Abstract

A class of electromagnetic sources with multi-cosine Gaussian Schell-model correlation function is introduced. The realizability conditions for such sources and the beam conditions for the beams generated by them are established. Analytical formulas for the cross-spectral density matrix of such beams propagating in free space are derived and used to examine their statistical properties by numerical simulations. The results demonstrate that such beams possess invariant far-field concentric rings-like intensity patterns, uniform polarization state on all rings, and generally different degree of polarization values on different rings. By changing the summation index and other source parameters, the number of rings along with the behavior of various beam characteristics can be tuned at will.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Electromagnetic multi-Gaussian Schell-model vortex light sources and their radiation field properties

Zhangrong Mei, Yonghua Mao, and Yuyan Wang
Opt. Express 26(17) 21992-22000 (2018)

Electromagnetic sinc Schell-model beams and their statistical properties

Zhangrong Mei and Yonghua Mao
Opt. Express 22(19) 22534-22546 (2014)

Source coherence-based far-field intensity filtering

Zhangrong Mei, Olga Korotkova, and Yonghua Mao
Opt. Express 23(19) 24748-24758 (2015)

References

  • View by:
  • |
  • |
  • |

  1. L. Amico, A. Osterloh, and F. Cataliotti, “Quantum many particle systems in ring-shaped optical lattices,” Phys. Rev. Lett. 95(6), 063201 (2005).
    [Crossref] [PubMed]
  2. G. Ruffato, M. Massari, and F. Romanato, “Generation of high-order Laguerre-Gaussian modes by means of spiral phase plates,” Opt. Lett. 39(17), 5094–5097 (2014).
    [Crossref] [PubMed]
  3. J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
    [Crossref]
  4. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary solitons in Bessel optical lattices,” Phys. Rev. Lett. 93(9), 093904 (2004).
    [Crossref] [PubMed]
  5. Z. Mei and O. Korotkova, “Alternating series of cross-spectral densities,” Opt. Lett. 40(11), 2473–2476 (2015).
    [Crossref] [PubMed]
  6. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  7. F. Gori and M. Santarsiero, “Devising genuine spatial correlation functions,” Opt. Lett. 32(24), 3531–3533 (2007).
    [Crossref] [PubMed]
  8. H. Lajunen and T. Saastamoinen, “Propagation characteristics of partially coherent beams with spatially varying correlations,” Opt. Lett. 36(20), 4104–4106 (2011).
    [Crossref] [PubMed]
  9. Z. Tong and O. Korotkova, “Nonuniformly correlated light beams in uniformly correlated media,” Opt. Lett. 37(15), 3240–3242 (2012).
    [Crossref] [PubMed]
  10. H. Lajunen and T. Saastamoinen, “Non-uniformly correlated partially coherent pulses,” Opt. Express 21(1), 190–195 (2013).
    [Crossref] [PubMed]
  11. S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. 37(14), 2970–2972 (2012).
    [Crossref] [PubMed]
  12. O. Korotkova, S. Sahin, and E. Shchepakina, “Multi-Gaussian Schell-model beams,” J. Opt. Soc. Am. A 29(10), 2159–2164 (2012).
    [Crossref] [PubMed]
  13. O. Korotkova, “Random sources for rectangular far fields,” Opt. Lett. 39(1), 64–67 (2014).
    [Crossref] [PubMed]
  14. Z. Mei, “Two types of sinc Schell-model beams and their propagation characteristics,” Opt. Lett. 39(14), 4188–4191 (2014).
    [Crossref] [PubMed]
  15. Z. Mei and O. Korotkova, “Cosine-Gaussian Schell-model sources,” Opt. Lett. 38(14), 2578–2580 (2013).
    [Crossref] [PubMed]
  16. C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39(4), 769–772 (2014).
    [Crossref] [PubMed]
  17. Z. Mei, “Light sources generating self-splitting beams and their propagation in non-Kolmogorov turbulence,” Opt. Express 22(11), 13029–13040 (2014).
    [Crossref] [PubMed]
  18. C. Ding, O. Korotkova, Y. Zhang, and L. Pan, “Sinc Schell-model pulses,” Opt. Commun. 339, 115–122 (2015).
    [Crossref]
  19. L. Ma and S. A. Ponomarenko, “Optical coherence gratings and lattices,” Opt. Lett. 39(23), 6656–6659 (2014).
    [Crossref] [PubMed]
  20. Z. Mei, D. Zhao, O. Korotkova, and Y. Mao, “Gaussian Schell-model arrays,” Opt. Lett. 40(23), 5662–5665 (2015).
    [Crossref] [PubMed]
  21. L. Ma and S. A. Ponomarenko, “Free-space propagation of optical coherence lattices and periodicity reciprocity,” Opt. Express 23(2), 1848–1856 (2015).
    [Crossref] [PubMed]
  22. M. Santarsiero, G. Piquero, J. C. G. de Sande, and F. Gori, “Difference of cross-spectral densities,” Opt. Lett. 39(7), 1713–1716 (2014).
    [Crossref] [PubMed]
  23. Z. Mei, O. Korotkova, and Y. Mao, “Products of Schell-model cross-spectral densities,” Opt. Lett. 39(24), 6879–6882 (2014).
