Abstract

Based on the intensity moments and Wigner distribution function, the second-order moments for broadband partially coherent flat-topped (BPCFT) beams in atmospheric turbulence are studied. The beam width of BPCFT beams in atmospheric turbulence is larger than that in free space. The beam width of BPCFT beams in atmospheric turbulence is larger than that of broadband fully coherent flat-topped (BFCFT) beams in atmospheric turbulence. The broader the bandwidth is, the larger the beam width of BPCFT beams becomes. Similar conclusion can be obtained by analyzing the divergence angle and beam propagation factor of BPCFT beams. The beam width of BPCFT beams in atmospheric turbulence is less affected by the broad spectral bandwidth than that in free space. The beam width of BFCFT beams in atmospheric turbulence is less affected by the broad spectral bandwidth than that of BPCFT beams in atmospheric turbulence.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Ishimaru, "Theory and application of wave propagation and scattering in random media," Proc. IEEE 65(7), 1030-1061 (1977).
    [CrossRef]
  2. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).
  3. J. Wu, "Propagation of a Gaussian-Schell beam through turbulent media," J. Mod. Opt. 37(4), 671-684 (1990).
    [CrossRef]
  4. J. Wu, and A. Boardman, "Coherence length of a Gaussian-Schell beam and atmospheric turbulence," J. Mod. Opt. 38(7), 1355-1363 (1991).
    [CrossRef]
  5. G. Gbur, and E. Wolf, "Spreading of partially coherent beams in random media," J. Opt. Soc. Am. A 19(8), 1592-1598 (2002).
    [CrossRef]
  6. S. Ponomarenko, J.-J. Greffet, and E. Wolf, "The diffusion of partially coherent beams in turbulent media," Opt. Commun. 208(1-3), 1-8 (2002).
    [CrossRef]
  7. J. Li, A. Yang, and B. Lu, "Comparative study of the beam-width spreading of partially coherent Hermite-sinh-Gaussian beams in atmospheric turbulence," J. Opt. Soc. Am. A 25, 2670-2679 (2008).
  8. X. Ji, X. Chen, and B. Lu, "Spreading and directionality of partially coherent Hermite-Gaussian beams propagating through atmospheric turbulence," J. Opt. Soc. Am. A 25(1), 21-28 (2008).
    [CrossRef]
  9. G. Zhou, and X. Chu, "Propagation of a partially coherent cosine-Gaussian beam through an ABCD optical system in turbulent atmosphere," Opt. Express 17(13), 10529-10534 (2009).
    [CrossRef] [PubMed]
  10. T. Shirai, A. Dogariu, and E. Wolf, "Mode analysis of spreading of partially coherent beams propagating through atmospheric turbulence," J. Opt. Soc. Am. A 20(6), 1094-1102 (2003).
    [CrossRef]
  11. A. Dogariu, and S. Amarande, "Propagation of partially coherent beams: turbulence-induced degradation," Opt. Lett. 28(1), 10-12 (2003).
    [CrossRef] [PubMed]
  12. M. Mahdieh, "Numerical approach to laser beam propagation through turbulent atmosphere and evaluation of beam quality factor," Opt. Commun. 281(13), 3395-3402 (2008).
    [CrossRef]
  13. Y. Dan, and B. Zhang, "Second moments of partially coherent beams in atmospheric turbulence," Opt. Lett. 34(5), 563-565 (2009).
    [CrossRef] [PubMed]
  14. R. Haas, and P. Banks, "Generation of high intensity broad-bandwidth light for inertial confinement fusion," Opt. Commun. 107(3-4), 265-270 (1994).
    [CrossRef]
  15. B. Schenkel, J. Biegert, U. Keller, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, and O. Svelto, "Generation of 3.8-fs pulses from adaptive compression of a cascaded hollow fiber supercontinuum," Opt. Lett. 28(20), 1987-1989 (2003).
    [CrossRef] [PubMed]
  16. G. Samelsohn, and V. Freilikher, "Two-frequency mutual coherence function and pulse propagation in random media," Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(4), 046617 (2002).
    [CrossRef] [PubMed]
