Abstract

With the help of a tensor method, we investigate the evolution properties of the state of polarization of an electromagnetic Gaussian Schell-model beam propagating through a gradient-index (GRIN) fiber. We find that the Stokes parameters and the polarization ellipse exhibit periodicity. The initial beam parameters affect the values of the Stokes parameters and the parameters of the polarization ellipse. Furthermore, based on the second-order moments of the Wigner distribution function, the explicit expression for the propagation factor (known as the M2 factor) in the GRIN fiber is derived. It is shown that the M2 factor remains invariant on propagation and is determined only by the initial beam parameters.

© 2013 Optical Society of America

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  1. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).
  2. F. Gori, “Matrix treatment for partially polarized, partially coherent beams,” Opt. Lett. 23, 241–243 (1998).
    [CrossRef]
  3. F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A 3, 1–9 (2001).
    [CrossRef]
  4. E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003).
    [CrossRef]
  5. H. Roychowdhury, S. A. Ponomarenko, and E. Wolf, “Change in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmosphere,” J. Mod. Opt. 52, 1611–1618 (2005).
    [CrossRef]
  6. H. Wang, X. Wang, A. Zeng, and K. Yang, “Effects of coherence on anisotropic electromagnetic Gaussian–Schell model beams on propagation,” Opt. Lett. 32, 2215–2217 (2007).
    [CrossRef]
  7. X. Ji, E. Zhang, and B. Lu, “Changes in the spectrum and polarization of polychromatic partially coherent electromagnetic beams in the turbulent atmosphere,” Opt. Commun. 275, 292–300 (2007).
    [CrossRef]
  8. Z. Chen and J. Pu, “Propagation characteristics of aberrant stochastic electromagnetic beams in a turbulent atmosphere,” J. Opt. A 9, 1123–1130 (2007).
    [CrossRef]
  9. O. Korotkova, “Scintillation index of a stochastic electromagnetic beam propagating in random media,” Opt. Commun. 281, 2342–2348 (2008).
    [CrossRef]
  10. 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]
  11. L. Pan, M. Sun, C. Ding, Z. Zhao, and B. Lü, “Effects of astigmatism on spectra, coherence and polarization of stochastic electromagnetic beams passing through an astigmatic optical system,” Opt. Express 17, 7310–7321 (2009).
    [CrossRef]
  12. Y. Cai and O. Korotkova, “Twist phase-induced polarization changes in electromagnetic Gaussian Schell-model beams,” Appl. Phys. B 96, 499–507 (2009).
    [CrossRef]
  13. Z. Tong, Y. Cai, and O. Korotkova, “Ghost imaging with electromagnetic stochastic beams,” Opt. Commun. 283, 3838–3845 (2010).
    [CrossRef]
  14. Z. Tong and O. Korotkova, “Stochastic electromagnetic beams in positive-and negative-phase materials,” Opt. Lett. 35, 175–177 (2010).
    [CrossRef]
  15. O. Korotkova, Y. Cai, and E. Watson, “Stochastic electromagnetic beams for LIDAR systems operating through turbulent atmosphere,” Appl. Phys. B 94, 681–690 (2009).
    [CrossRef]
  16. S. Zhu, Y. Cai, and O. Korotkova, “Propagation factor of a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Express 18, 12587–12598 (2010).
    [CrossRef]
  17. T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A 7, 232–237 (2005).
    [CrossRef]
  18. 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]
  19. F. Zhou, S. Zhu, and Y. Cai, “Spectral shift of an electromagnetic Gaussian Schell-model beam propagating through tissue,” J. Mod. Opt. 58, 38–44 (2011).
    [CrossRef]
  20. M. Yao, Y. Cai, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “Evolution of the degree of polarization of an electromagnetic Gaussian Schell-model beam in a Gaussian cavity,” Opt. Lett. 33, 2266–2268 (2008).
    [CrossRef]
  21. S. Zhu and Y. Cai, “M2-factor of a stochastic electromagnetic beam in a Gaussian cavity,” Opt. Express 18, 27567–27581 (2010).
    [CrossRef]
  22. 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]
  23. S. Zhu and Y. Cai, “Spectral shift of a twisted electromagnetic Gaussian Schell-model beam focused by a thin lens,” Appl. Phys. B 99, 317–323 (2010).
    [CrossRef]
  24. L. Zhang, F. Wang, Y. Cai, and O. Korotkova, “Degree of paraxiality of a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Commun. 284, 1111–1117 (2011).
    [CrossRef]
  25. E. Shchepakina and O. Korotkova, “Second-order statistics of stochastic electromagnetic beams propagating through non-Kolmogorov turbulence,” Opt. Express 18, 10650–10658 (2010).
    [CrossRef]
  26. 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]
  27. C. Zhao, Y. Dong, G. Wu, F. Wang, Y. Cai, and O. Korotkova, “Experimental demonstration of coupling of an electromagnetic Gaussian Schell-model beam into a single-mode optical fiber,” Appl. Phys. B 108, 891–895 (2012).
    [CrossRef]
  28. F. Wang, S. Zhu, X. Hu, and Y. Cai, “Coincidence fractional Fourier transform with a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Commun. 284, 5275–5280 (2011).
    [CrossRef]
  29. D. F. V. James, “Changes of polarization of light beams on propagation in free space,” J. Opt. Soc. Am. A 11, 1641–1643 (1994).
