Abstract

The nonzero response time of the Kerr [χ3] nonlinearity determines the quantum-limited noise figure of χ3 parametric amplifiers. This nonzero response time of the nonlinearity requires coupling of the parametric amplification process to a molecular-vibration phonon bath, causing the addition of excess noise through Raman gain or loss at temperatures above 0 K. The effect of this excess noise on the noise figure can be surprisingly significant. We derive analytical expressions for this quantum-limited noise figure for phase-insensitive operation of a χ3 amplifier and show good agreement with published noise-figure measurements.

© 2004 Optical Society of America

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2003 (4)

K. K. Y. Wong, K. Shimizu, M. E. Marhic, K. Uesaka, G. Kalogerakis, and L. G. Kazovsky, Opt. Lett. 28, 692 (2003).
[CrossRef] [PubMed]

R. Y. Tang, J. Lasri, P. Devgan, J. E. Sharping, and P. Kumar, Electron. Lett. 39, 195 (2003).
[CrossRef]

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin, and G. P. Agrawal, Electron. Lett. 39, 838 (2003).
[CrossRef]

P. L. Voss, R.-Y. Tang, and P. Kumar, Opt. Lett. 28, 549 (2003).
[CrossRef] [PubMed]

2002 (4)

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

L. Wang, A. Agarwal, Y. Su, and P. Kumar, IEEE J. Quantum Electron. 38, 614 (2002).
[CrossRef]

J. L. Blows and S. E. French, Opt. Lett. 27, 491 (2002).
[CrossRef]

K. Inoue and T. Mukai, IEEE J. Lightwave Technol. 20, 969 (2002).
[CrossRef]

2001 (2)

F. Koch, S. A. E. Lewis, S. V. Chernikov, and J. R. Taylor, Electron. Lett. 37, 1437 (2001).
[CrossRef]

M.-C. Ho, K. Uesaka, M. Marhic, Y. Akasaka, and L. G. Kazovsky, J. Lightwave Technol. 19, 977 (2001).
[CrossRef]

2000 (1)

Y. Su, L. Wang, A. Agarwal, and P. Kumar, Electron. Lett. 36, 1103 (2000).
[CrossRef]

1996 (1)

1995 (2)

1994 (1)

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

1989 (1)

Agarwal, A.

L. Wang, A. Agarwal, Y. Su, and P. Kumar, IEEE J. Quantum Electron. 38, 614 (2002).
[CrossRef]

Y. Su, L. Wang, A. Agarwal, and P. Kumar, Electron. Lett. 36, 1103 (2000).
[CrossRef]

Agrawal, G. P.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin, and G. P. Agrawal, Electron. Lett. 39, 838 (2003).
[CrossRef]

Akasaka, Y.

Andrekson, P. A.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

Blows, J. L.

Boivin, L.

J. H. Shapiro and L. Boivin, Opt. Lett. 20, 925 (1995).
[CrossRef] [PubMed]

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

Boskovic, A.

Centanni, J. C.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin, and G. P. Agrawal, Electron. Lett. 39, 838 (2003).
[CrossRef]

Chernikov, S. V.

F. Koch, S. A. E. Lewis, S. V. Chernikov, and J. R. Taylor, Electron. Lett. 37, 1437 (2001).
[CrossRef]

A. Boskovic, S. V. Chernikov, J. R. Taylor, L. Gruner-Nielsen, and O. A. Levring, Opt. Lett. 21, 1966 (1996).
[CrossRef] [PubMed]

Devgan, P.

R. Y. Tang, J. Lasri, P. Devgan, J. E. Sharping, and P. Kumar, Electron. Lett. 39, 195 (2003).
[CrossRef]

Dougherty, D. J.

French, S. E.

Gordon, J. P.

Gruner-Nielsen, L.

Hansryd, J.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

Haus, H. A.

Hedekvist, P. O.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

Ho, M.-C.

Inoue, K.

K. Inoue and T. Mukai, IEEE J. Lightwave Technol. 20, 969 (2002).
[CrossRef]

Ippen, E. P.

Jopson, R. M.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin, and G. P. Agrawal, Electron. Lett. 39, 838 (2003).
[CrossRef]

Kalogerakis, G.

Kärtner, F. X.

Kazovsky, L. G.

Koch, F.

F. Koch, S. A. E. Lewis, S. V. Chernikov, and J. R. Taylor, Electron. Lett. 37, 1437 (2001).
[CrossRef]

Kumar, P.

P. L. Voss, R.-Y. Tang, and P. Kumar, Opt. Lett. 28, 549 (2003).
[CrossRef] [PubMed]

R. Y. Tang, J. Lasri, P. Devgan, J. E. Sharping, and P. Kumar, Electron. Lett. 39, 195 (2003).
[CrossRef]

L. Wang, A. Agarwal, Y. Su, and P. Kumar, IEEE J. Quantum Electron. 38, 614 (2002).
[CrossRef]

Y. Su, L. Wang, A. Agarwal, and P. Kumar, Electron. Lett. 36, 1103 (2000).
[CrossRef]

Lasri, J.

R. Y. Tang, J. Lasri, P. Devgan, J. E. Sharping, and P. Kumar, Electron. Lett. 39, 195 (2003).
[CrossRef]

Levring, O. A.

Lewis, S. A. E.

