Abstract

On the basis of the unified theory of coherence and polarization, we investigate the behavior of the state of polarization of a stochastic electromagnetic beam in a Gaussian cavity. Formulations both in terms of Stokes parameters and in terms of polarization ellipse are given. We show that the state of polarization stabilizes, except in the case of a lossless cavity, after several passages between the mirrors, exhibiting monotonic or oscillatory behavior depending on the parameters of the resonator. We also find that an initially (spatially) uniformly polarized beam remains nonuniformly polarized even for a large number of passages between the mirrors of the cavity.

© 2008 Optical Society of America

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References

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  1. A. G. Fox and T. Li, “Resonate modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453-488 (1961).
  2. G. D. Boyd and J. P. Gordon, “Confocal multimode resonator for millimeter through optical wavelength masers,” Bell Syst. Tech. J. 40, 489-508 (1961).
  3. E. Wolf, “Spatial coherence of resonant modes in a maser interferometer,” Phys. Lett. 3, 166-168 (1963).
    [CrossRef]
  4. E. Wolf and G. S. Agarwal, “Coherence theory of laser resonator modes,” J. Opt. Soc. Am. A 1, 541-546 (1984).
    [CrossRef]
  5. F. Gori, “Propagation of the mutual intensity through a periodic structure,” Atti Fond. Giorgio Ronchi 35, 434-447 (1980).
  6. P. DeSantis, A. Mascello, C. Palma, and M. R. Perrone, “Coherence growth of laser radiation in Gaussian cavities,” IEEE J. Quantum Electron. 32, 802-812 (1996).
    [CrossRef]
  7. C. Palma, G. Cardone, and G. Cincotti, “Spectral changes in Gaussian-cavity lasers,” IEEE J. Quantum Electron. 34, 1082-1088 (1998).
    [CrossRef]
  8. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge U. Press, 2007).
  9. F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3, 1-9 (2001).
    [CrossRef]
  10. O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of partially coherent beams propagating through atmospheric turbulence,” Opt. Commun. 233, 225-230 (2004).
    [CrossRef]
  11. O. Korotkova and E. Wolf, “Effects of linear non-image forming devices on coherence and polarization properties of random electromagnetic beams. Part I. General theory,” J. Mod. Opt. 52, 2659-2671 (2005).
    [CrossRef]
  12. W. Gao, “Changes of polarization of light beams on propagation through tissue,” Opt. Commun. 260, 749-754 (2006).
    [CrossRef]
  13. X. Du, D. Zhao, and O. Korotkova, “Changes in the degree of polarization of a random electromagnetic beam propagating through an apertured optical system,” Phys. Lett. A 372, 4135-4140 (2008).
    [CrossRef]
  14. E. Wolf, “Coherence and polarization properties of electromagnetic laser modes,” Opt. Commun. 265, 60-62 (2006).
    [CrossRef]
  15. T. Saastamoinen, J. Turunen, J. Tervo, T. Setala, and A. T. Friberg, “Electromagnetic coherence theory of laser resonator modes,” J. Opt. Soc. Am. A 22, 103-108 (2005).
    [CrossRef]
  16. Y. Min, 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]
  17. G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Philos. Soc. 9, 399-416 (1852).
  18. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
  19. 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]
  20. H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550-1567 (1966).
    [CrossRef] [PubMed]
  21. 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] [PubMed]
  22. H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249, 379-385 (2005).
    [CrossRef]
  23. W. Casperson and S. D. Lunnam, “Gaussian modes in high loss laser resonators,” Appl. Opt. 14, 1193-1199 (1975).
    [CrossRef] [PubMed]
  24. O. Korotkova and E. Wolf, “Generalized Stokes parameters of random electromagnetic beams,” Opt. Lett. 30, 198-200 (2005).
    [CrossRef] [PubMed]
  25. Q. Lin and Y. Cai, “Tensor ABCD law for partially coherent twisted anisotropic Gaussian Schell-model beams,” Opt. Lett. 27, 216-218 (2002).
    [CrossRef]
  26. Y. Cai, D. Ge, and Q. Lin, “Fractional Fourier transform for partially coherent and partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 5, 453-459 (2003).
    [CrossRef]
  27. D. Ge, Y. Cai, and Q. Lin, “Propagation of partially polarized Gaussian Schell-model beams through aligned and misaligned optical system,” Chin. Phys. 14, 128-132 (2005).
    [CrossRef]
  28. R. K. Luneburg, Mathematical Theory of Optics (University of California Press, 1964), Chap. 4.