    [CrossRef]
  30. E. Wolf, “Polarization invariance in beam propagation,” Opt. Lett. 32, 3400–3401 (2007).
    [CrossRef]
  31. D. Zhao and E. Wolf, “Light beams whose degree of polarization does not changes in propagation,” Opt. Commun. 281, 3067–3070 (2008).
    [CrossRef]
  32. O. Korotkova and E. Wolf, “Generalized Stokes parameters of random electromagnetic beams,” Opt. Lett. 30, 198–200 (2005).
    [CrossRef]
  33. O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246, 35–43 (2005).
    [CrossRef]
  34. T. Setälä, M. Kaivola, and A. T. Friberg, “Degree of polarization in near fields of thermal sources: effects of surface waves,” Phys. Rev. Lett. 88, 123902 (2002).
    [CrossRef]
  35. T. Setälä, K. Lindfors, and A. T. Friberg, “Degree of polarization in 3D optical fields generated from a partially polarized plane wave,” Opt. Lett. 34, 3394–3396 (2009).
    [CrossRef]
  36. A. Luis, “Degree of polarization for three-dimensional fields as a distance between correlation matrices,” Opt. Commun. 253, 10–14 (2005).
    [CrossRef]
  37. A. Luis, “Polarization distribution and degree of polarization for three-dimensional quantum light fields,” Phys. Rev. A 71, 063815 (2005).
    [CrossRef]
  38. Z. Mei, “Generalized Stokes parameters of three-dimensional stochastic electromagnetic beams,” Opt. Express 18, 22826–22832 (2010).
    [CrossRef]
  39. B. Kanseri and H. C. Kandpal, “Experimental determination of electric cross-spectral density matrix and generalized Stokes parameters for a laser beam,” Opt. Lett. 33, 2410–2412 (2008).
    [CrossRef]
  40. B. Kanseri, S. Rath, and H. C. Kandpal, “Direct determination of the generalized Stokes parameters from the usual Stokes parameters,” Opt. Lett. 34, 719–721 (2009).
    [CrossRef]
  41. O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15, 353–364 (2005).
  42. O. Korotkova, M. Yao, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “State of polarization of a stochastic electromagnetic beam in an optical resonator,” J. Opt. Soc. Am. A 25, 2710–2720 (2008).
    [CrossRef]
  43. J. Li, C. Ding, and B. Lü, “Generalized Stokes parameters of random electromagnetic vortex beams propagating through atmospheric turbulence,” Appl. Phys. B 103, 245–255 (2011).
    [CrossRef]
  44. D. Liu and Z. Zhou, “Generalized stokes parameters of stochastic electromagnetic beams propagating through uniaxial crystals orthogonal to the optical axis” J. Opt. A 11, 065710 (2009).
    [CrossRef]
  45. W. Gao and O. Korotkova, “Changes in the state of polarization of a random electromagnetic beam propagating through tissue,” Opt. Commun. 270, 474–478 (2007).
    [CrossRef]
  46. V. Bhatia and A. M. Vengsarkar, “Optical fiber long-period grating sensors,” Opt. Lett. 21, 692–694 (1996).
    [CrossRef]
  47. G. P. Agrawal, A. K. Ghatak, and C. L. Mehta, “Propagation of partially coherent beam through Selfoc fibers,” Opt. Commun. 12, 333–337 (1974).
    [CrossRef]
  48. 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]
  49. S. Zhu, C. Zhao, Y. Chen, and Y. Cai, “Experimental generation of a polychromatic partially coherent dark hollow beam,” Optik 124, 5271–5273 (2013).
    [CrossRef]
  50. M. Van Buren and N. A. Riza, “Foundations for low-loss fiber gradient-index lens pair coupling with the self-imaging mechanism,” Appl. Opt. 42, 550–565 (2003).
    [CrossRef]
  51. G. P. Agarwal, Fiber-Optic Communication Systems, 3rd ed. (Wiley, 2002).
  52. A. Gamliel and G. P. Agrawal, “Wolf effect in homogenous and inhomogenous media,” J. Opt. Soc. Am. A 7, 2184–2192 (1990).
    [CrossRef]
  53. H. Roychowdhury, G. P. Agarwal, and E. Wolf, “Changes in the spectrum, in the spectral degree of polarization, and in the spectral degree of coherence of a partially coherent beam propagating through a gradient-index fiber,” J. Opt. Soc. Am. A 23, 940–948 (2006).
    [CrossRef]
  54. A. E. Siegman, Lasers (University Science Books, 1986), Chap. 20.
  55. J. Collins and A. Stuart, “Lens-system diffraction integral written in terms of matrix optics,” J. Opt. Soc. Am. 60, 1168–1177 (1970).
    [CrossRef]
  56. Q. Lin and Y. Cai, “Tensor ABCD law for partially coherent twisted anisotropic Gaussian–Schell model beams,” Opt. Lett. 27, 216–218 (2002).
    [CrossRef]
  57. A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2C14 (1990).
    [CrossRef]
  58. M. Santarsiero, F. Gori, R. Borghi, G. Cincotti, and P. Vahimaa, “Spreading properties of beams radiated by partially coherent Schell-model sources,” J. Opt. Soc. Am. A 16, 106–112 (1999).
    [CrossRef]
  59. J. Serna, R. Martinez-Herrero, and P. M. Mejfas, “Parametric characterization of general partially coherent beams propagating through ABCD optical systems,” J. Opt. Soc. Am. A 8, 1094–1098 (1991).
    [CrossRef]
  60. R. Martinez-Herrero and P. M. Mejias, “Second-order spatial characterization of hard-edge diffracted beams,” Opt. Lett. 18, 1669–1671 (1993).
    [CrossRef]
  61. M. J. Bastiaans, “Application of the Wigner distribution function to partially coherent light,” J. Opt. Soc. Am. A 3, 1227–1238 (1986).
    [CrossRef]

