang and Y. Cai, “Random source generating far field with elliptical flat-topped beam profile,” J. Opt. 16, 075704 (2014).
  59. Y. Zhang, L. Liu, C. Zhao, and Y. Cai, “Multi-Gaussian Schell-model vortex beam,” Phys. Lett. A 378, 750–754 (2014).
    [CrossRef]
  60. Z. Mei and O. Korotkova, “Random sources generating ring-shaped beams,” Opt. Lett. 38, 91–93 (2013).
    [CrossRef]
  61. Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre–Gaussian correlated Schell-model beam,” Opt. Express 22, 13975–13987 (2014).
    [CrossRef]
  62. Y. Chen, F. Wang, C. Zhao, and Y. Cai, “Experimental demonstration of a Laguerre–Gaussian correlated Schell-model vortex beam,” Opt. Express 22, 5826–5838 (2014).
    [CrossRef]
  63. Z. Mei and O. Korotkova, “Cosine-Gaussian Schell-model sources,” Opt. Lett. 38, 2578–2580 (2013).
    [CrossRef]
  64. C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39, 769–772 (2014).
    [CrossRef]
  65. C. Ding, O. Korotkova, Y. Zhang, and L. Pan, “Cosine-Gaussian correlated Schell-model pulsed beams,” Opt. Express 22, 931–942 (2014).
    [CrossRef]
  66. Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89, 013801 (2014).
    [CrossRef]
  67. Z. Tong and O. Korotkova, “Non-uniformly correlated light beams in uniformly correlated media,” Opt. Lett. 37, 3240–3242 (2012).
    [CrossRef]
  68. Y. Gu and G. Gbur, “Scintillation of nonuniformly correlated beams in atmospheric turbulence,” Opt. Lett. 38, 1395–1397 (2013).
    [CrossRef]
  69. S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
    [CrossRef]
  70. Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
    [CrossRef]
  71. J. Cang, P. Xiu, and X. Liu, “Propagation of Laguerre–Gaussian and Bessel–Gaussian Schell-model beams through paraxial optical system in turbulent atmosphere,” Opt. Laser Technol. 54, 35–41 (2013).
    [CrossRef]
  72. Z. Mei, E. Shchepakin, and O. Korotkova, “Electromagnetic non-uniformly correlated beams in turbulent atmosphere,” Opt. Express 21, 17512–17519 (2013).
    [CrossRef]
  73. R. Chen, L. Liu, S. Zhu, G. Wu, F. Wang, and Y. Cai, “Statistical properties of a Laguerre–Gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 22, 1871–1883 (2014).
    [CrossRef]
  74. O. Korotkova and E. Shchepakina, “Rectangular multi-Gaussian Schell-model beams in atmospheric turbulence,” J. Opt. 16, 045704 (2014).
    [CrossRef]
  75. Y. Chen and Y. Cai, “Generation of a controllable optical cage by focusing a Laguerre–Gaussian correlated Schell-model beam,” Opt. Lett. 39, 2549–2552 (2014).
    [CrossRef]
  76. Y. Zhan and D. Zhao, “Scattering of multi-Gaussian Schell-model beams on a random medium,” Opt. Express 21, 24781–24792 (2013).
    [CrossRef]
  77. F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38, 1814–1816 (2013).
    [CrossRef]
  78. F. Gori, “Matrix treatment for partially polarized partially coherent beams,” Opt. Lett. 23, 241–243 (1998).
    [CrossRef]
  79. Y. Zhang, B. Ding, and T. Suyama, “Trapping two types of particles using a double-ring-shaped radially polarized beam,” Phys. Rev. A 81, 023831 (2010).
    [CrossRef]
  80. P. Xu, X. He, J. Wang, and M. Zhan, “Trapping a single atom in a blue detuned optical bottle beam trap,” Opt. Lett. 35, 2164–2166 (2010).
    [CrossRef]
  81. Z. Wang, Q. Lin, and Y. Wang, “Control of atomic rotation by elliptical hollow beam carrying zero angular momentum,” Opt. Commun. 240, 357–362 (2004).
    [CrossRef]
  82. J. Lancis, V. Torres-Company, E. Silvestre, and P. Andrés, “Space–time analogy for partially coherent plane-wave-type pulses,” Opt. Lett. 30, 2973–2975 (2005).
    [CrossRef]
  83. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57 (2009).
    [CrossRef]
  84. Y. Dong, Y. Cai, C. Zhao, and M. Yao, “Statistics properties of a cylindrical vector partially coherent beam,” Opt. Express 19, 5979–5992 (2011).
    [CrossRef]
  85. J. Tervo, T. Setälä, and A. T. Friberg, “Degree of coherence for electromagnetic fields,” Opt. Express 11, 1137–1143 (2003).
    [CrossRef]
  86. G. Wu, F. Wang, and Y. Cai, “Coherence and polarization properties of a radially polarized beam with variable spatial coherence,” Opt. Express 20, 28301–28318 (2012).
    [CrossRef]
  87. S. Zhu, X. Zhu, L. Liu, F. Wang, and Y. Cai, “Theoretical and experimental studies of the spectral changes of a polychromatic partially coherent radially polarized beam,” Opt. Express 21, 27682–27696 (2013).
    [CrossRef]
  88. Y. Cai and Q. Lin, “Hollow elliptical Gaussian beam and its propagation through aligned and misaligned paraxial optical systems,” J. Opt. Soc. Am. A 21, 1058–1065 (2004).
    [CrossRef]
  89. Y. Cai, X. Lu, and Q. Lin, “Hollow Gaussian beam and its propagation properties,” Opt. Lett. 28, 1084–1086 (2003).
    [CrossRef]

2014 (12)

X. Liu, F. Wang, C. Wei, and Y. Cai, “Experimental study of turbulence-induced beam wander and deformation of a partially coherent beam,” Opt. Lett. 39, 3336–3339 (2014).
[CrossRef]

O. Korotkova, “Random sources for rectangularly-shaped far fields,” Opt. Lett. 39, 64–67 (2014).
[CrossRef]

Y. Zhang and Y. Cai, “Random source generating far field with elliptical flat-topped beam profile,” J. Opt. 16, 075704 (2014).

Y. Zhang, L. Liu, C. Zhao, and Y. Cai, “Multi-Gaussian Schell-model vortex beam,” Phys. Lett. A 378, 750–754 (2014).
[CrossRef]

Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre–Gaussian correlated Schell-model beam,” Opt. Express 22, 13975–13987 (2014).
[CrossRef]

Y. Chen, F. Wang, C. Zhao, and Y. Cai, “Experimental demonstration of a Laguerre–Gaussian correlated Schell-model vortex beam,” Opt. Express 22, 5826–5838 (2014).
[CrossRef]

C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39, 769–772 (2014).
[CrossRef]

C. Ding, O. Korotkova, Y. Zhang, and L. Pan, “Cosine-Gaussian correlated Schell-model pulsed beams,” Opt. Express 22, 931–942 (2014).
[CrossRef]

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89, 013801 (2014).
[CrossRef]

R. Chen, L. Liu, S. Zhu, G. Wu, F. Wang, and Y. Cai, “Statistical properties of a Laguerre–Gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 22, 1871–1883 (2014).
[CrossRef]

O. Korotkova and E. Shchepakina, “Rectangular multi-Gaussian Schell-model beams in atmospheric turbulence,” J. Opt. 16, 045704 (2014).
[CrossRef]

Y. Chen and Y. Cai, “Generation of a controllable optical cage by focusing a Laguerre–Gaussian correlated Schell-model beam,” Opt. Lett. 39, 2549–2552 (2014).
[CrossRef]

2013 (16)

Y. Zhan and D. Zhao, “Scattering of multi-Gaussian Schell-model beams on a random medium,” Opt. Express 21, 24781–24792 (2013).
[CrossRef]

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38, 1814–1816 (2013).
[CrossRef]

Y. Gu and G. Gbur, “Scintillation of nonuniformly correlated beams in atmospheric turbulence,” Opt. Lett. 38, 1395–1397 (2013).
[CrossRef]

S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
[CrossRef]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[CrossRef]

J. Cang, P. Xiu, and X. Liu, “Propagation of Laguerre–Gaussian and Bessel–Gaussian Schell-model beams through paraxial optical system in turbulent atmosphere,” Opt. Laser Technol. 54, 35–41 (2013).
[CrossRef]

Z. Mei, E. Shchepakin, and O. Korotkova, “Electromagnetic non-uniformly correlated beams in turbulent atmosphere,” Opt. Express 21, 17512–17519 (2013).
[CrossRef]

Z. Mei and O. Korotkova, “Cosine-Gaussian Schell-model sources,” Opt. Lett. 38, 2578–2580 (2013).
[CrossRef]

Z. Mei and O. Korotkova, “Random sources generating ring-shaped beams,” Opt. Lett. 38, 91–93 (2013).
[CrossRef]

H. Lajunen and T. Saastamoinen, “Non-uniformly correlated partially coherent pulses,” Opt. Lett. 21, 190–195 (2013).

C. Ding, Y. Cai, Y. Zhang, H. Wang, Z. Zhao, and L. Pan, “Stochastic electromagnetic plane-wave pulse with non-uniform correlation distribution,” Phys. Lett. A 377, 1563–1565 (2013).
[CrossRef]

X. Liu, Y. Shen, L. Liu, F. Wang, and Y. Cai, “Experimental demonstration of vortex phase-induced reduction in scintillation of a partially coherent beam,” Opt. Lett. 38, 5323–5326 (2013).
[CrossRef]

