Abstract

A new class of sources generating ensemble of random pulses is introduced based on superposition of the mutual coherence functions of several Multi-Gaussian Schell-model sources that separately are capable of shaping the propagating pulse’s average intensity into flat profiles with adjustable duration and edge sharpness. Under certain conditions that we discuss in detail such superposition allows for production of a pulse ensemble that after a sufficiently long propagation distance in a dispersive medium reshapes its average intensity from an arbitrary initial profile to a train whose parts have flat intensities of different levels and durations and can be either temporarily separated or adjacent.

© 2014 Optical Society of America

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  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  2. E. Wolf and D. F. V. James, “Correlation-induced spectral changes,” Rep. Prog. Phys.59(6), 771–818 (1996).
    [CrossRef]
  3. D. F. V. James, “Change of polarization of light beams on propagation in free space,” J. Opt. Soc. Am. A11(5), 1641–1643 (1994).
    [CrossRef]
  4. 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]
  5. O. Korotkova and E. Wolf, “Generalized Stokes parameters of random electromagnetic beams,” Opt. Lett.30(2), 198–200 (2005).
    [CrossRef] [PubMed]
  6. F. Gori, G. Guattari, and C. Padovani, “Modal expansion for J0-correlated Schell- model sources,” Opt. Commun.64(4), 311–316 (1987).
    [CrossRef]
  7. C. Palma, R. Borghi, and G. Cincotti, “Beams originated by J0-correlated Schell-model planar sources,” Opt. Commun.125(1–3), 113–121 (1996).
    [CrossRef]
  8. F. Gori, M. Santarsiero, and R. Borghi, “Modal expansion for J0-correlated electromagnetic sources,” Opt. Lett.33(16), 1857–1859 (2008).
    [CrossRef] [PubMed]
  9. Z. Mei and O. Korotkova, “Random sources generating ring-shaped beams,” Opt. Lett.38(2), 91–93 (2013).
    [CrossRef] [PubMed]
  10. Z. Mei and O. Korotkova, “Cosine-Gaussian Schell-model sources,” Opt. Lett.38(14), 2578–2580 (2013).
    [CrossRef] [PubMed]
  11. Z. Mei and O. Korotkova, “Electromagnetic cosine-Gaussian Schell-model beams in free space and atmospheric turbulence,” Opt. Express21(22), 27246–27259 (2013).
    [CrossRef] [PubMed]
  12. L. Pan, C. Ding, and H. Wang, “Diffraction of cosine-Gaussian-correlated Schell-model beams,” Opt. Express22(10), 11670–11679 (2014).
    [CrossRef] [PubMed]
  13. H. Lajunen and T. Saastamoinen, “Propagation characteristics of partially coherent beams with spatially varying correlations,” Opt. Lett.36(20), 4104–4106 (2011).
    [CrossRef] [PubMed]
  14. Z. Tong and O. Korotkova, “Electromagnetic non-uniformly correlated beams,” J. Opt. Soc. Am. A29(10), 2154–2158 (2012).
    [CrossRef]
  15. S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett.37(14), 2970–2972 (2012).
    [CrossRef] [PubMed]
  16. O. Korotkova, S. Sahin, and E. Shchepakina, “Multi-Gaussian Schell-model beams,” J. Opt. Soc. Am. A29(10), 2159–2164 (2012).
    [CrossRef] [PubMed]
  17. Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic Multi-Gaussian Schell-model beams,” J. Opt.15(2), 025705 (2013).
    [CrossRef]
  18. O. Korotkova, “Random sources for rectangular far fields,” Opt. Lett.39(1), 64–67 (2014).
    [CrossRef] [PubMed]
  19. O. Korotkova and E. Shchepakina, “Random sources for optical frames,” Opt. Express22(9), 10622–10633 (2014).
    [CrossRef] [PubMed]
  20. F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett.38(11), 1814–1816 (2013).