2013 (1)

S. Zhu, C. Zhao, Y. Chen, and Y. Cai, “Experimental generation of a polychromatic partially coherent dark hollow beam,” Optik 124, 5271–5273 (2013).
[CrossRef]

2012 (2)

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]

C. Zhao, Y. Dong, G. Wu, F. Wang, Y. Cai, and O. Korotkova, “Experimental demonstration of coupling of an electromagnetic Gaussian Schell-model beam into a single-mode optical fiber,” Appl. Phys. B 108, 891–895 (2012).
[CrossRef]

2011 (5)

F. Wang, S. Zhu, X. Hu, and Y. Cai, “Coincidence fractional Fourier transform with a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Commun. 284, 5275–5280 (2011).
[CrossRef]

L. Zhang, F. Wang, Y. Cai, and O. Korotkova, “Degree of paraxiality of a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Commun. 284, 1111–1117 (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]

F. Zhou, S. Zhu, and Y. Cai, “Spectral shift of an electromagnetic Gaussian Schell-model beam propagating through tissue,” J. Mod. Opt. 58, 38–44 (2011).
[CrossRef]

J. Li, C. Ding, and B. Lü, “Generalized Stokes parameters of random electromagnetic vortex beams propagating through atmospheric turbulence,” Appl. Phys. B 103, 245–255 (2011).
[CrossRef]

2010 (7)

2009 (7)

2008 (7)

2007 (5)

E. Wolf, “Polarization invariance in beam propagation,” Opt. Lett. 32, 3400–3401 (2007).
[CrossRef]

H. Wang, X. Wang, A. Zeng, and K. Yang, “Effects of coherence on anisotropic electromagnetic Gaussian–Schell model beams on propagation,” Opt. Lett. 32, 2215–2217 (2007).
[CrossRef]

X. Ji, E. Zhang, and B. Lu, “Changes in the spectrum and polarization of polychromatic partially coherent electromagnetic beams in the turbulent atmosphere,” Opt. Commun. 275, 292–300 (2007).
[CrossRef]

Z. Chen and J. Pu, “Propagation characteristics of aberrant stochastic electromagnetic beams in a turbulent atmosphere,” J. Opt. A 9, 1123–1130 (2007).
[CrossRef]

W. Gao and O. Korotkova, “Changes in the state of polarization of a random electromagnetic beam propagating through tissue,” Opt. Commun. 270, 474–478 (2007).
[CrossRef]

2006 (1)

2005 (7)

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15, 353–364 (2005).

H. Roychowdhury, S. A. Ponomarenko, and E. Wolf, “Change in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmosphere,” J. Mod. Opt. 52, 1611–1618 (2005).
[CrossRef]

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A 7, 232–237 (2005).
[CrossRef]

A. Luis, “Degree of polarization for three-dimensional fields as a distance between correlation matrices,” Opt. Commun. 253, 10–14 (2005).
[CrossRef]

A. Luis, “Polarization distribution and degree of polarization for three-dimensional quantum light fields,” Phys. Rev. A 71, 063815 (2005).
[CrossRef]

O. Korotkova and E. Wolf, “Generalized Stokes parameters of random electromagnetic beams,” Opt. Lett. 30, 198–200 (2005).
[CrossRef]

O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246, 35–43 (2005).
[CrossRef]

2003 (2)

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003).
[CrossRef]

M. Van Buren and N. A. Riza, “Foundations for low-loss fiber gradient-index lens pair coupling with the self-imaging mechanism,” Appl. Opt. 42, 550–565 (2003).
[CrossRef]

2002 (2)

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

T. Setälä, M. Kaivola, and A. T. Friberg, “Degree of polarization in near fields of thermal sources: effects of surface waves,” Phys. Rev. Lett. 88, 123902 (2002).
[CrossRef]

2001 (1)

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A 3, 1–9 (2001).
[CrossRef]

1999 (1)

1998 (1)

1996 (1)

1994 (1)

1993 (1)

1991 (1)

1990 (2)

1986 (1)

1974 (1)

G. P. Agrawal, A. K. Ghatak, and C. L. Mehta, “Propagation of partially coherent beam through Selfoc fibers,” Opt. Commun. 12, 333–337 (1974).
[CrossRef]

1970 (1)

Agarwal, G. P.

Agrawal, G. P.

A. Gamliel and G. P. Agrawal, “Wolf effect in homogenous and inhomogenous media,” J. Opt. Soc. Am. A 7, 2184–2192 (1990).
[CrossRef]

G. P. Agrawal, A. K. Ghatak, and C. L. Mehta, “Propagation of partially coherent beam through Selfoc fibers,” Opt. Commun. 12, 333–337 (1974).
[CrossRef]

Bastiaans, M. J.

Baykal, Y.

Bhatia, V.

Borghi, R.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A 3, 1–9 (2001).
[CrossRef]

M. Santarsiero, F. Gori, R. Borghi, G. Cincotti, and P. Vahimaa, “Spreading properties of beams radiated by partially coherent Schell-model sources,” J. Opt. Soc. Am. A 16, 106–112 (1999).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

Cai, Y.

S. Zhu, C. Zhao, Y. Chen, and Y. Cai, “Experimental generation of a polychromatic partially coherent dark hollow beam,” Optik 124, 5271–5273 (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]

C. Zhao, Y. Dong, G. Wu, F. Wang, Y. Cai, and O. Korotkova, “Experimental demonstration of coupling of an electromagnetic Gaussian Schell-model beam into a single-mode optical fiber,” Appl. Phys. B 108, 891–895 (2012).
[CrossRef]

F. Wang, S. Zhu, X. Hu, and Y. Cai, “Coincidence fractional Fourier transform with a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Commun. 284, 5275–5280 (2011).
[CrossRef]

F. Zhou, S. Zhu, and Y. Cai, “Spectral shift of an electromagnetic Gaussian Schell-model beam propagating through tissue,” J. Mod. Opt. 58, 38–44 (2011).
[CrossRef]

L. Zhang, F. Wang, Y. Cai, and O. Korotkova, “Degree of paraxiality of a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Commun. 284, 1111–1117 (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]

Z. Tong, Y. Cai, and O. Korotkova, “Ghost imaging with electromagnetic stochastic beams,” Opt. Commun. 283, 3838–3845 (2010).
[CrossRef]

S. Zhu, Y. Cai, and O. Korotkova, “Propagation factor of a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Express 18, 12587–12598 (2010).
[CrossRef]

S. Zhu and Y. Cai, “Spectral shift of a twisted electromagnetic Gaussian Schell-model beam focused by a thin lens,” Appl. Phys. B 99, 317–323 (2010).
[CrossRef]

