Abstract

In this Letter we extend the well-known space–time duality to partially coherent wave fields and, as a limit case, to incoherent sources. We show that there is a general analogy between the paraxial diffraction of quasi-monochromatic beams of limited spatial coherence and the temporal distortion of partially coherent plane-wave pulses in parabolic dispersive media. Next, coherence-dependent effects in the propagation of Gaussian Schell-model pulses are retrieved from that of their spatial counterpart, the Gaussian Schell-model beam. Finally, the last result allows us to present a source linewidth analysis in an optical fiber communication system operating around the 1.55μm wavelength window.

© 2005 Optical Society of America

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References

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  1. S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, IEEE J. Quantum Electron. QE-4, 598 (1968).
    [CrossRef]
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2004 (1)

M. Brunel and S. Coëtmelec, Opt. Commun. 230, 1 (2004).
[CrossRef]

2003 (3)

H. Lajunen, J. Tervo, J. Turunen, and P. Vahimaa, Opt. Express 21, 1894 (2003).
[CrossRef]

Q. Lin, L. Wang, and S. Zhu, Opt. Commun. 219, 65 (2003).
[CrossRef]

J. Capmany, D. Pastor, S. Sales, and M. A. Muriel, J. Opt. Soc. Am. B 20, 2523 (2003).
[CrossRef]

2002 (1)

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, Opt. Commun. 204, 53 (2002).
[CrossRef]

1995 (1)

1980 (1)

1978 (1)

1969 (1)

E. B. Treacy, IEEE J. Quantum Electron. QE-5, 454 (1969).
[CrossRef]

1968 (1)

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, IEEE J. Quantum Electron. QE-4, 598 (1968).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, 1997), Chap. 2.

Akhmanov, S. A.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, IEEE J. Quantum Electron. QE-4, 598 (1968).
[CrossRef]

Bertolotti, M.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

Brunel, M.

M. Brunel and S. Coëtmelec, Opt. Commun. 230, 1 (2004).
[CrossRef]

Capmany, J.

Chirkin, A. S.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, IEEE J. Quantum Electron. QE-4, 598 (1968).
[CrossRef]

Coëtmelec, S.

M. Brunel and S. Coëtmelec, Opt. Commun. 230, 1 (2004).
[CrossRef]

Drabovich, K. N.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, IEEE J. Quantum Electron. QE-4, 598 (1968).
[CrossRef]

Ferrari, A.

Friberg, A. T.

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, Opt. Commun. 204, 53 (2002).
[CrossRef]

Jurgensen, K.

Khokhlov, R. V.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, IEEE J. Quantum Electron. QE-4, 598 (1968).
[CrossRef]

Kovrigin, A. I.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, IEEE J. Quantum Electron. QE-4, 598 (1968).
[CrossRef]

Lajunen, H.

H. Lajunen, J. Tervo, J. Turunen, and P. Vahimaa, Opt. Express 21, 1894 (2003).
[CrossRef]

Lin, Q.

Q. Lin, L. Wang, and S. Zhu, Opt. Commun. 219, 65 (2003).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
[CrossRef]

Marcuse, D.

Muriel, M. A.

Pääkkönen, P.

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, Opt. Commun. 204, 53 (2002).
[CrossRef]

Pastor, D.

Sales, S.

Sereda, L.

Sukhorukov, A. P.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, IEEE J. Quantum Electron. QE-4, 598 (1968).
[CrossRef]

Tervo, J.

H. Lajunen, J. Tervo, J. Turunen, and P. Vahimaa, Opt. Express 21, 1894 (2003).
[CrossRef]

Treacy, E. B.

E. B. Treacy, IEEE J. Quantum Electron. QE-5, 454 (1969).
[CrossRef]

Turunen, J.

H. Lajunen, J. Tervo, J. Turunen, and P. Vahimaa, Opt. Express 21, 1894 (2003).
[CrossRef]

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, Opt. Commun. 204, 53 (2002).
[CrossRef]

Vahimaa, P.