F. Wang, X. Liu, L. Liu, Y. Yuan, and Y. Cai, “Experimental study of the scintillation index of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 103, 091102 (2013).
[CrossRef]

J. Zhang, Z. Wang, B. Cheng, Q. Wang, B. Wu, X. Shen, L. Zheng, Y. Xu, and Q. Lin, “Atom cooling by partially spatially coherent lasers,” Phys. Rev. A 88, 023416 (2013).
[CrossRef]

Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. 15, 025705 (2013).
[CrossRef]

S. Zhu, X. Zhu, L. Liu, F. Wang, and Y. Cai, “Theoretical and experimental studies of the spectral changes of a polychromatic partially coherent radially polarized beam,” Opt. Express 21, 27682–27696 (2013).
[CrossRef]

2012 (9)

G. Wu, F. Wang, and Y. Cai, “Coherence and polarization properties of a radially polarized beam with variable spatial coherence,” Opt. Express 20, 28301–28318 (2012).
[CrossRef]

Y. Dong, F. Wang, C. Zhao, and Y. Cai, “Effect of spatial coherence on propagation, tight focusing and radiation forces of an azimuthally polarized beam,” Phys. Rev. A 86, 013840 (2012).
[CrossRef]

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, “Effect of spatial coherence on determining the topological charge of a vortex beam,” Appl. Phys. Lett. 101, 261104 (2012).
[CrossRef]

F. Wang, Y. Cai, Y. Dong, and O. Korotkova, “Experimental generation of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 100, 051108 (2012).
[CrossRef]

S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. 37, 2970–2972 (2012).
[CrossRef]

O. Korotkova, S. Sahin, and E. Shchepakina, “Multi-Gaussian Schell-model beams,” J. Opt. Soc. Am. A 29, 2159–2164 (2012).
[CrossRef]

L. Waller, G. Situ, and J. W. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nat. Photonics 6, 474–479 (2012).
[CrossRef]

Z. Tong and O. Korotkova, “Electromagnetic nonuniformly correlated beam,” J. Opt. Soc. Am. A 29, 2154–2158 (2012).
[CrossRef]

Z. Tong and O. Korotkova, “Non-uniformly correlated light beams in uniformly correlated media,” Opt. Lett. 37, 3240–3242 (2012).
[CrossRef]

2011 (6)

2010 (6)

Y. Zhang, B. Ding, and T. Suyama, “Trapping two types of particles using a double-ring-shaped radially polarized beam,” Phys. Rev. A 81, 023831 (2010).
[CrossRef]

P. Xu, X. He, J. Wang, and M. Zhan, “Trapping a single atom in a blue detuned optical bottle beam trap,” Opt. Lett. 35, 2164–2166 (2010).
[CrossRef]

T. van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, “Effects of spatial coherence on the angular distribution of radiant intensity generated by scattering on a sphere,” Phys. Rev. Lett. 104, 173902 (2010).
[CrossRef]

Y. Cai and F. Wang, “Tensor method for treating the propagation of scalar and electromagnetic Gaussian Schell-model beams: a review,” Open Opt. J. 4, 1–20 (2010).

S. B. Raghunathan, T. van Dijk, E. J. G. Peterman, and T. D. Visser, “Experimental demonstration of an intensity minimum at the focus of a laser beam created by spatial coherence: application to the optical trapping of dielectric particles,” Opt. Lett. 35, 4166–4168 (2010).
[CrossRef]

Y. Gu and G. Gbur, “Scintillation of pseudo-Bessel correlated beams in atmospheric turbulence,” J. Opt. Soc. Am. A 27, 2621–2629 (2010).
[CrossRef]

2009 (6)

2008 (4)

2007 (4)

2006 (1)

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

2005 (2)

Y. Cai and S. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E 71, 056607 (2005).
[CrossRef]

J. Lancis, V. Torres-Company, E. Silvestre, and P. Andrés, “Space–time analogy for partially coherent plane-wave-type pulses,” Opt. Lett. 30, 2973–2975 (2005).
[CrossRef]

2004 (3)

Z. Wang, Q. Lin, and Y. Wang, “Control of atomic rotation by elliptical hollow beam carrying zero angular momentum,” Opt. Commun. 240, 357–362 (2004).
[CrossRef]

Y. Cai and Q. Lin, “Hollow elliptical Gaussian beam and its propagation through aligned and misaligned paraxial optical systems,” J. Opt. Soc. Am. A 21, 1058–1065 (2004).
[CrossRef]

T. E. Gureyev, D. M. Paganin, A. W. Stevenson, S. C. Mayo, and S. W. Wilkins, “Generalized eikonal of partially coherent beams and its use in quantitative imaging,” Phys. Rev. Lett. 93, 068103 (2004).
[CrossRef]

2003 (3)

2002 (2)

1998 (1)

1996 (1)

C. Palma, R. Borghi, and G. Cincotti, “Beams originated by J0-correlated Schell-model planar sources,” Opt. Commun. 125, 113–121 (1996).
[CrossRef]

1993 (1)

A. Belendez, L. Carretero, and A. Fimia, “The use of partially coherent light to reduce the efficiency of silver halide noise gratings,” Opt. Commun. 98, 236–240 (1993).
[CrossRef]

1992 (1)

1987 (2)

F. Gori and G. Guattari, “Modal expansion for J0-correlated Schell-model sources,” Opt. Commun. 64, 311–316 (1987).
[CrossRef]

M. S. Zubairy and J. K. McIver, “Second-harmonic generation by a partially coherent beam,” Phys. Rev. A 36, 202–206 (1987).
[CrossRef]

1984 (1)

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[CrossRef]

1982 (1)

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

1980 (1)

F. Gori, “Collet–Wolf sources and multimode lasers,” Opt. Commun. 34, 301–305 (1980).
[CrossRef]

1979 (1)

P. de Santis, F. Gori, G. Guattari, and C. Palma, “An example of a Collett–Wolf source,” Opt. Commun. 29, 256–260 (1979).
[CrossRef]

1978 (1)

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

1975 (1)

Andrés, P.

Arinaga, S.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[CrossRef]

Belendez, A.

A. Belendez, L. Carretero, and A. Fimia, “The use of partially coherent light to reduce the efficiency of silver halide noise gratings,” Opt. Commun. 98, 236–240 (1993).
[CrossRef]

Borghi, R.

F. Gori, M. Santarsiero, and R. Borghi, “Modal expansion for J0-correlated electromagnetic sources,” Opt. Lett. 33, 1857–1859 (2008).
[CrossRef]

C. Palma, R. Borghi, and G. Cincotti, “Beams originated by J0-correlated Schell-model planar sources,” Opt. Commun. 125, 113–121 (1996).
[CrossRef]

Cai, Y.

X. Liu, F. Wang, C. Wei, and Y. Cai, “Experimental study of turbulence-induced beam wander and deformation of a partially coherent beam,” Opt. Lett. 39, 3336–3339 (2014).
[CrossRef]

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89, 013801 (2014).
[CrossRef]

R. Chen, L. Liu, S. Zhu, G. Wu, F. Wang, and Y. Cai, “Statistical properties of a Laguerre–Gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 22, 1871–1883 (2014).
[CrossRef]

Y. Chen and Y. Cai, “Generation of a controllable optical cage by focusing a Laguerre–Gaussian correlated Schell-model beam,” Opt. Lett. 39, 2549–2552 (2014).
[CrossRef]

Y. Zhang and Y. Cai, “Random source generating far field with elliptical flat-topped beam profile,” J. Opt. 16, 075704 (2014).

Y. Zhang, L. Liu, C. Zhao, and Y. Cai, “Multi-Gaussian Schell-model vortex beam,” Phys. Lett. A 378, 750–754 (2014).
[CrossRef]

Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre–Gaussian correlated Schell-model beam,” Opt. Express 22, 13975–13987 (2014).
[CrossRef]

Y. Chen, F. Wang, C. Zhao, and Y. Cai, “Experimental demonstration of a Laguerre–Gaussian correlated Schell-model vortex beam,” Opt. Express 22, 5826–5838 (2014).
[CrossRef]

C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39, 769–772 (2014).
[CrossRef]

C. Ding, Y. Cai, Y. Zhang, H. Wang, Z. Zhao, and L. Pan, “Stochastic electromagnetic plane-wave pulse with non-uniform correlation distribution,” Phys. Lett. A 377, 1563–1565 (2013).
[CrossRef]

S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
[CrossRef]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[CrossRef]

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38, 1814–1816 (2013).
[CrossRef]

S. Zhu, X. Zhu, L. Liu, F. Wang, and Y. Cai, “Theoretical and experimental studies of the spectral changes of a polychromatic partially coherent radially polarized beam,” Opt. Express 21, 27682–27696 (2013).
[CrossRef]

X. Liu, Y. Shen, L. Liu, F. Wang, and Y. Cai, “Experimental demonstration of vortex phase-induced reduction in scintillation of a partially coherent beam,” Opt. Lett. 38, 5323–5326 (2013).
[CrossRef]

F. Wang, X. Liu, L. Liu, Y. Yuan, and Y. Cai, “Experimental study of the scintillation index of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 103, 091102 (2013).
[CrossRef]

Y. Dong, F. Wang, C. Zhao, and Y. Cai, “Effect of spatial coherence on propagation, tight focusing and radiation forces of an azimuthally polarized beam,” Phys. Rev. A 86, 013840 (2012).
[CrossRef]

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, “Effect of spatial coherence on determining the topological charge of a vortex beam,” Appl. Phys. Lett. 101, 261104 (2012).
[CrossRef]

F. Wang, Y. Cai, Y. Dong, and O. Korotkova, “Experimental generation of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 100, 051108 (2012).
[CrossRef]