S. Zhu and Y. Cai, “M2-factor of a stochastic electromagnetic beam in a Gaussian cavity,” Opt. Express 18, 27567–27581 (2010).
[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]

O. Korotkova, Y. Cai, and E. Watson, “Stochastic electromagnetic beams for LIDAR systems operating through turbulent atmosphere,” Appl. Phys. B 94, 681–690 (2009).
[CrossRef]

Y. Cai and O. Korotkova, “Twist phase-induced polarization changes in electromagnetic Gaussian Schell-model beams,” Appl. Phys. B 96, 499–507 (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]

M. Yao, Y. Cai, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “Evolution of the degree of polarization of an electromagnetic Gaussian Schell-model beam in a Gaussian cavity,” Opt. Lett. 33, 2266–2268 (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]

O. Korotkova, M. Yao, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “State of polarization of a stochastic electromagnetic beam in an optical resonator,” J. Opt. Soc. Am. A 25, 2710–2720 (2008).
[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]

Chen, Y.

S. Zhu, C. Zhao, Y. Chen, and Y. Cai, “Experimental generation of a polychromatic partially coherent dark hollow beam,” Optik 124, 5271–5273 (2013).
[CrossRef]

Chen, Z.

Z. Chen and J. Pu, “Propagation characteristics of aberrant stochastic electromagnetic beams in a turbulent atmosphere,” J. Opt. A 9, 1123–1130 (2007).
[CrossRef]

Cincotti, G.

Collins, J.

Ding, C.

J. Li, C. Ding, and B. Lü, “Generalized Stokes parameters of random electromagnetic vortex beams propagating through atmospheric turbulence,” Appl. Phys. B 103, 245–255 (2011).
[CrossRef]

L. Pan, M. Sun, C. Ding, Z. Zhao, and B. Lü, “Effects of astigmatism on spectra, coherence and polarization of stochastic electromagnetic beams passing through an astigmatic optical system,” Opt. Express 17, 7310–7321 (2009).
[CrossRef]

Dogariu, A.

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15, 353–364 (2005).

Dong, Y.

C. Zhao, Y. Dong, G. Wu, F. Wang, Y. Cai, and O. Korotkova, “Experimental demonstration of coupling of an electromagnetic Gaussian Schell-model beam into a single-mode optical fiber,” Appl. Phys. B 108, 891–895 (2012).
[CrossRef]

Eyyuboglu, H. T.

Friberg, A. T.

T. Setälä, K. Lindfors, and A. T. Friberg, “Degree of polarization in 3D optical fields generated from a partially polarized plane wave,” Opt. Lett. 34, 3394–3396 (2009).
[CrossRef]

T. Setälä, M. Kaivola, and A. T. Friberg, “Degree of polarization in near fields of thermal sources: effects of surface waves,” Phys. Rev. Lett. 88, 123902 (2002).
[CrossRef]

Gamliel, A.

Gao, W.

W. Gao and O. Korotkova, “Changes in the state of polarization of a random electromagnetic beam propagating through tissue,” Opt. Commun. 270, 474–478 (2007).
[CrossRef]

Ghatak, A. K.

G. P. Agrawal, A. K. Ghatak, and C. L. Mehta, “Propagation of partially coherent beam through Selfoc fibers,” Opt. Commun. 12, 333–337 (1974).
[CrossRef]

Gori, F.

Hu, X.

F. Wang, S. Zhu, X. Hu, and Y. Cai, “Coincidence fractional Fourier transform with a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Commun. 284, 5275–5280 (2011).
[CrossRef]

James, D. F. V.

Ji, X.

X. Ji, E. Zhang, and B. Lu, “Changes in the spectrum and polarization of polychromatic partially coherent electromagnetic beams in the turbulent atmosphere,” Opt. Commun. 275, 292–300 (2007).
[CrossRef]

Kaivola, M.

T. Setälä, M. Kaivola, and A. T. Friberg, “Degree of polarization in near fields of thermal sources: effects of surface waves,” Phys. Rev. Lett. 88, 123902 (2002).
[CrossRef]

Kandpal, H. C.

Kanseri, B.

Korotkova, O.

C. Zhao, Y. Dong, G. Wu, F. Wang, Y. Cai, and O. Korotkova, “Experimental demonstration of coupling of an electromagnetic Gaussian Schell-model beam into a single-mode optical fiber,” Appl. Phys. B 108, 891–895 (2012).
[CrossRef]

L. Zhang, F. Wang, Y. Cai, and O. Korotkova, “Degree of paraxiality of a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Commun. 284, 1111–1117 (2011).
[CrossRef]

E. Shchepakina and O. Korotkova, “Second-order statistics of stochastic electromagnetic beams propagating through non-Kolmogorov turbulence,” Opt. Express 18, 10650–10658 (2010).
[CrossRef]

S. Zhu, Y. Cai, and O. Korotkova, “Propagation factor of a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Express 18, 12587–12598 (2010).
[CrossRef]

Z. Tong, Y. Cai, and O. Korotkova, “Ghost imaging with electromagnetic stochastic beams,” Opt. Commun. 283, 3838–3845 (2010).
[CrossRef]

Z. Tong and O. Korotkova, “Stochastic electromagnetic beams in positive-and negative-phase materials,” Opt. Lett. 35, 175–177 (2010).
[CrossRef]

O. Korotkova, Y. Cai, and E. Watson, “Stochastic electromagnetic beams for LIDAR systems operating through turbulent atmosphere,” Appl. Phys. B 94, 681–690 (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]

Y. Cai and O. Korotkova, “Twist phase-induced polarization changes in electromagnetic Gaussian Schell-model beams,” Appl. Phys. B 96, 499–507 (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]

O. Korotkova, “Scintillation index of a stochastic electromagnetic beam propagating in random media,” Opt. Commun. 281, 2342–2348 (2008).
[CrossRef]

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

O. Korotkova, M. Yao, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “State of polarization of a stochastic electromagnetic beam in an optical resonator,” J. Opt. Soc. Am. A 25, 2710–2720 (2008).
[CrossRef]

W. Gao and O. Korotkova, “Changes in the state of polarization of a random electromagnetic beam propagating through tissue,” Opt. Commun. 270, 474–478 (2007).
[CrossRef]

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15, 353–364 (2005).

