Abstract

We numerically investigate partially coherent short pulse propagation in nonlinear media near optical resonance. We examine how the pulse state of coherence at the source affects the evolution of the ensemble averaged intensity, mutual coherence function, and temporal degree of coherence of the pulse ensemble. We report evidence of self-induced transparency random phase soliton formation for the relatively coherent incident pulses with sufficiently large average areas. We also show that random pulses lose their coherence on propagation in resonant media and we explain this phenomenon in qualitative terms.

© 2015 Optical Society of America

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References

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  1. R. W. Boyd, Nonlinear Optics (Academic Press, 2008).
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  4. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007).
  5. M. Bertolotti, A. Ferrari, and L. Sereda, “Coherence properties of nonstationary polychromatic light sources,” J. Opt. Soc. Am. B 12, 341–347 (1995).
    [Crossref]
  6. L. Sereda, M. Bertolotti, and A. Ferrari, “Coherence properties of nonstationary light wave fields,” J. Opt. Soc. Am. B 15, 695–705 (1998).
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  7. H. Lajunen, J. Tervo, J. Turunen, P. Vahimaa, and F. Wyrowski, “Spectral coherence properties of temporarily modulated stationary light sources,” Opt. Express 11, 1894–1899 (2003).
    [Crossref] [PubMed]
  8. L. Ma and S. A. Ponomarenko, “Optical coherence gratings and lattices,” Opt. Lett. 39, 6656 (2014).
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  9. P. Paakkonen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun. 204, 53–58 (2002).
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  10. S. A. Ponomarenko, G. P. Agrawal, and E. Wolf, “Energy spectrum of a nonstationary ensemble of pulses,” Opt. Lett. 29, 394–396 (2004).
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  11. P. Vahimaa and J. Turunen, “Independent-elementary-pulse representation for non-stationary fields,” Opt. Express 14, 5007–5012 (2006).
    [Crossref] [PubMed]
  12. S. A. Ponomarenko, “Complex Gaussian representation of statistical pulses,” Opt. Express 19, 17086–17091 (2011).
    [Crossref] [PubMed]
  13. Q. Lin, L. Wang, and S. Zhu, “Partially coherent light pulse and its propagation,” Opt. Commun. 219, 65–70 (2003).
    [Crossref]
  14. M. Brunel and S. Coëtlemec, “Fractional-order Fourier formulation of the propagation of partially coherent light pulses,” Opt. Commun. 230, 1–5 (2004).
    [Crossref]
  15. W. Huang, S. A. Ponomarenko, M. Cada, and G. P. Agrawal, “Polarization changes of partially coherent pulses propagating in optical fibers,” J. Opt. Soc. Am. A 24, 3063–3068 (2007).
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  18. S. A. Ponomarenko, “Degree of phase-space separability of statistical pulses,” Opt. Express 20, 2548–2555 (2012).
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  19. S. A. Ponomarenko, “Self-imaging of partially coherent light in graded-index media,” Opt. Lett. 40, 566 (2015).
    [Crossref] [PubMed]
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    [Crossref]
  22. S. B. Cavalcanti, G. P. Agrawal, and M. Yu, “Noise amplification in dispersive nonlinear media,” Phys. Rev. A 51, 4086–4092 (1995).
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  23. H. Lajunen, V. Torres-Company, J. Lancis, E. Silvestre, and P. Andrés, “Pulse-by-pulse method to characterize partially coherent pulse propagation in instantaneous nonlinear media,” Opt. Express 18, 14979–14991 (2011).
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  24. L. Mokhtarpour and S. A. Ponomarenko, “Complex area correlation theorem for statistical pulses in coherent linear absorbers,” Opt. Lett. 37, 3498–3500 (2012).
    [Crossref] [PubMed]
  25. L. Mokhtarpour and S. A. Ponomarenko, “Ultrashort pulse coherence properties in coherent linear amplifiers,” J. Opt. Soc. Am. A 30, 627–630 (2013).
    [Crossref]
  26. L. Mokhtarpour, G. H. Akter, and S. A. Ponomarenko, “Partially coherent self-similar pulses in resonant linear absorbers,” Opt. Express 20, 17816–17822 (2012).
    [Crossref] [PubMed]
  27. L. Allen and J. H. Eberly, Optical Resonance and Two-level Atoms (Dover, 1975).
  28. J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic Press, 2006)
  29. L. Banyai and S. W. Koch, Semiconductor Quantum Dots (World Scientific, 1993).
  30. Y. Wu and L. Deng, “Ultraslow bright and dark optical solitons in a cold three-state system,” Opt. Lett. 29, 2064–2066 (2004).
    [Crossref] [PubMed]
  31. C. Hang and G. Huang, “Giant Kerr nonlinearity and weak-light superluminal optical solitons in a four-state atomic system with gain doublet,” Opt. Express 18, 2952–2966 (2010).
    [Crossref] [PubMed]
  32. W-X. Yang, Ai-Xi Chen, L-G. Si, K. Jiang, X. Yang, and R-K. Lee, “Three coupled ultraslow solitons in a five-level tripod system,” Phys. Rev. A 81023814 (2010).
    [Crossref]
  33. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1997).
  34. S. A. Ponomarenko and E. Wolf, “Coherence properties of light in Young’s interference pattern formed with partially coherent light,” Opt. Commun. 170, 1–8 (1999).
    [Crossref]
  35. S. A. Ponomarenko, H. Roychoudhury, and E. Wolf, “Physical significance of complete spatial coherence of optical fields,” Phys. Lett. A,  345, 10–12 (2005).
    [Crossref]
  36. S. A. Ponomarenko and E. Wolf, “The spectral degree of coherence of fully spatially coherent electromagnetic beams,” Opt. Commun. 227, 73–74 (2003).
    [Crossref]
  37. A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics: Mechanics of Turbulence, Vols. 1& 2, (Dover, 2007).
  38. G. A. Pasmanik, “Self-interaction of incoherent light beams,” Sov. Phys. JETP,  39, 234–238 (1974).
  39. M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Theory of Self-Trapped Spatially Incoherent Light Beams,” Phys. Rev. Lett. 79, 4990–4993 (1997).
    [Crossref]
  40. D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, “Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media,” Phys. Rev. E 63, 035601(R) (2001).
    [Crossref]
  41. S. A. Ponomarenko, N. M. Litchinitser, and G. P. Agrawal, “Theory of incoherent solitons: Beyond the mean-field approximation,” Phys. Rev. E 70, 015603(R) (2004).
    [Crossref]
  42. V. P. Kandidov, “Monte Carlo method in nonlinear statistical optics”, Sov. Phys.Usp. 39, 1243–1272 (1996).
  43. X. Xiao and D. Voelz, “Wave optics simulation approach for partial spatially coherent beams,” Opt. Express 16, 6986–6992 (2006).
    [Crossref]
  44. S. A. Parhl, D. G. Fischer, and D. D. Duncan, “Monte Carlo Green’s function for the propagation of partially coherent light,” J. Opt. Soc. Am. A 260, 1533–1543 (2009).
    [Crossref]
  45. E. Wolf, “New spectral representation of random sources and of the partially coherent fields that they generate,” Opt. Commun. 38, 3–6 (1981).
    [Crossref]
  46. F. Gori, “Collett-Wolf sources and multimode lasers,” Opt. Commun. 34, 301–305 (1980).
    [Crossref]
  47. A. Starikov and E. Wolf, “Coherent-mode representation of Gaussian Schell-model sources and of their radiation fields,” J. Opt. Soc. Am. A 72, 923–928 (1982).
  48. P. W. Milonni and J. H. Eberly, Lasers (Wiley, 1985).

