Abstract

Optical frequency conversion by four-wave mixing (Bragg scattering) in a fiber is considered. If the frequencies and polarizations of the waves are chosen judiciously, Bragg scattering enables the translation of individual and entangled states, without the noise pollution associated with parametric amplification (modulation instability or phase conjugation), and with reduced noise pollution associated with stimulated Raman scattering.

© 2005 Optical Society of America

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References

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Appl. Opt.

Appl. Phys. Lett.

R. H. Stolen and E. P. Ippen, �??Raman gain in glass optical waveguides,�?? Appl. Phys. Lett. 22, 276�??278 (1973).
[CrossRef]

IEEE J. Quantum Electron.

R. H. Stolen, �??Polarization effects in fiber Raman and Brillouin lasers,�?? IEEE J. Quantum Electron. 15, 1157�??1160 (1979).
[CrossRef]

C. R. Menyuk, �??Nonlinear pulse propagation in birefringent optical fibers,�?? IEEE J. Quantum Electron. 23, 174�??176 (1987).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li and P. O. Hedekvist, �??Fiber-based optical parametric amplifiers and their applications,�?? IEEE J. Sel. Top. Quantum Electron. 8, 506�??520 (2002).
[CrossRef]

C. J. McKinstrie, S. Radic and A. R. Chraplyvy, �??Parametric amplifiers driven by two pump waves,�?? IEEE J. Sel. Top. Quantum Electron. 8, 538�??547 and 956 (2002).
[CrossRef]

IEEE Photon. Technol. Lett.

T. Tanemura, J. Suzuki, K. Katoh and K. Kikuchi, �??Polarization-insensitive all-optical wavelength conversion using cross-phase modulation in twisted fiber and optical filtering,�?? IEEE Photon. Technol. Lett. 17, 1052�??1054 (2005).
[CrossRef]

J. Lightwave Technol.

S. G. Evangelides, L. F. Mollenauer, J. P. Gordon and N. S. Bergano, �??Polarization muliplexing with solitons,�?? J. Lightwave Technol. 10, 28�??35 (1992).
[CrossRef]

J. Mod. Opt.

M. G. Raymer, �??Quantum state entanglement and readout of collective atomic-ensemble modes and optical wave packets by stimulated Raman scattering,�?? J. Mod. Opt. 51, 1739�??1759 (2004).

Opt. Express

Opt. Fiber Technol.

S. Radic and C. J. McKinstrie, �??Two-pump fiber parametric amplifiers,�?? Opt. Fiber Technol. 9, 7�??23 (2003).
[CrossRef]

Opt. Lett.

Phys. Rev.

P. D. Maker and R.W. Terhune, �??Study of optical effects due to an induced polarization third order in the electric field strength,�?? Phys. Rev. 137, A801�??A818 (1965).
[CrossRef]

Phys. Rev. E

M. Yu, C. J. McKinstrie and G. P. Agrawal, �??Modulational instabilities in dispersion-flattened fibers,�?? Phys. Rev. E 52, 1072�??1080 (1995).
[CrossRef]

Other

M. G. Raymer and I. A.Walmsley, �??Quantum coherence properties of stimulated Raman scattering,�?? in Progress in Optics, Vol. 28, edited by E. Wolf (North-Holland, 1990), pp. 181�??270.
[CrossRef]

W. H. Louisell, Radiation and Noise in Quantum Electronics (McGraw-Hill, 1964).

R. Loudon, The Quantum Theory of Light, 3rd Ed. (Oxford University Press, 2000).

H. Kogelnik, R. M. Jopson and L. E. Nelson, �??Polarization-mode dispersion,�?? in Optical Fiber Telecommunications IVB, edited by I. Kaminow and T. Li (Academic Press, 2002), pp. 725�??861.

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Figures (7)

Fig. 1.
Fig. 1.

Illustration of the constituent two-mode processes in a four-mode parametric interaction driven by two pump waves.

Fig. 2.
Fig. 2.

Eigenpolarizations of BS driven by parallel pumps.

Fig. 3.
Fig. 3.

Eigenpolarizations of BS driven by perpendicular pumps. The dashed lines denote sidebands that propagate independently.

Fig. 4.
Fig. 4.