    [Crossref] [PubMed]
  24. O. Korotkova and Z. Mei, “Convolution of degrees of coherence,” Opt. Lett. 40(13), 3073–3076 (2015).
    [Crossref] [PubMed]
  25. Z. Mei, O. Korotkova, and Y. Mao, “Powers of the degree of coherence,” Opt. Express 23(7), 8519–8531 (2015).
    [Crossref] [PubMed]
  26. F. Gori, “Matrix treatment for partially polarized, partially coherent beams,” Opt. Lett. 23(4), 241–243 (1998).
    [Crossref] [PubMed]
  27. E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 32(5-6), 263–267 (2003).
    [Crossref]
  28. E. Wolf, Introduction to the Theories of Coherence and Polarization of Light (Cambridge University, 2007).
  29. S. R. Seshadri, “Partially coherent Gaussian Schell-model electromagnetic beams,” J. Opt. Soc. Am. A 16(6), 1373–1380 (1999).
    [Crossref]
  30. 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), 1–9 (2001).
    [Crossref]
  31. T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7(5), 232–237 (2005).
    [Crossref]
  32. O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246(1-3), 35–43 (2005).
    [Crossref]
  33. X. Du, D. Zhao, and O. Korotkova, “Changes in the statistical properties of stochastic anisotropic electromagnetic beams on propagation in the turbulent atmosphere,” Opt. Express 15(25), 16909–16915 (2007).
    [Crossref] [PubMed]
  34. F. Gori, M. Santarsiero, and R. Borghi, “Modal expansion for J0-correlated electromagnetic sources,” Opt. Lett. 33(16), 1857–1859 (2008).
    [Crossref] [PubMed]
  35. D. Zhao and X. Du, “Polarization modulation of stochastic electromagnetic beams on propagation through the turbulent atmosphere,” Opt. Express 17(6), 4257–4262 (2009).
    [Crossref] [PubMed]
  36. X. Ji, E. Zhang, and B. Lü, “Changes in the spectrum and polarization of polychromatic partially coherent electromagnetic beams in the turbulent atomosphere,” Opt. Commun. 275(2), 292–300 (2007).
    [Crossref]
  37. Y. Cai, Q. Lin, H. T. Eyyuboğlu, and Y. Baykal, “Average irradiance and polarization properties of a radially or azimuthally polarized beam in a turbulent atmosphere,” Opt. Express 16(11), 7665–7673 (2008).
    [Crossref] [PubMed]
  38. J. Pu and O. Korotkova, “Propagation of the degree of cross-polarization of a stochastic electromagnetic beam through the turbulent atmosphere,” Opt. Commun. 282(9), 1691–1698 (2009).
    [Crossref]
  39. E. Shchepakina and O. Korotkova, “Second-order statistics of stochastic electromagnetic beams propagating through non-Kolmogorov turbulence,” Opt. Express 18(10), 10650–10658 (2010).
    [Crossref] [PubMed]
  40. G. Zhou and X. Chu, “Average intensity and spreading of a Lorentz-Gauss beam in turbulent atmosphere,” Opt. Express 18(2), 726–731 (2010).
    [Crossref] [PubMed]
  41. X. Chu, C. Qiao, X. Feng, and R. Chen, “Propagation of Gaussian-Schell beam in turbulent atmosphere of three-layer altitude model,” Appl. Opt. 50(21), 3871–3878 (2011).
    [Crossref] [PubMed]
  42. F. Wang, Y. Cai, Y. Dong, and O. Korotkova, “Experimental generation of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 100(5), 051108 (2012).
    [Crossref]
  43. M. Yao, I. Toselli, and O. Korotkova, “Propagation of electromagnetic stochastic beams in anisotropic turbulence,” Opt. Express 22(26), 31608–31619 (2014).
    [Crossref] [PubMed]
  44. O. Korotkova, M. Salem, and E. Wolf, “Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source,” Opt. Lett. 29(11), 1173–1175 (2004).
    [Crossref] [PubMed]
  45. H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249(4-6), 379–385 (2005).
    [Crossref]
  46. F. Gori, M. Santarsiero, R. Borghi, and V. Ramírez-Sánchez, “Realizability condition for electromagnetic Schell-model sources,” J. Opt. Soc. Am. A 25(5), 1016–1021 (2008).
    [Crossref] [PubMed]
  47. F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A: Pure Appl. Opt. 11(8), 085706 (2009).
    [Crossref]
  48. Z. Tong and O. Korotkova, “Electromagnetic nonuniformly correlated beams,” J. Opt. Soc. Am. A 29(10), 2154–2158 (2012).
    [Crossref] [PubMed]
  49. Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. 15(2), 025705 (2013).
    [Crossref]
  50. Z. Mei and O. Korotkova, “Electromagnetic cosine-Gaussian Schell-model beams in free space and atmospheric turbulence,” Opt. Express 21(22), 27246–27259 (2013).
    [Crossref] [PubMed]
  51. O. Korotkova and Z. Mei, “Random electromagnetic model beams with correlations described by two families of functions,” Opt. Lett. 40(23), 5534–5537 (2015).
    [Crossref] [PubMed]
  52. J. Tervo, T. Setälä, and A. Friberg, “Degree of coherence for electromagnetic fields,” Opt. Express 11(10), 1137–1143 (2003).
    [Crossref] [PubMed]

