Abstract

We analyze the coherence properties of supercontinuum generated in photonic crystal fibers by applying the second-order coherence theory of nonstationary light. Using an ensemble of simulated realizations, we construct two-frequency cross-spectral density and two-time mutual coherence functions. This allows us to introduce measures of temporal and spectral coherence. We show that, in the long-pulse regime, supercontinuum light can be decomposed into a sum of coherent and quasi-stationary contributions. Our approach and findings are also applicable in the short-pulse regime.

© 2010 Optical Society of America

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  1. J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
    [CrossRef]
  2. J. M. Dudley and S. Coen, Opt. Lett. 27, 1180 (2002).
    [CrossRef]
  3. J. M. Dudley and S. Coen, IEEE J. Sel. Top. Quantum Electron. 8, 651 (2002).
    [CrossRef]
  4. I. Zeylikovich, V. Kartazaev, and R. R. Alfano, J. Opt. Soc. Am. B 22, 1453 (2005).
    [CrossRef]
  5. F. Lu and W. Knox, Opt. Express 12, 347 (2004).
    [CrossRef] [PubMed]
  6. M. Bertolotti, L. Sereda, and A. Ferrari, Pure Appl. Opt. 6, 153 (1997).
    [CrossRef]
  7. C. Iaconis, V. Wong, and I. A. Walmsley, IEEE J. Sel. Top. Quantum Electron. 4, 285 (1998).
    [CrossRef]
  8. I. A. Walmsley and C. Dorrer, Adv. Opt. Photon. 1, 308 (2009).
    [CrossRef]
  9. S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
    [CrossRef]
  10. P. Bejot, J. Kasparian, E. Salomon, R. Ackermann, and J.-P. Wolf, Appl. Phys. B 87, 1 (2007).
    [CrossRef]
  11. B. Cairns and E. Wolf, Opt. Commun. 62, 215 (1987).
    [CrossRef]

2009 (1)

2007 (1)

P. Bejot, J. Kasparian, E. Salomon, R. Ackermann, and J.-P. Wolf, Appl. Phys. B 87, 1 (2007).
[CrossRef]

2006 (1)

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

2005 (1)

2004 (1)

2002 (2)

J. M. Dudley and S. Coen, Opt. Lett. 27, 1180 (2002).
[CrossRef]

J. M. Dudley and S. Coen, IEEE J. Sel. Top. Quantum Electron. 8, 651 (2002).
[CrossRef]

1998 (2)

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

C. Iaconis, V. Wong, and I. A. Walmsley, IEEE J. Sel. Top. Quantum Electron. 4, 285 (1998).
[CrossRef]

1997 (1)

M. Bertolotti, L. Sereda, and A. Ferrari, Pure Appl. Opt. 6, 153 (1997).
[CrossRef]

1987 (1)

B. Cairns and E. Wolf, Opt. Commun. 62, 215 (1987).
[CrossRef]

Ackermann, R.

P. Bejot, J. Kasparian, E. Salomon, R. Ackermann, and J.-P. Wolf, Appl. Phys. B 87, 1 (2007).
[CrossRef]

Alfano, R. R.

Bejot, P.

P. Bejot, J. Kasparian, E. Salomon, R. Ackermann, and J.-P. Wolf, Appl. Phys. B 87, 1 (2007).
[CrossRef]

Bertolotti, M.

M. Bertolotti, L. Sereda, and A. Ferrari, Pure Appl. Opt. 6, 153 (1997).
[CrossRef]

Cairns, B.

B. Cairns and E. Wolf, Opt. Commun. 62, 215 (1987).
[CrossRef]

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

J. M. Dudley and S. Coen, IEEE J. Sel. Top. Quantum Electron. 8, 651 (2002).
[CrossRef]

J. M. Dudley and S. Coen, Opt. Lett. 27, 1180 (2002).
[CrossRef]

Dorrer, C.

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

J. M. Dudley and S. Coen, IEEE J. Sel. Top. Quantum Electron. 8, 651 (2002).
[CrossRef]

J. M. Dudley and S. Coen, Opt. Lett. 27, 1180 (2002).
[CrossRef]

Ferrari, A.

M. Bertolotti, L. Sereda, and A. Ferrari, Pure Appl. Opt. 6, 153 (1997).
[CrossRef]

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Iaconis, C.

C. Iaconis, V. Wong, and I. A. Walmsley, IEEE J. Sel. Top. Quantum Electron. 4, 285 (1998).
[CrossRef]

Kartazaev, V.

Kasparian, J.