2008 (2)

X. Du, D. Zhao, and O. Korotkova, “Changes in the degree of polarization of a random electromagnetic beam propagating through an apertured optical system,” Phys. Lett. A 372, 4135-4140 (2008).
[CrossRef]

Y. Min, 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]

2006 (2)

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

W. Gao, “Changes of polarization of light beams on propagation through tissue,” Opt. Commun. 260, 749-754 (2006).
[CrossRef]

2005 (6)

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

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

D. Ge, Y. Cai, and Q. Lin, “Propagation of partially polarized Gaussian Schell-model beams through aligned and misaligned optical system,” Chin. Phys. 14, 128-132 (2005).
[CrossRef]

T. Saastamoinen, J. Turunen, J. Tervo, T. Setala, 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, “Effects of linear non-image forming devices on coherence and polarization properties of random electromagnetic beams. Part I. General theory,” J. Mod. Opt. 52, 2659-2671 (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]

2004 (2)

O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of partially coherent 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] [PubMed]

2003 (1)

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

2002 (1)

2001 (1)

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

1998 (1)

C. Palma, G. Cardone, and G. Cincotti, “Spectral changes in Gaussian-cavity lasers,” IEEE J. Quantum Electron. 34, 1082-1088 (1998).
[CrossRef]

1996 (1)

P. DeSantis, A. Mascello, C. Palma, and M. R. Perrone, “Coherence growth of laser radiation in Gaussian cavities,” IEEE J. Quantum Electron. 32, 802-812 (1996).
[CrossRef]

1984 (1)

1980 (1)

F. Gori, “Propagation of the mutual intensity through a periodic structure,” Atti Fond. Giorgio Ronchi 35, 434-447 (1980).

1975 (1)

1966 (1)

1963 (1)

E. Wolf, “Spatial coherence of resonant modes in a maser interferometer,” Phys. Lett. 3, 166-168 (1963).
[CrossRef]

1961 (2)

A. G. Fox and T. Li, “Resonate modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453-488 (1961).

G. D. Boyd and J. P. Gordon, “Confocal multimode resonator for millimeter through optical wavelength masers,” Bell Syst. Tech. J. 40, 489-508 (1961).

1852 (1)

G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Philos. Soc. 9, 399-416 (1852).

Agarwal, G. S.

Baykal, Y.

Borghi, R.

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

Born, M.

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

Boyd, G. D.

G. D. Boyd and J. P. Gordon, “Confocal multimode resonator for millimeter through optical wavelength masers,” Bell Syst. Tech. J. 40, 489-508 (1961).

Cai, Y.

Y. Min, 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]

D. Ge, Y. Cai, and Q. Lin, “Propagation of partially polarized Gaussian Schell-model beams through aligned and misaligned optical system,” Chin. Phys. 14, 128-132 (2005).
[CrossRef]

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

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

Cardone, G.

C. Palma, G. Cardone, and G. Cincotti, “Spectral changes in Gaussian-cavity lasers,” IEEE J. Quantum Electron. 34, 1082-1088 (1998).
[CrossRef]

Casperson, W.

Cincotti, G.

C. Palma, G. Cardone, and G. Cincotti, “Spectral changes in Gaussian-cavity lasers,” IEEE J. Quantum Electron. 34, 1082-1088 (1998).
[CrossRef]

DeSantis, P.

P. DeSantis, A. Mascello, C. Palma, and M. R. Perrone, “Coherence growth of laser radiation in Gaussian cavities,” IEEE J. Quantum Electron. 32, 802-812 (1996).
[CrossRef]

Du, X.