2015 (7)

2014 (9)

2013 (4)

2012 (5)

2011 (2)

2010 (2)

2009 (3)

J. Pu and O. Korotkova, “Propagation of the degree of cross-polarization of a stochastic electromagnetic beam through the turbulent atmosphere,” Opt. Commun. 282(9), 1691–1698 (2009).
[Crossref]

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A: Pure Appl. Opt. 11(8), 085706 (2009).
[Crossref]

D. Zhao and X. Du, “Polarization modulation of stochastic electromagnetic beams on propagation through the turbulent atmosphere,” Opt. Express 17(6), 4257–4262 (2009).
[Crossref] [PubMed]

2008 (3)

2007 (3)

2005 (4)

L. Amico, A. Osterloh, and F. Cataliotti, “Quantum many particle systems in ring-shaped optical lattices,” Phys. Rev. Lett. 95(6), 063201 (2005).
[Crossref] [PubMed]

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7(5), 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(1-3), 35–43 (2005).
[Crossref]

H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249(4-6), 379–385 (2005).
[Crossref]

2004 (2)

2003 (2)

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 32(5-6), 263–267 (2003).
[Crossref]

J. Tervo, T. Setälä, and A. Friberg, “Degree of coherence for electromagnetic fields,” Opt. Express 11(10), 1137–1143 (2003).
[Crossref] [PubMed]

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), 1–9 (2001).
[Crossref]

2000 (1)

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
[Crossref]

1999 (1)

1998 (1)

Amico, L.

L. Amico, A. Osterloh, and F. Cataliotti, “Quantum many particle systems in ring-shaped optical lattices,” Phys. Rev. Lett. 95(6), 063201 (2005).
[Crossref] [PubMed]

Arlt, J.

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
[Crossref]

Baykal, Y.

Borghi, R.

Cai, Y.

Cataliotti, F.

L. Amico, A. Osterloh, and F. Cataliotti, “Quantum many particle systems in ring-shaped optical lattices,” Phys. Rev. Lett. 95(6), 063201 (2005).
[Crossref] [PubMed]

Chen, R.

Chu, X.

de Sande, J. C. G.

Dholakia, K.

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
[Crossref]

Ding, C.

C. Ding, O. Korotkova, Y. Zhang, and L. Pan, “Sinc Schell-model pulses,” Opt. Commun. 339, 115–122 (2015).
[Crossref]

Dong, Y.

F. Wang, Y. Cai, Y. Dong, and O. Korotkova, “Experimental generation of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 100(5), 051108 (2012).
[Crossref]

Du, X.

Eyyuboglu, H. T.

Feng, X.

Friberg, A.

Gori, F.

Ji, X.

X. Ji, E. Zhang, and B. Lü, “Changes in the spectrum and polarization of polychromatic partially coherent electromagnetic beams in the turbulent atomosphere,” Opt. Commun. 275(2), 292–300 (2007).
[Crossref]

Kartashov, Y. V.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary solitons in Bessel optical lattices,” Phys. Rev. Lett. 93(9), 093904 (2004).
[Crossref] [PubMed]

Korotkova, O.

C. Ding, O. Korotkova, Y. Zhang, and L. Pan, “Sinc Schell-model pulses,” Opt. Commun. 339, 115–122 (2015).
[Crossref]

Z. Mei, O. Korotkova, and Y. Mao, “Powers of the degree of coherence,” Opt. Express 23(7), 8519–8531 (2015).
[Crossref] [PubMed]

O. Korotkova and Z. Mei, “Random electromagnetic model beams with correlations described by two families of functions,” Opt. Lett. 40(23), 5534–5537 (2015).
[Crossref] [PubMed]

Z. Mei and O. Korotkova, “Alternating series of cross-spectral densities,” Opt. Lett. 40(11), 2473–2476 (2015).
[Crossref] [PubMed]