  17. R. L. Fante, "Two-position, two-frequency mutual-coherence function in turbulence," J. Opt. Soc. Am. A 71(12), 1446-1461 (1981).
    [CrossRef]
  18. C. Y. Young, A. Ishimaru, and L. C. Andrews, "Two-frequency mutual coherence function of a Gaussian beam pulse in weak optical turbulence: an analytic solution," Appl. Opt. 35(33), 6522-6526 (1996).
    [CrossRef] [PubMed]
  19. I. Sreenivasiah, and A. Ishimaru, "Beam wave two-frequency mutual-coherence function and pulse propagation in random media: an analytic solution," Appl. Opt. 18(10), 1613-1618 (1979).
    [CrossRef] [PubMed]
  20. A. V. Morozov, "Two-frequency mutual coherence function of electromagnetic waves in random media: a path-integral variational solution," J. Opt. Soc. Am. A 19(10), 2074-2084 (2002).
    [CrossRef]
  21. P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, "Partially coherent Gaussian pulses," Opt. Commun.  204(1-6), 53 -58 (2002).
    [CrossRef]
  22. H. Lajunen, P. Vahimaa, and J. Tervo, "Theory of spatially and spectrally partially coherent pulses," J. Opt. Soc. Am. A 22(8), 1536-1545 (2005).
    [CrossRef]
  23. L. Mandel, and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).
  24. Q1. X. Deng, W. Yu, S. Chen, L. Ding, and W. Tan, "Improvement of the output power by increasing the spectral bandwidth of high-power laser," Acta Opt. Sin. 3, 97-101 (1983).
  25. R. Peng, Y. Ye, Z. Tang, C. Zhao, S. Wen, and D. Fan, "Smoothing effect in the broadband laser through a dispersive wedge," Opt. Commun. 265(1), 106-110 (2006).
    [CrossRef]
  26. Q2. X. Ji, X. Xi, and B. Lu, "Effect of atmospheric turbulence on the propagation properties of spatially partially coherent polychromatic light," Acta Phys. Sinica 53, 3996-4001 (2004).
  27. Q3. X. Ji, E. Zhang, and B. Lu, "Spreading of spatially partially coherent polychromatic beams in atmospheric turbulence," Optik (Stuttg.) 119(14), 689-694 (2008).
  28. Y. J. Li, "Light beams with flat-topped profiles," Opt. Lett. 27(12), 1007-1009 (2002).
    [CrossRef]
  29. Y. J. Li, "New expressions for flat-topped light beams," Opt. Commun. 206(4-6), 225-234 (2002).
    [CrossRef]
  30. Y. Q. Dan, B. Zhang, and P. P. Pan, "Propagation of partially coherent flat-topped beams through a turbulent atmosphere," J. Opt. Soc. Am. A 25(9), 2223-2231 (2008).
    [CrossRef]
  31. L. C. Andrews, and R. L. Phillips, Laser Beam Propagation through Random Media, (SPIE Press, Bellingham, WA, 1998).
  32. S. C. H. Wang, and M. A. Plonus, "Optical beam propagation for a partially coherent source in the turbulent atmosphere," J. Opt. Soc. Am. 69(9), 1297-1304 (1979).
    [CrossRef]
  33. J. C. Leader, "Atmospheric propagation of partially coherent radiation," J. Opt. Soc. Am. 68(2), 175-185 (1978).
    [CrossRef]
  34. Y. B. Zhu, D. M. Zhao, and X. Y. Du, "Propagation of stochastic Gaussian-Schell model array beams in turbulent atmosphere," Opt. Express 16(22), 18437-18442 (2008).
    [CrossRef] [PubMed]
  35. H. T. Eyyuboğlu, and Y. K. Baykal, "Average intensity and spreading of cosh-Gaussian laser beams in the turbulent atmosphere," Appl. Opt. 44(6), 976-983 (2005).
    [CrossRef] [PubMed]
  36. H. T. Eyyuboglu, C. Arpali, and Y. K. Baykal, "Flat topped beams and their characteristics in turbulent media," Opt. Express 14(10), 4196-4207 (2006).
    [CrossRef] [PubMed]
  37. A. Erdelyi, Tables of Integral Transforms (McGraw-Hill, New York, 1954).
  38. M. J. Bastiaans, "Application of the Wigner distribution function to partially coherent light," J. Opt. Soc. Am. A 3(8), 1227-1238 (1986).
    [CrossRef]
  39. J. Serna, R. Martínez-Herrero, and P. M. Mejías, "Parametric characterization of general partially coherent beams propagating through ABCD optical systems," J. Opt. Soc. Am. A 8(7), 1094-1098 (1991).
    [CrossRef]

