Abstract

We derive the analytical expressions for the second-order moments of an electromagnetic Gaussian Schell-model (EGSM) beam propagating in a uniaxial crystal. With the help of the derived formulas, we study the evolution properties of the propagation factor, the effective radius of curvature and the Rayleigh range of an EGSM beam in a uniaxial crystal. It is found that the evolution properties of an EGSM beam in a uniaxial crystal are much different from its evolution properties in free space and are closely determined by the initial beam parameters and the parameters of the uniaxial crystal. The uniaxial crystal provides one way for modulating the properties of an EGSM beam.

© 2014 Optical Society of America

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2013 (3)

D. Deng, C. Chen, X. Zhao, and H. Li, “Propagation of an Airy vortex beam in uniaxial crystals,” Appl. Phys. B 110, 433–436 (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]

S. Zhu, L. Liu, Y. Chen, and Y. Cai, “State of polarization and propagation factor of a stochastic electromagnetic beam in a gradient-index fiber,” J. Opt. Soc. Am. A 30, 2306–2313 (2013).
[CrossRef]

2012 (2)

G. Zhou, R. Chen, and X. Chu, “Propagation of Airy beams in uniaxial crystals orthogonal to the optical axis,” Opt. Express 20, 2196–2205 (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 (7)

2010 (9)

X. Ji, H. T. Eyyuboğlu, and Y. Baykal, “Influence of turbulence on the effective radius of curvature of radial Gaussian array beams,” Opt. Express 18, 6922–6928 (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]

M. Yao, Y. Cai, O. Korotkova, Q. Lin, and Z. Wang, “Spatio-temporal coupling of random electromagnetic pulses interacting with reflecting gratings,” Opt. Express 18, 22503–22514 (2010).
[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]

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

H. T. Eyyuboğlu, Y. Baykal, and X. Ji, “Radius of curvature variations for annular, dark hollow and flat topped beams in turbulence,” Appl. Phys. B 99, 801–807 (2010).
[CrossRef]

X. Du and D. Zhao, “Propagation of uniformly polarized stochastic electromagnetic beams in uniaxial crystals,” J. Electromagn. Waves Appl. 24, 971–981 (2010).
[CrossRef]

C. Zhao and Y. Cai, “Paraxial propagation of Lorentz and Lorentz–Gauss beams in uniaxial crystals orthogonal to the optical axis,” J. Mod. Opt. 57, 375–384 (2010).
[CrossRef]

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

2009 (9)

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]

D. Liu and Z. Zhou, “Propagation of partially polarized, partially coherent beams in uniaxially crystals orthogonal to the optical axis,” Eur. Phys. J. D 54, 95–101 (2009).
[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]

M. Salem and G. P. Agrawal, “Coupling of stochastic electromagnetic beams into optical fibers,” Opt. Lett. 34, 2829–2831 (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]

M. Salem and G. P. Agrawal, “Effects of coherence and polarization on the coupling of stochastic electromagnetic beams into optical fibers,” J. Opt. Soc. Am. A 26, 2452–2458 (2009).
[CrossRef]

B. Tang, “Hermite–cosine–Gaussian beams propagating in uniaxial crystals orthogonal to the optical axis,” J. Opt. Soc. Am. A 26, 2480–2487 (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]

2008 (6)

2007 (1)

2006 (1)

E. Wolf, “Coherence and polarization properties of electromagnetic laser modes,” Opt. Commun. 265, 60–62 (2006).
[CrossRef]

2005 (6)

H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249, 379–385 (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]

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, “Degree of polarization of statistically stationary electromagnetic fields,” Opt. Commun. 248, 333–337 (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. Saastamoinen, J. Turunen, J. Tervo, T. Setälä, and A. T. Friberg, “Electromagnetic coherence theory of laser resonator modes,” J. Opt. Soc. Am. A 22, 103–108 (2005).
[CrossRef]

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

2004 (3)

O. Korotkova, M. Salem, and E. Wolf, “Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source,” Opt. Lett. 29, 1173–1175 (2004).
[CrossRef]

O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233, 225–230 (2004).
[CrossRef]

A. Ciattoni and C. Palma, “Anisotropic beam spreading in uniaxial crystals,” Opt. Commun. 231, 79–92 (2004).
[CrossRef]

2003 (3)

Y. Cai, D. Ge, and Q. Lin, “Fractional Fourier transform for partially coherent and partially polarized Gaussian–Schell-model beams,” J. Opt. A 5, 453–459 (2003).
[CrossRef]