2015 (1)

2014 (1)

2013 (1)

2012 (3)

2011 (2)

2010 (2)

W-X. Yang, Ai-Xi Chen, L-G. Si, K. Jiang, X. Yang, and R-K. Lee, “Three coupled ultraslow solitons in a five-level tripod system,” Phys. Rev. A 81023814 (2010).
[Crossref]

C. Hang and G. Huang, “Giant Kerr nonlinearity and weak-light superluminal optical solitons in a four-state atomic system with gain doublet,” Opt. Express 18, 2952–2966 (2010).
[Crossref] [PubMed]

2009 (3)

2007 (1)

2006 (3)

P. Vahimaa and J. Turunen, “Independent-elementary-pulse representation for non-stationary fields,” Opt. Express 14, 5007–5012 (2006).
[Crossref] [PubMed]

S. A. Ponomarenko and G. P. Agrawal, “Linear optical bullets,” Opt. Commun. 261, 1–4 (2006).
[Crossref]

X. Xiao and D. Voelz, “Wave optics simulation approach for partial spatially coherent beams,” Opt. Express 16, 6986–6992 (2006).
[Crossref]

2005 (1)

S. A. Ponomarenko, H. Roychoudhury, and E. Wolf, “Physical significance of complete spatial coherence of optical fields,” Phys. Lett. A,  345, 10–12 (2005).
[Crossref]

2004 (4)

S. A. Ponomarenko, N. M. Litchinitser, and G. P. Agrawal, “Theory of incoherent solitons: Beyond the mean-field approximation,” Phys. Rev. E 70, 015603(R) (2004).
[Crossref]

M. Brunel and S. Coëtlemec, “Fractional-order Fourier formulation of the propagation of partially coherent light pulses,” Opt. Commun. 230, 1–5 (2004).
[Crossref]

S. A. Ponomarenko, G. P. Agrawal, and E. Wolf, “Energy spectrum of a nonstationary ensemble of pulses,” Opt. Lett. 29, 394–396 (2004).
[Crossref] [PubMed]