2009

2008

2006

H. T. Eyyuboglu, C. Arpali, and Y. K. Baykal, "Flat topped beams and their characteristics in turbulent media," Opt. Express 14(10), 4196-4207 (2006).
[CrossRef] [PubMed]

R. Peng, Y. Ye, Z. Tang, C. Zhao, S. Wen, and D. Fan, "Smoothing effect in the broadband laser through a dispersive wedge," Opt. Commun. 265(1), 106-110 (2006).
[CrossRef]

2005

2004

Q2. X. Ji, X. Xi, and B. Lu, "Effect of atmospheric turbulence on the propagation properties of spatially partially coherent polychromatic light," Acta Phys. Sinica 53, 3996-4001 (2004).

2003

2002

G. Samelsohn, and V. Freilikher, "Two-frequency mutual coherence function and pulse propagation in random media," Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(4), 046617 (2002).
[CrossRef] [PubMed]

G. Gbur, and E. Wolf, "Spreading of partially coherent beams in random media," J. Opt. Soc. Am. A 19(8), 1592-1598 (2002).
[CrossRef]

S. Ponomarenko, J.-J. Greffet, and E. Wolf, "The diffusion of partially coherent beams in turbulent media," Opt. Commun. 208(1-3), 1-8 (2002).
[CrossRef]

Y. J. Li, "Light beams with flat-topped profiles," Opt. Lett. 27(12), 1007-1009 (2002).
[CrossRef]

Y. J. Li, "New expressions for flat-topped light beams," Opt. Commun. 206(4-6), 225-234 (2002).
[CrossRef]

A. V. Morozov, "Two-frequency mutual coherence function of electromagnetic waves in random media: a path-integral variational solution," J. Opt. Soc. Am. A 19(10), 2074-2084 (2002).
[CrossRef]

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, "Partially coherent Gaussian pulses," Opt. Commun.  204(1-6), 53 -58 (2002).
[CrossRef]

1996

1994

R. Haas, and P. Banks, "Generation of high intensity broad-bandwidth light for inertial confinement fusion," Opt. Commun. 107(3-4), 265-270 (1994).
[CrossRef]

1991

1990

J. Wu, "Propagation of a Gaussian-Schell beam through turbulent media," J. Mod. Opt. 37(4), 671-684 (1990).
[CrossRef]

1986

1983

Q1. X. Deng, W. Yu, S. Chen, L. Ding, and W. Tan, "Improvement of the output power by increasing the spectral bandwidth of high-power laser," Acta Opt. Sin. 3, 97-101 (1983).

1981

R. L. Fante, "Two-position, two-frequency mutual-coherence function in turbulence," J. Opt. Soc. Am. A 71(12), 1446-1461 (1981).
[CrossRef]

1979

1978

1977

A. Ishimaru, "Theory and application of wave propagation and scattering in random media," Proc. IEEE 65(7), 1030-1061 (1977).
[CrossRef]

58, 53

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, "Partially coherent Gaussian pulses," Opt. Commun.  204(1-6), 53 -58 (2002).
[CrossRef]

Amarande, S.

Andrews, L. C.

Arpali, C.

Banks, P.

R. Haas, and P. Banks, "Generation of high intensity broad-bandwidth light for inertial confinement fusion," Opt. Commun. 107(3-4), 265-270 (1994).
[CrossRef]

Bastiaans, M. J.

Baykal, Y. K.

Biegert, J.

Boardman, A.

J. Wu, and A. Boardman, "Coherence length of a Gaussian-Schell beam and atmospheric turbulence," J. Mod. Opt. 38(7), 1355-1363 (1991).
[CrossRef]

Chen, S.

Q1. X. Deng, W. Yu, S. Chen, L. Ding, and W. Tan, "Improvement of the output power by increasing the spectral bandwidth of high-power laser," Acta Opt. Sin. 3, 97-101 (1983).

Chen, X.

Chu, X.

Dan, Y.

Dan, Y. Q.

De Silvestri, S.

Deng, X.

Q1. X. Deng, W. Yu, S. Chen, L. Ding, and W. Tan, "Improvement of the output power by increasing the spectral bandwidth of high-power laser," Acta Opt. Sin. 3, 97-101 (1983).

Ding, L.

Q1. X. Deng, W. Yu, S. Chen, L. Ding, and W. Tan, "Improvement of the output power by increasing the spectral bandwidth of high-power laser," Acta Opt. Sin. 3, 97-101 (1983).