O. Korotkova and Z. Mei, “Convolution of degrees of coherence,” Opt. Lett. 40(13), 3073–3076 (2015).
[Crossref] [PubMed]

Z. Mei, D. Zhao, O. Korotkova, and Y. Mao, “Gaussian Schell-model arrays,” Opt. Lett. 40(23), 5662–5665 (2015).
[Crossref] [PubMed]

M. Yao, I. Toselli, and O. Korotkova, “Propagation of electromagnetic stochastic beams in anisotropic turbulence,” Opt. Express 22(26), 31608–31619 (2014).
[Crossref] [PubMed]

Z. Mei, O. Korotkova, and Y. Mao, “Products of Schell-model cross-spectral densities,” Opt. Lett. 39(24), 6879–6882 (2014).
[Crossref] [PubMed]

C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39(4), 769–772 (2014).
[Crossref] [PubMed]

O. Korotkova, “Random sources for rectangular far fields,” Opt. Lett. 39(1), 64–67 (2014).
[Crossref] [PubMed]

Z. Mei and O. Korotkova, “Electromagnetic cosine-Gaussian Schell-model beams in free space and atmospheric turbulence,” Opt. Express 21(22), 27246–27259 (2013).
[Crossref] [PubMed]

Z. Mei and O. Korotkova, “Cosine-Gaussian Schell-model sources,” Opt. Lett. 38(14), 2578–2580 (2013).
[Crossref] [PubMed]

Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. 15(2), 025705 (2013).
[Crossref]

F. Wang, Y. Cai, Y. Dong, and O. Korotkova, “Experimental generation of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 100(5), 051108 (2012).
[Crossref]

Z. Tong and O. Korotkova, “Electromagnetic nonuniformly correlated beams,” J. Opt. Soc. Am. A 29(10), 2154–2158 (2012).
[Crossref] [PubMed]

O. Korotkova, S. Sahin, and E. Shchepakina, “Multi-Gaussian Schell-model beams,” J. Opt. Soc. Am. A 29(10), 2159–2164 (2012).
[Crossref] [PubMed]

S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. 37(14), 2970–2972 (2012).
[Crossref] [PubMed]

Z. Tong and O. Korotkova, “Nonuniformly correlated light beams in uniformly correlated media,” Opt. Lett. 37(15), 3240–3242 (2012).
[Crossref] [PubMed]

E. Shchepakina and O. Korotkova, “Second-order statistics of stochastic electromagnetic beams propagating through non-Kolmogorov turbulence,” Opt. Express 18(10), 10650–10658 (2010).
[Crossref] [PubMed]

J. Pu and O. Korotkova, “Propagation of the degree of cross-polarization of a stochastic electromagnetic beam through the turbulent atmosphere,” Opt. Commun. 282(9), 1691–1698 (2009).
[Crossref]

X. Du, D. Zhao, and O. Korotkova, “Changes in the statistical properties of stochastic anisotropic electromagnetic beams on propagation in the turbulent atmosphere,” Opt. Express 15(25), 16909–16915 (2007).
[Crossref] [PubMed]

H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249(4-6), 379–385 (2005).
[Crossref]

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7(5), 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(1-3), 35–43 (2005).
[Crossref]

O. Korotkova, M. Salem, and E. Wolf, “Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source,” Opt. Lett. 29(11), 1173–1175 (2004).
[Crossref] [PubMed]

Lajunen, H.

Liang, C.

Lin, Q.

Liu, X.

Lü, B.

X. Ji, E. Zhang, and B. Lü, “Changes in the spectrum and polarization of polychromatic partially coherent electromagnetic beams in the turbulent atomosphere,” Opt. Commun. 275(2), 292–300 (2007).
[Crossref]

Ma, L.

Mao, Y.

Massari, M.

Mei, Z.

Z. Mei and O. Korotkova, “Alternating series of cross-spectral densities,” Opt. Lett. 40(11), 2473–2476 (2015).
[Crossref] [PubMed]

O. Korotkova and Z. Mei, “Convolution of degrees of coherence,” Opt. Lett. 40(13), 3073–3076 (2015).
[Crossref] [PubMed]

O. Korotkova and Z. Mei, “Random electromagnetic model beams with correlations described by two families of functions,” Opt. Lett. 40(23), 5534–5537 (2015).
[Crossref] [PubMed]

Z. Mei, D. Zhao, O. Korotkova, and Y. Mao, “Gaussian Schell-model arrays,” Opt. Lett. 40(23), 5662–5665 (2015).
[Crossref] [PubMed]

Z. Mei, O. Korotkova, and Y. Mao, “Powers of the degree of coherence,” Opt. Express 23(7), 8519–8531 (2015).
[Crossref] [PubMed]

Z. Mei, O. Korotkova, and Y. Mao, “Products of Schell-model cross-spectral densities,” Opt. Lett. 39(24), 6879–6882 (2014).
[Crossref] [PubMed]