F. Koch, S. A. E. Lewis, S. V. Chernikov, and J. R. Taylor, Electron. Lett. 37, 1437 (2001).
[CrossRef]

Li, J.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

Lin, Q.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin, and G. P. Agrawal, Electron. Lett. 39, 838 (2003).
[CrossRef]

Marhic, M.

Marhic, M. E.

McKinstrie, C. J.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin, and G. P. Agrawal, Electron. Lett. 39, 838 (2003).
[CrossRef]

Mukai, T.

K. Inoue and T. Mukai, IEEE J. Lightwave Technol. 20, 969 (2002).
[CrossRef]

Radic, S.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin, and G. P. Agrawal, Electron. Lett. 39, 838 (2003).
[CrossRef]

Shapiro, J. H.

Sharping, J. E.

R. Y. Tang, J. Lasri, P. Devgan, J. E. Sharping, and P. Kumar, Electron. Lett. 39, 195 (2003).
[CrossRef]

Shimizu, K.

Stolen, R. H.

Su, Y.

L. Wang, A. Agarwal, Y. Su, and P. Kumar, IEEE J. Quantum Electron. 38, 614 (2002).
[CrossRef]

Y. Su, L. Wang, A. Agarwal, and P. Kumar, Electron. Lett. 36, 1103 (2000).
[CrossRef]

Tang, R. Y.

R. Y. Tang, J. Lasri, P. Devgan, J. E. Sharping, and P. Kumar, Electron. Lett. 39, 195 (2003).
[CrossRef]

Tang, R.-Y.

Taylor, J. R.

F. Koch, S. A. E. Lewis, S. V. Chernikov, and J. R. Taylor, Electron. Lett. 37, 1437 (2001).
[CrossRef]

A. Boskovic, S. V. Chernikov, J. R. Taylor, L. Gruner-Nielsen, and O. A. Levring, Opt. Lett. 21, 1966 (1996).
[CrossRef] [PubMed]

Tomlinson, W. J.

Uesaka, K.

Voss, P. L.

Wang, L.

L. Wang, A. Agarwal, Y. Su, and P. Kumar, IEEE J. Quantum Electron. 38, 614 (2002).
[CrossRef]

Y. Su, L. Wang, A. Agarwal, and P. Kumar, Electron. Lett. 36, 1103 (2000).
[CrossRef]

Westlund, M.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

Wong, K. K. Y.

Electron. Lett. (4)

Y. Su, L. Wang, A. Agarwal, and P. Kumar, Electron. Lett. 36, 1103 (2000).
[CrossRef]

R. Y. Tang, J. Lasri, P. Devgan, J. E. Sharping, and P. Kumar, Electron. Lett. 39, 195 (2003).
[CrossRef]

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin, and G. P. Agrawal, Electron. Lett. 39, 838 (2003).
[CrossRef]

F. Koch, S. A. E. Lewis, S. V. Chernikov, and J. R. Taylor, Electron. Lett. 37, 1437 (2001).
[CrossRef]

IEEE J. Lightwave Technol. (1)

K. Inoue and T. Mukai, IEEE J. Lightwave Technol. 20, 969 (2002).
[CrossRef]

IEEE J. Quantum Electron. (1)

L. Wang, A. Agarwal, Y. Su, and P. Kumar, IEEE J. Quantum Electron. 38, 614 (2002).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

J. Lightwave Technol. (1)

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

Opt. Lett. (6)

Phys. Rev. Lett. (1)

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

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Figures (2)

Fig. 1
Fig. 1

Gain and NF spectra for 1-km-long FOPA pumped at 1537.6 nm with 1.5 W of power. The fiber’s dispersion zero is at 1537 nm, the dispersion slope is 0.064 ps/nm2 km, and the nonlinear coefficient is H0=1.8 W-1 km-1. ImHΩ calculated from Raman measurements11-13 (dotted curve) and ImHΩ=0 (solid curve).

Fig. 2
Fig. 2

High-gain NF versus pump-signal detuning for a FOPA phase matched at each detuning. Solid curve, DSF; dotted curve, SMF; circle, experimental data point from Voss et al.9 Inset, NF versus gain for a (a) phase-matched ideal PIA, (b) PIA made with SMF-28, and (c) PIA made with DSF at 1.38-THz pump-signal detuning and 300 K. Experimental data points for DSF are from Voss et al.9 No fitting parameters are used, and HΩ is calculated from measured nonlinear coefficients.11-13

Equations (10)

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

Aˆtz=idτht-τAˆτAˆτAˆt+mˆz,t,
dAˆadz=iH0+HΩA¯p2Aˆa+iHΩA¯p2Aˆsexp-iΔkz+Mˆz,ΩA¯p,
dAˆsdz=iH0+H-ΩA¯p2Aˆs+iH-ΩA¯p2Aˆaexp-iΔkz+Mˆz,-ΩA¯p,
μaz=expiϕczcoshgz+iκ2gsinhgz,
μsz=expiϕczcoshg*z+iκ*2g*sinhg*z,
νaz=expiϕcziHΩA¯p2gsinhgz,
νsz=expiϕcziH-ΩA¯p2g*sinhg*z,
Aˆaz=μazAˆa0+νazAˆs0+ca1tˆ1+ca2tˆ2,
Aˆsz=μszAˆs0+νszAˆa0+cstˆ1,
NFj,PIA=1+νj2+1+2nth-1+μj2-νj2μj2,

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