O. Korotkova and E. Wolf, “Generalized Stokes parameters of random electromagnetic beams,” Opt. Lett. 30, 198–200 (2005).
[CrossRef]

O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246, 35–43 (2005).
[CrossRef]

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A 7, 232–237 (2005).
[CrossRef]

Li, J.

J. Li, C. Ding, and B. Lü, “Generalized Stokes parameters of random electromagnetic vortex beams propagating through atmospheric turbulence,” Appl. Phys. B 103, 245–255 (2011).
[CrossRef]

Lin, Q.

Lindfors, K.

Liu, D.

D. Liu and Z. Zhou, “Generalized stokes parameters of stochastic electromagnetic beams propagating through uniaxial crystals orthogonal to the optical axis” J. Opt. A 11, 065710 (2009).
[CrossRef]

Liu, X.

Lu, B.

X. Ji, E. Zhang, and B. Lu, “Changes in the spectrum and polarization of polychromatic partially coherent electromagnetic beams in the turbulent atmosphere,” Opt. Commun. 275, 292–300 (2007).
[CrossRef]

Lu, X.

Lü, B.

J. Li, C. Ding, and B. Lü, “Generalized Stokes parameters of random electromagnetic vortex beams propagating through atmospheric turbulence,” Appl. Phys. B 103, 245–255 (2011).
[CrossRef]

L. Pan, M. Sun, C. Ding, Z. Zhao, and B. Lü, “Effects of astigmatism on spectra, coherence and polarization of stochastic electromagnetic beams passing through an astigmatic optical system,” Opt. Express 17, 7310–7321 (2009).
[CrossRef]

Luis, A.

A. Luis, “Degree of polarization for three-dimensional fields as a distance between correlation matrices,” Opt. Commun. 253, 10–14 (2005).
[CrossRef]

A. Luis, “Polarization distribution and degree of polarization for three-dimensional quantum light fields,” Phys. Rev. A 71, 063815 (2005).
[CrossRef]

Martinez-Herrero, R.

Mehta, C. L.

G. P. Agrawal, A. K. Ghatak, and C. L. Mehta, “Propagation of partially coherent beam through Selfoc fibers,” Opt. Commun. 12, 333–337 (1974).
[CrossRef]

Mei, Z.

Mejfas, P. M.

Mejias, P. M.

Mondello, A.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A 3, 1–9 (2001).
[CrossRef]

Pan, L.

Piquero, G.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A 3, 1–9 (2001).
[CrossRef]

Ponomarenko, S. A.

H. Roychowdhury, S. A. Ponomarenko, and E. Wolf, “Change in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmosphere,” J. Mod. Opt. 52, 1611–1618 (2005).
[CrossRef]

Pu, J.

Z. Chen and J. Pu, “Propagation characteristics of aberrant stochastic electromagnetic beams in a turbulent atmosphere,” J. Opt. A 9, 1123–1130 (2007).
[CrossRef]

Rath, S.

Riza, N. A.

Roychowdhury, H.

H. Roychowdhury, G. P. Agarwal, and E. Wolf, “Changes in the spectrum, in the spectral degree of polarization, and in the spectral degree of coherence of a partially coherent beam propagating through a gradient-index fiber,” J. Opt. Soc. Am. A 23, 940–948 (2006).
[CrossRef]

H. Roychowdhury, S. A. Ponomarenko, and E. Wolf, “Change in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmosphere,” J. Mod. Opt. 52, 1611–1618 (2005).
[CrossRef]

Salem, M.

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15, 353–364 (2005).

Santarsiero, M.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A 3, 1–9 (2001).
[CrossRef]

M. Santarsiero, F. Gori, R. Borghi, G. Cincotti, and P. Vahimaa, “Spreading properties of beams radiated by partially coherent Schell-model sources,” J. Opt. Soc. Am. A 16, 106–112 (1999).
[CrossRef]

Serna, J.

Setälä, T.

T. Setälä, K. Lindfors, and A. T. Friberg, “Degree of polarization in 3D optical fields generated from a partially polarized plane wave,” Opt. Lett. 34, 3394–3396 (2009).
[CrossRef]

T. Setälä, M. Kaivola, and A. T. Friberg, “Degree of polarization in near fields of thermal sources: effects of surface waves,” Phys. Rev. Lett. 88, 123902 (2002).
[CrossRef]

Shchepakina, E.

Shirai, T.

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A 7, 232–237 (2005).
[CrossRef]

Siegman, A. E.

A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2C14 (1990).
[CrossRef]

A. E. Siegman, Lasers (University Science Books, 1986), Chap. 20.

Simon, R.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A 3, 1–9 (2001).
[CrossRef]

Stuart, A.

Sun, M.

Tong, Z.

Z. Tong, Y. Cai, and O. Korotkova, “Ghost imaging with electromagnetic stochastic beams,” Opt. Commun. 283, 3838–3845 (2010).
[CrossRef]

Z. Tong and O. Korotkova, “Stochastic electromagnetic beams in positive-and negative-phase materials,” Opt. Lett. 35, 175–177 (2010).
[CrossRef]

Vahimaa, P.

Van Buren, M.

Vengsarkar, A. M.

Wang, F.

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]

C. Zhao, Y. Dong, G. Wu, F. Wang, Y. Cai, and O. Korotkova, “Experimental demonstration of coupling of an electromagnetic Gaussian Schell-model beam into a single-mode optical fiber,” Appl. Phys. B 108, 891–895 (2012).
[CrossRef]

L. Zhang, F. Wang, Y. Cai, and O. Korotkova, “Degree of paraxiality of a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Commun. 284, 1111–1117 (2011).
[CrossRef]

F. Wang, S. Zhu, X. Hu, and Y. Cai, “Coincidence fractional Fourier transform with a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Commun. 284, 5275–5280 (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]

Wang, H.