    [CrossRef] [PubMed]
  21. 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]
  22. S. Avramov-Zamurovic, O. Korotkova, C. Nelson, O. Korotkova, and R. Malek-Madani, “Generation of Multi-Gaussian Schell-model beams,” Opt. Express, submitted.
  23. 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]
  24. Q. Lin, L. G. Wang, and S. Y. Zhu, “Partially coherent light pulse and its propagation,” Opt. Commun.219(1–6), 65–70 (2003).
    [CrossRef]
  25. L. G. Wang, Q. Lin, H. Chen, and S. Y. Zhu, “Propagation of partially coherent pulsed beams in the spatiotemporal domain,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(5), 056613 (2003).
    [CrossRef] [PubMed]
  26. H. Lajunen, J. Tervo, J. Turunen, P. Vahimaa, and F. Wyrowski, “Spectral coherence properties of temporally modulated stationary light sources,” Opt. Express11(16), 1894–1899 (2003).
    [CrossRef] [PubMed]
  27. H. Lajunen, J. Tervo, and P. Vahimaa, “Overall coherence and coherent-mode expansion of spectrally partially coherent plane-wave pulses,” J. Opt. Soc. Am. A21(11), 2117–2123 (2004).
    [CrossRef] [PubMed]
  28. H. Lajunen, P. Vahimaa, and J. Tervo, “Theory of spatially and spectrally partially coherent pulses,” J. Opt. Soc. Am. A22(8), 1536–1545 (2005).
    [CrossRef] [PubMed]
  29. J. Lancis, V. Torres-Company, E. Silvestre, and P. Andrés, “Space-time analogy for partially coherent plane-wave-type pulses,” Opt. Lett.30(22), 2973–2975 (2005).
    [CrossRef] [PubMed]
  30. H. Lajunen and T. Saastamoinen, “Non-uniformly correlated partially coherent pulses,” Opt. Express21(1), 190–195 (2013).
    [CrossRef] [PubMed]
  31. C. Ding, O. Korotkova, Y. Zhang, and L. Pan, “Cosine-Gaussian correlated Schell-model pulsed beams,” Opt. Express22(1), 931–942 (2014).
    [CrossRef] [PubMed]
  32. C. Ding, O. Korotkova, Y. Zhang, and L. Pan, “The control of pulse profiles with tunable temporal coherence,” Phys. Lett. A, in press.
  33. V. Torres-Company, G. Mínguez-Vega, J. Lancis, and A. T. Friberg, “Controllable generation of partially coherent light pulses with direct space-to-time pulse shaper,” Opt. Lett.32(12), 1608–1610 (2007).
    [CrossRef] [PubMed]
  34. Y. Li, H. Lee, and E. Wolf, “Effect of edge rounding and sloping of sidewalls on the readout signal of the information pits,” Opt. Eng.42(9), 2707–2720 (2003).
    [CrossRef]
  35. 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]
  36. F. Gori and M. Santarsiero, “Difference of two Gaussian Schell-model cross-spectral densities,” Opt. Lett.39(9), 2731–2734 (2014).
    [CrossRef] [PubMed]
  37. R. M. Gagliardi and S. Karp, Optical Communications (Wiley-Interscience, 1995).
  38. F. Gori, “Flattened Gaussian beams,” Opt. Commun.107(5–6), 335–341 (1994).
    [CrossRef]
  39. Y. Li, “New expressions for flat-topped light beams,” Opt. Commun.206(4–6), 225–234 (2002).
    [CrossRef]
  40. S. Sahin, G. Gbur, and O. Korotkova, “Scattering of light from particles with semisoft boundaries,” Opt. Lett.36(20), 3957–3959 (2011).
    [CrossRef] [PubMed]
  41. F. Gori and M. Santarsiero, “Devising genuine spatial correlation functions,” Opt. Lett.32(24), 3531–3533 (2007).
    [CrossRef] [PubMed]

2014 (7)

2013 (6)

2012 (3)

2011 (2)

2008 (1)

2007 (2)

2005 (4)

2004 (1)

2003 (4)

H. Lajunen, J. Tervo, J. Turunen, P. Vahimaa, and F. Wyrowski, “Spectral coherence properties of temporally modulated stationary light sources,” Opt. Express11(16), 1894–1899 (2003).
[CrossRef] [PubMed]

