Abstract

We propose a method to determine the radius of curvature of an isotropic Gaussian Schell-model (GSM) beam by measuring the transverse beam widths and the transverse coherence widths at two different planes. Furthermore, we carry out experimental determination of the radius of curvature of a GSM beam. Using the measured beam parameters, we carry out a comparative study of the propagation properties of a GSM beam both theoretically and experimentally. Our experimental results agree well with theoretical predictions.

© 2013 Optical Society of America

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  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  2. 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]
  3. J. N. Clark, X. Huang, R. Harder, and I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
    [CrossRef]
  4. T. E. Gureyev, D. M. Paganin, A. W. Stevenson, S. C. Mayo, and S. W. Wilkin, “Generalized eikonal of partially coherent beams and its use in quantitative imaging,” Phys. Rev. Lett. 93, 068103 (2004).
    [CrossRef]
  5. Y. Cai and S. Zhu, “Ghost interference with partially coherent radiation,” Opt. Lett. 29, 2716–2718 (2004).
    [CrossRef]
  6. Y. Cai and S. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E 71, 056607 (2005).
    [CrossRef]
  7. D. Kermisch, “Partially coherent image processing by laser scanning,” J. Opt. Soc. Am. 65, 887–891 (1975).
    [CrossRef]
  8. 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]
  9. 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]
  10. Y. Cai and U. Peschel, “Second-harmonic generation by an astigmatic partially coherent beam,” Opt. Express 15, 15480–15492 (2007).
    [CrossRef]
  11. 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]
  12. Y. Cai, O. Korotkova, H. T. Eyyuboğlu, and Y. Baykal, “Active laser radar systems with stochastic electromagnetic beams in turbulent atmosphere,” Opt. Express 16, 15834–15846 (2008).
    [CrossRef]
  13. Y. Yuan, Y. Cai, J. Qu, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “M2-factor of coherent and partially coherent dark hollow beams propagating in turbulent atmosphere,” Opt. Express 17, 17344–17356 (2009).
    [CrossRef]
  14. F. Wang and Y. Cai, “Second-order statistics of a twisted Gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 18, 24661–24672 (2010).
    [CrossRef]
  15. G. Wu and Y. Cai, “Detection of a semi-rough target in turbulent atmosphere by a partially coherent beam,” Opt. Lett. 36, 1939–1942 (2011).
    [CrossRef]
  16. 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]
  17. 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]
  18. F. Wang, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “Twist phase-induced reduction in scintillation of a partially coherent beam in turbulent atmosphere,” Opt. Lett. 37, 184–186 (2012).
    [CrossRef]
  19. E. Wolf and E. Collett, “Partially coherent sources which produce same far-field intensity distribution as a laser,” Opt. Commun. 25, 293–296 (1978).
    [CrossRef]
  20. P. de Santis, F. Gori, G. Guattari, and C. Palma, “An example of a Collett–Wolf source,” Opt. Commun. 29, 256–260 (1979).
    [CrossRef]
  21. F. Gori, “Collet–Wolf sources and multimode lasers,” Opt. Commun. 34, 301–305 (1980).
    [CrossRef]
  22. A. T. Friberg, and R. J. Sudol, “Propagation parameters of Gaussian Schell-model beams,” Opt. Commun. 41, 383–387 (1982).
    [CrossRef]
  23. A. T. Friberg and J. Turunen, “Algebraic and graphical propagation methods for Gaussian Schell-model beams,” Opt. Eng. 25, 857–864 (1986).
    [CrossRef]
  24. 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]
  25. M. J. Bastiaans, “Application of the Wigner distribution function to partially coherent light,” J. Opt. Soc. Am. A 3, 1227–1238 (1986).
    [CrossRef]
  26. Q. Lin and Y. Cai, “Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams,” Opt. Lett. 27, 216–218 (2002).
    [CrossRef]
  27. Q. Lin and Y. Cai, “Fractional Fourier transform for partially coherent Gaussian Schell-model beams,” Opt. Lett. 27, 1672–1674 (2002).
    [CrossRef]
  28. 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]
  29. F. Wang, Y. Cai, and O. Korotkova, “Experimental observation of focal shifts in focused partially coherent beams,” Opt. Commun. 282, 3408–3413 (2009).
    [CrossRef]
  30. X. Ji and X. Li, “Effective radius of curvature of partially coherent Hermite–Gaussian beams propagating through atmospheric turbulence,” J. Opt. 12, 035403 (2010).
    [CrossRef]

2012

J. N. Clark, X. Huang, R. Harder, and I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[CrossRef]

F. Wang, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “Twist phase-induced reduction in scintillation of a partially coherent beam in turbulent atmosphere,” Opt. Lett. 37, 184–186 (2012).
[CrossRef]