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

A. Ciattoni and C. Palma, “Optical propagation in uniaxial crystals orthogonal to the optical axis: paraxial theory and beyond,” J. Opt. Soc. Am. A 20, 2163–2171 (2003).
[CrossRef]

2002 (3)

A. Ciattoni, G. Cincotti, and C. Palma, “Propagation of cylindrically symmetric fields in uniaxial crystals,” J. Opt. Soc. Am. A 19, 792–796 (2002).
[CrossRef]

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208, 9–16 (2002).
[CrossRef]

T. Setälä, A. Shevchenko, M. Kaivola, and A. Friberg, “Degree of polarization for optical near fields,” Phys. Rev. E 66, 016615 (2002).
[CrossRef]

2001 (2)

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]

J. J. Stamnes and V. Dhayalan, “Transmission of a two-dimensional Gaussian beam into a uniaxial crystal,” J. Opt. Soc. Am. A 18, 1662–1669 (2001).
[CrossRef]

2000 (2)

1999 (1)

1998 (1)

1995 (1)

1994 (1)

1993 (1)

1992 (1)

H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron. 24, S1027–S1049 (1992).
[CrossRef]

1991 (1)

F. Gori, M. Santarsiero, and A. Sona, “The change of width for a partially coherent beam on paraxial propagation,” Opt. Commun. 82, 197–203 (1991).
[CrossRef]

1990 (1)

A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2–14 (1990).

Agrawal, G. P.

Arias, M.

Baykal, Y.

Borghi, R.

Brosseau, C.

C. Brosseau, Fundamentals of Polarized Light: A Statistical Approach (Wiley, 1998).

Cai, Y.

S. Zhu, L. Liu, Y. Chen, and Y. Cai, “State of polarization and propagation factor of a stochastic electromagnetic beam in a gradient-index fiber,” J. Opt. Soc. Am. A 30, 2306–2313 (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]

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]

L. Zhang and Y. Cai, “Statistical properties of a nonparaxial Gaussian Schell-model beam in a uniaxial crystal,” Opt. Express 19, 13312–13325 (2011).
[CrossRef]

G. Wu and Y. Cai, “Modulation of spectral intensity, polarization and coherence of a stochastic electromagnetic beam,” Opt. Express 19, 8700–8714 (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]

L. Zhang and Y. Cai, “Evolution properties of a twisted Gaussian Schell-model beam in a uniaxial crystal,” J. Mod. Opt. 58, 1224–1232 (2011).
[CrossRef]

C. Zhao and Y. Cai, “Paraxial propagation of Lorentz and Lorentz–Gauss beams in uniaxial crystals orthogonal to the optical axis,” J. Mod. Opt. 57, 375–384 (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]

M. Yao, Y. Cai, O. Korotkova, Q. Lin, and Z. Wang, “Spatio-temporal coupling of random electromagnetic pulses interacting with reflecting gratings,” Opt. Express 18, 22503–22514 (2010).
[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]

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

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]

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]

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, D. Ge, and Q. Lin, “Fractional Fourier transform for partially coherent and partially polarized Gaussian–Schell-model beams,” J. Opt. A 5, 453–459 (2003).
[CrossRef]

Chen, C.

D. Deng, C. Chen, X. Zhao, and H. Li, “Propagation of an Airy vortex beam in uniaxial crystals,” Appl. Phys. B 110, 433–436 (2013).
[CrossRef]

Chen, R.

Chen, Y.

Chu, X.

Ciattoni, A.

Cincotti, G.

Deng, D.

D. Deng, C. Chen, X. Zhao, and H. Li, “Propagation of an Airy vortex beam in uniaxial crystals,” Appl. Phys. B 110, 433–436 (2013).
[CrossRef]

Dhayalan, V.

Dogariu, A.

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, “Degree of polarization of statistically stationary electromagnetic fields,” Opt. Commun. 248, 333–337 (2005).
[CrossRef]

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]

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]

Du, X.

X. Du and D. Zhao, “Propagation of uniformly polarized stochastic electromagnetic beams in uniaxial crystals,” J. Electromagn. Waves Appl. 24, 971–981 (2010).
[CrossRef]

Ellis, J.

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, “Degree of polarization of statistically stationary electromagnetic fields,” Opt. Commun. 248, 333–337 (2005).
[CrossRef]

Eyyuboglu, H. T.

Friberg, A.

T. Setälä, A. Shevchenko, M. Kaivola, and A. Friberg, “Degree of polarization for optical near fields,” Phys. Rev. E 66, 016615 (2002).
[CrossRef]

Friberg, A. T.

Gbur, G.