Q. Lin, L. G. Wang, and S. Y. Zhu, “Partially coherent light pulse and its propagation,” Opt. Commun.219(1–6), 65–70 (2003).
[CrossRef]

L. G. Wang, Q. Lin, H. Chen, and S. Y. Zhu, “Propagation of partially coherent pulsed beams in the spatiotemporal domain,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(5), 056613 (2003).
[CrossRef] [PubMed]

Y. Li, H. Lee, and E. Wolf, “Effect of edge rounding and sloping of sidewalls on the readout signal of the information pits,” Opt. Eng.42(9), 2707–2720 (2003).
[CrossRef]

2002 (2)

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]

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

1996 (2)

E. Wolf and D. F. V. James, “Correlation-induced spectral changes,” Rep. Prog. Phys.59(6), 771–818 (1996).
[CrossRef]

C. Palma, R. Borghi, and G. Cincotti, “Beams originated by J0-correlated Schell-model planar sources,” Opt. Commun.125(1–3), 113–121 (1996).
[CrossRef]

1994 (2)

1987 (1)

F. Gori, G. Guattari, and C. Padovani, “Modal expansion for J0-correlated Schell- model sources,” Opt. Commun.64(4), 311–316 (1987).
[CrossRef]

Andrés, P.

Borghi, R.

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

C. Palma, R. Borghi, and G. Cincotti, “Beams originated by J0-correlated Schell-model planar sources,” Opt. Commun.125(1–3), 113–121 (1996).
[CrossRef]

Cai, Y.

Chen, H.

L. G. Wang, Q. Lin, H. Chen, and S. Y. Zhu, “Propagation of partially coherent pulsed beams in the spatiotemporal domain,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(5), 056613 (2003).
[CrossRef] [PubMed]

Cincotti, G.

C. Palma, R. Borghi, and G. Cincotti, “Beams originated by J0-correlated Schell-model planar sources,” Opt. Commun.125(1–3), 113–121 (1996).
[CrossRef]

de Sande, J. C. G.

Ding, C.

Friberg, A. T.

Gbur, G.

Gori, F.

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, “Modal expansion for J0-correlated Schell- model sources,” Opt. Commun.64(4), 311–316 (1987).
[CrossRef]

James, D. F. V.

E. Wolf and D. F. V. James, “Correlation-induced spectral changes,” Rep. Prog. Phys.59(6), 771–818 (1996).
[CrossRef]

D. F. V. James, “Change of polarization of light beams on propagation in free space,” J. Opt. Soc. Am. A11(5), 1641–1643 (1994).
[CrossRef]

Korotkova, O.

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

O. Korotkova and E. Shchepakina, “Random sources for optical frames,” Opt. Express22(9), 10622–10633 (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]

C. Ding, O. Korotkova, Y. Zhang, and L. Pan, “Cosine-Gaussian correlated Schell-model pulsed beams,” Opt. Express22(1), 931–942 (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, “Random sources generating ring-shaped beams,” Opt. Lett.38(2), 91–93 (2013).
[CrossRef] [PubMed]

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

Z. Mei and O. Korotkova, “Electromagnetic cosine-Gaussian Schell-model beams in free space and atmospheric turbulence,” Opt. Express21(22), 27246–27259 (2013).
[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]

O. Korotkova, S. Sahin, and E. Shchepakina, “Multi-Gaussian Schell-model beams,” J. Opt. Soc. Am. A29(10), 2159–2164 (2012).
[CrossRef] [PubMed]

Z. Tong and O. Korotkova, “Electromagnetic non-uniformly correlated beams,” J. Opt. Soc. Am. A29(10), 2154–2158 (2012).
[CrossRef]

S. Sahin, G. Gbur, and O. Korotkova, “Scattering of light from particles with semisoft boundaries,” Opt. Lett.36(20), 3957–3959 (2011).
[CrossRef] [PubMed]

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 and E. Wolf, “Generalized Stokes parameters of random electromagnetic beams,” Opt. Lett.30(2), 198–200 (2005).
[CrossRef] [PubMed]

Lajunen, H.