Z. Mei, “Light sources generating self-splitting beams and their propagation in non-Kolmogorov turbulence,” Opt. Express 22(11), 13029–13040 (2014).
[Crossref] [PubMed]

Z. Mei, “Two types of sinc Schell-model beams and their propagation characteristics,” Opt. Lett. 39(14), 4188–4191 (2014).
[Crossref] [PubMed]

Z. Mei and O. Korotkova, “Cosine-Gaussian Schell-model sources,” Opt. Lett. 38(14), 2578–2580 (2013).
[Crossref] [PubMed]

Z. Mei and O. Korotkova, “Electromagnetic cosine-Gaussian Schell-model beams in free space and atmospheric turbulence,” Opt. Express 21(22), 27246–27259 (2013).
[Crossref] [PubMed]

Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. 15(2), 025705 (2013).
[Crossref]

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), 1–9 (2001).
[Crossref]

Osterloh, A.

L. Amico, A. Osterloh, and F. Cataliotti, “Quantum many particle systems in ring-shaped optical lattices,” Phys. Rev. Lett. 95(6), 063201 (2005).
[Crossref] [PubMed]

Pan, L.

C. Ding, O. Korotkova, Y. Zhang, and L. Pan, “Sinc Schell-model pulses,” Opt. Commun. 339, 115–122 (2015).
[Crossref]

Piquero, G.

M. Santarsiero, G. Piquero, J. C. G. de Sande, and F. Gori, “Difference of cross-spectral densities,” Opt. Lett. 39(7), 1713–1716 (2014).
[Crossref] [PubMed]

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), 1–9 (2001).
[Crossref]

Ponomarenko, S. A.

Pu, J.

J. Pu and O. Korotkova, “Propagation of the degree of cross-polarization of a stochastic electromagnetic beam through the turbulent atmosphere,” Opt. Commun. 282(9), 1691–1698 (2009).
[Crossref]

Qiao, C.

Ramírez-Sánchez, V.

Romanato, F.

Roychowdhury, H.

H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249(4-6), 379–385 (2005).
[Crossref]

Ruffato, G.

Saastamoinen, T.

Sahin, S.

Salem, M.

Sanchez, V. R.

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A: Pure Appl. Opt. 11(8), 085706 (2009).
[Crossref]

Santarsiero, M.

Seshadri, S. R.

Setälä, T.

Shchepakina, E.

Shirai, T.

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A: Pure Appl. Opt. 11(8), 085706 (2009).
[Crossref]

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7(5), 232–237 (2005).
[Crossref]

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), 1–9 (2001).
[Crossref]

Tervo, J.

Tong, Z.

Torner, L.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary solitons in Bessel optical lattices,” Phys. Rev. Lett. 93(9), 093904 (2004).
[Crossref] [PubMed]

Toselli, I.

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary solitons in Bessel optical lattices,” Phys. Rev. Lett. 93(9), 093904 (2004).
[Crossref] [PubMed]

Wang, F.

C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39(4), 769–772 (2014).
[Crossref] [PubMed]

F. Wang, Y. Cai, Y. Dong, and O. Korotkova, “Experimental generation of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 100(5), 051108 (2012).
[Crossref]

Wolf, E.

O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246(1-3), 35–43 (2005).
[Crossref]

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7(5), 232–237 (2005).
[Crossref]

O. Korotkova, M. Salem, and E. Wolf, “Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source,” Opt. Lett. 29(11), 1173–1175 (2004).
[Crossref] [PubMed]

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 32(5-6), 263–267 (2003).
[Crossref]

Yao, M.

Zhang, E.

X. Ji, E. Zhang, and B. Lü, “Changes in the spectrum and polarization of polychromatic partially coherent electromagnetic beams in the turbulent atomosphere,” Opt. Commun. 275(2), 292–300 (2007).
[Crossref]

Zhang, Y.

C. Ding, O. Korotkova, Y. Zhang, and L. Pan, “Sinc Schell-model pulses,” Opt. Commun. 339, 115–122 (2015).
[Crossref]

Zhao, D.