X. Du, D. Zhao, and O. Korotkova, “Changes in the degree of polarization of a random electromagnetic beam propagating through an apertured optical system,” Phys. Lett. A 372, 4135-4140 (2008).
[CrossRef]

Eyyuboglu, H. T.

Fox, A. G.

A. G. Fox and T. Li, “Resonate modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453-488 (1961).

Friberg, A. T.

Gao, W.

W. Gao, “Changes of polarization of light beams on propagation through tissue,” Opt. Commun. 260, 749-754 (2006).
[CrossRef]

Ge, D.

D. Ge, Y. Cai, and Q. Lin, “Propagation of partially polarized Gaussian Schell-model beams through aligned and misaligned optical system,” Chin. Phys. 14, 128-132 (2005).
[CrossRef]

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

Gordon, J. P.

G. D. Boyd and J. P. Gordon, “Confocal multimode resonator for millimeter through optical wavelength masers,” Bell Syst. Tech. J. 40, 489-508 (1961).

Gori, F.

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

F. Gori, “Propagation of the mutual intensity through a periodic structure,” Atti Fond. Giorgio Ronchi 35, 434-447 (1980).

Kogelnik, H.

Korotkova, O.

Y. Min, 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]

X. Du, D. Zhao, and O. Korotkova, “Changes in the degree of polarization of a random electromagnetic beam propagating through an apertured optical system,” Phys. Lett. A 372, 4135-4140 (2008).
[CrossRef]

O. Korotkova and E. Wolf, “Effects of linear non-image forming devices on coherence and polarization properties of random electromagnetic beams. Part I. General theory,” J. Mod. Opt. 52, 2659-2671 (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 and E. Wolf, “Generalized Stokes parameters of random electromagnetic beams,” Opt. Lett. 30, 198-200 (2005).
[CrossRef] [PubMed]

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] [PubMed]

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

Li, T.

H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550-1567 (1966).
[CrossRef] [PubMed]

A. G. Fox and T. Li, “Resonate modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453-488 (1961).

Lin, Q.

D. Ge, Y. Cai, and Q. Lin, “Propagation of partially polarized Gaussian Schell-model beams through aligned and misaligned optical system,” Chin. Phys. 14, 128-132 (2005).
[CrossRef]

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

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

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, 1964), Chap. 4.

Lunnam, S. D.

Mascello, A.

P. DeSantis, A. Mascello, C. Palma, and M. R. Perrone, “Coherence growth of laser radiation in Gaussian cavities,” IEEE J. Quantum Electron. 32, 802-812 (1996).
[CrossRef]

Min, Y.

Mondello, A.

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

Palma, C.

C. Palma, G. Cardone, and G. Cincotti, “Spectral changes in Gaussian-cavity lasers,” IEEE J. Quantum Electron. 34, 1082-1088 (1998).
[CrossRef]

P. DeSantis, A. Mascello, C. Palma, and M. R. Perrone, “Coherence growth of laser radiation in Gaussian cavities,” IEEE J. Quantum Electron. 32, 802-812 (1996).
[CrossRef]

Perrone, M. R.

P. DeSantis, A. Mascello, C. Palma, and M. R. Perrone, “Coherence growth of laser radiation in Gaussian cavities,” IEEE J. Quantum Electron. 32, 802-812 (1996).
[CrossRef]

Piquero, G.

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

O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of partially coherent 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] [PubMed]

Santarsiero, M.

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

Setala, T.

Simon, R.

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

Stokes, G. G.

G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Philos. Soc. 9, 399-416 (1852).

Tervo, J.

Turunen, J.

Wolf, E.

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

O. Korotkova and E. Wolf, “Effects of linear non-image forming devices on coherence and polarization properties of random electromagnetic beams. Part I. General theory,” J. Mod. Opt. 52, 2659-2671 (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]

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

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] [PubMed]

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

E. Wolf and G. S. Agarwal, “Coherence theory of laser resonator modes,” J. Opt. Soc. Am. A 1, 541-546 (1984).
[CrossRef]

E. Wolf, “Spatial coherence of resonant modes in a maser interferometer,” Phys. Lett. 3, 166-168 (1963).
[CrossRef]

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

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

Zhao, D.