Lancis, J.

Lee, H.

Y. Li, H. Lee, and E. Wolf, “Effect of edge rounding and sloping of sidewalls on the readout signal of the information pits,” Opt. Eng.42(9), 2707–2720 (2003).
[CrossRef]

Li, Y.

Y. Li, H. Lee, and E. Wolf, “Effect of edge rounding and sloping of sidewalls on the readout signal of the information pits,” Opt. Eng.42(9), 2707–2720 (2003).
[CrossRef]

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

Liang, C.

Lin, Q.

Q. Lin, L. G. Wang, and S. Y. Zhu, “Partially coherent light pulse and its propagation,” Opt. Commun.219(1–6), 65–70 (2003).
[CrossRef]

L. G. Wang, Q. Lin, H. Chen, and S. Y. Zhu, “Propagation of partially coherent pulsed beams in the spatiotemporal domain,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(5), 056613 (2003).
[CrossRef] [PubMed]

Liu, X.

Mei, Z.

Mínguez-Vega, G.

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]

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, “Modal expansion for J0-correlated Schell- model sources,” Opt. Commun.64(4), 311–316 (1987).
[CrossRef]

Palma, C.

C. Palma, R. Borghi, and G. Cincotti, “Beams originated by J0-correlated Schell-model planar sources,” Opt. Commun.125(1–3), 113–121 (1996).
[CrossRef]

Pan, L.

Piquero, G.

Saastamoinen, T.

Sahin, S.

Santarsiero, M.

Shchepakina, E.

Silvestre, E.

Tervo, J.

Tong, Z.

Torres-Company, V.

Turunen, J.

H. Lajunen, J. Tervo, J. Turunen, P. Vahimaa, and F. Wyrowski, “Spectral coherence properties of temporally modulated stationary light sources,” Opt. Express11(16), 1894–1899 (2003).
[CrossRef] [PubMed]

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.

Wang, F.

Wang, H.

Wang, L. G.

L. G. Wang, Q. Lin, H. Chen, and S. Y. Zhu, “Propagation of partially coherent pulsed beams in the spatiotemporal domain,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(5), 056613 (2003).
[CrossRef] [PubMed]

Q. Lin, L. G. Wang, and S. Y. Zhu, “Partially coherent light pulse and its propagation,” Opt. Commun.219(1–6), 65–70 (2003).
[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]

O. Korotkova and E. Wolf, “Generalized Stokes parameters of random electromagnetic beams,” Opt. Lett.30(2), 198–200 (2005).
[CrossRef] [PubMed]

Y. Li, H. Lee, and E. Wolf, “Effect of edge rounding and sloping of sidewalls on the readout signal of the information pits,” Opt. Eng.42(9), 2707–2720 (2003).
[CrossRef]

E. Wolf and D. F. V. James, “Correlation-induced spectral changes,” Rep. Prog. Phys.59(6), 771–818 (1996).
[CrossRef]

Wyrowski, F.

H. Lajunen, J. Tervo, J. Turunen, P. Vahimaa, and F. Wyrowski, “Spectral coherence properties of temporally modulated stationary light sources,” Opt. Express11(16), 1894–1899 (2003).
[CrossRef] [PubMed]

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]

Yuan, Y.

Zhang, Y.

Zhu, S. Y.

Q. Lin, L. G. Wang, and S. Y. Zhu, “Partially coherent light pulse and its propagation,” Opt. Commun.219(1–6), 65–70 (2003).
[CrossRef]

L. G. Wang, Q. Lin, H. Chen, and S. Y. Zhu, “Propagation of partially coherent pulsed beams in the spatiotemporal domain,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(5), 056613 (2003).
[CrossRef] [PubMed]

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. Soc. Am. A (5)

Opt. Commun. (7)

F. Gori, “Flattened Gaussian beams,” Opt. Commun.107(5–6), 335–341 (1994).
[CrossRef]

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

F. Gori, G. Guattari, and C. Padovani, “Modal expansion for J0-correlated Schell- model sources,” Opt. Commun.64(4), 311–316 (1987).
[CrossRef]