Zhou, G.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

F. Wang, Y. Cai, Y. Dong, and O. Korotkova, “Experimental generation of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 100(5), 051108 (2012).
[Crossref]

J. Opt. (1)

Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. 15(2), 025705 (2013).
[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), 1–9 (2001).
[Crossref]

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7(5), 232–237 (2005).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

F. Gori, V. R. Sanchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A: Pure Appl. Opt. 11(8), 085706 (2009).
[Crossref]

J. Opt. Soc. Am. A (4)

Opt. Commun. (6)

C. Ding, O. Korotkova, Y. Zhang, and L. Pan, “Sinc Schell-model pulses,” Opt. Commun. 339, 115–122 (2015).
[Crossref]

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
[Crossref]

X. Ji, E. Zhang, and B. Lü, “Changes in the spectrum and polarization of polychromatic partially coherent electromagnetic beams in the turbulent atomosphere,” Opt. Commun. 275(2), 292–300 (2007).
[Crossref]

O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246(1-3), 35–43 (2005).
[Crossref]

J. Pu and O. Korotkova, “Propagation of the degree of cross-polarization of a stochastic electromagnetic beam through the turbulent atmosphere,” Opt. Commun. 282(9), 1691–1698 (2009).
[Crossref]

H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249(4-6), 379–385 (2005).
[Crossref]

Opt. Express (12)

D. Zhao and X. Du, “Polarization modulation of stochastic electromagnetic beams on propagation through the turbulent atmosphere,” Opt. Express 17(6), 4257–4262 (2009).
[Crossref] [PubMed]

E. Shchepakina and O. Korotkova, “Second-order statistics of stochastic electromagnetic beams propagating through non-Kolmogorov turbulence,” Opt. Express 18(10), 10650–10658 (2010).
[Crossref] [PubMed]

G. Zhou and X. Chu, “Average intensity and spreading of a Lorentz-Gauss beam in turbulent atmosphere,” Opt. Express 18(2), 726–731 (2010).
[Crossref] [PubMed]

M. Yao, I. Toselli, and O. Korotkova, “Propagation of electromagnetic stochastic beams in anisotropic turbulence,” Opt. Express 22(26), 31608–31619 (2014).
[Crossref] [PubMed]

J. Tervo, T. Setälä, and A. Friberg, “Degree of coherence for electromagnetic fields,” Opt. Express 11(10), 1137–1143 (2003).
[Crossref] [PubMed]

Z. Mei and O. Korotkova, “Electromagnetic cosine-Gaussian Schell-model beams in free space and atmospheric turbulence,” Opt. Express 21(22), 27246–27259 (2013).
[Crossref] [PubMed]

X. Du, D. Zhao, and O. Korotkova, “Changes in the statistical properties of stochastic anisotropic electromagnetic beams on propagation in the turbulent atmosphere,” Opt. Express 15(25), 16909–16915 (2007).
[Crossref] [PubMed]

Y. Cai, Q. Lin, H. T. Eyyuboğlu, and Y. Baykal, “Average irradiance and polarization properties of a radially or azimuthally polarized beam in a turbulent atmosphere,” Opt. Express 16(11), 7665–7673 (2008).
[Crossref] [PubMed]

Z. Mei, “Light sources generating self-splitting beams and their propagation in non-Kolmogorov turbulence,” Opt. Express 22(11), 13029–13040 (2014).
[Crossref] [PubMed]

L. Ma and S. A. Ponomarenko, “Free-space propagation of optical coherence lattices and periodicity reciprocity,” Opt. Express 23(2), 1848–1856 (2015).
[Crossref] [PubMed]

Z. Mei, O. Korotkova, and Y. Mao, “Powers of the degree of coherence,” Opt. Express 23(7), 8519–8531 (2015).
[Crossref] [PubMed]

H. Lajunen and T. Saastamoinen, “Non-uniformly correlated partially coherent pulses,” Opt. Express 21(1), 190–195 (2013).
[Crossref] [PubMed]

Opt. Lett. (19)

S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. 37(14), 2970–2972 (2012).
[Crossref] [PubMed]

L. Ma and S. A. Ponomarenko, “Optical coherence gratings and lattices,” Opt. Lett. 39(23), 6656–6659 (2014).
[Crossref] [PubMed]

Z. Mei, D. Zhao, O. Korotkova, and Y. Mao, “Gaussian Schell-model arrays,” Opt. Lett. 40(23), 5662–5665 (2015).
[Crossref] [PubMed]

O. Korotkova, “Random sources for rectangular far fields,” Opt. Lett. 39(1), 64–67 (2014).
[Crossref] [PubMed]

Z. Mei, “Two types of sinc Schell-model beams and their propagation characteristics,” Opt. Lett. 39(14), 4188–4191 (2014).
[Crossref] [PubMed]

Z. Mei and O. Korotkova, “Cosine-Gaussian Schell-model sources,” Opt. Lett. 38(14), 2578–2580 (2013).
[Crossref] [PubMed]

C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39(4), 769–772 (2014).
[Crossref] [PubMed]

G. Ruffato, M. Massari, and F. Romanato, “Generation of high-order Laguerre-Gaussian modes by means of spiral phase plates,” Opt. Lett. 39(17), 5094–5097 (2014).
[Crossref] [PubMed]

Z. Mei and O. Korotkova, “Alternating series of cross-spectral densities,” Opt. Lett. 40(11), 2473–2476 (2015).
[Crossref] [PubMed]