Y. Wu and L. Deng, “Ultraslow bright and dark optical solitons in a cold three-state system,” Opt. Lett. 29, 2064–2066 (2004).
[Crossref] [PubMed]

2003 (3)

H. Lajunen, J. Tervo, J. Turunen, P. Vahimaa, and F. Wyrowski, “Spectral coherence properties of temporarily modulated stationary light sources,” Opt. Express 11, 1894–1899 (2003).
[Crossref] [PubMed]

Q. Lin, L. Wang, and S. Zhu, “Partially coherent light pulse and its propagation,” Opt. Commun. 219, 65–70 (2003).
[Crossref]

S. A. Ponomarenko and E. Wolf, “The spectral degree of coherence of fully spatially coherent electromagnetic beams,” Opt. Commun. 227, 73–74 (2003).
[Crossref]

2002 (1)

P. Paakkonen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun. 204, 53–58 (2002).
[Crossref]

2001 (1)

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, “Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media,” Phys. Rev. E 63, 035601(R) (2001).
[Crossref]

1999 (1)

S. A. Ponomarenko and E. Wolf, “Coherence properties of light in Young’s interference pattern formed with partially coherent light,” Opt. Commun. 170, 1–8 (1999).
[Crossref]

1998 (1)

L. Sereda, M. Bertolotti, and A. Ferrari, “Coherence properties of nonstationary light wave fields,” J. Opt. Soc. Am. B 15, 695–705 (1998).
[Crossref]

1997 (1)

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Theory of Self-Trapped Spatially Incoherent Light Beams,” Phys. Rev. Lett. 79, 4990–4993 (1997).
[Crossref]

1996 (1)

V. P. Kandidov, “Monte Carlo method in nonlinear statistical optics”, Sov. Phys.Usp. 39, 1243–1272 (1996).

1995 (2)

S. B. Cavalcanti, G. P. Agrawal, and M. Yu, “Noise amplification in dispersive nonlinear media,” Phys. Rev. A 51, 4086–4092 (1995).
[Crossref] [PubMed]

M. Bertolotti, A. Ferrari, and L. Sereda, “Coherence properties of nonstationary polychromatic light sources,” J. Opt. Soc. Am. B 12, 341–347 (1995).
[Crossref]

1991 (1)

1988 (1)

V. A. Aleshkevich, V. A. Vysloukh, G. D. Kozhoridze, A. N. Matveev, and S. I. Terzieva, “Nonlinear propagation of partially coherent pulse in fiber waveguide and the role of higher order dispersion,” Sov. J. Quantum Electron. 18, 207–211 (1988).
[Crossref]

1982 (1)

A. Starikov and E. Wolf, “Coherent-mode representation of Gaussian Schell-model sources and of their radiation fields,” J. Opt. Soc. Am. A 72, 923–928 (1982).

1981 (1)

E. Wolf, “New spectral representation of random sources and of the partially coherent fields that they generate,” Opt. Commun. 38, 3–6 (1981).
[Crossref]

1980 (1)

F. Gori, “Collett-Wolf sources and multimode lasers,” Opt. Commun. 34, 301–305 (1980).
[Crossref]

1974 (1)

G. A. Pasmanik, “Self-interaction of incoherent light beams,” Sov. Phys. JETP,  39, 234–238 (1974).

Agrawal, G. P.

W. Huang, S. A. Ponomarenko, M. Cada, and G. P. Agrawal, “Polarization changes of partially coherent pulses propagating in optical fibers,” J. Opt. Soc. Am. A 24, 3063–3068 (2007).
[Crossref]

S. A. Ponomarenko and G. P. Agrawal, “Linear optical bullets,” Opt. Commun. 261, 1–4 (2006).
[Crossref]

S. A. Ponomarenko, G. P. Agrawal, and E. Wolf, “Energy spectrum of a nonstationary ensemble of pulses,” Opt. Lett. 29, 394–396 (2004).
[Crossref] [PubMed]

S. A. Ponomarenko, N. M. Litchinitser, and G. P. Agrawal, “Theory of incoherent solitons: Beyond the mean-field approximation,” Phys. Rev. E 70, 015603(R) (2004).
[Crossref]

S. B. Cavalcanti, G. P. Agrawal, and M. Yu, “Noise amplification in dispersive nonlinear media,” Phys. Rev. A 51, 4086–4092 (1995).
[Crossref] [PubMed]

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007).

Akter, G. H.

Aleshkevich, V. A.

V. A. Aleshkevich, V. A. Vysloukh, G. D. Kozhoridze, A. N. Matveev, and S. I. Terzieva, “Nonlinear propagation of partially coherent pulse in fiber waveguide and the role of higher order dispersion,” Sov. J. Quantum Electron. 18, 207–211 (1988).
[Crossref]

Allen, L.

L. Allen and J. H. Eberly, Optical Resonance and Two-level Atoms (Dover, 1975).

Andrés, P.

Banerjee, P. P.