2011

2010

F. Wang and Y. Cai, “Second-order statistics of a twisted Gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 18, 24661–24672 (2010).
[CrossRef]

X. Ji and X. Li, “Effective radius of curvature of partially coherent Hermite–Gaussian beams propagating through atmospheric turbulence,” J. Opt. 12, 035403 (2010).
[CrossRef]

2009

F. Wang, Y. Cai, and O. Korotkova, “Experimental observation of focal shifts in focused partially coherent beams,” Opt. Commun. 282, 3408–3413 (2009).
[CrossRef]

Y. Yuan, Y. Cai, J. Qu, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “M2-factor of coherent and partially coherent dark hollow beams propagating in turbulent atmosphere,” Opt. Express 17, 17344–17356 (2009).
[CrossRef]

2008

2007

2006

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

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

2004

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

Y. Cai and S. Zhu, “Ghost interference with partially coherent radiation,” Opt. Lett. 29, 2716–2718 (2004).
[CrossRef]

2002

1993

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

1986

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

A. T. Friberg and J. Turunen, “Algebraic and graphical propagation methods for Gaussian Schell-model beams,” Opt. Eng. 25, 857–864 (1986).
[CrossRef]

1984

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

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

1980

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

1979

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

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

1975

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]

Bastiaans, M. J.

Baykal, Y.

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]

Cai, Y.

F. Wang, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “Twist phase-induced reduction in scintillation of a partially coherent beam in turbulent atmosphere,” Opt. Lett. 37, 184–186 (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]

G. Wu and Y. Cai, “Detection of a semi-rough target in turbulent atmosphere by a partially coherent beam,” Opt. Lett. 36, 1939–1942 (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]

F. Wang and Y. Cai, “Second-order statistics of a twisted Gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 18, 24661–24672 (2010).
[CrossRef]

F. Wang, Y. Cai, and O. Korotkova, “Experimental observation of focal shifts in focused partially coherent beams,” Opt. Commun. 282, 3408–3413 (2009).
[CrossRef]

Y. Yuan, Y. Cai, J. Qu, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “M2-factor of coherent and partially coherent dark hollow beams propagating in turbulent atmosphere,” Opt. Express 17, 17344–17356 (2009).
[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, 15834–15846 (2008).
[CrossRef]

Y. Cai and U. Peschel, “Second-harmonic generation by an astigmatic partially coherent beam,” Opt. Express 15, 15480–15492 (2007).
[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 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 S. Zhu, “Ghost interference with partially coherent radiation,” Opt. Lett. 29, 2716–2718 (2004).
[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]

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

Clark, J. N.

J. N. Clark, X. Huang, R. Harder, and I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[CrossRef]

Collett, E.

E. Wolf and E. Collett, “Partially coherent sources which produce 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, C.

Eyyuboglu, H. T.

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]

Friberg, A. T.

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]

A. T. Friberg and J. Turunen, “Algebraic and graphical propagation methods for Gaussian Schell-model beams,” Opt. Eng. 25, 857–864 (1986).
[CrossRef]

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

Gori, F.

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]

Guattari, G.

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. Wilkin, “Generalized eikonal of partially coherent beams and its use in quantitative imaging,” Phys. Rev. Lett. 93, 068103 (2004).
[CrossRef]

Harder, R.

J. N. Clark, X. Huang, R. Harder, and I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (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]

Huang, X.

J. N. Clark, X. Huang, R. Harder, and I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[CrossRef]

Ji, X.

X. Ji and X. Li, “Effective radius of curvature of partially coherent Hermite–Gaussian beams propagating through atmospheric turbulence,” J. Opt. 12, 035403 (2010).
[CrossRef]

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.

Li, X.

X. Ji and X. Li, “Effective radius of curvature of partially coherent Hermite–Gaussian beams propagating through atmospheric turbulence,” J. Opt. 12, 035403 (2010).
[CrossRef]

Lin, Q.

Mandel, L.

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

Mayo, S. C.

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

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. Wilkin, “Generalized eikonal of partially coherent beams and its use in quantitative imaging,” Phys. Rev. Lett. 93, 068103 (2004).
[CrossRef]

Palma, C.

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.

Qu, J.

Ricklin, J. C.

Robinson, I. K.

J. N. Clark, X. Huang, R. Harder, and I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[CrossRef]

Stevenson, A. W.

T. E. Gureyev, D. M. Paganin, A. W. Stevenson, S. C. Mayo, and S. W. Wilkin, “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]

Tervonen, E.

Turunen, J.

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]

A. T. Friberg and J. Turunen, “Algebraic and graphical propagation methods for Gaussian Schell-model beams,” Opt. Eng. 25, 857–864 (1986).
[CrossRef]

Wang, F.