Dogariu, A.

Du, X. Y.

Eyyuboglu, H. T.

Fan, D.

R. Peng, Y. Ye, Z. Tang, C. Zhao, S. Wen, and D. Fan, "Smoothing effect in the broadband laser through a dispersive wedge," Opt. Commun. 265(1), 106-110 (2006).
[CrossRef]

Fante, R. L.

R. L. Fante, "Two-position, two-frequency mutual-coherence function in turbulence," J. Opt. Soc. Am. A 71(12), 1446-1461 (1981).
[CrossRef]

Freilikher, V.

G. Samelsohn, and V. Freilikher, "Two-frequency mutual coherence function and pulse propagation in random media," Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(4), 046617 (2002).
[CrossRef] [PubMed]

Friberg, A. T.

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, "Partially coherent Gaussian pulses," Opt. Commun.  204(1-6), 53 -58 (2002).
[CrossRef]

Gbur, G.

Greffet, J.-J.

S. Ponomarenko, J.-J. Greffet, and E. Wolf, "The diffusion of partially coherent beams in turbulent media," Opt. Commun. 208(1-3), 1-8 (2002).
[CrossRef]

Haas, R.

R. Haas, and P. Banks, "Generation of high intensity broad-bandwidth light for inertial confinement fusion," Opt. Commun. 107(3-4), 265-270 (1994).
[CrossRef]

Ishimaru, A.

Ji, X.

X. Ji, X. Chen, and B. Lu, "Spreading and directionality of partially coherent Hermite-Gaussian beams propagating through atmospheric turbulence," J. Opt. Soc. Am. A 25(1), 21-28 (2008).
[CrossRef]

Q3. X. Ji, E. Zhang, and B. Lu, "Spreading of spatially partially coherent polychromatic beams in atmospheric turbulence," Optik (Stuttg.) 119(14), 689-694 (2008).

Q2. X. Ji, X. Xi, and B. Lu, "Effect of atmospheric turbulence on the propagation properties of spatially partially coherent polychromatic light," Acta Phys. Sinica 53, 3996-4001 (2004).

Keller, U.

Lajunen, H.

Leader, J. C.

Li, J.

Li, Y. J.

Y. J. Li, "Light beams with flat-topped profiles," Opt. Lett. 27(12), 1007-1009 (2002).
[CrossRef]

Y. J. Li, "New expressions for flat-topped light beams," Opt. Commun. 206(4-6), 225-234 (2002).
[CrossRef]

Lu, B.

J. Li, A. Yang, and B. Lu, "Comparative study of the beam-width spreading of partially coherent Hermite-sinh-Gaussian beams in atmospheric turbulence," J. Opt. Soc. Am. A 25, 2670-2679 (2008).

X. Ji, X. Chen, and B. Lu, "Spreading and directionality of partially coherent Hermite-Gaussian beams propagating through atmospheric turbulence," J. Opt. Soc. Am. A 25(1), 21-28 (2008).
[CrossRef]

Q3. X. Ji, E. Zhang, and B. Lu, "Spreading of spatially partially coherent polychromatic beams in atmospheric turbulence," Optik (Stuttg.) 119(14), 689-694 (2008).

Q2. X. Ji, X. Xi, and B. Lu, "Effect of atmospheric turbulence on the propagation properties of spatially partially coherent polychromatic light," Acta Phys. Sinica 53, 3996-4001 (2004).

Mahdieh, M.

M. Mahdieh, "Numerical approach to laser beam propagation through turbulent atmosphere and evaluation of beam quality factor," Opt. Commun. 281(13), 3395-3402 (2008).
[CrossRef]

Martínez-Herrero, R.

Mejías, P. M.

Morozov, A. V.

Nisoli, M.

Pääkkönen, P.

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, "Partially coherent Gaussian pulses," Opt. Commun.  204(1-6), 53 -58 (2002).
[CrossRef]

Pan, P. P.

Peng, R.

R. Peng, Y. Ye, Z. Tang, C. Zhao, S. Wen, and D. Fan, "Smoothing effect in the broadband laser through a dispersive wedge," Opt. Commun. 265(1), 106-110 (2006).
[CrossRef]

Plonus, M. A.

Ponomarenko, S.

S. Ponomarenko, J.-J. Greffet, and E. Wolf, "The diffusion of partially coherent beams in turbulent media," Opt. Commun. 208(1-3), 1-8 (2002).
[CrossRef]

Samelsohn, G.

