Abstract

We present a theory to quantify a fundamental limit on correlated photon pairs generated through four-wave mixing inside optical fibers in the presence of spontaneous Raman scattering (SpRS). Our theory is able to explain current experimental data. We show that if correlated photon pairs are generated with polarization orthogonal to the pump the effect of SpRS is significantly reduced over a broad spectral region extending from 5to15THz.

© 2006 Optical Society of America

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References

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2005

2004

2003

R. H. Stolen, in Raman Amplifiers for Telecommunications 1, M.N.Islam, ed. (Springer, 2003). The Raman spectra are provided by R. H. Stolen.

2001

L. J. Wang, C. K. Hong, and S. R. Friberg, J. Opt. B Quantum Semiclassical Opt. 3, 346 (2001).
[CrossRef]

1996

P. D. Drummond, in Coherence and Quantum Optics VII, J.H.Eberly, L.Mandel, and E.Wolf, eds. (Springer, 1996), p. 323.

1995

1994

L. Boivin, F. X. Kärtner, and H. A. Haus, Phys. Rev. Lett. 73, 240 (1994).
[CrossRef] [PubMed]

1977

R. W. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

Alibart, O.

Boivin, L.

L. Boivin, F. X. Kärtner, and H. A. Haus, Phys. Rev. Lett. 73, 240 (1994).
[CrossRef] [PubMed]

Chen, J.

Dogariu, A.

Drummond, P. D.

P. D. Drummond, in Coherence and Quantum Optics VII, J.H.Eberly, L.Mandel, and E.Wolf, eds. (Springer, 1996), p. 323.

Duligall, J.

Fan, J.

Friberg, S. R.

L. J. Wang, C. K. Hong, and S. R. Friberg, J. Opt. B Quantum Semiclassical Opt. 3, 346 (2001).
[CrossRef]

Fulconis, J.

Harvey, J. D.

Haus, H. A.

L. Boivin, F. X. Kärtner, and H. A. Haus, Phys. Rev. Lett. 73, 240 (1994).
[CrossRef] [PubMed]

Hellwarth, R. W.

R. W. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

Hong, C. K.

L. J. Wang, C. K. Hong, and S. R. Friberg, J. Opt. B Quantum Semiclassical Opt. 3, 346 (2001).
[CrossRef]

Inoue, K.

K. Inoue and K. Shimizu, Jpn. J. Appl. Phys. Part 1 43, 8048 (2004).
[CrossRef]

Kärtner, F. X.

L. Boivin, F. X. Kärtner, and H. A. Haus, Phys. Rev. Lett. 73, 240 (1994).
[CrossRef] [PubMed]

Kumar, P.

Leonhardt, R.

Li, X.

Migdall, A.

Murdoch, S. G.

Rarity, J. G.

Russell, P. St. J.

Sharping, J.

Shimizu, K.

K. Inoue and K. Shimizu, Jpn. J. Appl. Phys. Part 1 43, 8048 (2004).
[CrossRef]

Stolen, R. H.

R. H. Stolen, in Raman Amplifiers for Telecommunications 1, M.N.Islam, ed. (Springer, 2003). The Raman spectra are provided by R. H. Stolen.

Voss, P.

Wadsworth, W. J.

Wang, L. J.

J. Opt. B Quantum Semiclassical Opt.

L. J. Wang, C. K. Hong, and S. R. Friberg, J. Opt. B Quantum Semiclassical Opt. 3, 346 (2001).
[CrossRef]

Jpn. J. Appl. Phys. Part 1

K. Inoue and K. Shimizu, Jpn. J. Appl. Phys. Part 1 43, 8048 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A.

J. Chen, X. Li, and P. Kumar, Phys. Rev. A 72, 033801 (2005).

Phys. Rev. Lett.

L. Boivin, F. X. Kärtner, and H. A. Haus, Phys. Rev. Lett. 73, 240 (1994).
[CrossRef] [PubMed]

Prog. Quantum Electron.

R. W. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

Other

R. H. Stolen, in Raman Amplifiers for Telecommunications 1, M.N.Islam, ed. (Springer, 2003). The Raman spectra are provided by R. H. Stolen.

P. D. Drummond, in Coherence and Quantum Optics VII, J.H.Eberly, L.Mandel, and E.Wolf, eds. (Springer, 1996), p. 323.

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Figures (3)

Fig. 1
Fig. 1

Two eigenprocesses of FWM. The signal and idler are copolarized with the pump during process (a) but are orthogonally polarized during process (b).

Fig. 2
Fig. 2

Correlation ρ ( 0 ) versus pump–signal detuning, assuming perfect phase matching, for n 2 = 2.6 × 10 20 m 2 W , peak Raman gain of 0.62 × 10 13 m W (at 1550 nm ), and T = 300 K . The Raman spectra used are from Ref. [9]. The dotted and solid curves show the copolarized and orthogonally polarized cases, respectively.

Fig. 3
Fig. 3

Correlation enhancement factor plotted as a function of pump–signal detuning.

Equations (9)

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A ̂ i z = i j τ d τ R i j ( 1 ) ( τ τ ) A ̂ j ( z , τ ) + i j m ̂ i j ( z , τ ) A ̂ j ( z , τ ) + i j k l τ d τ R i j k l ( 3 ) ( τ τ ) A ̂ k ( z , τ ) A ̂ l ( z , τ ) A ̂ j ( z , τ ) ,
R i j k l ( 3 ) ( τ ) = γ 3 ( 1 f R ) δ ( τ ) ( δ i j δ k l + δ i k δ j l + δ i l δ j k ) + γ f R R a ( τ ) δ i j δ k l + γ 2 f R R b ( τ ) ( δ i k δ j l + δ i l δ j k ) ,
A ̂ j ( z , ω s ) z = i [ k j ( ω s ) + γ ξ j ( Ω s ) P 0 ] A ̂ j ( z , ω s ) + i γ η j ( Ω s ) A p x 2 A ̂ j ( z , ω i ) + i A p x m ̂ j x ( z , Ω s ) ,
A ̂ j ( L , ω s ) = [ α j ( L , ω s ) A ̂ j ( 0 , ω s ) + β j ( L , ω s ) A ̂ j ( 0 , ω i ) + N ̂ j ( L , ω s ) ] Φ ( L ) ,
α j ( L , ω s ) = [ cosh ( g j L ) + ( i κ j 2 g j ) sinh ( g j L ) ] e i K j L ,
β j ( L , ω s ) = ( i γ η j g j ) A p 2 sinh ( g j L ) e i K j L ,
N ̂ j ( L , ω s ) = i 0 L m ̂ j x ( z , Ω s ) [ A p α j ( L z , ω s ) A p * β j ( L z , ω s ) ] d z ,
ρ ( τ ) = A ̂ i ( t ) A ̂ s ( t + τ ) A ̂ s ( t + τ ) A ̂ i ( t ) ( I s I i ) 1 ,
ρ ( τ ) = φ ( τ ) 2 { [ γ Re ( η ) ] 2 + g R ( n th + 1 2 ) 2 } [ γ η 2 P 0 L + g R ( n th + 1 ) ] ( γ η 2 P 0 L + g R n th ) ,

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