X. Du, D. Zhao, and O. Korotkova, “Changes in the degree of polarization of a random electromagnetic beam propagating through an apertured optical system,” Phys. Lett. A 372, 4135-4140 (2008).
[CrossRef]

Appl. Opt. (2)

Atti Fond. Giorgio Ronchi (1)

F. Gori, “Propagation of the mutual intensity through a periodic structure,” Atti Fond. Giorgio Ronchi 35, 434-447 (1980).

Bell Syst. Tech. J. (2)

A. G. Fox and T. Li, “Resonate modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453-488 (1961).

G. D. Boyd and J. P. Gordon, “Confocal multimode resonator for millimeter through optical wavelength masers,” Bell Syst. Tech. J. 40, 489-508 (1961).

Chin. Phys. (1)

D. Ge, Y. Cai, and Q. Lin, “Propagation of partially polarized Gaussian Schell-model beams through aligned and misaligned optical system,” Chin. Phys. 14, 128-132 (2005).
[CrossRef]

IEEE J. Quantum Electron. (2)

P. DeSantis, A. Mascello, C. Palma, and M. R. Perrone, “Coherence growth of laser radiation in Gaussian cavities,” IEEE J. Quantum Electron. 32, 802-812 (1996).
[CrossRef]

C. Palma, G. Cardone, and G. Cincotti, “Spectral changes in Gaussian-cavity lasers,” IEEE J. Quantum Electron. 34, 1082-1088 (1998).
[CrossRef]

J. Mod. Opt. (1)

O. Korotkova and E. Wolf, “Effects of linear non-image forming devices on coherence and polarization properties of random electromagnetic beams. Part I. General theory,” J. Mod. Opt. 52, 2659-2671 (2005).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (2)

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

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

J. Opt. Soc. Am. A (2)

Opt. Commun. (5)

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

W. Gao, “Changes of polarization of light beams on propagation through tissue,” Opt. Commun. 260, 749-754 (2006).
[CrossRef]

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

Opt. Lett. (4)

Phys. Lett. (1)

E. Wolf, “Spatial coherence of resonant modes in a maser interferometer,” Phys. Lett. 3, 166-168 (1963).
[CrossRef]

Phys. Lett. A (1)

X. Du, D. Zhao, and O. Korotkova, “Changes in the degree of polarization of a random electromagnetic beam propagating through an apertured optical system,” Phys. Lett. A 372, 4135-4140 (2008).
[CrossRef]

Trans. Cambridge Philos. Soc. (1)

G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Philos. Soc. 9, 399-416 (1852).

Other (3)

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

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

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, 1964), Chap. 4.

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Figures (15)

Fig. 1
Fig. 1

Schematic diagram of a Gaussian cavity and its equivalent (unfolded) version.

Fig. 2
Fig. 2

The (on-axis) normalized Stokes parameters versus N for different values of cavity parameter g with δ x x = 0.15 mm and η = 0.8 mm .

Fig. 3
Fig. 3

The (on-axis) normalized Stokes parameters versus N for different values of the mirror spot size η in a Gaussian plane-parallel cavity ( g = 1 ) with δ x x = 0.15 mm .

Fig. 4
Fig. 4

Degree of ellipticity (on-axis) versus N for different values of cavity parameter g and the source correlation coefficients with η = 0.8 mm : (a) δ x x = 0.15 mm , (b) δ x x = 0.15 mm , (c) g = 0.5 , (d) g = 1.2 .

Fig. 5
Fig. 5

Orientation angle θ (on-axis) versus N for different values of cavity parameter g and the source correlation coefficients with η = 0.8 mm ; (a) δ x x = 0.15 mm , (b) δ x x = 0.15 mm , (c) g = 0.5 , (d) g = 1.2 .

Fig. 6
Fig. 6

Degree of ellipticity (on-axis) versus N for different values of mirror spot size η in a Gaussian plane-parallel cavity ( g = 1 ) with δ x x = 0.15 mm .