G. Wu, F. Wang, and Y. Cai, “Coherence and polarization properties of a radially polarized beam with variable spatial coherence,” Opt. Express 20, 28301–28318 (2012).
[CrossRef]

Y. Dong, Y. Cai, C. Zhao, and M. Yao, “Statistics properties of a cylindrical vector partially coherent beam,” Opt. Express 19, 5979–5992 (2011).
[CrossRef]

F. Wang, G. Wu, X. Liu, S. Zhu, and Y. Cai, “Experimental measurement of the beam parameters of an electromagnetic Gaussian Schell-model source,” Opt. Lett. 36, 2722–2724 (2011).
[CrossRef]

C. Zhao and Y. Cai, “Trapping two types of particles using a focused partially coherent elegant Laguerre–Gaussian beam,” Opt. Lett. 36, 2251–2253 (2011).
[CrossRef]

Y. Cai, “Generation of various partially coherent beams and their propagation properties in turbulent atmosphere: a review,” Proc. SPIE 7924, 792402 (2011).
[CrossRef]

C. Ding, Y. Cai, O. Korotkova, Y. Zhang, and L. Pan, “Scattering-induced changes in the temporal coherence length and the pulse duration of a partially coherent plane-wave pulse,” Opt. Lett. 36, 517–519 (2011).
[CrossRef]

Y. Cai and F. Wang, “Tensor method for treating the propagation of scalar and electromagnetic Gaussian Schell-model beams: a review,” Open Opt. J. 4, 1–20 (2010).

C. Zhao, Y. Cai, and O. Korotkova, “Radiation force of scalar and electromagnetic twisted Gaussian Schell-model beams,” Opt. Express 17, 21472–21487 (2009).
[CrossRef]

C. 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, 1753–1765 (2009).
[CrossRef]

C. Zhao, Y. Cai, F. Wang, X. Lu, and Y. Wang, “Generation of a high-quality partially coherent dark hollow beam with a multimode fiber,” Opt. Lett. 33, 1389–1391 (2008).
[CrossRef]

F. Wang and Y. Cai, “Experimental generation of a partially coherent flat-topped beam,” Opt. Lett. 33, 1795–1797 (2008).
[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, 1937–1944 (2007).
[CrossRef]

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

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

Y. Cai and S. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E 71, 056607 (2005).
[CrossRef]

Y. Cai and Q. Lin, “Hollow elliptical Gaussian beam and its propagation through aligned and misaligned paraxial optical systems,” J. Opt. Soc. Am. A 21, 1058–1065 (2004).
[CrossRef]

Y. Cai, X. Lu, and Q. Lin, “Hollow Gaussian beam and its propagation properties,” Opt. Lett. 28, 1084–1086 (2003).
[CrossRef]

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

Y. Cai, F. Wang, C. Zhao, S. Zhu, G. Wu, and Y. Dong, “Partially coherent vector beams: from theory to experiment,” in Vectorial Optical Fields: Fundamentals and Applications, Q. Zhen, ed. (World Scientific, 2013), Chap. 7, pp. 221–273.

Cang, J.

J. Cang, P. Xiu, and X. Liu, “Propagation of Laguerre–Gaussian and Bessel–Gaussian Schell-model beams through paraxial optical system in turbulent atmosphere,” Opt. Laser Technol. 54, 35–41 (2013).
[CrossRef]

Carretero, L.

A. Belendez, L. Carretero, and A. Fimia, “The use of partially coherent light to reduce the efficiency of silver halide noise gratings,” Opt. Commun. 98, 236–240 (1993).
[CrossRef]

Chen, R.

Chen, Y.

Y. Chen and Y. Cai, “Generation of a controllable optical cage by focusing a Laguerre–Gaussian correlated Schell-model beam,” Opt. Lett. 39, 2549–2552 (2014).
[CrossRef]

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89, 013801 (2014).
[CrossRef]

Y. Chen, F. Wang, C. Zhao, and Y. Cai, “Experimental demonstration of a Laguerre–Gaussian correlated Schell-model vortex beam,” Opt. Express 22, 5826–5838 (2014).
[CrossRef]

Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre–Gaussian correlated Schell-model beam,” Opt. Express 22, 13975–13987 (2014).
[CrossRef]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[CrossRef]

Cheng, B.

J. Zhang, Z. Wang, B. Cheng, Q. Wang, B. Wu, X. Shen, L. Zheng, Y. Xu, and Q. Lin, “Atom cooling by partially spatially coherent lasers,” Phys. Rev. A 88, 023416 (2013).
[CrossRef]

Cincotti, G.

C. Palma, R. Borghi, and G. Cincotti, “Beams originated by J0-correlated Schell-model planar sources,” Opt. Commun. 125, 113–121 (1996).
[CrossRef]

Collett, E.

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

Davidson, F. M.

de Santis, P.

P. de Santis, F. Gori, G. Guattari, and C. Palma, “An example of a Collett–Wolf source,” Opt. Commun. 29, 256–260 (1979).
[CrossRef]

Ding, B.

Y. Zhang, B. Ding, and T. Suyama, “Trapping two types of particles using a double-ring-shaped radially polarized beam,” Phys. Rev. A 81, 023831 (2010).
[CrossRef]

Ding, C.

Dong, Y.

F. Wang, Y. Cai, Y. Dong, and O. Korotkova, “Experimental generation of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 100, 051108 (2012).
[CrossRef]

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, “Effect of spatial coherence on determining the topological charge of a vortex beam,” Appl. Phys. Lett. 101, 261104 (2012).
[CrossRef]

Y. Dong, F. Wang, C. Zhao, and Y. Cai, “Effect of spatial coherence on propagation, tight focusing and radiation forces of an azimuthally polarized beam,” Phys. Rev. A 86, 013840 (2012).
[CrossRef]

Y. Dong, Y. Cai, C. Zhao, and M. Yao, “Statistics properties of a cylindrical vector partially coherent beam,” Opt. Express 19, 5979–5992 (2011).
[CrossRef]

Y. Cai, F. Wang, C. Zhao, S. Zhu, G. Wu, and Y. Dong, “Partially coherent vector beams: from theory to experiment,” in Vectorial Optical Fields: Fundamentals and Applications, Q. Zhen, ed. (World Scientific, 2013), Chap. 7, pp. 221–273.

Du, S.

S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
[CrossRef]

Eyyuboglu, H. T.

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[CrossRef]

C. 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, 1753–1765 (2009).
[CrossRef]

Fimia, A.

A. Belendez, L. Carretero, and A. Fimia, “The use of partially coherent light to reduce the efficiency of silver halide noise gratings,” Opt. Commun. 98, 236–240 (1993).
[CrossRef]

Firth, W. J.

G. R. M. Robb and W. J. Firth, “Collective atomic recoil lasing with a partially coherent pump,” Phys. Rev. Lett. 99, 253601 (2007).
[CrossRef]

Fischer, D. G.

T. van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, “Effects of spatial coherence on the angular distribution of radiant intensity generated by scattering on a sphere,” Phys. Rev. Lett. 104, 173902 (2010).
[CrossRef]

Fleischer, J. W.

L. Waller, G. Situ, and J. W. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nat. Photonics 6, 474–479 (2012).
[CrossRef]

Friberg, A. T.

Gbur, G.

Gori, F.

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A 11, 085706 (2009).
[CrossRef]

R. Martínez-Herrero, P. M. Mejías, and F. Gori, “Genuine cross-spectral densities and pseudo-modal expansions,” Opt. Lett. 34, 1399–1401 (2009).
[CrossRef]

F. Gori, M. Santarsiero, and R. Borghi, “Modal expansion for J0-correlated electromagnetic sources,” Opt. Lett. 33, 1857–1859 (2008).
[CrossRef]

F. Gori and M. Santarsiero, “Devising genuine spatial correlation functions,” Opt. Lett. 32, 3531–3533 (2007).
[CrossRef]

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

F. Gori and G. Guattari, “Modal expansion for J0-correlated Schell-model sources,” Opt. Commun. 64, 311–316 (1987).
[CrossRef]

F. Gori, “Collet–Wolf sources and multimode lasers,” Opt. Commun. 34, 301–305 (1980).
[CrossRef]

P. de Santis, F. Gori, G. Guattari, and C. Palma, “An example of a Collett–Wolf source,” Opt. Commun. 29, 256–260 (1979).
[CrossRef]

Gu, Y.

Guattari, G.

F. Gori and G. Guattari, “Modal expansion for J0-correlated Schell-model sources,” Opt. Commun. 64, 311–316 (1987).
[CrossRef]

P. de Santis, F. Gori, G. Guattari, and C. Palma, “An example of a Collett–Wolf source,” Opt. Commun. 29, 256–260 (1979).
[CrossRef]

Gureyev, T. E.

T. E. Gureyev, D. M. Paganin, A. W. Stevenson, S. C. Mayo, and S. W. Wilkins, “Generalized eikonal of partially coherent beams and its use in quantitative imaging,” Phys. Rev. Lett. 93, 068103 (2004).
[CrossRef]

Han, Y.

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, “Effect of spatial coherence on determining the topological charge of a vortex beam,” Appl. Phys. Lett. 101, 261104 (2012).
[CrossRef]

He, S.

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

He, X.

Kato, Y.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[CrossRef]

Kermisch, D.

Kitagawa, Y.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[CrossRef]

Korotkova, O.