G. Gbur and E. Wolf, “The Rayleigh range of Gaussian Schell-model beams,” J. Mod. Opt. 48, 1735–1741 (2011).

Ge, D.

Y. Cai, D. Ge, and Q. Lin, “Fractional Fourier transform for partially coherent and partially polarized Gaussian–Schell-model beams,” J. Opt. A 5, 453–459 (2003).
[CrossRef]

Gori, F.

F. Gori, M. Santarsiero, R. Borghi, and V. Ramírez-Sánchez, “Realizability condition for electromagnetic Schell-model sources,” J. Opt. Soc. Am. A 25, 1016–1021 (2008).
[CrossRef]

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208, 9–16 (2002).
[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]

F. Gori, M. Santarsiero, R. Borghi, and G. Piquero, “Use of the van Cittert–Zernike theorem for partially polarized sources,” Opt. Lett. 25, 1291–1293 (2000).
[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]

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

F. Gori, M. Santarsiero, and A. Sona, “The change of width for a partially coherent beam on paraxial propagation,” Opt. Commun. 82, 197–203 (1991).
[CrossRef]

James, D. F. V.

Ji, X.

X. Ji, H. T. Eyyuboğlu, and Y. Baykal, “Influence of turbulence on the effective radius of curvature of radial Gaussian array beams,” Opt. Express 18, 6922–6928 (2010).
[CrossRef]

H. T. Eyyuboğlu, Y. Baykal, and X. Ji, “Radius of curvature variations for annular, dark hollow and flat topped beams in turbulence,” Appl. Phys. B 99, 801–807 (2010).
[CrossRef]

Kaivola, M.

T. Setälä, A. Shevchenko, M. Kaivola, and A. Friberg, “Degree of polarization for optical near fields,” Phys. Rev. E 66, 016615 (2002).
[CrossRef]

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]

M. Yao, Y. Cai, O. Korotkova, Q. Lin, and Z. Wang, “Spatio-temporal coupling of random electromagnetic pulses interacting with reflecting gratings,” Opt. Express 18, 22503–22514 (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]

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

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, 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, 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]

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 and E. Wolf, “Generalized Stokes parameters of random electromagnetic beams,” Opt. Lett. 30, 198–200 (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]

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]

H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249, 379–385 (2005).
[CrossRef]

O. Korotkova, M. Salem, and E. Wolf, “Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source,” Opt. Lett. 29, 1173–1175 (2004).
[CrossRef]

O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233, 225–230 (2004).
[CrossRef]

Li, H.

D. Deng, C. Chen, X. Zhao, and H. Li, “Propagation of an Airy vortex beam in uniaxial crystals,” Appl. Phys. B 110, 433–436 (2013).
[CrossRef]

Liang, C.

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.

M. Yao, Y. Cai, O. Korotkova, Q. Lin, and Z. Wang, “Spatio-temporal coupling of random electromagnetic pulses interacting with reflecting gratings,” Opt. Express 18, 22503–22514 (2010).
[CrossRef]

Y. Cai, D. Ge, and Q. Lin, “Fractional Fourier transform for partially coherent and partially polarized Gaussian–Schell-model beams,” J. Opt. A 5, 453–459 (2003).
[CrossRef]

Liu, D.

D. Liu and Z. Zhou, “Propagation of partially polarized, partially coherent beams in uniaxially crystals orthogonal to the optical axis,” Eur. Phys. J. D 54, 95–101 (2009).
[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]

Liu, L.

Liu, X.

Mandel, L.

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

Martinez-Herrero, R.

Mejias, P. M.

Mondello, A.

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208, 9–16 (2002).
[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]

Palma, C.

Piquero, G.

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208, 9–16 (2002).
[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]

F. Gori, M. Santarsiero, R. Borghi, and G. Piquero, “Use of the van Cittert–Zernike theorem for partially polarized sources,” Opt. Lett. 25, 1291–1293 (2000).
[CrossRef]

Ponomarenko, S.

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, “Degree of polarization of statistically stationary electromagnetic fields,” Opt. Commun. 248, 333–337 (2005).
[CrossRef]

Qu, J.

Ramírez-Sánchez, V.

Romanini, P.

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208, 9–16 (2002).
[CrossRef]

Roychowdhury, H.

H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249, 379–385 (2005).
[CrossRef]

Saastamoinen, T.

Salem, M.

Santarsiero, M.