P. P. Banerjee, Nonlinear Optics: Theory, Numerical Modeling and Applications (Marcel Decker, 2004).

Banyai, L.

L. Banyai and S. W. Koch, Semiconductor Quantum Dots (World Scientific, 1993).

Bartels, R. A.

Bertolotti, M.

L. Sereda, M. Bertolotti, and A. Ferrari, “Coherence properties of nonstationary light wave fields,” J. Opt. Soc. Am. B 15, 695–705 (1998).
[Crossref]

M. Bertolotti, A. Ferrari, and L. Sereda, “Coherence properties of nonstationary polychromatic light sources,” J. Opt. Soc. Am. B 12, 341–347 (1995).
[Crossref]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic Press, 2008).

Brunel, M.

M. Brunel and S. Coëtlemec, “Fractional-order Fourier formulation of the propagation of partially coherent light pulses,” Opt. Commun. 230, 1–5 (2004).
[Crossref]

Cada, M.

Carney, P. S.

Cavalcanti, S. B.

S. B. Cavalcanti, G. P. Agrawal, and M. Yu, “Noise amplification in dispersive nonlinear media,” Phys. Rev. A 51, 4086–4092 (1995).
[Crossref] [PubMed]

Chen, Ai-Xi

W-X. Yang, Ai-Xi Chen, L-G. Si, K. Jiang, X. Yang, and R-K. Lee, “Three coupled ultraslow solitons in a five-level tripod system,” Phys. Rev. A 81023814 (2010).
[Crossref]

Christodoulides, D. N.

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, “Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media,” Phys. Rev. E 63, 035601(R) (2001).
[Crossref]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Theory of Self-Trapped Spatially Incoherent Light Beams,” Phys. Rev. Lett. 79, 4990–4993 (1997).
[Crossref]

Coëtlemec, S.

M. Brunel and S. Coëtlemec, “Fractional-order Fourier formulation of the propagation of partially coherent light pulses,” Opt. Commun. 230, 1–5 (2004).
[Crossref]

Coskun, T. H.

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, “Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media,” Phys. Rev. E 63, 035601(R) (2001).
[Crossref]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Theory of Self-Trapped Spatially Incoherent Light Beams,” Phys. Rev. Lett. 79, 4990–4993 (1997).
[Crossref]

Davis, B. J.

Deng, L.

Diels, J. C.

J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic Press, 2006)

Ding, C. L.

Duncan, D. D.

S. A. Parhl, D. G. Fischer, and D. D. Duncan, “Monte Carlo Green’s function for the propagation of partially coherent light,” J. Opt. Soc. Am. A 260, 1533–1543 (2009).
[Crossref]

Eberly, J. H.

P. W. Milonni and J. H. Eberly, Lasers (Wiley, 1985).

L. Allen and J. H. Eberly, Optical Resonance and Two-level Atoms (Dover, 1975).

Eugenieva, E. D.

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, “Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media,” Phys. Rev. E 63, 035601(R) (2001).
[Crossref]

Ferrari, A.

L. Sereda, M. Bertolotti, and A. Ferrari, “Coherence properties of nonstationary light wave fields,” J. Opt. Soc. Am. B 15, 695–705 (1998).
[Crossref]

M. Bertolotti, A. Ferrari, and L. Sereda, “Coherence properties of nonstationary polychromatic light sources,” J. Opt. Soc. Am. B 12, 341–347 (1995).
[Crossref]

Fischer, D. G.

S. A. Parhl, D. G. Fischer, and D. D. Duncan, “Monte Carlo Green’s function for the propagation of partially coherent light,” J. Opt. Soc. Am. A 260, 1533–1543 (2009).
[Crossref]

Friberg, A. T.

P. Paakkonen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun. 204, 53–58 (2002).
[Crossref]

Gori, F.

F. Gori, “Collett-Wolf sources and multimode lasers,” Opt. Commun. 34, 301–305 (1980).
[Crossref]

Gross, B.

Hang, C.

Huang, G.

Huang, W.

Jiang, K.

W-X. Yang, Ai-Xi Chen, L-G. Si, K. Jiang, X. Yang, and R-K. Lee, “Three coupled ultraslow solitons in a five-level tripod system,” Phys. Rev. A 81023814 (2010).
[Crossref]

Kandidov, V. P.

V. P. Kandidov, “Monte Carlo method in nonlinear statistical optics”, Sov. Phys.Usp. 39, 1243–1272 (1996).

Koch, S. W.

L. Banyai and S. W. Koch, Semiconductor Quantum Dots (World Scientific, 1993).

Kozhoridze, G. D.

V. A. Aleshkevich, V. A. Vysloukh, G. D. Kozhoridze, A. N. Matveev, and S. I. Terzieva, “Nonlinear propagation of partially coherent pulse in fiber waveguide and the role of higher order dispersion,” Sov. J. Quantum Electron. 18, 207–211 (1988).
[Crossref]

Lajunen, H.

Lancis, J.