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89, 013801 (2014).
[CrossRef]

O. Korotkova and E. Shchepakina, “Rectangular multi-Gaussian Schell-model beams in atmospheric turbulence,” J. Opt. 16, 045704 (2014).
[CrossRef]

C. Ding, O. Korotkova, Y. Zhang, and L. Pan, “Cosine-Gaussian correlated Schell-model pulsed beams,” Opt. Express 22, 931–942 (2014).
[CrossRef]

C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39, 769–772 (2014).
[CrossRef]

O. Korotkova, “Random sources for rectangularly-shaped far fields,” Opt. Lett. 39, 64–67 (2014).
[CrossRef]

Z. Mei and O. Korotkova, “Cosine-Gaussian Schell-model sources,” Opt. Lett. 38, 2578–2580 (2013).
[CrossRef]

Z. Mei and O. Korotkova, “Random sources generating ring-shaped beams,” Opt. Lett. 38, 91–93 (2013).
[CrossRef]

Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. 15, 025705 (2013).
[CrossRef]

Z. Mei, E. Shchepakin, and O. Korotkova, “Electromagnetic non-uniformly correlated beams in turbulent atmosphere,” Opt. Express 21, 17512–17519 (2013).
[CrossRef]

Z. Tong and O. Korotkova, “Non-uniformly correlated light beams in uniformly correlated media,” Opt. Lett. 37, 3240–3242 (2012).
[CrossRef]

S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. 37, 2970–2972 (2012).
[CrossRef]

O. Korotkova, S. Sahin, and E. Shchepakina, “Multi-Gaussian Schell-model beams,” J. Opt. Soc. Am. A 29, 2159–2164 (2012).
[CrossRef]

Z. Tong and O. Korotkova, “Electromagnetic nonuniformly correlated beam,” J. Opt. Soc. Am. A 29, 2154–2158 (2012).
[CrossRef]

F. Wang, Y. Cai, Y. Dong, and O. Korotkova, “Experimental generation of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 100, 051108 (2012).
[CrossRef]

C. Ding, Y. Cai, O. Korotkova, Y. Zhang, and L. Pan, “Scattering-induced changes in the temporal coherence length and the pulse duration of a partially coherent plane-wave pulse,” Opt. Lett. 36, 517–519 (2011).
[CrossRef]

C. Zhao, Y. Cai, and O. Korotkova, “Radiation force of scalar and electromagnetic twisted Gaussian Schell-model beams,” Opt. Express 17, 21472–21487 (2009).
[CrossRef]

Lajunen, H.

H. Lajunen and T. Saastamoinen, “Non-uniformly correlated partially coherent pulses,” Opt. Lett. 21, 190–195 (2013).

H. Lajunen and T. Saastamoinen, “Propagation characteristics of partially coherent beams with spatially varying correlations,” Opt. Lett. 36, 4104–4106 (2011).
[CrossRef]

Lancis, J.

Liang, C.

C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39, 769–772 (2014).
[CrossRef]

S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
[CrossRef]

Lin, Q.

J. Zhang, Z. Wang, B. Cheng, Q. Wang, B. Wu, X. Shen, L. Zheng, Y. Xu, and Q. Lin, “Atom cooling by partially spatially coherent lasers,” Phys. Rev. A 88, 023416 (2013).
[CrossRef]

Z. Wang, Q. Lin, and Y. Wang, “Control of atomic rotation by elliptical hollow beam carrying zero angular momentum,” Opt. Commun. 240, 357–362 (2004).
[CrossRef]

Y. Cai and Q. Lin, “Hollow elliptical Gaussian beam and its propagation through aligned and misaligned paraxial optical systems,” J. Opt. Soc. Am. A 21, 1058–1065 (2004).
[CrossRef]

Y. Cai, X. Lu, and Q. Lin, “Hollow Gaussian beam and its propagation properties,” Opt. Lett. 28, 1084–1086 (2003).
[CrossRef]

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

Liu, L.

Liu, X.

X. Liu, F. Wang, C. Wei, and Y. Cai, “Experimental study of turbulence-induced beam wander and deformation of a partially coherent beam,” Opt. Lett. 39, 3336–3339 (2014).
[CrossRef]

C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39, 769–772 (2014).
[CrossRef]

J. Cang, P. Xiu, and X. Liu, “Propagation of Laguerre–Gaussian and Bessel–Gaussian Schell-model beams through paraxial optical system in turbulent atmosphere,” Opt. Laser Technol. 54, 35–41 (2013).
[CrossRef]

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38, 1814–1816 (2013).
[CrossRef]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[CrossRef]

X. Liu, Y. Shen, L. Liu, F. Wang, and Y. Cai, “Experimental demonstration of vortex phase-induced reduction in scintillation of a partially coherent beam,” Opt. Lett. 38, 5323–5326 (2013).
[CrossRef]

F. Wang, X. Liu, L. Liu, Y. Yuan, and Y. Cai, “Experimental study of the scintillation index of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 103, 091102 (2013).
[CrossRef]

F. Wang, G. Wu, X. Liu, S. Zhu, and Y. Cai, “Experimental measurement of the beam parameters of an electromagnetic Gaussian Schell-model source,” Opt. Lett. 36, 2722–2724 (2011).
[CrossRef]

Lu, X.

Mandel, L.

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

Martínez-Herrero, R.

Mayo, S. C.

T. E. Gureyev, D. M. Paganin, A. W. Stevenson, S. C. Mayo, and S. W. Wilkins, “Generalized eikonal of partially coherent beams and its use in quantitative imaging,” Phys. Rev. Lett. 93, 068103 (2004).
[CrossRef]

McIver, J. K.

M. S. Zubairy and J. K. McIver, “Second-harmonic generation by a partially coherent beam,” Phys. Rev. A 36, 202–206 (1987).
[CrossRef]

Mei, Z.

Mejías, P. M.

Mima, K.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[CrossRef]

Miyanaga, N.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[CrossRef]

Nakatsuka, M.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[CrossRef]

Paganin, D. M.

T. E. Gureyev, D. M. Paganin, A. W. Stevenson, S. C. Mayo, and S. W. Wilkins, “Generalized eikonal of partially coherent beams and its use in quantitative imaging,” Phys. Rev. Lett. 93, 068103 (2004).
[CrossRef]

Palma, C.

C. Palma, R. Borghi, and G. Cincotti, “Beams originated by J0-correlated Schell-model planar sources,” Opt. Commun. 125, 113–121 (1996).
[CrossRef]

P. de Santis, F. Gori, G. Guattari, and C. Palma, “An example of a Collett–Wolf source,” Opt. Commun. 29, 256–260 (1979).
[CrossRef]

Pan, L.

Peschel, U.

Peterman, E. J. G.

Qu, J.

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[CrossRef]

Raghunathan, S. B.

Ricklin, J. C.

Robb, G. R. M.

G. R. M. Robb and W. J. Firth, “Collective atomic recoil lasing with a partially coherent pump,” Phys. Rev. Lett. 99, 253601 (2007).
[CrossRef]

Saastamoinen, T.

H. Lajunen and T. Saastamoinen, “Non-uniformly correlated partially coherent pulses,” Opt. Lett. 21, 190–195 (2013).

H. Lajunen and T. Saastamoinen, “Propagation characteristics of partially coherent beams with spatially varying correlations,” Opt. Lett. 36, 4104–4106 (2011).
[CrossRef]

Sahin, S.

Sanchez, V. R.

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A 11, 085706 (2009).
[CrossRef]

Santarsiero, M.

Setälä, T.

Shchepakin, E.

Shchepakina, E.

O. Korotkova and E. Shchepakina, “Rectangular multi-Gaussian Schell-model beams in atmospheric turbulence,” J. Opt. 16, 045704 (2014).
[CrossRef]

Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. 15, 025705 (2013).
[CrossRef]

O. Korotkova, S. Sahin, and E. Shchepakina, “Multi-Gaussian Schell-model beams,” J. Opt. Soc. Am. A 29, 2159–2164 (2012).
[CrossRef]

Shen, X.

J. Zhang, Z. Wang, B. Cheng, Q. Wang, B. Wu, X. Shen, L. Zheng, Y. Xu, and Q. Lin, “Atom cooling by partially spatially coherent lasers,” Phys. Rev. A 88, 023416 (2013).
[CrossRef]

Shen, Y.

Shirai, T.

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A 11, 085706 (2009).
[CrossRef]

Silvestre, E.

Situ, G.

L. Waller, G. Situ, and J. W. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nat. Photonics 6, 474–479 (2012).
[CrossRef]

Stevenson, A. W.

T. E. Gureyev, D. M. Paganin, A. W. Stevenson, S. C. Mayo, and S. W. Wilkins, “Generalized eikonal of partially coherent beams and its use in quantitative imaging,” Phys. Rev. Lett. 93, 068103 (2004).
[CrossRef]

Sudol, R. J.

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

Suyama, T.

Y. Zhang, B. Ding, and T. Suyama, “Trapping two types of particles using a double-ring-shaped radially polarized beam,” Phys. Rev. A 81, 023831 (2010).
[CrossRef]

Tervo, J.

Tervonen, E.

Tong, Z.

Torres-Company, V.

Turunen, J.

van Dijk, T.

Visse, T. D.

Visser, T. D.

Waller, L.

L. Waller, G. Situ, and J. W. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nat. Photonics 6, 474–479 (2012).
[CrossRef]

Wang, F.