Wilkin, S. W.

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

Wolf, E.

E. Wolf and E. Collett, “Partially coherent sources which produce 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).

Wu, G.

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]

Yuan, Y.

Zhang, Y.

Zhao, C.

Zhu, S.

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

Y. Cai and S. Zhu, “Ghost interference with partially coherent radiation,” Opt. Lett. 29, 2716–2718 (2004).
[CrossRef]

Appl. Phys. Lett.

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.

X. Ji and X. Li, “Effective radius of curvature of partially coherent Hermite–Gaussian beams propagating through atmospheric turbulence,” J. Opt. 12, 035403 (2010).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Nat. Commun.

J. N. Clark, X. Huang, R. Harder, and I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[CrossRef]

Opt. Commun.

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

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

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

F. Wang, Y. Cai, and O. Korotkova, “Experimental observation of focal shifts in focused partially coherent beams,” Opt. Commun. 282, 3408–3413 (2009).
[CrossRef]

Opt. Eng.

A. T. Friberg and J. Turunen, “Algebraic and graphical propagation methods for Gaussian Schell-model beams,” Opt. Eng. 25, 857–864 (1986).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. E

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

Phys. Rev. Lett.

T. E. Gureyev, D. M. Paganin, A. W. Stevenson, S. C. Mayo, and S. W. Wilkin, “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]

Other

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

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Figures (7)

Fig. 1.
Fig. 1.

Experimental setup for generating an isotropic GSM beam and measuring its beam profile. P, linear polarizer; M, reflecting mirror; L1, L2, L3, thin lenses; RGGP, rotating ground-glass plate; P1, P2, plane 1 and plane 2; GAF, Gaussian amplitude filter; BPA, beam profile analyzer; PC, personal computer.

Fig. 2.
Fig. 2.

Experimental results of the intensity distribution of the generated GSM beam at P2 and the corresponding cross line (dotted curve). The solid curve is a result of the Gaussian fit of the experimental result.

Fig. 3.
Fig. 3.

Experimental setup for measuring the transverse coherence width δ0 of the generated GSM beam at P2. BS, 5050 beam splitter; D1, D2, single-photon detectors.

Fig. 4.
Fig. 4.

Experimental result (dotted curve) of the normalized fourth-order correlation function of the generated GSM beam at P2 and the corresponding Gaussian fit (solid curve) of the experimental result.

Fig. 5.
Fig. 5.

Experimental result (dotted curve) of the normalized intensity distribution of the generated GSM beam at z=30cm and the corresponding Gaussian fit (solid curve) of the experimental result.

Fig. 6.
Fig. 6.

Experimental results (dotted curves) of the normalized intensity distribution of the generated GSM beam at several propagation distances and the corresponding Gaussian fit (solid curve) of the experimental result.

Fig. 7.
Fig. 7.

Experimental results (dotted curves) of the normalized fourth-order correlation function of the generated GSM beam at several propagation distances. The solid curves are calculated by the theoretical formulas.

Equations (18)

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

W(r1,r2)=exp[r12+r224σ02(r1r2)22δ02ik(r12r22)2R0],
W(r˜)=exp[ik2r˜TM01r˜],
M01=((1R0i2kσ02ikδ02)Iikδ02Iikδ02I(1R0i2kσ02ikδ02)I),
W(v˜)=1[Det(A˜+B˜M01)]1/2exp(ik2v˜TM1v˜),
M1=(C˜+D˜M01)(A˜+B˜M01)1,
A˜=(AI0I0IAI),B˜=(BI0I0IBI),C˜=(CI0I0ICI),D˜=(DI0I0IDI),
M1=(m11m12m13m14m21m22m23m24m31m32m33m34m41m42m43m44)=((1Ri2kσ2ikδ2)Iikδ2Iikδ2I(1Ri2kσ2ikδ2)I),
1R=12(m11m33),1σ2=ik(m11+m33+2m13),1δ2=ikm13.
σ2=σ02[(A+BR0)2+B2Ni44k2σ04],
δ2=δ02[(A+BR0)2+B2Ni44k2σ04],
R=[(BDR02+AD+BCR0+AC)σ02σ2+BDNi44k2σ02σ2]1,
Ni2=(1+4σ02δ02)1/2.
1R0=±σ2B2σ02Ni44k2σ04AB.
(ABCD)=(1z01).
R=4k2σ04(1+4σ02δ02)z+z.
g(2)(v1v2,τ)=I(v1,t)I(v2,t+τ)I(v1,t)I(v2,t+τ),
g(2)(v1v2,τ=0)=1+exp[(v1v2)2/δ02].
ΔR0=|R0R¯0|R¯0.

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