Lee, R-K.

W-X. Yang, Ai-Xi Chen, L-G. Si, K. Jiang, X. Yang, and R-K. Lee, “Three coupled ultraslow solitons in a five-level tripod system,” Phys. Rev. A 81023814 (2010).
[Crossref]

Lin, Q.

Q. Lin, L. Wang, and S. Zhu, “Partially coherent light pulse and its propagation,” Opt. Commun. 219, 65–70 (2003).
[Crossref]

Litchinitser, N. M.

S. A. Ponomarenko, N. M. Litchinitser, and G. P. Agrawal, “Theory of incoherent solitons: Beyond the mean-field approximation,” Phys. Rev. E 70, 015603(R) (2004).
[Crossref]

Lu, B. D.

Ma, L.

Manassah, J. T.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1997).

Matveev, A. N.

V. A. Aleshkevich, V. A. Vysloukh, G. D. Kozhoridze, A. N. Matveev, and S. I. Terzieva, “Nonlinear propagation of partially coherent pulse in fiber waveguide and the role of higher order dispersion,” Sov. J. Quantum Electron. 18, 207–211 (1988).
[Crossref]

Milonni, P. W.

P. W. Milonni and J. H. Eberly, Lasers (Wiley, 1985).

Mitchell, M.

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, “Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media,” Phys. Rev. E 63, 035601(R) (2001).
[Crossref]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Theory of Self-Trapped Spatially Incoherent Light Beams,” Phys. Rev. Lett. 79, 4990–4993 (1997).
[Crossref]

Mokhtarpour, L.

Monin, A. S.

A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics: Mechanics of Turbulence, Vols. 1& 2, (Dover, 2007).

Paakkonen, P.

P. Paakkonen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun. 204, 53–58 (2002).
[Crossref]

Pan, L. Z.

Parhl, S. A.

S. A. Parhl, D. G. Fischer, and D. D. Duncan, “Monte Carlo Green’s function for the propagation of partially coherent light,” J. Opt. Soc. Am. A 260, 1533–1543 (2009).
[Crossref]

Pasmanik, G. A.

G. A. Pasmanik, “Self-interaction of incoherent light beams,” Sov. Phys. JETP,  39, 234–238 (1974).

Ponomarenko, S. A.

S. A. Ponomarenko, “Self-imaging of partially coherent light in graded-index media,” Opt. Lett. 40, 566 (2015).
[Crossref] [PubMed]

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

L. Mokhtarpour and S. A. Ponomarenko, “Ultrashort pulse coherence properties in coherent linear amplifiers,” J. Opt. Soc. Am. A 30, 627–630 (2013).
[Crossref]

L. Mokhtarpour, G. H. Akter, and S. A. Ponomarenko, “Partially coherent self-similar pulses in resonant linear absorbers,” Opt. Express 20, 17816–17822 (2012).
[Crossref] [PubMed]

L. Mokhtarpour and S. A. Ponomarenko, “Complex area correlation theorem for statistical pulses in coherent linear absorbers,” Opt. Lett. 37, 3498–3500 (2012).
[Crossref] [PubMed]

S. A. Ponomarenko, “Degree of phase-space separability of statistical pulses,” Opt. Express 20, 2548–2555 (2012).
[Crossref] [PubMed]

S. A. Ponomarenko, “Complex Gaussian representation of statistical pulses,” Opt. Express 19, 17086–17091 (2011).
[Crossref] [PubMed]

W. Huang, S. A. Ponomarenko, M. Cada, and G. P. Agrawal, “Polarization changes of partially coherent pulses propagating in optical fibers,” J. Opt. Soc. Am. A 24, 3063–3068 (2007).
[Crossref]

S. A. Ponomarenko and G. P. Agrawal, “Linear optical bullets,” Opt. Commun. 261, 1–4 (2006).
[Crossref]

S. A. Ponomarenko, H. Roychoudhury, and E. Wolf, “Physical significance of complete spatial coherence of optical fields,” Phys. Lett. A,  345, 10–12 (2005).
[Crossref]

S. A. Ponomarenko, N. M. Litchinitser, and G. P. Agrawal, “Theory of incoherent solitons: Beyond the mean-field approximation,” Phys. Rev. E 70, 015603(R) (2004).
[Crossref]

S. A. Ponomarenko, G. P. Agrawal, and E. Wolf, “Energy spectrum of a nonstationary ensemble of pulses,” Opt. Lett. 29, 394–396 (2004).
[Crossref] [PubMed]

S. A. Ponomarenko and E. Wolf, “The spectral degree of coherence of fully spatially coherent electromagnetic beams,” Opt. Commun. 227, 73–74 (2003).
[Crossref]

S. A. Ponomarenko and E. Wolf, “Coherence properties of light in Young’s interference pattern formed with partially coherent light,” Opt. Commun. 170, 1–8 (1999).
[Crossref]

Roychoudhury, H.