F. Gori and M. Santarsiero, “Devising genuine spatial correlation functions,” Opt. Lett. 32(24), 3531–3533 (2007).
[Crossref] [PubMed]

H. Lajunen and T. Saastamoinen, “Propagation characteristics of partially coherent beams with spatially varying correlations,” Opt. Lett. 36(20), 4104–4106 (2011).
[Crossref] [PubMed]

Z. Tong and O. Korotkova, “Nonuniformly correlated light beams in uniformly correlated media,” Opt. Lett. 37(15), 3240–3242 (2012).
[Crossref] [PubMed]

F. Gori, “Matrix treatment for partially polarized, partially coherent beams,” Opt. Lett. 23(4), 241–243 (1998).
[Crossref] [PubMed]

M. Santarsiero, G. Piquero, J. C. G. de Sande, and F. Gori, “Difference of cross-spectral densities,” Opt. Lett. 39(7), 1713–1716 (2014).
[Crossref] [PubMed]

Z. Mei, O. Korotkova, and Y. Mao, “Products of Schell-model cross-spectral densities,” Opt. Lett. 39(24), 6879–6882 (2014).
[Crossref] [PubMed]

O. Korotkova and Z. Mei, “Convolution of degrees of coherence,” Opt. Lett. 40(13), 3073–3076 (2015).
[Crossref] [PubMed]

F. Gori, M. Santarsiero, and R. Borghi, “Modal expansion for J0-correlated electromagnetic sources,” Opt. Lett. 33(16), 1857–1859 (2008).
[Crossref] [PubMed]

O. Korotkova and Z. Mei, “Random electromagnetic model beams with correlations described by two families of functions,” Opt. Lett. 40(23), 5534–5537 (2015).
[Crossref] [PubMed]

O. Korotkova, M. Salem, and E. Wolf, “Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source,” Opt. Lett. 29(11), 1173–1175 (2004).
[Crossref] [PubMed]

Phys. Lett. A (1)

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 32(5-6), 263–267 (2003).
[Crossref]

Phys. Rev. Lett. (2)

L. Amico, A. Osterloh, and F. Cataliotti, “Quantum many particle systems in ring-shaped optical lattices,” Phys. Rev. Lett. 95(6), 063201 (2005).
[Crossref] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary solitons in Bessel optical lattices,” Phys. Rev. Lett. 93(9), 093904 (2004).
[Crossref] [PubMed]

Other (2)

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

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

Cited By

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

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1 Transverse distributions of the spectral density of an EM CRSM beam with N=6 , R=1mm , δ xx =0.4mm and δ yy =0.45mm at several different propagation distances in free space.
Fig. 2
Fig. 2 Transverse distributions of the spectral density of the EM CRSM beams with different values of parameters N, R, δ xx and δ yy in the plane z=3m .
Fig. 3
Fig. 3 Transverse cross-sections of (a) the degree of polarization, (b) the orientation angle (rad) and (c) the degree of ellipticity of an EM CRSM beam with the same parameters as in Fig. 1 except for δ xy =0.426mm and B xy =0.2exp(iπ/3) in the plane z=3m .
Fig. 4
Fig. 4 Spectral degrees of polarization of the EM CRSM beams, (a) at several different propagation distances; (b)-(d) in the plane z=3m for different N, R and δ xy , respectively, and other source parameters as in Fig. 1.
Fig. 5
Fig. 5 Spectral degrees of coherence of the EM CRSM beams versus ρ d , (a) at several propagation distances; (b)-(d) in the plane z=0 and z=3m for different N, R and δ xx , respectively, other source parameters as in Fig. 1 unless specified in Figure.

Tables (1)

Tables Icon

Table 1 The effective ranges of δ xy for different values of N, R, | B xy |, δ xx and δ yy .

Equations (29)