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89, 013801 (2014).
[CrossRef]

C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39, 769–772 (2014).
[CrossRef]

Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre–Gaussian correlated Schell-model beam,” Opt. Express 22, 13975–13987 (2014).
[CrossRef]

Y. Chen, F. Wang, C. Zhao, and Y. Cai, “Experimental demonstration of a Laguerre–Gaussian correlated Schell-model vortex beam,” Opt. Express 22, 5826–5838 (2014).
[CrossRef]

R. Chen, L. Liu, S. Zhu, G. Wu, F. Wang, and Y. Cai, “Statistical properties of a Laguerre–Gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 22, 1871–1883 (2014).
[CrossRef]

X. Liu, F. Wang, C. Wei, and Y. Cai, “Experimental study of turbulence-induced beam wander and deformation of a partially coherent beam,” Opt. Lett. 39, 3336–3339 (2014).
[CrossRef]

X. Liu, Y. Shen, L. Liu, F. Wang, and Y. Cai, “Experimental demonstration of vortex phase-induced reduction in scintillation of a partially coherent beam,” Opt. Lett. 38, 5323–5326 (2013).
[CrossRef]

F. Wang, X. Liu, L. Liu, Y. Yuan, and Y. Cai, “Experimental study of the scintillation index of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 103, 091102 (2013).
[CrossRef]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[CrossRef]

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38, 1814–1816 (2013).
[CrossRef]

S. Zhu, X. Zhu, L. Liu, F. Wang, and Y. Cai, “Theoretical and experimental studies of the spectral changes of a polychromatic partially coherent radially polarized beam,” Opt. Express 21, 27682–27696 (2013).
[CrossRef]

G. Wu, F. Wang, and Y. Cai, “Coherence and polarization properties of a radially polarized beam with variable spatial coherence,” Opt. Express 20, 28301–28318 (2012).
[CrossRef]

Y. Dong, F. Wang, C. Zhao, and Y. Cai, “Effect of spatial coherence on propagation, tight focusing and radiation forces of an azimuthally polarized beam,” Phys. Rev. A 86, 013840 (2012).
[CrossRef]

F. Wang, Y. Cai, Y. Dong, and O. Korotkova, “Experimental generation of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 100, 051108 (2012).
[CrossRef]

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, “Effect of spatial coherence on determining the topological charge of a vortex beam,” Appl. Phys. Lett. 101, 261104 (2012).
[CrossRef]

F. Wang, G. Wu, X. Liu, S. Zhu, and Y. Cai, “Experimental measurement of the beam parameters of an electromagnetic Gaussian Schell-model source,” Opt. Lett. 36, 2722–2724 (2011).
[CrossRef]

Y. Cai and F. Wang, “Tensor method for treating the propagation of scalar and electromagnetic Gaussian Schell-model beams: a review,” Open Opt. J. 4, 1–20 (2010).

F. Wang and Y. Cai, “Experimental generation of a partially coherent flat-topped beam,” Opt. Lett. 33, 1795–1797 (2008).
[CrossRef]

C. Zhao, Y. Cai, F. Wang, X. Lu, and Y. Wang, “Generation of a high-quality partially coherent dark hollow beam with a multimode fiber,” Opt. Lett. 33, 1389–1391 (2008).
[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, 1937–1944 (2007).
[CrossRef]

Y. Cai, F. Wang, C. Zhao, S. Zhu, G. Wu, and Y. Dong, “Partially coherent vector beams: from theory to experiment,” in Vectorial Optical Fields: Fundamentals and Applications, Q. Zhen, ed. (World Scientific, 2013), Chap. 7, pp. 221–273.

Wang, H.

C. Ding, Y. Cai, Y. Zhang, H. Wang, Z. Zhao, and L. Pan, “Stochastic electromagnetic plane-wave pulse with non-uniform correlation distribution,” Phys. Lett. A 377, 1563–1565 (2013).
[CrossRef]

Wang, J.

Wang, Q.

J. Zhang, Z. Wang, B. Cheng, Q. Wang, B. Wu, X. Shen, L. Zheng, Y. Xu, and Q. Lin, “Atom cooling by partially spatially coherent lasers,” Phys. Rev. A 88, 023416 (2013).
[CrossRef]

Wang, Y.

C. Zhao, Y. Cai, F. Wang, X. Lu, and Y. Wang, “Generation of a high-quality partially coherent dark hollow beam with a multimode fiber,” Opt. Lett. 33, 1389–1391 (2008).
[CrossRef]

Z. Wang, Q. Lin, and Y. Wang, “Control of atomic rotation by elliptical hollow beam carrying zero angular momentum,” Opt. Commun. 240, 357–362 (2004).
[CrossRef]

Wang, Z.

J. Zhang, Z. Wang, B. Cheng, Q. Wang, B. Wu, X. Shen, L. Zheng, Y. Xu, and Q. Lin, “Atom cooling by partially spatially coherent lasers,” Phys. Rev. A 88, 023416 (2013).
[CrossRef]

Z. Wang, Q. Lin, and Y. Wang, “Control of atomic rotation by elliptical hollow beam carrying zero angular momentum,” Opt. Commun. 240, 357–362 (2004).
[CrossRef]

Wei, C.

Wilkins, S. W.

T. E. Gureyev, D. M. Paganin, A. W. Stevenson, S. C. Mayo, and S. W. Wilkins, “Generalized eikonal of partially coherent beams and its use in quantitative imaging,” Phys. Rev. Lett. 93, 068103 (2004).
[CrossRef]

Wolf, E.

T. van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, “Effects of spatial coherence on the angular distribution of radiant intensity generated by scattering on a sphere,” Phys. Rev. Lett. 104, 173902 (2010).
[CrossRef]

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

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

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

Wu, B.

J. Zhang, Z. Wang, B. Cheng, Q. Wang, B. Wu, X. Shen, L. Zheng, Y. Xu, and Q. Lin, “Atom cooling by partially spatially coherent lasers,” Phys. Rev. A 88, 023416 (2013).
[CrossRef]

Wu, G.

Xiu, P.

J. Cang, P. Xiu, and X. Liu, “Propagation of Laguerre–Gaussian and Bessel–Gaussian Schell-model beams through paraxial optical system in turbulent atmosphere,” Opt. Laser Technol. 54, 35–41 (2013).
[CrossRef]

Xu, P.

Xu, Y.

J. Zhang, Z. Wang, B. Cheng, Q. Wang, B. Wu, X. Shen, L. Zheng, Y. Xu, and Q. Lin, “Atom cooling by partially spatially coherent lasers,” Phys. Rev. A 88, 023416 (2013).
[CrossRef]

Yamanaka, C.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[CrossRef]

Yao, M.

Yuan, Y.

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38, 1814–1816 (2013).
[CrossRef]

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[CrossRef]

S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
[CrossRef]

F. Wang, X. Liu, L. Liu, Y. Yuan, and Y. Cai, “Experimental study of the scintillation index of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 103, 091102 (2013).
[CrossRef]

Zhan, M.

Zhan, Q.

Zhan, Y.

Zhang, J.

J. Zhang, Z. Wang, B. Cheng, Q. Wang, B. Wu, X. Shen, L. Zheng, Y. Xu, and Q. Lin, “Atom cooling by partially spatially coherent lasers,” Phys. Rev. A 88, 023416 (2013).
[CrossRef]

Zhang, Y.

Y. Zhang and Y. Cai, “Random source generating far field with elliptical flat-topped beam profile,” J. Opt. 16, 075704 (2014).

Y. Zhang, L. Liu, C. Zhao, and Y. Cai, “Multi-Gaussian Schell-model vortex beam,” Phys. Lett. A 378, 750–754 (2014).
[CrossRef]

C. Ding, O. Korotkova, Y. Zhang, and L. Pan, “Cosine-Gaussian correlated Schell-model pulsed beams,” Opt. Express 22, 931–942 (2014).
[CrossRef]

C. Ding, Y. Cai, Y. Zhang, H. Wang, Z. Zhao, and L. Pan, “Stochastic electromagnetic plane-wave pulse with non-uniform correlation distribution,” Phys. Lett. A 377, 1563–1565 (2013).
[CrossRef]

C. Ding, Y. Cai, O. Korotkova, Y. Zhang, and L. Pan, “Scattering-induced changes in the temporal coherence length and the pulse duration of a partially coherent plane-wave pulse,” Opt. Lett. 36, 517–519 (2011).
[CrossRef]

Y. Zhang, B. Ding, and T. Suyama, “Trapping two types of particles using a double-ring-shaped radially polarized beam,” Phys. Rev. A 81, 023831 (2010).
[CrossRef]

Zhao, C.

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89, 013801 (2014).
[CrossRef]

Y. Zhang, L. Liu, C. Zhao, and Y. Cai, “Multi-Gaussian Schell-model vortex beam,” Phys. Lett. A 378, 750–754 (2014).
[CrossRef]

Y. Chen, F. Wang, C. Zhao, and Y. Cai, “Experimental demonstration of a Laguerre–Gaussian correlated Schell-model vortex beam,” Opt. Express 22, 5826–5838 (2014).
[CrossRef]

Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre–Gaussian correlated Schell-model beam,” Opt. Express 22, 13975–13987 (2014).
[CrossRef]

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, “Effect of spatial coherence on determining the topological charge of a vortex beam,” Appl. Phys. Lett. 101, 261104 (2012).
[CrossRef]

Y. Dong, F. Wang, C. Zhao, and Y. Cai, “Effect of spatial coherence on propagation, tight focusing and radiation forces of an azimuthally polarized beam,” Phys. Rev. A 86, 013840 (2012).
[CrossRef]

C. Zhao and Y. Cai, “Trapping two types of particles using a focused partially coherent elegant Laguerre–Gaussian beam,” Opt. Lett. 36, 2251–2253 (2011).
[CrossRef]

Y. Dong, Y. Cai, C. Zhao, and M. Yao, “Statistics properties of a cylindrical vector partially coherent beam,” Opt. Express 19, 5979–5992 (2011).
[CrossRef]

C. Zhao, Y. Cai, and O. Korotkova, “Radiation force of scalar and electromagnetic twisted Gaussian Schell-model beams,” Opt. Express 17, 21472–21487 (2009).
[CrossRef]

C. 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, 1753–1765 (2009).
[CrossRef]

C. Zhao, Y. Cai, F. Wang, X. Lu, and Y. Wang, “Generation of a high-quality partially coherent dark hollow beam with a multimode fiber,” Opt. Lett. 33, 1389–1391 (2008).
[CrossRef]

Y. Cai, F. Wang, C. Zhao, S. Zhu, G. Wu, and Y. Dong, “Partially coherent vector beams: from theory to experiment,” in Vectorial Optical Fields: Fundamentals and Applications, Q. Zhen, ed. (World Scientific, 2013), Chap. 7, pp. 221–273.