C. Palma, R. Borghi, and G. Cincotti, “Beams originated by J0-correlated Schell-model planar sources,” Opt. Commun.125(1–3), 113–121 (1996).
[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]

Q. Lin, L. G. Wang, and S. Y. Zhu, “Partially coherent light pulse and its propagation,” Opt. Commun.219(1–6), 65–70 (2003).
[CrossRef]

Opt. Eng. (1)

Y. Li, H. Lee, and E. Wolf, “Effect of edge rounding and sloping of sidewalls on the readout signal of the information pits,” Opt. Eng.42(9), 2707–2720 (2003).
[CrossRef]

Opt. Express (6)

Opt. Lett. (15)

F. Gori and M. Santarsiero, “Difference of two Gaussian Schell-model cross-spectral densities,” Opt. Lett.39(9), 2731–2734 (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]

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 and O. Korotkova, “Random sources generating ring-shaped beams,” Opt. Lett.38(2), 91–93 (2013).
[CrossRef] [PubMed]

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett.38(11), 1814–1816 (2013).
[CrossRef] [PubMed]

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

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

O. Korotkova and E. Wolf, “Generalized Stokes parameters of random electromagnetic beams,” Opt. Lett.30(2), 198–200 (2005).
[CrossRef] [PubMed]

J. Lancis, V. Torres-Company, E. Silvestre, and P. Andrés, “Space-time analogy for partially coherent plane-wave-type pulses,” Opt. Lett.30(22), 2973–2975 (2005).
[CrossRef] [PubMed]

V. Torres-Company, G. Mínguez-Vega, J. Lancis, and A. T. Friberg, “Controllable generation of partially coherent light pulses with direct space-to-time pulse shaper,” Opt. Lett.32(12), 1608–1610 (2007).
[CrossRef] [PubMed]

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

S. Sahin, G. Gbur, and O. Korotkova, “Scattering of light from particles with semisoft boundaries,” Opt. Lett.36(20), 3957–3959 (2011).
[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]

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

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

L. G. Wang, Q. Lin, H. Chen, and S. Y. Zhu, “Propagation of partially coherent pulsed beams in the spatiotemporal domain,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(5), 056613 (2003).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

E. Wolf and D. F. V. James, “Correlation-induced spectral changes,” Rep. Prog. Phys.59(6), 771–818 (1996).
[CrossRef]

Other (4)

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

C. Ding, O. Korotkova, Y. Zhang, and L. Pan, “The control of pulse profiles with tunable temporal coherence,” Phys. Lett. A, in press.

R. M. Gagliardi and S. Karp, Optical Communications (Wiley-Interscience, 1995).

S. Avramov-Zamurovic, O. Korotkova, C. Nelson, O. Korotkova, and R. Malek-Madani, “Generation of Multi-Gaussian Schell-model beams,” Opt. Express, submitted.

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Figures (6)

Fig. 1
Fig. 1

The temporal degree of coherence of random optical pulses at the source plane for several different sources: (a) for two parts in the far field, δ b t = 1 p s , δ f t = 2 p s , (b) for two parts in the far field, δ b t = 1 p s , δ f t = 10 p s , (c) for four parts in the far field, δ 1 f t = 10 p s , δ 1 b t = 1.5 p s , δ 2 f t = 0.8 p s , δ 2 b t = 0.4 p s , (d) for six parts in the far field, δ 1 f t = 10 p s , δ 1 b t = 5 p s , δ 2 f t = 2 p s , δ 2 b t = 1.2 p s , δ 3 f t = 0.4 p s , δ 3 b t = 0.3 p s . Several curves correspond to different values of M. Other pulse and media parameters are σ t 0 = 15 p s , β 2 = 50 p s 2 / k m .

Fig. 2
Fig. 2

Normalized intensity distribution I ( t , z ) of random optical pulse ensembles (split to two parts at far field) versus distance z and time t for different values of parameters: (a), (c) for δ f t = 2 p s ; (b), (d) for δ f t = 10 p s ; (a), (b) for M = 1 ; (c), (d) for M = 30 . The parameter δ b t = 1 p s and the other parameters as in Fig. 1.