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

W ^ (0) ( ρ 1 , ρ 2 ;ω)[ W αβ (0) ( ρ 1 , ρ 2 ;ω) ], (α=x,y; β=x,y).
W αβ (0) ( ρ 1 , ρ 2 ;ω)= E α * ( ρ 1 ;ω) E β ( ρ 2 ;ω),
W αβ (0) ( ρ 1 , ρ 2 )= p αβ (v) H α ( ρ 1 ,v ) H β ( ρ 2 ,v) d 2 v,
p αα (v)0,
p xx (v) p yy (v) p xy (v) p yx (v)0.
H α ( ρ 1 ,v)= A α τ( ρ 1 )exp(2πiv ρ 1 ),
H β ( ρ 2 ,v)= A β τ( ρ 2 )exp(2πiv ρ 2 ),
W αβ (0) ( ρ 1 , ρ 2 )= A α A β τ ( ρ 1 )τ( ρ 2 ) μ αβ ( ρ 1 ρ 2 ),
p αβ (v)=2π B αβ δ αβ 2 exp( 2π δ 2 αβ 2 v 2 ) 1 N n=(N1)/2 (N1)/2 cosh(4 π 2 δ αβ nRv) exp( 2 π 2 n 2 R 2 ),
W αβ (0) ( ρ 1 , ρ 2 )= A α A β B αβ exp( ρ 1 2 + ρ 2 2 4 σ 2 )exp[ ( ρ 2 ρ 1 ) 2 2 δ αβ 2 ] × 1 N n=(N1)/2 (N1)/2 cos[ 2πnR δ αβ ( ρ 1 ρ 2 ) ] .
B xx = B yy =1, | B xy |=| B yx |, δ xy = δ yx .
δ xx 2 exp( 2π δ 2 xx 2 v 2 ) n=(N1)/2 (N1)/2 cosh(4 π 2 δ xx nRv) exp( 2 π 2 n 2 R 2 ) × δ yy 2 exp( 2π δ 2 yy 2 v 2 ) n=(N1)/2 (N1)/2 cosh(4 π 2 δ yy nRv) exp( 2 π 2 n 2 R 2 ) | B xy | 2 δ xy 4 exp( 4π δ 2 xy 2 v 2 ) [ n=(N1)/2 (N1)/2 cosh(4 π 2 δ xy nRv) exp( 2 π 2 n 2 R 2 ) ] 2 .
δ xy ( δ xx 2 + δ yy 2 )/2 ,
S (r)= (2πk/r) 2 cos 2 θ[ W ˜ xx (0) (k s ,k s )+ W ˜ yy (0) (k s ,k s ) ],
W ˜ αα (0) ( f 1 , f 2 )= (2π) 4 W αα (0) ( ρ 1 , ρ 2 ) exp[i( f 1 ρ 1 + f 2 ρ 2 ) d 2 ρ 1 d 2 ρ 2 .
S (r)= k 2 σ 2 cos 2 θ 2N r 2 [ A x 2 a xx exp( k 2 s 2 4 a xx ) n=(N1)/2 (N1)/2 exp( 2 π 2 n 2 R 2 2 a xx δ xx 2 )cosh( 2πnRk s 2 a xx δ xx ) + A y 2 a yy exp( k 2 s 2 4 a yy ) n=(N1)/2 (N1)/2 exp( 2 π 2 n 2 R 2 2 a yy δ yy 2 )cosh( 2πnRk s 2 a yy δ yy ) ],
4 a xx << k 2 , 4 a yy << k 2 ,
1 4 σ 2 + 1 δ xx 2 << 2 π 2 λ 2 , 1 4 σ 2 + 1 δ yy 2 << 2 π 2 λ 2 .
W αβ ( ρ 1 , ρ 2 ,z)= ( k 2πz ) 2 W αβ (0) ( ρ 1 , ρ 2 ) ×exp{ ik ( ρ 1 ρ 1 ) 2 ( ρ 2 ρ 2 ) 2 2z } d 2 ρ 1 d 2 ρ 2 .
W αβ ( ρ 1 , ρ 2 ,z)= A α A β B αβ k 2 σ 2 4 z 2 Δ(z) exp[ k 2 σ 2 ( ρ 1 ρ 2 ) 2 2 z 2 ]exp[ ik 2z ( ρ 1 2 ρ 2 2 ) ] × 1 N n=(N1)/2 (N1)/2 [ exp( γ + 2 Δ(z) )+exp( γ 2 Δ(z) ) ] ,
Δ(z)= k 2 σ 2 2 z 2 + 1 8 σ 2 + 1 2 δ αβ 2 ,
γ ± = 3 k 2 σ 2 2 z 2 ( ρ 1 ρ 2 )+ ik 4z ( ρ 1 + ρ 2 )± i2πnR 2 δ αβ .
S(ρ,z)=Tr W ^ (ρ,ρ,z),
μ( ρ 1 , ρ 2 ,z)= Tr W ^ ( ρ 1 , ρ 2 ,z) Tr W ^ ( ρ 1 , ρ 1 ,z)Tr W ^ ( ρ 2 , ρ 2 ,z) ,
P(ρ,z)= 1 4Det W ^ (ρ,ρ,z) [Tr W ^ (ρ,ρ,z)] 2 .
θ(ρ,z)= 1 2 arctan( 2Re[ W xy (ρ,z)] W xx (ρ,z) W yy (ρ,z) ),
ε(ρ,z)= A minor (ρ,z)/ A major (ρ,z),
A major 2 (ρ,z)= 1 2 ( ( W xx W yy ) 2 +4 | W xy | 2 + ( W xx W yy ) 2 +4 [ Re W xy ] 2 ),
A minor 2 (ρ,z)= 1 2 ( ( W xx W yy ) 2 +4 | W xy | 2 ( W xx W yy ) 2 +4 [ Re W xy ] 2 ).

Metrics