S. A. Ponomarenko, H. Roychoudhury, and E. Wolf, “Physical significance of complete spatial coherence of optical fields,” Phys. Lett. A,  345, 10–12 (2005).
[Crossref]

Rudolph, W.

J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic Press, 2006)

Schoonover, R. W.

Segev, M.

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, “Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media,” Phys. Rev. E 63, 035601(R) (2001).
[Crossref]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Theory of Self-Trapped Spatially Incoherent Light Beams,” Phys. Rev. Lett. 79, 4990–4993 (1997).
[Crossref]

Sereda, L.

L. Sereda, M. Bertolotti, and A. Ferrari, “Coherence properties of nonstationary light wave fields,” J. Opt. Soc. Am. B 15, 695–705 (1998).
[Crossref]

M. Bertolotti, A. Ferrari, and L. Sereda, “Coherence properties of nonstationary polychromatic light sources,” J. Opt. Soc. Am. B 12, 341–347 (1995).
[Crossref]

Si, L-G.

W-X. Yang, Ai-Xi Chen, L-G. Si, K. Jiang, X. Yang, and R-K. Lee, “Three coupled ultraslow solitons in a five-level tripod system,” Phys. Rev. A 81023814 (2010).
[Crossref]

Silvestre, E.

Starikov, A.

A. Starikov and E. Wolf, “Coherent-mode representation of Gaussian Schell-model sources and of their radiation fields,” J. Opt. Soc. Am. A 72, 923–928 (1982).

Tervo, J.

Terzieva, S. I.

V. A. Aleshkevich, V. A. Vysloukh, G. D. Kozhoridze, A. N. Matveev, and S. I. Terzieva, “Nonlinear propagation of partially coherent pulse in fiber waveguide and the role of higher order dispersion,” Sov. J. Quantum Electron. 18, 207–211 (1988).
[Crossref]

Torres-Company, V.

Turunen, J.

Vahimaa, P.

Voelz, D.

X. Xiao and D. Voelz, “Wave optics simulation approach for partial spatially coherent beams,” Opt. Express 16, 6986–6992 (2006).
[Crossref]

Vysloukh, V. A.

V. A. Aleshkevich, V. A. Vysloukh, G. D. Kozhoridze, A. N. Matveev, and S. I. Terzieva, “Nonlinear propagation of partially coherent pulse in fiber waveguide and the role of higher order dispersion,” Sov. J. Quantum Electron. 18, 207–211 (1988).
[Crossref]

Wang, L.

Q. Lin, L. Wang, and S. Zhu, “Partially coherent light pulse and its propagation,” Opt. Commun. 219, 65–70 (2003).
[Crossref]

Wolf, E.

S. A. Ponomarenko, H. Roychoudhury, and E. Wolf, “Physical significance of complete spatial coherence of optical fields,” Phys. Lett. A,  345, 10–12 (2005).
[Crossref]

S. A. Ponomarenko, G. P. Agrawal, and E. Wolf, “Energy spectrum of a nonstationary ensemble of pulses,” Opt. Lett. 29, 394–396 (2004).
[Crossref] [PubMed]

S. A. Ponomarenko and E. Wolf, “The spectral degree of coherence of fully spatially coherent electromagnetic beams,” Opt. Commun. 227, 73–74 (2003).
[Crossref]

S. A. Ponomarenko and E. Wolf, “Coherence properties of light in Young’s interference pattern formed with partially coherent light,” Opt. Commun. 170, 1–8 (1999).
[Crossref]

A. Starikov and E. Wolf, “Coherent-mode representation of Gaussian Schell-model sources and of their radiation fields,” J. Opt. Soc. Am. A 72, 923–928 (1982).

E. Wolf, “New spectral representation of random sources and of the partially coherent fields that they generate,” Opt. Commun. 38, 3–6 (1981).
[Crossref]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1997).

Wu, Y.

Wyrowski, F.

H. Lajunen, J. Tervo, J. Turunen, P. Vahimaa, and F. Wyrowski, “Spectral coherence properties of temporarily modulated stationary light sources,” Opt. Express 11, 1894–1899 (2003).
[Crossref] [PubMed]

P. Paakkonen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun. 204, 53–58 (2002).
[Crossref]

Xiao, X.

X. Xiao and D. Voelz, “Wave optics simulation approach for partial spatially coherent beams,” Opt. Express 16, 6986–6992 (2006).
[Crossref]

Yaglom, A. M.

A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics: Mechanics of Turbulence, Vols. 1& 2, (Dover, 2007).

Yang, W-X.

W-X. Yang, Ai-Xi Chen, L-G. Si, K. Jiang, X. Yang, and R-K. Lee, “Three coupled ultraslow solitons in a five-level tripod system,” Phys. Rev. A 81023814 (2010).
[Crossref]

Yang, X.