Fig. 3
Fig. 3

Normalized average intensity distribution I ( t , z ) of random optical pulse ensemble split to four parts versus distance z and time t. The source parameters are as in Figs. 1(c) and (d), respectively.

Fig. 4
Fig. 4

Normalized average intensity distribution I ( t , z ) of random optical pulse ensemble (split to four parts in the far field) versus time t for different values of pulse coherent gap ( δ 1 b t δ 2 f t ): (a) δ 2 f t = 0.8 p s , (b) δ 2 f t = 1.2 p s , (c) δ 2 f t = 1.5 p s , (d) δ 2 f t = 1.8 p s . The parameter δ 1 b t = 1.5 p s and the other parameters are as in Fig. 1(c).

Fig. 5
Fig. 5

Normalized average intensity distribution I ( t , z ) of random optical pulse ensemble (split to four parts in the far field) versus time t for different values of pulse weight parameter a 2 A 2 t / ( a 1 A 1 t ) : (a) 0.5 , (b) 0.8 , (c) 1.0 , (d) 1.2 , The parameter δ 1 b t = δ 2 f t = 1.5 p s and the other parameters are as in Fig. 1(c).

Fig. 6
Fig. 6

Normalized average intensity distribution I ( t , z ) of random optical pulse ensemble (split to six parts at far field) versus time t for different values of gap parameter: (a) with gaps δ 1 b t = 5 p s , δ 2 f t = 2 p s , δ 2 b t = 1.2 p s , δ 3 f t = 0.4 p s . (b) without gaps δ 1 b t = δ 2 f t = 2 p s , δ 2 b t = δ 3 f t = 0.7 p s . The values of the pulse weight parameter are a 2 A 2 t / ( a 1 A 1 t ) = 1.2 , a 3 A 3 t / ( a 1 A 1 t ) = 0.8 and other parameters as in Fig. 1(c).

Equations (29)