G. Samelsohn, and V. Freilikher, "Two-frequency mutual coherence function and pulse propagation in random media," Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(4), 046617 (2002).
[CrossRef] [PubMed]

Sansone, G.

Schenkel, B.

Serna, J.

Shirai, T.

Sreenivasiah, I.

Stagira, S.

Svelto, O.

Tan, W.

Q1. X. Deng, W. Yu, S. Chen, L. Ding, and W. Tan, "Improvement of the output power by increasing the spectral bandwidth of high-power laser," Acta Opt. Sin. 3, 97-101 (1983).

Tang, Z.

R. Peng, Y. Ye, Z. Tang, C. Zhao, S. Wen, and D. Fan, "Smoothing effect in the broadband laser through a dispersive wedge," Opt. Commun. 265(1), 106-110 (2006).
[CrossRef]

Tervo, J.

Turunen, J.

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, "Partially coherent Gaussian pulses," Opt. Commun.  204(1-6), 53 -58 (2002).
[CrossRef]

Vahimaa, P.

H. Lajunen, P. Vahimaa, and J. Tervo, "Theory of spatially and spectrally partially coherent pulses," J. Opt. Soc. Am. A 22(8), 1536-1545 (2005).
[CrossRef]

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, "Partially coherent Gaussian pulses," Opt. Commun.  204(1-6), 53 -58 (2002).
[CrossRef]

Vozzi, C.

Wang, S. C. H.

Wen, S.

R. Peng, Y. Ye, Z. Tang, C. Zhao, S. Wen, and D. Fan, "Smoothing effect in the broadband laser through a dispersive wedge," Opt. Commun. 265(1), 106-110 (2006).
[CrossRef]

Wolf, E.

Wu, J.

J. Wu, and A. Boardman, "Coherence length of a Gaussian-Schell beam and atmospheric turbulence," J. Mod. Opt. 38(7), 1355-1363 (1991).
[CrossRef]

J. Wu, "Propagation of a Gaussian-Schell beam through turbulent media," J. Mod. Opt. 37(4), 671-684 (1990).
[CrossRef]

Wyrowski, F.

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, "Partially coherent Gaussian pulses," Opt. Commun.  204(1-6), 53 -58 (2002).
[CrossRef]

Xi, X.

Q2. X. Ji, X. Xi, and B. Lu, "Effect of atmospheric turbulence on the propagation properties of spatially partially coherent polychromatic light," Acta Phys. Sinica 53, 3996-4001 (2004).

Yang, A.

Ye, Y.

R. Peng, Y. Ye, Z. Tang, C. Zhao, S. Wen, and D. Fan, "Smoothing effect in the broadband laser through a dispersive wedge," Opt. Commun. 265(1), 106-110 (2006).
[CrossRef]

Young, C. Y.

Yu, W.

Q1. X. Deng, W. Yu, S. Chen, L. Ding, and W. Tan, "Improvement of the output power by increasing the spectral bandwidth of high-power laser," Acta Opt. Sin. 3, 97-101 (1983).

Zhang, B.

Zhang, E.

Q3. X. Ji, E. Zhang, and B. Lu, "Spreading of spatially partially coherent polychromatic beams in atmospheric turbulence," Optik (Stuttg.) 119(14), 689-694 (2008).

Zhao, C.

R. Peng, Y. Ye, Z. Tang, C. Zhao, S. Wen, and D. Fan, "Smoothing effect in the broadband laser through a dispersive wedge," Opt. Commun. 265(1), 106-110 (2006).
[CrossRef]

Zhao, D. M.

Zhou, G.

Zhu, Y. B.

Acta Opt. Sin.

Q1. X. Deng, W. Yu, S. Chen, L. Ding, and W. Tan, "Improvement of the output power by increasing the spectral bandwidth of high-power laser," Acta Opt. Sin. 3, 97-101 (1983).

Acta Phys. Sinica

Q2. X. Ji, X. Xi, and B. Lu, "Effect of atmospheric turbulence on the propagation properties of spatially partially coherent polychromatic light," Acta Phys. Sinica 53, 3996-4001 (2004).

Appl. Opt.