P. Bejot, J. Kasparian, E. Salomon, R. Ackermann, and J.-P. Wolf, Appl. Phys. B 87, 1 (2007).
[CrossRef]

Knox, W.

König, F.

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

Korolkova, N.

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

Leuchs, G.

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

Lu, F.

Salomon, E.

P. Bejot, J. Kasparian, E. Salomon, R. Ackermann, and J.-P. Wolf, Appl. Phys. B 87, 1 (2007).
[CrossRef]

Sereda, L.

M. Bertolotti, L. Sereda, and A. Ferrari, Pure Appl. Opt. 6, 153 (1997).
[CrossRef]

Sizmann, A.

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

Spälter, S.

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

Walmsley, I. A.

I. A. Walmsley and C. Dorrer, Adv. Opt. Photon. 1, 308 (2009).
[CrossRef]

C. Iaconis, V. Wong, and I. A. Walmsley, IEEE J. Sel. Top. Quantum Electron. 4, 285 (1998).
[CrossRef]

Wolf, E.

B. Cairns and E. Wolf, Opt. Commun. 62, 215 (1987).
[CrossRef]

Wolf, J.-P.

P. Bejot, J. Kasparian, E. Salomon, R. Ackermann, and J.-P. Wolf, Appl. Phys. B 87, 1 (2007).
[CrossRef]

Wong, V.

C. Iaconis, V. Wong, and I. A. Walmsley, IEEE J. Sel. Top. Quantum Electron. 4, 285 (1998).
[CrossRef]

Zeylikovich, I.

Adv. Opt. Photon. (1)

Appl. Phys. B (1)

P. Bejot, J. Kasparian, E. Salomon, R. Ackermann, and J.-P. Wolf, Appl. Phys. B 87, 1 (2007).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

C. Iaconis, V. Wong, and I. A. Walmsley, IEEE J. Sel. Top. Quantum Electron. 4, 285 (1998).
[CrossRef]

J. M. Dudley and S. Coen, IEEE J. Sel. Top. Quantum Electron. 8, 651 (2002).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

B. Cairns and E. Wolf, Opt. Commun. 62, 215 (1987).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

Pure Appl. Opt. (1)

M. Bertolotti, L. Sereda, and A. Ferrari, Pure Appl. Opt. 6, 153 (1997).
[CrossRef]

Rev. Mod. Phys. (1)

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic (a) | γ ( t ¯ , Δ t ) | and (b) | μ ( ω ¯ , Δ ω ) | for SC light. Here t 0 is the initial temporal center of mass of the pump pulse; ω 0 is the initial spectral center of mass; c s is the coherent square; q s is the quasi-stationary segment; and S , I , G , and U represent the width of the coherent square and quasi-stationary segment in the temporal and spectral domain, respectively.

Fig. 2
Fig. 2

Simulated (a) | γ ( t ¯ , Δ t ) | and (b) | μ ( ω ¯ , Δ ω ) | for SC generated as described in the text.

Fig. 3
Fig. 3

Top, (a) normalized temporal intensity and (b) normalized spectrum corresponding to Fig. 2. Bottom, dashed curves show the quasi-coherent contributions I c and S c , and gray curves illustrate the quasi-stationary contributions I q and S q .

Equations (9)

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Γ ( t ¯ , Δ t ) = E * ( t ¯ Δ t / 2 ) E ( t ¯ + Δ t / 2 ) .
γ ( t ¯ , Δ t ) = Γ ( t ¯ , Δ t ) I ( t ¯ Δ t / 2 ) I ( t ¯ + Δ t / 2 ) ,
W ( ω ¯ , Δ ω ) = E ˜ * ( ω ¯ Δ ω / 2 ) E ˜ ( ω ¯ + Δ ω / 2 ) ,
μ ( ω ¯ , Δ ω ) = W ( ω ¯ , Δ ω ) S ( ω ¯ Δ ω / 2 ) S ( ω ¯ + Δ ω / 2 )
μ ¯ 2 = 1 2 π E 0 2 | Γ ( t ¯ , Δ t ) | 2 d t ¯ d Δ t ,
Γ ( t ¯ , Δ t ) = Γ c ( t ¯ , Δ t ) + Γ q ( t ¯ , Δ t ) ,
W ( ω ¯ , Δ ω ) = W c ( ω ¯ , Δ ω ) + W q ( ω ¯ , Δ ω ) ,
μ q ( Δ ω ) = 1 2 π E 0 I q ( t ¯ ) exp ( i Δ ω t ¯ ) d t ¯ ,
γ q ( Δ t ) = 1 E 0 0 S q ( ω ¯ ) exp ( i ω ¯ Δ t ) d ω ¯ ,

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