W-X. Yang, Ai-Xi Chen, L-G. Si, K. Jiang, X. Yang, and R-K. Lee, “Three coupled ultraslow solitons in a five-level tripod system,” Phys. Rev. A 81023814 (2010).
[Crossref]

Yu, M.

S. B. Cavalcanti, G. P. Agrawal, and M. Yu, “Noise amplification in dispersive nonlinear media,” Phys. Rev. A 51, 4086–4092 (1995).
[Crossref] [PubMed]

Zhu, S.

Q. Lin, L. Wang, and S. Zhu, “Partially coherent light pulse and its propagation,” Opt. Commun. 219, 65–70 (2003).
[Crossref]

J. Opt. Soc. Am. A (5)

J. Opt. Soc. Am. B (3)

Opt. Commun. (8)

E. Wolf, “New spectral representation of random sources and of the partially coherent fields that they generate,” Opt. Commun. 38, 3–6 (1981).
[Crossref]

F. Gori, “Collett-Wolf sources and multimode lasers,” Opt. Commun. 34, 301–305 (1980).
[Crossref]

S. A. Ponomarenko and G. P. Agrawal, “Linear optical bullets,” Opt. Commun. 261, 1–4 (2006).
[Crossref]

P. Paakkonen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun. 204, 53–58 (2002).
[Crossref]

Q. Lin, L. Wang, and S. Zhu, “Partially coherent light pulse and its propagation,” Opt. Commun. 219, 65–70 (2003).
[Crossref]

M. Brunel and S. Coëtlemec, “Fractional-order Fourier formulation of the propagation of partially coherent light pulses,” Opt. Commun. 230, 1–5 (2004).
[Crossref]

S. A. Ponomarenko and E. Wolf, “Coherence properties of light in Young’s interference pattern formed with partially coherent light,” Opt. Commun. 170, 1–8 (1999).
[Crossref]

S. A. Ponomarenko and E. Wolf, “The spectral degree of coherence of fully spatially coherent electromagnetic beams,” Opt. Commun. 227, 73–74 (2003).
[Crossref]

Opt. Express (8)

Opt. Lett. (6)

Phys. Lett. A (1)

S. A. Ponomarenko, H. Roychoudhury, and E. Wolf, “Physical significance of complete spatial coherence of optical fields,” Phys. Lett. A,  345, 10–12 (2005).
[Crossref]

Phys. Rev. A (2)

S. B. Cavalcanti, G. P. Agrawal, and M. Yu, “Noise amplification in dispersive nonlinear media,” Phys. Rev. A 51, 4086–4092 (1995).
[Crossref] [PubMed]

W-X. Yang, Ai-Xi Chen, L-G. Si, K. Jiang, X. Yang, and R-K. Lee, “Three coupled ultraslow solitons in a five-level tripod system,” Phys. Rev. A 81023814 (2010).
[Crossref]

Phys. Rev. E (2)

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, “Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media,” Phys. Rev. E 63, 035601(R) (2001).
[Crossref]

S. A. Ponomarenko, N. M. Litchinitser, and G. P. Agrawal, “Theory of incoherent solitons: Beyond the mean-field approximation,” Phys. Rev. E 70, 015603(R) (2004).
[Crossref]

Phys. Rev. Lett. (1)

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Theory of Self-Trapped Spatially Incoherent Light Beams,” Phys. Rev. Lett. 79, 4990–4993 (1997).
[Crossref]

Sov. J. Quantum Electron. (1)

V. A. Aleshkevich, V. A. Vysloukh, G. D. Kozhoridze, A. N. Matveev, and S. I. Terzieva, “Nonlinear propagation of partially coherent pulse in fiber waveguide and the role of higher order dispersion,” Sov. J. Quantum Electron. 18, 207–211 (1988).
[Crossref]

Sov. Phys. JETP (1)

G. A. Pasmanik, “Self-interaction of incoherent light beams,” Sov. Phys. JETP,  39, 234–238 (1974).

Sov. Phys.Usp. (1)

V. P. Kandidov, “Monte Carlo method in nonlinear statistical optics”, Sov. Phys.Usp. 39, 1243–1272 (1996).

Other (9)

L. Allen and J. H. Eberly, Optical Resonance and Two-level Atoms (Dover, 1975).

J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic Press, 2006)

L. Banyai and S. W. Koch, Semiconductor Quantum Dots (World Scientific, 1993).

P. W. Milonni and J. H. Eberly, Lasers (Wiley, 1985).

A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics: Mechanics of Turbulence, Vols. 1& 2, (Dover, 2007).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1997).

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007).