J. Mod. Opt.

J. Wu, "Propagation of a Gaussian-Schell beam through turbulent media," J. Mod. Opt. 37(4), 671-684 (1990).
[CrossRef]

J. Wu, and A. Boardman, "Coherence length of a Gaussian-Schell beam and atmospheric turbulence," J. Mod. Opt. 38(7), 1355-1363 (1991).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

R. L. Fante, "Two-position, two-frequency mutual-coherence function in turbulence," J. Opt. Soc. Am. A 71(12), 1446-1461 (1981).
[CrossRef]

Y. Q. Dan, B. Zhang, and P. P. Pan, "Propagation of partially coherent flat-topped beams through a turbulent atmosphere," J. Opt. Soc. Am. A 25(9), 2223-2231 (2008).
[CrossRef]

H. Lajunen, P. Vahimaa, and J. Tervo, "Theory of spatially and spectrally partially coherent pulses," J. Opt. Soc. Am. A 22(8), 1536-1545 (2005).
[CrossRef]

G. Gbur, and E. Wolf, "Spreading of partially coherent beams in random media," J. Opt. Soc. Am. A 19(8), 1592-1598 (2002).
[CrossRef]

J. Li, A. Yang, and B. Lu, "Comparative study of the beam-width spreading of partially coherent Hermite-sinh-Gaussian beams in atmospheric turbulence," J. Opt. Soc. Am. A 25, 2670-2679 (2008).

X. Ji, X. Chen, and B. Lu, "Spreading and directionality of partially coherent Hermite-Gaussian beams propagating through atmospheric turbulence," J. Opt. Soc. Am. A 25(1), 21-28 (2008).
[CrossRef]

A. V. Morozov, "Two-frequency mutual coherence function of electromagnetic waves in random media: a path-integral variational solution," J. Opt. Soc. Am. A 19(10), 2074-2084 (2002).
[CrossRef]

T. Shirai, A. Dogariu, and E. Wolf, "Mode analysis of spreading of partially coherent beams propagating through atmospheric turbulence," J. Opt. Soc. Am. A 20(6), 1094-1102 (2003).
[CrossRef]

M. J. Bastiaans, "Application of the Wigner distribution function to partially coherent light," J. Opt. Soc. Am. A 3(8), 1227-1238 (1986).
[CrossRef]

J. Serna, R. Martínez-Herrero, and P. M. Mejías, "Parametric characterization of general partially coherent beams propagating through ABCD optical systems," J. Opt. Soc. Am. A 8(7), 1094-1098 (1991).
[CrossRef]

Opt. Commun

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, "Partially coherent Gaussian pulses," Opt. Commun.  204(1-6), 53 -58 (2002).
[CrossRef]

Opt. Commun.

M. Mahdieh, "Numerical approach to laser beam propagation through turbulent atmosphere and evaluation of beam quality factor," Opt. Commun. 281(13), 3395-3402 (2008).
[CrossRef]

S. Ponomarenko, J.-J. Greffet, and E. Wolf, "The diffusion of partially coherent beams in turbulent media," Opt. Commun. 208(1-3), 1-8 (2002).
[CrossRef]

R. Haas, and P. Banks, "Generation of high intensity broad-bandwidth light for inertial confinement fusion," Opt. Commun. 107(3-4), 265-270 (1994).
[CrossRef]

R. Peng, Y. Ye, Z. Tang, C. Zhao, S. Wen, and D. Fan, "Smoothing effect in the broadband laser through a dispersive wedge," Opt. Commun. 265(1), 106-110 (2006).
[CrossRef]

Y. J. Li, "New expressions for flat-topped light beams," Opt. Commun. 206(4-6), 225-234 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

Optik (Stuttg.)

Q3. X. Ji, E. Zhang, and B. Lu, "Spreading of spatially partially coherent polychromatic beams in atmospheric turbulence," Optik (Stuttg.) 119(14), 689-694 (2008).

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

G. Samelsohn, and V. Freilikher, "Two-frequency mutual coherence function and pulse propagation in random media," Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(4), 046617 (2002).
[CrossRef] [PubMed]

Proc. IEEE

A. Ishimaru, "Theory and application of wave propagation and scattering in random media," Proc. IEEE 65(7), 1030-1061 (1977).
[CrossRef]

Other

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

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

L. C. Andrews, and R. L. Phillips, Laser Beam Propagation through Random Media, (SPIE Press, Bellingham, WA, 1998).

A. Erdelyi, Tables of Integral Transforms (McGraw-Hill, New York, 1954).

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 (6)

Fig. 1.
Fig. 1.