Zhao, D.

Zhao, Z.

C. Ding, Y. Cai, Y. Zhang, H. Wang, Z. Zhao, and L. Pan, “Stochastic electromagnetic plane-wave pulse with non-uniform correlation distribution,” Phys. Lett. A 377, 1563–1565 (2013).
[CrossRef]

Zheng, L.

J. Zhang, Z. Wang, B. Cheng, Q. Wang, B. Wu, X. Shen, L. Zheng, Y. Xu, and Q. Lin, “Atom cooling by partially spatially coherent lasers,” Phys. Rev. A 88, 023416 (2013).
[CrossRef]

Zhu, S.

Zhu, X.

Zubairy, M. S.

M. S. Zubairy and J. K. McIver, “Second-harmonic generation by a partially coherent beam,” Phys. Rev. A 36, 202–206 (1987).
[CrossRef]

Adv. Opt. Photon. (1)

Appl. Phys. Lett. (4)

F. Wang, X. Liu, L. Liu, Y. Yuan, and Y. Cai, “Experimental study of the scintillation index of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 103, 091102 (2013).
[CrossRef]

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, “Effect of spatial coherence on determining the topological charge of a vortex beam,” Appl. Phys. Lett. 101, 261104 (2012).
[CrossRef]

F. Wang, Y. Cai, Y. Dong, and O. Korotkova, “Experimental generation of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 100, 051108 (2012).
[CrossRef]

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

J. Opt. (3)

Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. 15, 025705 (2013).
[CrossRef]

Y. Zhang and Y. Cai, “Random source generating far field with elliptical flat-topped beam profile,” J. Opt. 16, 075704 (2014).

O. Korotkova and E. Shchepakina, “Rectangular multi-Gaussian Schell-model beams in atmospheric turbulence,” J. Opt. 16, 045704 (2014).
[CrossRef]

J. Opt. A (1)

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A 11, 085706 (2009).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (8)

Nat. Photonics (1)

L. Waller, G. Situ, and J. W. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nat. Photonics 6, 474–479 (2012).
[CrossRef]

Open Opt. J. (1)

Y. Cai and F. Wang, “Tensor method for treating the propagation of scalar and electromagnetic Gaussian Schell-model beams: a review,” Open Opt. J. 4, 1–20 (2010).

Opt. Commun (1)

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

Opt. Commun. (8)

Y. Yuan, X. Liu, F. Wang, Y. Chen, Y. Cai, J. Qu, and H. T. Eyyuboğlu, “Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Commun. 305, 57–65 (2013).
[CrossRef]

F. Gori and G. Guattari, “Modal expansion for J0-correlated Schell-model sources,” Opt. Commun. 64, 311–316 (1987).
[CrossRef]

C. Palma, R. Borghi, and G. Cincotti, “Beams originated by J0-correlated Schell-model planar sources,” Opt. Commun. 125, 113–121 (1996).
[CrossRef]

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

F. Gori, “Collet–Wolf sources and multimode lasers,” Opt. Commun. 34, 301–305 (1980).
[CrossRef]

P. de Santis, F. Gori, G. Guattari, and C. Palma, “An example of a Collett–Wolf source,” Opt. Commun. 29, 256–260 (1979).
[CrossRef]

A. Belendez, L. Carretero, and A. Fimia, “The use of partially coherent light to reduce the efficiency of silver halide noise gratings,” Opt. Commun. 98, 236–240 (1993).
[CrossRef]

Z. Wang, Q. Lin, and Y. Wang, “Control of atomic rotation by elliptical hollow beam carrying zero angular momentum,” Opt. Commun. 240, 357–362 (2004).
[CrossRef]

Opt. Express (13)

Y. Zhan and D. Zhao, “Scattering of multi-Gaussian Schell-model beams on a random medium,” Opt. Express 21, 24781–24792 (2013).
[CrossRef]

Y. Dong, Y. Cai, C. Zhao, and M. Yao, “Statistics properties of a cylindrical vector partially coherent beam,” Opt. Express 19, 5979–5992 (2011).
[CrossRef]

J. Tervo, T. Setälä, and A. T. Friberg, “Degree of coherence for electromagnetic fields,” Opt. Express 11, 1137–1143 (2003).
[CrossRef]

G. Wu, F. Wang, and Y. Cai, “Coherence and polarization properties of a radially polarized beam with variable spatial coherence,” Opt. Express 20, 28301–28318 (2012).
[CrossRef]

S. Zhu, X. Zhu, L. Liu, F. Wang, and Y. Cai, “Theoretical and experimental studies of the spectral changes of a polychromatic partially coherent radially polarized beam,” Opt. Express 21, 27682–27696 (2013).
[CrossRef]

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

C. 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, 1753–1765 (2009).
[CrossRef]

C. Zhao, Y. Cai, and O. Korotkova, “Radiation force of scalar and electromagnetic twisted Gaussian Schell-model beams,” Opt. Express 17, 21472–21487 (2009).
[CrossRef]

Z. Mei, E. Shchepakin, and O. Korotkova, “Electromagnetic non-uniformly correlated beams in turbulent atmosphere,” Opt. Express 21, 17512–17519 (2013).
[CrossRef]

R. Chen, L. Liu, S. Zhu, G. Wu, F. Wang, and Y. Cai, “Statistical properties of a Laguerre–Gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 22, 1871–1883 (2014).
[CrossRef]

C. Ding, O. Korotkova, Y. Zhang, and L. Pan, “Cosine-Gaussian correlated Schell-model pulsed beams,” Opt. Express 22, 931–942 (2014).
[CrossRef]

Y. Chen, L. Liu, F. Wang, C. Zhao, and Y. Cai, “Elliptical Laguerre–Gaussian correlated Schell-model beam,” Opt. Express 22, 13975–13987 (2014).
[CrossRef]

Y. Chen, F. Wang, C. Zhao, and Y. Cai, “Experimental demonstration of a Laguerre–Gaussian correlated Schell-model vortex beam,” Opt. Express 22, 5826–5838 (2014).
[CrossRef]

Opt. Laser Technol. (2)

J. Cang, P. Xiu, and X. Liu, “Propagation of Laguerre–Gaussian and Bessel–Gaussian Schell-model beams through paraxial optical system in turbulent atmosphere,” Opt. Laser Technol. 54, 35–41 (2013).
[CrossRef]

S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013).
[CrossRef]

Opt. Lett. (29)

P. Xu, X. He, J. Wang, and M. Zhan, “Trapping a single atom in a blue detuned optical bottle beam trap,” Opt. Lett. 35, 2164–2166 (2010).
[CrossRef]

J. Lancis, V. Torres-Company, E. Silvestre, and P. Andrés, “Space–time analogy for partially coherent plane-wave-type pulses,” Opt. Lett. 30, 2973–2975 (2005).
[CrossRef]

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38, 1814–1816 (2013).
[CrossRef]

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

Y. Cai, X. Lu, and Q. Lin, “Hollow Gaussian beam and its propagation properties,” Opt. Lett. 28, 1084–1086 (2003).
[CrossRef]

Z. Tong and O. Korotkova, “Non-uniformly correlated light beams in uniformly correlated media,” Opt. Lett. 37, 3240–3242 (2012).
[CrossRef]

Y. Gu and G. Gbur, “Scintillation of nonuniformly correlated beams in atmospheric turbulence,” Opt. Lett. 38, 1395–1397 (2013).
[CrossRef]

Y. Chen and Y. Cai, “Generation of a controllable optical cage by focusing a Laguerre–Gaussian correlated Schell-model beam,” Opt. Lett. 39, 2549–2552 (2014).
[CrossRef]

Z. Mei and O. Korotkova, “Cosine-Gaussian Schell-model sources,” Opt. Lett. 38, 2578–2580 (2013).
[CrossRef]

C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39, 769–772 (2014).
[CrossRef]

Z. Mei and O. Korotkova, “Random sources generating ring-shaped beams,” Opt. Lett. 38, 91–93 (2013).
[CrossRef]

S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. 37, 2970–2972 (2012).
[CrossRef]

H. Lajunen and T. Saastamoinen, “Non-uniformly correlated partially coherent pulses,” Opt. Lett. 21, 190–195 (2013).

O. Korotkova, “Random sources for rectangularly-shaped far fields,” Opt. Lett. 39, 64–67 (2014).
[CrossRef]

H. Lajunen and T. Saastamoinen, “Propagation characteristics of partially coherent beams with spatially varying correlations,” Opt. Lett. 36, 4104–4106 (2011).
[CrossRef]

R. Martínez-Herrero, P. M. Mejías, and F. Gori, “Genuine cross-spectral densities and pseudo-modal expansions,” Opt. Lett. 34, 1399–1401 (2009).
[CrossRef]