Wang, X.

Wang, Y.

Watson, E.

O. Korotkova, Y. Cai, and E. Watson, “Stochastic electromagnetic beams for LIDAR systems operating through turbulent atmosphere,” Appl. Phys. B 94, 681–690 (2009).
[CrossRef]

Wolf, E.

D. Zhao and E. Wolf, “Light beams whose degree of polarization does not changes in propagation,” Opt. Commun. 281, 3067–3070 (2008).
[CrossRef]

E. Wolf, “Polarization invariance in beam propagation,” Opt. Lett. 32, 3400–3401 (2007).
[CrossRef]

H. Roychowdhury, G. P. Agarwal, and E. Wolf, “Changes in the spectrum, in the spectral degree of polarization, and in the spectral degree of coherence of a partially coherent beam propagating through a gradient-index fiber,” J. Opt. Soc. Am. A 23, 940–948 (2006).
[CrossRef]

O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246, 35–43 (2005).
[CrossRef]

O. Korotkova and E. Wolf, “Generalized Stokes parameters of random electromagnetic beams,” Opt. Lett. 30, 198–200 (2005).
[CrossRef]

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15, 353–364 (2005).

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A 7, 232–237 (2005).
[CrossRef]

H. Roychowdhury, S. A. Ponomarenko, and E. Wolf, “Change in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmosphere,” J. Mod. Opt. 52, 1611–1618 (2005).
[CrossRef]

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003).
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

Wu, G.

Yang, K.

Yao, M.

Zeng, A.

Zhang, E.

X. Ji, E. Zhang, and B. Lu, “Changes in the spectrum and polarization of polychromatic partially coherent electromagnetic beams in the turbulent atmosphere,” Opt. Commun. 275, 292–300 (2007).
[CrossRef]

Zhang, L.

L. Zhang, F. Wang, Y. Cai, and O. Korotkova, “Degree of paraxiality of a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Commun. 284, 1111–1117 (2011).
[CrossRef]

Zhao, C.

S. Zhu, C. Zhao, Y. Chen, and Y. Cai, “Experimental generation of a polychromatic partially coherent dark hollow beam,” Optik 124, 5271–5273 (2013).
[CrossRef]

C. Zhao, Y. Dong, G. Wu, F. Wang, Y. Cai, and O. Korotkova, “Experimental demonstration of coupling of an electromagnetic Gaussian Schell-model beam into a single-mode optical fiber,” Appl. Phys. B 108, 891–895 (2012).
[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, 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]

Zhao, D.

D. Zhao and E. Wolf, “Light beams whose degree of polarization does not changes in propagation,” Opt. Commun. 281, 3067–3070 (2008).
[CrossRef]

Zhao, Z.

Zhou, F.

F. Zhou, S. Zhu, and Y. Cai, “Spectral shift of an electromagnetic Gaussian Schell-model beam propagating through tissue,” J. Mod. Opt. 58, 38–44 (2011).
[CrossRef]

Zhou, Z.

D. Liu and Z. Zhou, “Generalized stokes parameters of stochastic electromagnetic beams propagating through uniaxial crystals orthogonal to the optical axis” J. Opt. A 11, 065710 (2009).
[CrossRef]

Zhu, S.

S. Zhu, C. Zhao, Y. Chen, and Y. Cai, “Experimental generation of a polychromatic partially coherent dark hollow beam,” Optik 124, 5271–5273 (2013).
[CrossRef]

F. Wang, S. Zhu, X. Hu, and Y. Cai, “Coincidence fractional Fourier transform with a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Commun. 284, 5275–5280 (2011).
[CrossRef]

F. Zhou, S. Zhu, and Y. Cai, “Spectral shift of an electromagnetic Gaussian Schell-model beam propagating through tissue,” J. Mod. Opt. 58, 38–44 (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]

S. Zhu, Y. Cai, and O. Korotkova, “Propagation factor of a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Express 18, 12587–12598 (2010).
[CrossRef]

S. Zhu and Y. Cai, “M2-factor of a stochastic electromagnetic beam in a Gaussian cavity,” Opt. Express 18, 27567–27581 (2010).
[CrossRef]

S. Zhu and Y. Cai, “Spectral shift of a twisted electromagnetic Gaussian Schell-model beam focused by a thin lens,” Appl. Phys. B 99, 317–323 (2010).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (5)

J. Li, C. Ding, and B. Lü, “Generalized Stokes parameters of random electromagnetic vortex beams propagating through atmospheric turbulence,” Appl. Phys. B 103, 245–255 (2011).
[CrossRef]

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

O. Korotkova, Y. Cai, and E. Watson, “Stochastic electromagnetic beams for LIDAR systems operating through turbulent atmosphere,” Appl. Phys. B 94, 681–690 (2009).
[CrossRef]

S. Zhu and Y. Cai, “Spectral shift of a twisted electromagnetic Gaussian Schell-model beam focused by a thin lens,” Appl. Phys. B 99, 317–323 (2010).
[CrossRef]

C. Zhao, Y. Dong, G. Wu, F. Wang, Y. Cai, and O. Korotkova, “Experimental demonstration of coupling of an electromagnetic Gaussian Schell-model beam into a single-mode optical fiber,” Appl. Phys. B 108, 891–895 (2012).
[CrossRef]

J. Mod. Opt. (2)

F. Zhou, S. Zhu, and Y. Cai, “Spectral shift of an electromagnetic Gaussian Schell-model beam propagating through tissue,” J. Mod. Opt. 58, 38–44 (2011).
[CrossRef]

H. Roychowdhury, S. A. Ponomarenko, and E. Wolf, “Change in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmosphere,” J. Mod. Opt. 52, 1611–1618 (2005).
[CrossRef]