Fig. 7
Fig. 7

Orientation angle θ (on-axis) versus N for different values of mirror spot size η in a Gaussian plane-parallel cavity ( g = 1 ) with δ x x = 0.15 mm .

Fig. 8
Fig. 8

Degree of ellipticity (on-axis) versus N for different values of g in a lossless cavity ( η ) with δ x x = 0.15 mm .

Fig. 9
Fig. 9

Orientation angle θ (on-axis) versus N for different values of g in a lossless cavity ( η ) with δ x x = 0.15 mm .

Fig. 10
Fig. 10

Degree of ellipticity versus a transverse dimension x for different values of the mirror spot size η and the source correlation coefficients in a Gaussian plane-parallel cavity ( g = 1 ) with N = 30 .

Fig. 11
Fig. 11

Orientation angle θ versus a transverse dimension x for different values of the mirror spot size η and the source correlation coefficients in a Gaussian plane-parallel cavity ( g = 1 ) with N = 30 .

Fig. 12
Fig. 12

Spectral density S 0 of the beam versus a transverse dimension x for different values of the mirror spot size η and the source correlation coefficients in a Gaussian plane-parallel cavity ( g = 1 ) with N = 30 .

Fig. 13
Fig. 13

Spatial distribution of the degree of ellipticity of a typical EGSM beam for N = 30 and g = 1 for two different values of the mirror spot size η.

Fig. 14
Fig. 14

Spatial distribution of the orientation angle of a typical EGSM beam for N = 30 and g = 1 for two different values of the mirror spot size η.

Fig. 15
Fig. 15

Spatial distribution of spectral density S 0 of a typical EGSM beam for N = 30 and g = 1 for two different values of the mirror spot size η.

Equations (32)