R. W. Boyd, Nonlinear Optics (Academic Press, 2008).

P. P. Banerjee, Nonlinear Optics: Theory, Numerical Modeling and Applications (Marcel Decker, 2004).

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Figures (10)

Fig. 1
Fig. 1 Magnitude of 10 random field realizations of the GSM pulse at the source Z = 0 as a function of dimensionless time T = t/tp in three cases (a) tc = 10tp, (b) tc = 2tp and (c) tc = tp. Black thick line: ensemble average amplitude.
Fig. 2
Fig. 2 Profile of the mutual coherence function at the source, Z = 0 as a function of dimensionless time T1 and T2 in three cases : (a) tc = 10tp, (b) tc = 2tp and (c) tc = tp.
Fig. 3
Fig. 3 Average intensity evolution of relatively coherent pulses as a function of the propagation distance Z. The cases (a) and (b) correspond to the average input pulse areas ��0 = 0.8π and ��0 = 1.5π, respectively.
Fig. 4
Fig. 4 Evolution of the average pulse area as a function of the propagation distance Z for relatively coherent pulses with ��0 = 0.8π (dashed) and, ��0 = 1.5π (solid), respectively.
Fig. 5
Fig. 5 Average intensity evolution as a function of propagation distance Z for input pulses with (a) tc = 2tp and (b) tc = tp. The average pulse area at the source is ��0 = 1.5π.
Fig. 6
Fig. 6 Evolution of the averaged pulse area as a function of propagation distance Z, corresponding to tc = 2tp (dashed line) and, tc = tp (solid line) with the initial area ��0 = 1.5π. The red dotted-dashed line represents the �� = 2π limit.
Fig. 7
Fig. 7 Intensity of five relatively coherent, tc = 10tp, pulse realizations with ��0 = 1.5π at three sample points in Z: Z = 0 (a), Z = 5 (b), and Z = 10 (c), respectively.
Fig. 8
Fig. 8 Intensity of five rather incoherent, tc = tp pulse realizations with ��0 = 1.5π at three sample points in Z: Z = 0 (a), Z = 5 (b), and Z = 10 (c), respectively.
Fig. 9
Fig. 9 Magnitude of the mutual coherence function at Z = 0, (top row) and Z = 10, (bottom row); tc = 10tp, (a,d); tc = 2tp, (b,e); tc = tp, (c,f).
Fig. 10
Fig. 10 Magnitude of the complex degree of coherence function at Z = 0, (top row) and Z = 10, (bottom row); tc = 10tp, (a,d); tc = 2tp, (b,e); tc = tp, (c,f).

Equations (27)

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ζ Ω = i 2 ω N | d e g | 2 c ε 0 h ¯ σ ¯ Δ .
σ Δ ¯ = d Δ g ( Δ ) σ ( Δ ) .
g ( Δ ) = 1 2 π δ exp ( Δ 2 2 δ 2 ) ,
τ σ = ( 1 T + i Δ ) σ i Ω w ,
τ w = 1 T ( w + 1 ) i 2 ( Ω * σ Ω σ * ) .
T σ = i Δ σ i Ω w ,
T w = i 2 ( Ω * σ Ω σ * ) .
Γ ( τ 1 , τ 2 , ζ ) = Ω * ( τ 1 , ζ ) Ω ( τ 2 , ζ ) ,
I ( τ , ζ ) Γ ( τ , τ , ζ ) ,
γ ( τ 1 , τ 2 , ζ ) Γ ( τ 1 , τ 2 , ζ ) I ( τ 1 , ζ ) I ( τ 2 , ζ ) .
Γ L ( τ 1 , τ 2 , ζ ) = 1 L i = 1 L Ω * ( τ 1 , ζ ) Ω ( τ 2 , ζ ) ,
γ L ( τ 1 , τ 2 , ζ ) = Γ L ( τ 1 , τ 2 , ζ ) ) I L ( τ 1 , ζ ) I L ( τ 2 , ζ ) .
Ω ( τ , ζ ) = n a n ψ n ( τ , ζ ) ,
a n = λ n exp ( i φ n ) ,
exp [ i ( φ n φ m ) ] = δ m n ,
a n * a m = λ n δ m n .
Γ ( τ 1 , τ 2 , ζ ) = n λ n ψ n * ( τ 1 , ζ ) ψ n ( τ 2 , ζ ) .
d τ 1 Γ ( τ 1 , τ 2 , ζ ) ψ n ( τ 1 , ζ ) = λ n ψ n ( τ 2 , ζ ) .
Γ ( t 1 , t 2 ) = E π t p exp [ ( t 1 2 + t 2 2 ) 2 t p ] exp [ ( t 1 t 2 ) 2 2 t c 2 ] ,
ψ n ( t ) = 1 2 n n ! ( 2 π d ) 1 / 4 H n ( t 2 d ) exp ( t 2 4 d ) ,
λ n = ( π a + b + d ) 1 / 2 ( b a + b + d ) n .
a = t p 2 t c 2 2 ( t c 2 + 2 t p 2 ) , b = t p 4 2 ( t c 2 + 2 t p 2 ) ,
d = a 2 + 2 a b .
1 T = 1 T h + 1 T in ,
b = 4 ln 2 δ h δ in ,
1 T = 1 2 T + 1 T h .
𝒜 ( Z ) I ( T , Z ) d T ;

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