F. Gori, M. Santarsiero, R. Borghi, and V. Ramírez-Sánchez, “Realizability condition for electromagnetic Schell-model sources,” J. Opt. Soc. Am. A 25, 1016–1021 (2008).
[CrossRef]

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208, 9–16 (2002).
[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]

F. Gori, M. Santarsiero, R. Borghi, and G. Piquero, “Use of the van Cittert–Zernike theorem for partially polarized sources,” Opt. Lett. 25, 1291–1293 (2000).
[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]

F. Gori, M. Santarsiero, and A. Sona, “The change of width for a partially coherent beam on paraxial propagation,” Opt. Commun. 82, 197–203 (1991).
[CrossRef]

Setälä, T.

T. Saastamoinen, J. Turunen, J. Tervo, T. Setälä, and A. T. Friberg, “Electromagnetic coherence theory of laser resonator modes,” J. Opt. Soc. Am. A 22, 103–108 (2005).
[CrossRef]

T. Setälä, A. Shevchenko, M. Kaivola, and A. Friberg, “Degree of polarization for optical near fields,” Phys. Rev. E 66, 016615 (2002).
[CrossRef]

Shevchenko, A.

T. Setälä, A. Shevchenko, M. Kaivola, and A. Friberg, “Degree of polarization for optical near fields,” Phys. Rev. E 66, 016615 (2002).
[CrossRef]

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).
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A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2–14 (1990).

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]

Sona, A.

F. Gori, M. Santarsiero, and A. Sona, “The change of width for a partially coherent beam on paraxial propagation,” Opt. Commun. 82, 197–203 (1991).
[CrossRef]

Stamnes, J. J.

Tang, B.

Tervo, J.

Tong, Z.

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

Turunen, J.

Vahimaa, P.

Wang, F.

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

Wang, Z.

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).
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H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron. 24, S1027–S1049 (1992).
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G. Gbur and E. Wolf, “The Rayleigh range of Gaussian Schell-model beams,” J. Mod. Opt. 48, 1735–1741 (2011).

M. Salem and E. Wolf, “Coherence-induced polarization changes in light beams,” Opt. Lett. 33, 1180–1182 (2008).
[CrossRef]

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

E. Wolf, “Coherence and polarization properties of electromagnetic laser modes,” Opt. Commun. 265, 60–62 (2006).
[CrossRef]

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, “Degree of polarization of statistically stationary electromagnetic fields,” Opt. Commun. 248, 333–337 (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]

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

O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233, 225–230 (2004).
[CrossRef]

O. Korotkova, M. Salem, and E. Wolf, “Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source,” Opt. Lett. 29, 1173–1175 (2004).
[CrossRef]

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003).
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G. P. Agrawal and E. Wolf, “Propagation-induced polarization changes in partially coherent optical beams,” J. Opt. Soc. Am. A 17, 2019–2023 (2000).
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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, G.

Yao, M.

Yuan, Y.

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, 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]

Zhang, L.

L. Zhang and Y. Cai, “Evolution properties of a twisted Gaussian Schell-model beam in a uniaxial crystal,” J. Mod. Opt. 58, 1224–1232 (2011).
[CrossRef]

L. Zhang and Y. Cai, “Statistical properties of a nonparaxial Gaussian Schell-model beam in a uniaxial crystal,” Opt. Express 19, 13312–13325 (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]

Zhao, C.

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 and Y. Cai, “Paraxial propagation of Lorentz and Lorentz–Gauss beams in uniaxial crystals orthogonal to the optical axis,” J. Mod. Opt. 57, 375–384 (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]

Zhao, D.

X. Du and D. Zhao, “Propagation of uniformly polarized stochastic electromagnetic beams in uniaxial crystals,” J. Electromagn. Waves Appl. 24, 971–981 (2010).
[CrossRef]

Zhao, X.

D. Deng, C. Chen, X. Zhao, and H. Li, “Propagation of an Airy vortex beam in uniaxial crystals,” Appl. Phys. B 110, 433–436 (2013).
[CrossRef]

Zhou, G.

Zhou, Z.

D. Liu and Z. Zhou, “Propagation of partially polarized, partially coherent beams in uniaxially crystals orthogonal to the optical axis,” Eur. Phys. J. D 54, 95–101 (2009).
[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]

Zhu, S.