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W α β ( r ̃ ) = A α A β B α β exp [ i k 2 r ̃ T M 0 α β 1 r ̃ ] , ( α = x , y ; β = x , y ) ,
M 0 α β 1 = ( 1 i k ( 1 2 σ a 2 + 1 δ α β 2 ) I i k δ α β 2 I i k δ α β 2 I 1 i k ( 1 2 σ β 2 + 1 δ α β 2 ) I ) ,
W α β ( ρ ̃ ) = A α A β B α β [ det ( A ¯ + B ¯ M 0 α β 1 ) ] 1 2 exp [ i k 2 ρ ̃ T M 1 α β 1 ρ ̃ ] , ( α = x , y ; β = x , y ) ,
M 1 α β 1 = ( C ¯ + D ¯ M 0 α β 1 ) ( A ¯ + B ¯ M 0 α β 1 ) 1 ,
A ¯ = ( A 0 I 0 I A * ) , B ¯ = ( B 0 I 0 I B * ) ,
C ¯ = ( C 0 I 0 I C * ) , D ¯ = ( D 0 I 0 I D * ) ,
( A B C D ) = ( A 1 B 1 C 1 D 1 ) N ,
( A 1 B 1 C 1 D 1 ) = ( I L I ( 2 R i λ π η 2 ) I ( 1 2 L R i λ L π η 2 ) I ) ,
S 0 ( ρ ) = W x x ( ρ ) + W y y ( ρ ) ,
S 1 ( ρ ) = W x x ( ρ ) W y y ( ρ ) ,
S 2 ( ρ ) = W x y ( ρ ) + W y x ( ρ ) ,
S 3 ( ρ ) = i [ W y x ( ρ ) W x y ( ρ ) ] .
W ( ρ ) = W ( u ) ( ρ ) + W ( p ) ( ρ ) ,
W ( u ) ( ρ ) = ( A ( ρ ) 0 0 A ( ρ ) ) , W ( p ) ( ρ ) = ( B ( ρ ) D ( ρ ) D * ( ρ ) C ( ρ ) )
A ( ρ ) = 1 2 [ W x x ( ρ ) + W y y ( ρ ) + ( W x x ( ρ ) W y y ( ρ ) ) 2 + 4 W x y ( ρ ) 2 ] ,
B ( ρ ) = 1 2 [ W x x ( ρ ) W y y ( ρ ) + ( W x x ( ρ ) W y y ( ρ ) ) 2 + 4 W x y ( ρ ) 2 ] ,
C ( ρ ) = 1 2 [ W y y ( ρ ) W x x ( ρ ) + ( W x x ( ρ ) W y y ( ρ ) ) 2 + 4 W x y ( ρ ) 2 ] ,
D ( ρ ) = W x y .
C ( ρ ) E x ( r ) 2 ( ρ ) 2 Re D ( ρ ) E x ( r ) ( ρ ) E y ( r ) ( ρ ) + B ( ρ ) E y ( r ) 2 ( ρ )
= [ Im D ( ρ ) ] 2 ,
A 1 , 2 ( ρ ) = 1 2 [ ( W x x ( ρ ) W y y ( ρ ) ) 2 + 4 W x y ( ρ ) 2 ± ( W x x ( ρ ) W y y ( ρ ) ) 2 + 4 [ Re W x y ( ρ ) ] 2 ] 1 2 ,
ε ( ρ ) = A 2 ( ρ ) A 1 ( ρ ) ,
θ ( ρ ) = 1 2 arctan ( 2 Re W x y ( ρ ) W x x ( ρ ) W y y ( ρ ) ) .
W α β ( ρ ̃ ) = k 2 4 π 2 [ det ( B ¯ ) ] 1 2 W α β ( r ̃ ) exp [ i k 2 ( r ̃ T B ¯ 1 A ¯ r ̃ 2 r ̃ T B ¯ 1 ρ ̃ + ρ ̃ T D ¯ B ¯ 1 ρ ̃ ) ] d r ̃ ,
( B ¯ 1 A ¯ ) T = B ¯ 1 A ¯ , ( D ¯ B ¯ 1 ) T = D ¯ B ¯ 1 ,
C ¯ D ¯ B ¯ 1 A ¯ = ( B ¯ 1 ) T .
W α β ( ρ ̃ ) = k 2 A α A β B α β 4 π 2 [ det ( B ¯ ) ] 1 2 exp [ i k 2 ρ ̃ T D ¯ B ¯ 1 ρ ̃ + i k 2 ρ ̃ T B ¯ 1 T ( M 0 α β 1 + B ¯ 1 A ¯ ) 1 B ¯ 1 T ρ ̃ ] exp [ i k 2 ( M 0 α β 1 + B ¯ 1 A ¯ ) 1 2 r ̃ ( M 0 α β 1 + B ¯ 1 A ¯ ) 1 2 B ¯ 1 ρ ̃ 2 ] d r ̃ .
exp ( a x 2 ) d x = π a ,
W α β ( ρ ̃ ) = k 2 A α A β B α β 4 π 2 [ det ( B ¯ ) ] 1 2 [ det ( M 0 α β 1 + B ¯ 1 A ¯ ) ] 1 2 exp [ i k 2 ρ ̃ T D ¯ B ¯ 1 ρ ̃ + i k 2 ρ ̃ T B ¯ 1 T ( M 0 α β 1 + B ¯ 1 A ¯ ) 1 B ¯ 1 T ] .
[ det ( B ¯ ) ] 1 2 [ det ( M 0 α β 1 + B ¯ 1 A ¯ ) ] 1 2 = [ det ( A ¯ + B ¯ M 0 α β 1 ) ] 1 2 ,
D ¯ B ¯ 1 B ¯ 1 T ( M 0 α β 1 + B ¯ 1 A ¯ ) 1 B ¯ 1 = [ D ¯ B ¯ 1 ( A ¯ + B ¯ M 0 α β 1 ) B ¯ 1 ] ( A ¯ + B ¯ M 0 α β 1 ) 1 = ( C ¯ + D ¯ M 0 α β 1 ) ( A ¯ + B ¯ M 0 α β 1 ) 1 ,
M 1 α β 1 = ( C ¯ + D ¯ M 0 α β 1 ) ( A ¯ + B ¯ M 0 α β 1 ) 1 ,

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