Signal transmittance (solid curve) and idler transmittance (dashed curve) plotted as functions of the pump frequency ω 1. The vertical line denotes the signal frequency ωs . (a) ωs = -5.0 and ω 2 = 5.0 Tr/s. (b) ωs = -5.05 and ω 2 = 4.95.

Fig. 5.
Fig. 5.

Signal transmittance (solid curve) and idler transmittance (dashed curve) plotted as functions of the pump frequency ω 1. The vertical line denotes the signal frequency ωs . (a) ωs = -5.53 and ω 2 = 4.47 Tr/s. (b) ωs = -40.31 and ω 2 = 39.69.

Fig. 6.
Fig. 6.

Signal transmittance (solid curve) and idler transmittance (dashed curve) plotted as functions of the signal frequency ωs . (a) ω 1 = -20 and ω 2 = 5 Tr/s. (b) ω 1 = -10 and ω 2 = 10.

Fig. 7.
Fig. 7.

Signal transmittance (solid curve) and idler transmittance (dashed curve) plotted as functions of the signal frequency ωs . The pump frequencies ω 1 = -10 and ω 2 = 10 Tr/s. (a) β 3 = 0.1 ps3/Km, γ= 20/Km-W and P = 1.0 W. (b) β 3 = 0.01, γ = 10 and P = 0.3.

Equations (29)

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

H = δ ( a s a s a i a i ) + κ a s a i + κ * a s a i ,
d z a j = i [ a j , H ] ,
d z a s = i δ a s + i κ a i ,
d z a i = i κ * a s i δ a i .
a s ( z ) = μ ¯ ( z ) a s ( 0 ) + ν ¯ ( z ) a i ( 0 ) ,
a i ( z ) = ν ¯ * ( z ) a s ( 0 ) + μ ¯ * ( z ) a i ( 0 ) ,
μ ¯ ( z ) = cos ( k z ) + i δ sin ( k z ) k ,
ν ¯ ( z ) = i κ sin ( k z ) k
1,0 in = μ ¯ 1,0 out ν ¯ * 0,1 out .
1,0 ; 1,0 in = μ ¯ μ ' ¯ 1,0 ; 1,0 out μ ¯ ( ν ' ¯ ) * 1,0 ; 0,1 out
ν ¯ * μ ' ¯ 0,1 ; 1,0 out + ν ¯ * ( ν ' ¯ ) * 1,0 ; 0,1 out .
δ = β 2 ( ω b 2 ω c 2 ) / 2 + β 4 ( ω b 4 ω c 4 ) / 24 ,
= [ ( ω b 2 ω c 2 ) / 2 ] [ β 2 + β 4 ( ω b 2 + ω c 2 ) / 12 ] ,
d δ d ω 1 = ω c ( β 2 + β 4 ω c 2 6 ) ,
d 2 δ d ω 1 2 = ( β 2 + β 4 ω c 2 2 ) .
d δ / d ω s = β 3 ( ω b 2 ω c 2 ) / 4 β 3 ω a ( ω b + ω c ) / 2 β 4 ( ω b 3 + ω c 3 ) / 12 ,
d 2 δ / d ω s 2 = β 3 ( ω b + ω c ) / 2 + β 4 ( ω b 2 ω c 2 ) / 8 .
E ( t , z ) = A ( t , z ) exp [ i ( k 0 z ω 0 t ) ] ,
P = γ ¯ [ 2 ( A · A * ) A + ( A · A ) A * ] / 3 ,
i z A = β ( i t ) A + γ ( A 2 + A 2 ) A ,
i z A = β ( i t ) A + γ ( A 2 + A 2 ) A ,
P x = γ ¯ ( X 2 + 2 Y 2 / 3 ) X + γ ¯ Y 2 X * / 3 ,
P y = γ ¯ ( 2 X 2 / 3 + Y 2 ) Y + γ ¯ X 2 Y * / 3 .
i z X = β x ( i t ) X + γ ( X 2 + ε Y 2 ) X ,
i z Y = β y ( i t ) Y + γ ( ε X 2 + Y 2 ) Y ,
P r = ( 2 γ ¯ / 3 ) ( R 2 + 2 L 2 ) R ,
P l = ( 2 γ ¯ / 3 ) ( 2 R 2 + L 2 ) L .
i z R = β ( i t ) R + γ ( R 2 + ε L 2 ) R ,
i z L = β ( i t ) L + γ ( ε R 2 + L 2 ) L ,

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