Abstract

Using the quantum theory of light, we derive general analytical expressions of Stokes and anti-Stokes spectral photon-flux densities that are spontaneously generated by a single monochromatic pump wave propagating in a single-mode optical fiber. We validate our results by comparing them with experimental data. Limiting cases corresponding to interesting physical situations are discussed.

© 2007 Optical Society of America

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References

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2007 (1)

Q. Lin, F. Yaman, and G. P. Agrawal, Phys. Rev. A 75, 023803 (2007).
[CrossRef]

2006 (3)

2005 (2)

2004 (1)

2003 (1)

2002 (2)

1995 (1)

1994 (1)

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

1990 (1)

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, IEEE J. Quantum Electron. 26, 1815 (1990).
[CrossRef]

1986 (1)

1964 (1)

N. Bloembergen and Y. R. Shen, Phys. Rev. Lett. 12, 504 (1964).
[CrossRef]

IEEE J. Quantum Electron. (1)

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, IEEE J. Quantum Electron. 26, 1815 (1990).
[CrossRef]

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

Opt. Express (2)

Opt. Lett. (6)

Phys. Rev. A (1)

Q. Lin, F. Yaman, and G. P. Agrawal, Phys. Rev. A 75, 023803 (2007).
[CrossRef]

Phys. Rev. Lett. (3)

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

S. Coen, D. A. Wardle, and J. D. Harvey, Phys. Rev. Lett. 89, 273901 (2002).
[CrossRef]

N. Bloembergen and Y. R. Shen, Phys. Rev. Lett. 12, 504 (1964).
[CrossRef]

Rev. Mod. Phys. (1)

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

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

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Figures (2)

Fig. 1
Fig. 1

Ratio of anti-Stokes to Stokes photon fluxes at the peak of the Raman gain as a function of γ P Δ k .

Fig. 2
Fig. 2

Evolution of the Stokes and anti-Stokes spectral power densities with the pump peak power. The experimental data are from [6]. The simulation parameters are: γ = 23 W 1 km 1 , x = 2.85 m , β 2 = 50 ps 2 km 1 , T = 293 K , pulse width 60 ps (FWHM), the repetition rate 1.176 MHz. We discretized each sech 2 -shaped pump pulse into 13 time bins and summed the resulting spectra.

Equations (13)

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A ( x , t ) = e i ϕ ( x , t ) 0 ( ω s 2 π A s ( Ω , x ) e i Ω t + ω a 2 π A a ( Ω , x ) e i Ω t ) d Ω + h.c.
f s , a ( Ω , x ) = lim ϵ 0 1 2 π ϵ × Ω ϵ 2 Ω + ϵ 2 Ω ϵ 2 Ω + ϵ 2 A s , a ( Ω 1 , x ) A s , a ( Ω 2 , x ) d Ω 1 d Ω 2 .
f s ( Ω , x ) = 1 2 π χ ( Ω ) 2 κ ( Ω ) 2 sinh ( κ ( Ω ) x ) 2 + Im [ χ ( Ω ) ] π ρ + ( Ω , x ) ( n ( Ω ) + 1 ) ,
f a ( Ω , x ) = 1 2 π χ ( Ω ) 2 κ ( Ω ) 2 sinh ( κ ( Ω ) x ) 2 + Im [ χ ( Ω ) ] π ρ ( Ω , x ) n ( Ω ) ,
ρ ± ( Ω , x ) = 0 x d x cosh ( κ ( Ω ) x ) ± i Δ k ( Ω ) 2 κ ( Ω ) sinh ( κ x ) 2 .
n ( Ω ) = ( exp ( Ω k B T ) 1 ) 1
f s 1 π Im [ χ ] x ( n + 1 ) ,
f a 1 π Im [ χ ] x n ,
f s e 2 Re [ κ ] x 8 π ( χ 2 κ 2 + Im [ χ ] Re [ κ ] κ + i Δ k 2 2 κ 2 ( n + 1 ) ) ,
f a e 2 Re [ κ ] x 8 π ( χ 2 κ 2 + Im [ χ ] Re [ κ ] κ i Δ k 2 2 κ 2 n ) .
f s f a e 2 Re [ κ ] x 8 π χ 2 κ 2 .
f s e 2 Im [ χ ] x 2 π ( n + 1 ) ,
f a e 2 Im [ χ ] x 2 π χ 2 Δ k 2 ( n + 1 ) .

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