R. Martínez-Herrero and P. M. Mejías, “Elementary-field expansions of genuine cross-spectral density matrices,” Opt. Lett. 34, 2303–2305 (2009).
[CrossRef]

F. Gori and M. Santarsiero, “Devising genuine spatial correlation functions,” Opt. Lett. 32, 3531–3533 (2007).
[CrossRef]

S. B. Raghunathan, T. van Dijk, E. J. G. Peterman, and T. D. Visser, “Experimental demonstration of an intensity minimum at the focus of a laser beam created by spatial coherence: application to the optical trapping of dielectric particles,” Opt. Lett. 35, 4166–4168 (2010).
[CrossRef]

F. Gori, M. Santarsiero, and R. Borghi, “Modal expansion for J0-correlated electromagnetic sources,” Opt. Lett. 33, 1857–1859 (2008).
[CrossRef]

C. Zhao and Y. Cai, “Trapping two types of particles using a focused partially coherent elegant Laguerre–Gaussian beam,” Opt. Lett. 36, 2251–2253 (2011).
[CrossRef]

F. Wang, G. Wu, X. Liu, S. Zhu, and Y. Cai, “Experimental measurement of the beam parameters of an electromagnetic Gaussian Schell-model source,” Opt. Lett. 36, 2722–2724 (2011).
[CrossRef]

C. Zhao, Y. Cai, F. Wang, X. Lu, and Y. Wang, “Generation of a high-quality partially coherent dark hollow beam with a multimode fiber,” Opt. Lett. 33, 1389–1391 (2008).
[CrossRef]

F. Wang and Y. Cai, “Experimental generation of a partially coherent flat-topped beam,” Opt. Lett. 33, 1795–1797 (2008).
[CrossRef]

X. Liu, F. Wang, C. Wei, and Y. Cai, “Experimental study of turbulence-induced beam wander and deformation of a partially coherent beam,” Opt. Lett. 39, 3336–3339 (2014).
[CrossRef]

X. Liu, Y. Shen, L. Liu, F. Wang, and Y. Cai, “Experimental demonstration of vortex phase-induced reduction in scintillation of a partially coherent beam,” Opt. Lett. 38, 5323–5326 (2013).
[CrossRef]

C. Ding, Y. Cai, O. Korotkova, Y. Zhang, and L. Pan, “Scattering-induced changes in the temporal coherence length and the pulse duration of a partially coherent plane-wave pulse,” Opt. Lett. 36, 517–519 (2011).
[CrossRef]

G. Gbur and T. D. Visse, “Can spatial coherence effects produce a local minimum of intensity at focus?” Opt. Lett. 28, 1627–1629 (2003).
[CrossRef]

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

Phys. Lett. A (2)

Y. Zhang, L. Liu, C. Zhao, and Y. Cai, “Multi-Gaussian Schell-model vortex beam,” Phys. Lett. A 378, 750–754 (2014).
[CrossRef]

C. Ding, Y. Cai, Y. Zhang, H. Wang, Z. Zhao, and L. Pan, “Stochastic electromagnetic plane-wave pulse with non-uniform correlation distribution,” Phys. Lett. A 377, 1563–1565 (2013).
[CrossRef]

Phys. Rev. A (5)

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89, 013801 (2014).
[CrossRef]

M. S. Zubairy and J. K. McIver, “Second-harmonic generation by a partially coherent beam,” Phys. Rev. A 36, 202–206 (1987).
[CrossRef]

Y. Dong, F. Wang, C. Zhao, and Y. Cai, “Effect of spatial coherence on propagation, tight focusing and radiation forces of an azimuthally polarized beam,” Phys. Rev. A 86, 013840 (2012).
[CrossRef]

J. Zhang, Z. Wang, B. Cheng, Q. Wang, B. Wu, X. Shen, L. Zheng, Y. Xu, and Q. Lin, “Atom cooling by partially spatially coherent lasers,” Phys. Rev. A 88, 023416 (2013).
[CrossRef]

Y. Zhang, B. Ding, and T. Suyama, “Trapping two types of particles using a double-ring-shaped radially polarized beam,” Phys. Rev. A 81, 023831 (2010).
[CrossRef]

Phys. Rev. E (1)

Y. Cai and S. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E 71, 056607 (2005).
[CrossRef]

Phys. Rev. Lett. (4)

T. E. Gureyev, D. M. Paganin, A. W. Stevenson, S. C. Mayo, and S. W. Wilkins, “Generalized eikonal of partially coherent beams and its use in quantitative imaging,” Phys. Rev. Lett. 93, 068103 (2004).
[CrossRef]

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[CrossRef]

T. van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, “Effects of spatial coherence on the angular distribution of radiant intensity generated by scattering on a sphere,” Phys. Rev. Lett. 104, 173902 (2010).
[CrossRef]

G. R. M. Robb and W. J. Firth, “Collective atomic recoil lasing with a partially coherent pump,” Phys. Rev. Lett. 99, 253601 (2007).
[CrossRef]

Proc. SPIE (1)

Y. Cai, “Generation of various partially coherent beams and their propagation properties in turbulent atmosphere: a review,” Proc. SPIE 7924, 792402 (2011).
[CrossRef]

Other (3)

Y. Cai, F. Wang, C. Zhao, S. Zhu, G. Wu, and Y. Dong, “Partially coherent vector beams: from theory to experiment,” in Vectorial Optical Fields: Fundamentals and Applications, Q. Zhen, ed. (World Scientific, 2013), Chap. 7, pp. 221–273.

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

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (25)

Fig. 1.
Fig. 1.

Density plots of the degrees of coherence of (a) the nonuniformly correlated beam in the source plane with ρ0=0, δc=0.2mm and (b) the conventional Gaussian Schell-model beam with δ=0.2mm.

Fig. 2.
Fig. 2.

Density plot of the intensity distribution of a nonuniformly correlated beam on propagation in free space versus ρx and z for (a) ρ0=0 and (b) ρ0=0.5mm.

Fig. 3.
Fig. 3.

Density plots of the degrees of coherence of (a-1), (b-1) a circular multi-Gaussian correlated Schell-model beam with δ=0.2mm; (a-2), (b-2) an elliptical multi-Gaussian correlated Schell-model beam with δx=0.2mm, δx=0.1mm; and (a-3), (b-3) a rectangular multi-Gaussian correlated Schell-model beam with δx=δy=0.2mm in the source plane for two different values of M.

Fig. 4.
Fig. 4.

Density plots of the intensity distributions of (a-1), (b-1) a circular multi-Gaussian correlated Schell-model beam with δ=0.2mm; (a-2), (b-2) an elliptical multi-Gaussian correlated Schell-model beam with δx=0.2mm, δx=0.1mm; and (a-3), (b-3) a rectangular multi-Gaussian correlated Schell-model beam with δx=δy=0.2mm in the far field (z=20m) for two different values of M.

Fig. 5.
Fig. 5.

Density plot of the degree of coherence of a circular Laguerre–Gaussian correlated Schell-model beam in the source plane for two different values of n with δ=0.2mm.

Fig. 6.
Fig. 6.

Density plot of the intensity distribution of a circular Laguerre–Gaussian correlated Schell-model beam in the far field (z=20m) for different values of n with σ=1mm, δ=0.2mm.

Fig. 7.
Fig. 7.

Density plot of the intensity distribution of a circular Laguerre–Gaussian correlated Schell-model beam near the focal plane with n=1, σ=1mm, f=250mm for different value of δ.

Fig. 8.
Fig. 8.

Density plot of the degree of coherence of an elliptical Laguerre–Gaussian correlated Schell-model beam in the source plane for different values of δx and δy with n=5.

Fig. 9.
Fig. 9.

Density plot of the intensity distribution of an elliptical Laguerre–Gaussian correlated Schell-model beam in the far field (z=20m) for different values of δx and δy with n=5.

Fig. 10.
Fig. 10.

Density plots of the degrees of coherence of (a-1), (b-1) a circular cosine-Gaussian correlated Schell-model beam with δ=0.2mm; and (a-2), (b-2) a rectangular cosine-Gaussian correlated Schell-model beam with δx=δy=0.2mm in the source plane for different values of n.

Fig. 11.
Fig. 11.

Density plots of the intensity distributions of (a-1), (b-1) a circular cosine-Gaussian correlated Schell-model beam with δ=0.2mm; and (a-2), (b-2) a rectangular cosine-Gaussian correlated Schell-model beam with δx=δy=0.2mm in the far field (z=20m) for different values of n.

Fig. 12.
Fig. 12.

Density plot of the intensity distribution of a rectangular cosine-Gaussian correlated Schell-model beam on propagation in free space versus ρ(x=y) and z.

Fig. 13.
Fig. 13.

Density plots of (a) the square of the degree of coherence μ2(ρ1,ρ2=0) and (b), (d) the square of the correlation functions μxx2(ρ1,ρ2=0), μyy2(ρ1,ρ2=0), and μxy2(ρ1,ρ2=0) of a specially correlated radially polarized beam in the source plane.

Fig. 14.
Fig. 14.

Density plots of the intensity distribution of a specially correlated radially polarized beam in the focal plane for different values of the initial coherence width δ.

Fig. 15.
Fig. 15.

Schematic for generating a partially coherent beam with a nonconventional correlation function from an incoherent source. GAF: Gaussian amplitude filter.

Fig. 16.
Fig. 16.

Experimental setup for generating a partially coherent beam with nonconventional correlation, measuring the square of the modulus of its degree of coherence and its focused intensity. RM, reflecting mirror; BE, beam expander; SLM, spatial light modulator; CA, circular aperture; RGGD, rotating ground-disk; L, L1, L2, L3, thin lenses; GAF, Gaussian amplitude filter; CCD, charge-coupled device; BPA, beam profile analyzer; PC1, PC2, personal computers.