H. Lajunen, J. Tervo, J. Turunen, and P. Vahimaa, Opt. Express 21, 1894 (2003).
[CrossRef]

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, Opt. Commun. 204, 53 (2002).
[CrossRef]

Wang, L.

Q. Lin, L. Wang, and S. Zhu, Opt. Commun. 219, 65 (2003).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
[CrossRef]

Wyrowski, F.

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, Opt. Commun. 204, 53 (2002).
[CrossRef]

Zhu, S.

Q. Lin, L. Wang, and S. Zhu, Opt. Commun. 219, 65 (2003).
[CrossRef]

Appl. Opt. (2)

IEEE J. Quantum Electron. (2)

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kovrigin, R. V. Khokhlov, and A. P. Sukhorukov, IEEE J. Quantum Electron. QE-4, 598 (1968).
[CrossRef]

E. B. Treacy, IEEE J. Quantum Electron. QE-5, 454 (1969).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (3)

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, Opt. Commun. 204, 53 (2002).
[CrossRef]

Q. Lin, L. Wang, and S. Zhu, Opt. Commun. 219, 65 (2003).
[CrossRef]

M. Brunel and S. Coëtmelec, Opt. Commun. 230, 1 (2004).
[CrossRef]

Opt. Express (1)

H. Lajunen, J. Tervo, J. Turunen, and P. Vahimaa, Opt. Express 21, 1894 (2003).
[CrossRef]

Other (3)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
[CrossRef]

G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, 1997), Chap. 2.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

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Figures (2)

Fig. 1
Fig. 1

Plot of the temporal rms width in intensity of the GSMP as a function of the fiber length for a fixed spectral width of the source ( σ λ = 0.4 nm ) and σ T 0 = 5 ps (short-dashed curve), σ T 0 = 10 ps (solid curve), and σ T 0 = 30 ps (long-dashed curve).

Fig. 2
Fig. 2

Plot of the maximum bit rate as a function of the fiber length for λ 0 = 1.55 μ m , β 2 = 20 ps 2 km , and three different source linewidths, such that σ λ = 5 nm (long-dashed curve), σ λ = 1.3 nm (short-dashed curve), and the coherent limit σ λ 0 nm (solid curve).

Equations (8)

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

i ψ z = β 2 2 2 ψ τ 2 .
i Γ ( z 1 , z 2 , τ 1 , τ 2 ) z 1 = β 2 2 2 Γ ( z 1 , z 2 , τ 1 , τ 2 ) τ 1 2 .
i Γ ( z 1 , z 2 , τ 1 , z 2 ) z 2 = β 2 2 2 Γ ( z 1 , z 2 , τ 1 , τ 2 ) τ 2 2 .
i J ( z 1 , z 2 , x 1 , x 2 ) z 1 = 1 2 k ¯ Δ 1 J ( z 1 , z 2 , x 1 , x 2 ) ,
i J ( z 1 , z 2 , x 1 , x 2 ) z 2 = 1 2 k ¯ Δ 2 J ( z 1 , z 2 , x 1 , x 2 ) .
Γ ( z 1 = 0 , z 2 = 0 , τ 1 , τ 2 ) = Γ 0 exp [ ( τ 1 + τ 2 ) 2 8 σ T 0 2 ] exp [ ( τ 2 τ 1 ) 2 2 δ 0 2 ] exp [ i ω 0 ( τ 2 τ 1 ) ] ,
Γ ( z 1 = z , z 2 = z , τ 1 , τ 2 ) = Γ 0 Δ ( z ) exp [ ( τ 1 + τ 2 ) 2 8 σ T 0 2 [ Δ ( z ) ] 2 ] exp [ ( τ 2 τ 1 ) 2 2 δ 0 2 [ Δ ( z ) ] 2 ] × exp [ i τ 2 2 τ 1 2 2 β 2 R ( z ) ] exp [ i ω 0 ( τ 2 τ 1 ) ] ,
B = 1 4 ( z β 2 + ( σ ω z β 2 ) 2 ) 1 2

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