J. Opt. A (4)

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A 7, 232–237 (2005).
[CrossRef]

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A 3, 1–9 (2001).
[CrossRef]

Z. Chen and J. Pu, “Propagation characteristics of aberrant stochastic electromagnetic beams in a turbulent atmosphere,” J. Opt. A 9, 1123–1130 (2007).
[CrossRef]

D. Liu and Z. Zhou, “Generalized stokes parameters of stochastic electromagnetic beams propagating through uniaxial crystals orthogonal to the optical axis” J. Opt. A 11, 065710 (2009).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (7)

Opt. Commun. (10)

F. Wang, S. Zhu, X. Hu, and Y. Cai, “Coincidence fractional Fourier transform with a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Commun. 284, 5275–5280 (2011).
[CrossRef]

D. Zhao and E. Wolf, “Light beams whose degree of polarization does not changes in propagation,” Opt. Commun. 281, 3067–3070 (2008).
[CrossRef]

O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246, 35–43 (2005).
[CrossRef]

L. Zhang, F. Wang, Y. Cai, and O. Korotkova, “Degree of paraxiality of a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Commun. 284, 1111–1117 (2011).
[CrossRef]

O. Korotkova, “Scintillation index of a stochastic electromagnetic beam propagating in random media,” Opt. Commun. 281, 2342–2348 (2008).
[CrossRef]

Z. Tong, Y. Cai, and O. Korotkova, “Ghost imaging with electromagnetic stochastic beams,” Opt. Commun. 283, 3838–3845 (2010).
[CrossRef]

W. Gao and O. Korotkova, “Changes in the state of polarization of a random electromagnetic beam propagating through tissue,” Opt. Commun. 270, 474–478 (2007).
[CrossRef]

G. P. Agrawal, A. K. Ghatak, and C. L. Mehta, “Propagation of partially coherent beam through Selfoc fibers,” Opt. Commun. 12, 333–337 (1974).
[CrossRef]

X. Ji, E. Zhang, and B. Lu, “Changes in the spectrum and polarization of polychromatic partially coherent electromagnetic beams in the turbulent atmosphere,” Opt. Commun. 275, 292–300 (2007).
[CrossRef]

A. Luis, “Degree of polarization for three-dimensional fields as a distance between correlation matrices,” Opt. Commun. 253, 10–14 (2005).
[CrossRef]

Opt. Express (8)

Opt. Lett. (14)

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

O. Korotkova and E. Wolf, “Generalized Stokes parameters of random electromagnetic beams,” Opt. Lett. 30, 198–200 (2005).
[CrossRef]

E. Wolf, “Polarization invariance in beam propagation,” Opt. Lett. 32, 3400–3401 (2007).
[CrossRef]

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

Z. Tong and O. Korotkova, “Stochastic electromagnetic beams in positive-and negative-phase materials,” Opt. Lett. 35, 175–177 (2010).
[CrossRef]

H. Wang, X. Wang, A. Zeng, and K. Yang, “Effects of coherence on anisotropic electromagnetic Gaussian–Schell model beams on propagation,” Opt. Lett. 32, 2215–2217 (2007).
[CrossRef]

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

B. Kanseri, S. Rath, and H. C. Kandpal, “Direct determination of the generalized Stokes parameters from the usual Stokes parameters,” Opt. Lett. 34, 719–721 (2009).
[CrossRef]

T. Setälä, K. Lindfors, and A. T. Friberg, “Degree of polarization in 3D optical fields generated from a partially polarized plane wave,” Opt. Lett. 34, 3394–3396 (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]

V. Bhatia and A. M. Vengsarkar, “Optical fiber long-period grating sensors,” Opt. Lett. 21, 692–694 (1996).
[CrossRef]

R. Martinez-Herrero and P. M. Mejias, “Second-order spatial characterization of hard-edge diffracted beams,” Opt. Lett. 18, 1669–1671 (1993).
[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]

Optik (1)

S. Zhu, C. Zhao, Y. Chen, and Y. Cai, “Experimental generation of a polychromatic partially coherent dark hollow beam,” Optik 124, 5271–5273 (2013).
[CrossRef]

Phys. Lett. A (1)

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003).
[CrossRef]

Phys. Rev. A (1)

A. Luis, “Polarization distribution and degree of polarization for three-dimensional quantum light fields,” Phys. Rev. A 71, 063815 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

T. Setälä, M. Kaivola, and A. T. Friberg, “Degree of polarization in near fields of thermal sources: effects of surface waves,” Phys. Rev. Lett. 88, 123902 (2002).
[CrossRef]

Proc. SPIE (1)

A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2C14 (1990).
[CrossRef]

Waves Random Complex Media (1)

O. Korotkova, M. Salem, A. Dogariu, and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through the turbulent atmosphere,” Waves Random Complex Media 15, 353–364 (2005).

Other (3)

G. P. Agarwal, Fiber-Optic Communication Systems, 3rd ed. (Wiley, 2002).

A. E. Siegman, Lasers (University Science Books, 1986), Chap. 20.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

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Figures (9)

Fig. 1.
Fig. 1.

Schematic diagram of a GRIN fiber.

Fig. 2.
Fig. 2.

Normalized spectral intensity S0/S0max (y=0) of an EGSM beam versus the propagation distance z within a GRIN fiber.

Fig. 3.
Fig. 3.

Normalized on-axis Stokes parameters of an EGSM beam versus the propagation distance within a GRIN fiber for different values of the initial correlation coefficient δxx. A, δxx=2.25μm; B, δxx=2.5μm; C, δxx=3μm; D, δxx=3.5μm.

Fig. 4.
Fig. 4.

On-axis normalized Stokes parameters of an EGSM beam versus the propagation distance z within a GRIN fiber for different values of the initial degree of polarization. A, P0=0.3; B, P0=0.5; C, P0=0.8.

Fig. 5.
Fig. 5.