Appl. Phys. B (5)

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]

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]

D. Deng, C. Chen, X. Zhao, and H. Li, “Propagation of an Airy vortex beam in uniaxial crystals,” Appl. Phys. B 110, 433–436 (2013).
[CrossRef]

H. T. Eyyuboğlu, Y. Baykal, and X. Ji, “Radius of curvature variations for annular, dark hollow and flat topped beams in turbulence,” Appl. Phys. B 99, 801–807 (2010).
[CrossRef]

Eur. Phys. J. D (1)

D. Liu and Z. Zhou, “Propagation of partially polarized, partially coherent beams in uniaxially crystals orthogonal to the optical axis,” Eur. Phys. J. D 54, 95–101 (2009).
[CrossRef]

J. Electromagn. Waves Appl. (1)

X. Du and D. Zhao, “Propagation of uniformly polarized stochastic electromagnetic beams in uniaxial crystals,” J. Electromagn. Waves Appl. 24, 971–981 (2010).
[CrossRef]

J. Mod. Opt. (3)

L. Zhang and Y. Cai, “Evolution properties of a twisted Gaussian Schell-model beam in a uniaxial crystal,” J. Mod. Opt. 58, 1224–1232 (2011).
[CrossRef]

C. Zhao and Y. Cai, “Paraxial propagation of Lorentz and Lorentz–Gauss beams in uniaxial crystals orthogonal to the optical axis,” J. Mod. Opt. 57, 375–384 (2010).
[CrossRef]

G. Gbur and E. Wolf, “The Rayleigh range of Gaussian Schell-model beams,” J. Mod. Opt. 48, 1735–1741 (2011).

J. Opt. A (4)

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]

Y. Cai, D. Ge, and Q. Lin, “Fractional Fourier transform for partially coherent and partially polarized Gaussian–Schell-model beams,” J. Opt. A 5, 453–459 (2003).
[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]

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

J. Opt. Soc. Am. A (13)

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

J. J. Stamnes and V. Dhayalan, “Transmission of a two-dimensional Gaussian beam into a uniaxial crystal,” J. Opt. Soc. Am. A 18, 1662–1669 (2001).
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A. Ciattoni, G. Cincotti, and C. Palma, “Propagation of cylindrically symmetric fields in uniaxial crystals,” J. Opt. Soc. Am. A 19, 792–796 (2002).
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A. Ciattoni and C. Palma, “Optical propagation in uniaxial crystals orthogonal to the optical axis: paraxial theory and beyond,” J. Opt. Soc. Am. A 20, 2163–2171 (2003).
[CrossRef]

G. P. Agrawal and E. Wolf, “Propagation-induced polarization changes in partially coherent optical beams,” J. Opt. Soc. Am. A 17, 2019–2023 (2000).
[CrossRef]

T. Saastamoinen, J. Turunen, J. Tervo, T. Setälä, and A. T. Friberg, “Electromagnetic coherence theory of laser resonator modes,” J. Opt. Soc. Am. A 22, 103–108 (2005).
[CrossRef]

M. Salem and G. P. Agrawal, “Effects of coherence and polarization on the coupling of stochastic electromagnetic beams into optical fibers,” J. Opt. Soc. Am. A 26, 2452–2458 (2009).
[CrossRef]

B. Tang, “Hermite–cosine–Gaussian beams propagating in uniaxial crystals orthogonal to the optical axis,” J. Opt. Soc. Am. A 26, 2480–2487 (2009).
[CrossRef]

F. Gori, M. Santarsiero, R. Borghi, and V. Ramírez-Sánchez, “Realizability condition for electromagnetic Schell-model sources,” J. Opt. Soc. Am. A 25, 1016–1021 (2008).
[CrossRef]

M. Salem and G. P. Agrawal, “Effects of coherence and polarization on the coupling of stochastic electromagnetic beams into optical fibers: errata,” J. Opt. Soc. Am. A 28, 307 (2011).
[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]

S. Zhu, L. Liu, Y. Chen, and Y. Cai, “State of polarization and propagation factor of a stochastic electromagnetic beam in a gradient-index fiber,” J. Opt. Soc. Am. A 30, 2306–2313 (2013).
[CrossRef]

Opt. Commun. (11)

F. Gori, M. Santarsiero, and A. Sona, “The change of width for a partially coherent beam on paraxial propagation,” Opt. Commun. 82, 197–203 (1991).
[CrossRef]

A. Ciattoni and C. Palma, “Anisotropic beam spreading in uniaxial crystals,” Opt. Commun. 231, 79–92 (2004).
[CrossRef]

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, “Degree of polarization of statistically stationary electromagnetic fields,” Opt. Commun. 248, 333–337 (2005).
[CrossRef]

H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249, 379–385 (2005).
[CrossRef]

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208, 9–16 (2002).
[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, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233, 225–230 (2004).
[CrossRef]

E. Wolf, “Coherence and polarization properties of electromagnetic laser modes,” Opt. Commun. 265, 60–62 (2006).
[CrossRef]

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

Opt. Express (11)

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]

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[CrossRef]

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