The relative beam width of BPCFT beams with different spectral bandwidth in atmospheric turbulence and in free space. Solid signs in (a) and (b) denote the cases of Cn 2 = 1.0×10-14 m-2/3 and Cn 2 = 1.0×10-15 m-2/3, respectively. Hollow signs in (a) and (b) denote the case of free space.

Fig. 2.
Fig. 2.

The divergence angle and relative divergence angle of BPCFT beams with different spectral bandwidth in atmospheric turbulence and in free space. Other captions are the same as Fig. 1.

Fig. 3.
Fig. 3.

The relative beam width of BPCFT and BFCFT beams with different spectral bandwidth in atmospheric turbulence. Solid signs in (a) and (b) denote the cases of σ 0 = 0.2w 0 and σ 0 = 2w 0, respectively. Hollow signs in (a) and (b) denote the case of BFCFT beams.

Fig. 4.
Fig. 4.

The divergence angle and relative divergence angle of BPCFT and BFCFT beams with different spectral bandwidth in atmospheric turbulence, other captions are the same as Fig. 3.

Fig. 5.
Fig. 5.

The beam propagation factor and relative beam propagation factor of BPCFT beams with different spectral bandwidth in atmospheric turbulence and in free space. Solid signs in (a) and (b) denote the cases of Cn 2 = 1.0 × 10-14 m-2/3 and Cn2 = 1.0 × 10-15 m-2/3, respectively. Hollow signs in (a) and (b) denote the case of free space.

Fig. 6.
Fig. 6.

The beam propagation factor and relative beam propagation factor of BPCFT and BFCFT beams with different spectral bandwidth in atmospheric turbulence. Solid signs in (a) and (b) denote the cases of σ 0 = 0.2w 0 and σ 0 = 2w 0, respectively. Hollow signs in (a) and (b) denote the case of BFCFT beams.

Equations (40)