Fig. 17.
Fig. 17.

Phase gratings for generating elliptical dark hollow beams (n=5) of different values of ωx/ωy with ω0x=0.8mm. (a) ωx/ωy=0.4, (b) ωx/ωy=0.8, (c) ωx/ωy=1, (d) ωx/ωy=1.2, (e) ωx/ωy=2.5.

Fig. 18.
Fig. 18.

Phase gratings for generating cosh–Gaussian beams with n=1 and n=2.

Fig. 19.
Fig. 19.

Experimental results of the square of the modulus of the degree of coherence and the corresponding cross lines (dotted curves) of the generated elliptical Laguerre–Gaussian correlated Schell-model beam (n=5) just behind the GAF for different values of coherence widths δx and δy.

Fig. 20.
Fig. 20.

Experimental results of the square of the modulus of the degree of coherence of the generated rectangular cosine-Gaussian correlated Schell-model beam just behind the GAF for two values of the beam order n.

Fig. 21.
Fig. 21.

Experimental results of the intensity distribution of the generated elliptical Laguerrre–Gaussian correlated Schell-model beam (n=5) in the geometrical focal plane for different values of coherence widths δx and δy.

Fig. 22.
Fig. 22.

Experimental results of the intensity distribution of the generated rectangular cosine-Gaussian correlated Schell-model beam for two values of the beam order n in the geometrical focal plane.

Fig. 23.
Fig. 23.

Experimental results of the square of the degree of coherence μ2(ρ1,ρ2=0), the square of the correlation functions μxx2(ρ1,ρ2=0), μyy2(ρ1,ρ2=0), and μxy2(ρ1,ρ2=0) of the generated specially correlated radially polarized beam just behind the GAF.

Fig. 24.
Fig. 24.

Experimental results of the intensity distribution of the generated specially correlated radially polarized beam in the geometrical focal plane for different values of the initial coherence width δ.

Fig. 25.
Fig. 25.

Experimental results of the degree of polarization of the generated specially correlated radially polarized beam after passing a thin lens for different values of the initial coherence width δ and the propagation distance. The solid curve is the theoretical result.

Equations (58)

Equations on this page are rendered with MathJax. Learn more.

W(ρ1,ρ2)=E*(ρ1)E(ρ2),
W(ρ1,ρ2)=p(v)H*(ρ1,v)H(ρ2,v)d2v,
W(ρ1,ρ2)=[Wxx(ρ1,ρ2)Wxy(ρ1,ρ2)Wyx(ρ1,ρ2)Wyy(ρ1,ρ2)],
Wαβ(ρ1,ρ2)=Eα*(ρ1)Eβ(ρ2),(α=x,y;β=x,y),
Wαβ(ρ1,ρ2)=pαβ(v)Hα*(ρ1,v)Hβ(ρ2,v)d2v,(α=x,y;β=x,y),
p^(v)=(pxx(v)pxy(v)pxy*(v)pyy(v)).
pxx(v)0,pyy(v)0,pxx(v)pyy(v)|pxy(v)|20.
p(vx)=(πa2)1/2exp(vx2/a2),
H(ρx,vx)=exp(ρx22σ2)exp[ik(ρxρ0)2vx],
W(ρ1x,ρ2x)=exp[ρ1x2+ρ2x24σ2]μ(ρ1x,ρ2x),
μ(ρ1x,ρ2x)=exp{[(ρ2xρ0)2(ρ1xρ0)2]2δc4},
p(v)=δ2C0m=1M(1)m1(Mm)exp[mδ2v22],
H(ρ,v)=τ(ρ)exp(iv·ρ),
τ(ρ)=exp(ρ2/4σ2),
C0=m=1M(1)m1m(Mm),
W(ρ1,ρ2)=exp[ρ12+ρ224σ2]μ(ρ1,ρ2),
μ(ρ1,ρ2)=1C0m=1M(Mm)(1)m1mexp[(ρ1ρ2)22mδ2].
μ(ρ1,ρ2)=1C0m=1M(1)m1m(Mm)×exp[(ρ1xρ2x)22mδx2(ρ1yρ2y)22mδy2].
μ(ρ1,ρ2)=1C2m=1M(1)m1m(Mm)exp[(ρ1xρ2x)22mδx2]×m=1M(1)m1m(Mm)exp[(ρ1yρ2y)22mδy2],
p(v)=(i)np(v)exp(inθ),
p(v)=(π2n+1δ2n+22n+1/n!)v2nexp(2π2δ2v2),
H(ρ,v)=τ(ρ)exp(iv·ρ),
τ(ρ)=exp(ρ2/4σ2),
W(ρ1,ρ2)=exp[ρ12+ρ224σ2]μ(ρ1,ρ2),
μ(ρ1,ρ2)=Ln0[(ρ1ρ2)22δ2]exp[(ρ1ρ2)22δ2],
μ(ρ1,ρ2)=exp[(ρ2xρ1x)22δx2(ρ2xρ1x)22δx2]×Ln0[(ρ2xρ1x)22δx2+(ρ2yρ1y)22δy2].
p(v)=2πδ2cosh(n2πδv)exp(δ2v2+2n2π2),
H(ρ,v)=τ(ρ)exp(iv·ρ),
τ(ρ)=exp(ρ2/4σ2),
W(ρ1,ρ2)=exp[ρ12+ρ224σ2]μ(ρ1,ρ2),
μ(ρ1,ρ2)=exp[(ρ2ρ1)22δ2]cos[n2π(ρ2ρ1)δ].
μ(ρ1,ρ2)=exp[(ρ2ρ1)22δ2]cos[n2π(ρ1xρ2x)2δx]×cos[n2π(ρ1yρ2y)2δy].
W(ρ1,ρ2)=exp[ρ12+ρ224σ2]1C0m=1M(Mm)(1)m1m×exp[(ρ1ρ2)22mδ2il(φ1φ2)],
W(ρ1,ρ2)=exp[ρ12+ρ224σ2(ρ1ρ2)22δ2]Ln0[(ρ1ρ2)22δ2]×exp[il(φ1φ2)],
μ(ρ1,ρ2)=Ln0[(ρ1ρ2)22δ2]exp[(ρ1ρ2)22δ2].
pαβ(v)=Bαβkδαβ22πexp(14k2δαβ4v2),
Ha(ρ,v)=Aαexp(ρ22σ2)exp[ik(ργa)2v],
Hβ(ρ,v)=Aβexp(ρ22σ2)exp[ik(ργβ)2v],
Wαβ(ρ1,ρ2)=AαAβBαβexp(ρ12+ρ222σ2)×exp{[(ρ1γa)2(ρ2γβ)2]2δαβ4}.
Wαβ(ρ1,ρ2)=AαAβBαβC0exp(ρ12+ρ224σ2)×m=1M(1)m1mM(Mm)exp[(ρ1ρ2)22mδαβ2].
Wαα(ρ1,ρ2)=exp(ρ12+ρ224σ2)(1(ρ1αρ2α)2δ2)×exp[(ρ1ρ2)22δ2],(α=x,y),
Wxy(ρ1,ρ2)=exp(ρ12+ρ224σ2(ρ1ρ2)22δ2)×(ρ2xρ1x)(ρ2yρ1y)δ2,
Wyx(ρ1,ρ2)=Wxy*(ρ2,ρ1).
μ2(ρ1,ρ2)=Tr[W(ρ1,ρ2)W(ρ1,ρ2)]Tr[W(ρ1,ρ1)]Tr[W(ρ2,ρ2)].
W(ρ1,ρ2)=W(v1,v2)H*(ρ1,v1)H(ρ2,v2)d2v1d2v2,
W(v1,v2)=p(v1)p(v2)δ(v1v2).
H(ρ,v)=iλfT(ρ)exp[iπλf(v22ρ·v)].
W(ρ1,ρ2)=exp[(ρ12+ρ22)/4σ2]μ[(ρ1ρ2)/λf],
μ[(ρ2ρ1)/λf]=1λ2f2I(v)exp[i2πv·(ρ2ρ1)λf]d2v.
p(v)=(vx2ωx2+vy2ωy2)nexp(2vx2ωx22vx2ωy2),
W(ρ1,ρ2)=G0exp[ρ12+ρ224σ2]Ln0[(ρ2xρ1x)22δx2+(ρ2yρ1y)22δy2],×exp[(ρ2xρ1x)22δx2(ρ2yρ1y)22δy2],
p(v)=cosh(2n2πvx/ωx)cosh(2n2πvy/ωy)×exp(2vx2/ωx22vy2/ωy2),
W(ρ1,ρ2)=G0exp[ρ12+ρ224σ2(ρ2xρ1x)22δx2]×exp[(ρ2yρ1y)22δy2]cos[n2π(ρ2xρ1x)δx]×cos[n2π(ρ2yρ1y)δy],
g(2)(ρ1,ρ2)=I(ρ1,t)I(ρ2,t)I(ρ1,t)I(ρ2,t),
g(2)(ρ1,ρ2)=1+|μ(ρ1,ρ2)|2.
|μ(ρ1,ρ2=0)|2=1Mm=1MI(m)(ρ1x,ρ1y)I(m)(0,0)I¯(ρ1x,ρ1y)I¯(0,0)1,
I¯(ρ1x,ρ1y)=m=1MI(m)(ρ1x,ρ1y)/M,
I¯(0,0)=m=1MI(m)(0,0)/M.

Metrics