On-axis degree of ellipticity and orientation angle of an EGSM beam versus the propagation distance z within a GRIN fiber for different values of the initial correlation coefficient δxx. A, δxx=2.25μm; B, δxx=2.5μm; C, δxx=3μm; D, δxx=3.5μm.

Fig. 6.
Fig. 6.

On-axis degree of ellipticity and orientation angle of an EGSM beam versus the propagation distance z within a GRIN fiber for different values of the initial degree of polarization. A, P0=0.3; B, P0=0.5; C, P0=0.8.

Fig. 7.
Fig. 7.

On-axis polarization ellipse of an EGSM beam versus the propagation distance z within a GRIN fiber.

Fig. 8.
Fig. 8.

On-axis polarization ellipse of a stochastic EGSM beam at z=1mm for different values of initial correlation coefficient δxx with P0=0.3.

Fig. 9.
Fig. 9.

On-axis polarization ellipse of an EGSM beam at z=1.2mm for different values of the initial degree of polarization with δxx=3μm.

Equations (26)

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

n2(x,y;ω)={n02(ω)[1α2(ω)(x2+y2)],x2+y2R02n02(ω)[1α2(ω)R02],x2+y2R02},
α(ω)=1R0[1n12(ω)n02(ω)]1/2.
(ABCD)=(cos(αz)Isin(αz)n0αIn0αsin(αz)Icos(αz)I).
W⃡(r1,r2;ω)=(Wxx(r1,r2;ω)Wxy(r1,r2;ω)Wyx(r1,r2;ω)Wyy(r1,r2;ω)),
Wαβ(r˜;ω)=AαAβBαβexp[ik2r˜TM0αβ1r˜],(α,β=x,y),
M0αβ1=(1ik(12σa2+1δαβ2)Iikδαβ2Iikδαβ2I1ik(12σβ2+1δαβ2)I),
Wαβ(ρ˜;ω)=k24π2[Det(B˜)]1/2Wαβ(r˜;ω)×exp[ik2(r˜TB˜1A˜r˜2r˜TB˜1ρ˜+ρ˜TD˜B˜1ρ˜)]dr˜,
A˜=(A0I0IA*),B˜=(B0I0IB*),C˜=(C0I0IC*),D˜=(D0I0ID*).
Wαβ(ρ˜;ω)=AαAβBαβ[Det(A˜+B˜M0αβ1)]1/2×exp[ik2ρ˜TM1αβ1ρ˜],(α,β=x,y),
M1αβ1=(C˜+D˜M0αβ1)(A˜+B˜M0αβ1)1.
S0(ρ;ω)=Wxx(ρ;ω)+Wyy(ρ;ω),S1(ρ;ω)=Wxx(ρ;ω)Wyy(ρ;ω),S2(ρ;ω)=Wxy(ρ;ω)+Wyx(ρ;ω),S3(ρ;ω)=i[Wyx(ρ;ω)Wxy(ρ;ω)].
P0(r,r;ω)=14DetW⃡(r,r;ω)[TrW⃡(r,r;ω)]2.
n2(ω)=1+i=13Ciωi2ωi2ω2.
W⃡(ρ;ω)W⃡(p)(ρ;ω)+W⃡(u)(ρ;ω),
W⃡(p)(ρ;ω)=(B(ρ;ω)D(ρ;ω)D*(ρ;ω)C(ρ;ω)),W⃡(u)(ρ;ω)=(A(ρ;ω)00A(ρ;ω))
A(ρ;ω)=12[Wxx(ρ;ω)+Wyy(ρ;ω)+[Wxx(ρ;ω)Wyy(ρ;ω)]2+4|Wxy(ρ;ω)|2],B(ρ;ω)=12[Wxx(ρ;ω)Wyy(ρ;ω)+[Wxx(ρ;ω)Wyy(ρ;ω)]2+4|Wxy(ρ;ω)|2],C(ρ;ω)=12[Wyy(ρ;ω)Wxx(ρ;ω)+[Wxx(ρ;ω)Wyy(ρ;ω)]2+4|Wxy(ρ;ω)|2],D(ρ;ω)=Wxy(ρ;ω),D*(ρ;ω)=Wyx(ρ;ω).
C(ρ;ω)εx[r]2(ρ;ω)2ReC(ρ;ω)εx[r](ρ;ω)εy[r](ρ;ω)+B(ρ;ω)εy[r]2(ρ;ω)=[ImD(ρ;ω)]2,
A1,2(ρ;ω)=12[[Wxx(ρ;ω)Wyy(ρ;ω)]2+4|Wxy(ρ;ω)|2±[Wxx(ρ;ω)Wyy(ρ;ω)]2+4[Wxy(ρ;ω)]2]1/2,
ε(ρ;ω)=A2(ρ;ω)A1(ρ;ω),θ(ρ;ω)=12arctan[2ReWxy(ρ;ω)Wxx(ρ;ω)Wyy(ρ;ω)].
H(ρ,θ;ω)=(k2π)2W⃡tr(ρ,ρs;ω)exp(ikθ·ρs)d2ρs,
M2(z)=k(ρ2θ2ρ·θ2)1/2=k[(ρ2xx+ρ2yy)(θ2xx+θ2yy)(ρ·θxx+ρ·θyy)2]1/2,
uv=1IuvH(ρ,θ;ω)d2ρd2θ×exp[ikρ·θ],u,v=ρx,ρy,θx,θy.
ρ2αα=4πσα4Aα2I(A2+2γααB2k2σα2),θ2αα=4πσα4Aα2B2I[(1AD)2+2γααB2D2k2σα2],ρ·θαα=4πσα4Aα2BI[A(1AD)2γααB2Dk2σα2],
M2(z)=[8γxxσx2Px2+8γyyσy2Py2+8PxPy(γxxσy2+γyyσx2)]1/2,
γαα=18σα2+12δαα2,Pα=Aα2σα2(Ax2σx2+Ay2σy2),(α=x,y).
M2(z)=(1+4σα2δαα2)1/2.

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