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

E ( r ) = l = 1 L α l exp [ l p L ( r w 0 ) 2 ] ,
α l = ( 1 ) l + 1 L ! l ! ( L l ) ! ,
p L = 2 l = 1 L l = 1 L α l α l l + l .
E r l v E * ( r 2 , v ) = W r 1 r 2 v δ ( v v ) ,
W ( 0 ) r 1 r 2 0 ω 1 ω 2 = E ( r 1 ) s ( ω 1 ) E * ( r 2 ) s * ( ω 2 ) δ ( ω 1 ω 2 ) ,
W ( 0 ) r 1 r 2 0 ω = l = 1 L l = 1 L α l α l exp { [ ( l p L r 1 ′2 w 0 2 ) + ( l p L r 2 ′2 w 0 2 ) + r 1 r 2 2 2 σ 0 2 ] } s 2 ( ω ) ,
W r 1 r 2 z ω = ( k 2 πz ) 2 + + d 2 r 1 + + d 2 r 2 W ( 0 ) r 1 r 2 0 ω × exp { ( ik 2 z ) [ ( r 1 r 1 ) 2 ( r 2 r 2 ) 2 ] } × exp [ ψ r 1 r 1 z ω + ψ * r 2 r 2 z ω ] m ,
exp [ ψ r 1 r 1 z ω + ψ * r 2 r 2 z ω ] m exp [ ( r 1 r 2 ) 2 + ( r 1 r 2 ) ( r 1 r 2 ) + ( r 1 r 2 ) 2 ρ 0 2 ] ,
ρ 0 = ( 0.545 C n 2 k 2 z ) 3 / 5 ,
+ exp [ ( a x 2 + 2 bx + c ) ] d x = ( π a ) 1 / 2 exp ( b 2 ac a ) ,
W r 1 r 2 z ω = ( k 2 z ) 2 s 2 ( ω ) exp [ ik 2 z ( r 1 2 r 2 2 ) 1 ρ 0 2 ( r 1 r 2 ) 2 ] × l = 1 L l = 1 L α l α l 1 AB C 2 exp { 1 A [ ik 2 z r 1 + 1 2 ρ 0 2 ( r 2 r 1 ) ] 2 } × exp { 1 A 2 B A C 2 [ ik 2 z ( A r 2 C r 1 ) + 1 2 ρ 0 2 ( A C ) ( r 2 r 1 ) ] 2 } ,
A = l p L w 0 2 + 1 2 σ 0 2 + ik 2 z + 1 ρ 0 2 ,
B = l p L w 0 2 + 1 2 σ 0 2 ik 2 z + 1 ρ 0 2 ,
C = 1 2 σ 0 2 + 1 ρ 0 2 .
S R z ω = W R R z ω = ( k 2 z ) 2 s 2 ( ω ) l = 1 L l = 1 L α l α l 1 AB C 2 exp [ 1 A ( ik 2 z R ) 2 ] × exp { 1 A 2 B A C 2 [ ik 2 z ( A C ) R ] 2 } .
I R z = 0 + S R z ω d ω .
W r 1 r 2 z ω = ( k 2 z ) 2 s 2 ( ω ) exp [ ik 2 z ( r 1 2 r 2 2 ) ] × 1 AB C 2 exp [ 1 A ( ik 2 z r 1 ) 2 ] × exp { 1 A 2 B A C 2 [ ik ( A r 2 C r 1 ) 2 z ] 2 } .
h r θ z = ( k 2 π ) 2 + + W r r d z ω exp ( ik θ r d ) d 2 r d ,
r = 1 2 ( r 1 + r 2 ) ,
r d = r 1 r 2 ,
W r r d z ω = ( k 2 z ) 2 s 2 ( ω ) l = 1 L l = 1 L α l α l 1 AB C 2 × exp [ A + B 2 C AB C 2 ( ik 2 z ) 2 r 2 D r d 2 2 E r r d ] ,
D = 1 4 ρ 0 4 A + B 2 C AB C 2 + 1 ρ 0 2 ( 1 1 2 ik 2 z A B AB C 2 ) ( ik 2 z ) 2 A + B + 2 C 4 ( AB C 2 ) ,
E = ik 2 z + ( ik 2 z ) 2 A B 2 ( AB C 2 ) + ik 2 z 1 2 ρ 0 2 A + B 2 C AB C 2 .
h r θ z ω = k 4 16 π z 2 s 2 ( ω ) l = 1 L l = 1 L α l α l 1 D ( AB C 2 ) × exp [ A + B 2 C AB C 2 ( ik 2 z ) 2 r 2 + 1 D ( E r + 1 2 ik θ ) 2 ] ,
x n 1 y n 2 θ x m 1 θ y m 2 = 1 P + + + + x n 1 y n 2 θ x m 1 θ y m 2 h r θ z ω d 2 r d 2 θ ,
x n 1 y n 2 θ x m 1 θ y m 2 = 1 P 0 + d ω + + + + x n 1 y n 2 θ x m 1 θ y m 2 h r θ z ω d 2 r d 2 θ ,
P = 0 + d ω + + + + h r θ z ω d 2 r d 2 θ .
r 2 = x 2 + y 2 ,
θ 2 = θ x 2 + θ y 2 ,
r θ = x θ x + y θ y .
+ x 2 exp [ ( a x 2 + 2 bx + c ) ] d x = a + 2 b 2 2 a 2 ( π a ) 1 / 2 exp ( b 2 ac a ) ,
+ x exp [ ( a x 2 + 2 bx + c ) ] d x = b a ( π a ) 1 / 2 exp ( b 2 ac a ) ,
x 2 = y 2 = 1 P 0 + d ω s 2 ( ω ) 2 π z 2 k 2 l = 1 L l = l L α l α l AB C 2 ( A + B 2 C ) 2 ,
θ x 2 = θ y 2 = 1 P 0 + d ω s 2 ( ω ) 2 π k 4 l = 1 L l = l L α l α l × k 2 D ( A + B 2 C ) 4 z 2 E 2 ( AB C 2 ) ( A + B 2 C ) 2 ,
x θ x = y θ y = 1 P 0 + d ω s 2 ( ω ) i 4 π z 2 k 3 l = 1 L l = l L α l α l E ( AB C 2 ) ( A + B 2 C ) 2 ,
P = 0 + d ω s 2 ( ω ) l = 1 L l = 1 L α l α l π ( A + B 2 C ) .
w ( z ) = w x ( z ) = w y ( z ) = x 2 1 / 2 = y 2 1 / 2 ,
θ ( z ) = θ x ( z ) = θ y ( z ) = θ x 2 1 / 2 = θ y 2 1 / 2 ,
M 2 = k 0 [ ( x 2 + y 2 ) ( θ x 2 + θ y 2 ) ( x θ x + y θ y ) 2 ] 1 / 2 ,
s ( ω ) = { 1 ω ω 0 Δ ω / 2 , 0 ω ω 0 > Δ ω / 2 .

Metrics