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Γ ( 0 ) ( t 1 , t 2 )=< U ( 0 )* ( t 1 ) U ( 0 ) ( t 2 )>,
Γ ( 0 ) ( t 1 , t 2 )= p( v ) H ( t 1 ,v )H( t 2 ,v )dv,
H( t,v )=exp( t 2 4 σ t0 2 )exp( ivt ).
Γ ( 0 ) ( t 1 , t 2 )=exp( t 1 2 + t 2 2 4 σ t0 2 )γ( t 1 , t 2 ),
γ ( 0 ) ( t 1 , t 2 )= p( v ) exp[ iv( t 2 t 1 ) ]dv.
p( v )= p b ( v ) p f ( v ),
p f ( v )= 1 2π A t C t m=1 M ( 1 ) m1 ( M m )exp[ m 2 δ ft 2 v 2 ] ,
p b ( v )= 1 2π A t C t m=1 M ( 1 ) m1 ( M m )exp[ m 2 δ bt 2 v 2 ] ,
p( v )= 1 2π A t C t m=1 M ( 1 ) m1 ( M m ) [ exp( m 2 δ bt 2 v 2 )exp( m 2 δ ft 2 v 2 ) ].
C t = m=1 M ( 1 ) m1 ( M m ) ,
δ bt < δ ft .
A t = ( 1 δ bt 1 δ ft ) 1 ,
γ ( 0 ) ( t 1 , t 2 )= A t C t m=1 M ( 1 ) m1 m ( M m ) { 1 δ bt exp[ 1 2m ( t 2 t 1 ) 2 δ bt 2 ] 1 δ ft exp[ 1 2m ( t 2 t 1 ) 2 δ ft 2 ] },
Γ( t 1 , t 2 ,z )= 1 2π β 2 z Γ ( 0 ) ( t 10 , t 20 ) ×exp{ i 2 β 2 z [ ( t 10 2 t 20 2 )2( t 10 t 1 t 20 t 2 )+( t 1 2 t 2 2 ) ] }d t 10 d t 20 ,
Γ( t 1 , t 2 ,z )= A t C t m=1 M ( 1 ) m1 m ( M m ) ( U b U f ),
U α = 1 δ αt Δ αm ( z ) exp[ ( t 2 + t 1 ) 2 8 σ t0 2 Δ αm 2 ( z ) ]exp[ ( t 2 t 1 ) 2 2 Q αm 2 Δ αm 2 ( z ) ]exp[ i ( t 2 2 t 1 2 ) 2 β 2 R αm ( z ) ],
Q αm 2 = ( 1 4 σ t0 2 + 1 m δ αt 2 ) 1 , Δ αm 2 ( z )=1+ β 2 2 z 2 σ t0 2 Q αm 2 , R αm ( z )=z( 1+ σ t0 2 Q αm 2 β 2 2 z 2 ),( α=b,f ).
I( t,z )=Γ( t,t,z )= A t C t m=1 M ( 1 ) m1 m ( M m ) ×{ 1 δ bt Δ bm ( z ) exp[ t 2 2 σ t0 2 Δ bm 2 ( z ) ] 1 δ ft Δ fm ( z ) exp[ t 2 2 σ t0 2 Δ fm 2 ( z ) ] }.
γ( t 1 , t 2 ,z )= Γ( t 1 , t 2 ,z ) I( t 1 ,z )I( t 2 ,z ) .
γ( t d , t d ,z )= m=1 M ( 1 ) m1 ( M m ) { 1 δ bt Δ bm ( z ) exp[ t d 2 2 Q bm 2 Δ bm 2 ( z ) ] 1 δ ft Δ fm ( z ) exp[ t d 2 2 Q fm 2 Δ fm 2 ( z ) ] } m=1 M ( 1 ) m1 ( M m ) { 1 δ bt Δ bm ( z ) exp[ t d 2 8 σ t0 2 Δ bm 2 ( z ) ] 1 δ ft Δ fm ( z ) exp[ t d 2 8 σ t0 2 Δ fm 2 ( z ) ] } .
γ ( 0 ) ( t 1 , t 2 )=B n=1 N A nt γ n ( 0 ) ( t 1 , t 2 ),B= ( n=1 N A nt ) 1 ,
Γ n ( 0 ) ( t 10 , t 20 )=exp( t 1 2 + t 2 2 4 σ t0 2 ) γ n ( t 1 , t 2 ).
Γ n ( t 1 , t 2 ,z )= 1 2π β 2 z Γ n ( 0 ) ( t 10 , t 20 ) ×exp{ i 2 β 2 z [ ( t 10 2 t 20 2 )( t 10 t 1 t 20 t 2 )+( t 1 2 t 2 2 ) ] }d t 10 d t 20 ,
Γ n ( t 1 , t 2 ,z )= A t C t m=1 M ( 1 ) m1 m ( M m ) ( U nbm U nfm ),
U nαm = 1 δ nαt Δ nαm ( z ) exp[ ( t 2 + t 1 ) 2 8 σ t0 2 Δ nαm 2 ( z ) ]exp[ Δ t 2 2 Q nαm 2 Δ nαm 2 ( z ) ]exp[ i ( t 2 2 t 1 2 ) 2 β 2 R nαm ( z ) ],
Q nαm 2 = ( 1 4 σ t0 2 + 1 m δ nαt 2 ) 1 , Δ nαm 2 ( z )=1+ β 2 2 z 2 σ t0 2 Q nαm 2 , R nαm ( z )=z( 1+ σ t0 2 Q nαm 2 β 2 2 z 2 ),( α=b,f ).
I=B n=1 N a n I n ,
I n ( t,z )= Γ n ( t,t,z )= A n t C n t m=1 M ( 1 ) m1 m ( M m ) ×{ 1 δ nbt Δ nbm ( z ) exp[ t 2 2 σ t0 2 Δ nbm 2 ( z ) ] 1 δ nft Δ nfm ( z ) exp[ t 2 2 σ t0 2 Δ nfm 2 ( z ) ] },
A nt = ( 1 δ nbt 1 δ nft ) 1 , δ nbt < δ nft .

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