Abstract

We propose a phase-sensitive amplifier scheme that balances fiber loss and parametric gain everywhere in a fiber span. We show that, for long links, such a distributed phase-sensitive amplifier has a 3-dB lower noise figure than an ideal distributed phase-insensitive amplifier (e.g. Raman), even if simple direct detection is employed. This sets the ultimate limit for the optimum noise-nonlinearity trade-off in transmission systems.

© 2005 Optical Society of America

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References

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  32. Here, conventional fiber is assumed to be averaging the nonlinear interaction over the signal states of polarization while preserving the relative orientation of the pump and signal. Coefficients a, b, ε, and εp are straightforwardly derived from Eq. (4.2.10) of [33], as done, for example, in [34].
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    [CrossRef]

9th International Conference on Squeezed

M. Vasilyev, �??Squeezing and fiber-optic communication,�?? 9th International Conference on Squeezed States and Uncertainty Relations 2005, May 2005, Besançon, France, paper I 79.

Conference on Lasers and Electro-Optics

G. Kalogerakis, K. K. Y. Wong, M. E. Marhic, and L. G. Kazovsky, �??Transmission of optical communication signals by distributed parametric amplification,�?? in Conference on Lasers and Electro-Optics 2005 (Optical Society of America, Washington, DC, 2005), paper CTuT2.
[CrossRef]

Electron. Lett.

I. Shake, H. Takara, K. Mori, S. Kawanishi, Y. Yamabayashi, �??Influence of inter-bit four-wave mixing in optical TDM transmission,�?? Electron. Lett. 34, 1600 (1998).
[CrossRef]

R. Tang, P. Devgan, V. S. Grigoryan, and P. Kumar, �??In-line frequency-non-degenerate phase-sensitive fiber parametric amplifier for fiber-optic communications,�?? to appear in Electron. Lett.

M. Vasilyev, B. Szalabofka, S. Tsuda, J. M. Grochocinski, and A. F. Evans, �??Reduction of Raman MPI and noise figure in dispersion-managed fibre,�?? Electron. Lett. 38, 271 (2002).
[CrossRef]

M. E. Marhic, C. H. Hsia, and J.-M. Jeong, Electron. Lett. 27, 210 (1991).
[CrossRef]

A. Takada and W. Imajuku, �??In-line optical phase-sensitive amplifier employing pump laser injection-locked to input signal light,�?? Electron. Lett. 34, 274 (1998).
[CrossRef]

W. Imajuku, A. Takada, Y. Yamabayashi, �??Low-noise amplification under the 3 dB noise figure in high-gain phase-sensitive fibre amplifier,�?? Electron. Lett. 35, 1954 (1999).
[CrossRef]

European Conference on Optical Communica

J.-C. Bouteiller, K. Brar, and C. Headley, �??Quasi-constant signal power transmission,�?? European Conference on Optical Communication 2002, paper S3.04.

IEEE Photonics Technol. Lett.

G. D. Bartolini, D. K. Serkland, P. Kumar, and W. L. Kath, �??All-optical storage of a picosecond-pulse packet using parametric amplification,�?? IEEE Photonics Technol. Lett. 9, 1020 (1997).
[CrossRef]

A. Mecozzi, C. B. Clausen, M. Shtaif, �??Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission,�?? IEEE Photonics Technol. Lett. 12, 392 (2000).
[CrossRef]

R. Tang, P. Devgan, P. L. Voss, V. S. Grigoryan, and P. Kumar, �??In-Line Frequency-Nondegenerate Phase-Sensitive Fiber-Optical Parametric Amplifier,�?? IEEE Photonics Technol. Lett. 17, 1845 (2005).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Opt. Express

Opt. Fiber Technol.

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

Opt. Lett.

Optical Fiber Communication Conference

M. Vasilyev, �??Raman-assisted transmission: toward ideal distributed amplification,�?? Optical Fiber Communication Conference 2003, Technical Digest (OSA, Washington, D.C. 2003), Vol. 1, pp. 303�??305, paper WB1.

Optical Fiber Telecommunications IIIA

L. F. Mollenauer, J. P. Gordon, and P. V. Mamyshev, �??Solitons in high bit-rate, long-distance transmission,�?? in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic Press, San Diego, 1997), pp. 373�??460.

Phys. Rev. B

R. M. Shelby, M. D. Levenson, and P. W. Bayer, �??Guided acoustic-wave Brillouin scattering,�?? Phys. Rev. B 31, 5244 (1985).
[CrossRef]

Phys. Rev. D

C. M. Caves, �??Quantum limits on noise in linear amplifiers,�?? Phys. Rev. D. 26, 1817 (1982).
[CrossRef]

Phys. Rev. Lett.

Z. Y. Ou, S. F. Pereira, H. J. Kimble, �??Quantum noise reduction in optical amplification,�?? Phys. Rev. Lett. 70, 3239 (1993).
[CrossRef] [PubMed]

S.-K. Choi, M. Vasilyev, and P. Kumar, �??Noiseless Optical Amplification of Images,�?? Phys. Rev. Lett. 83, 1938 (1999).
[CrossRef]

PRAMANA???Journal of Physics

D. Levandovsky, M. Vasilyev, and P. Kumar, �??Near-noiseless amplification of light by a phase-sensitive fibre amplifier,�?? PRAMANA�??Journal of Physics 56, 281 (2001).
[CrossRef]

Raman Amplifiers in Telecommunications 2

A. F. Evans, A. Kobyakov, and M. Vasilyev, �??Distributed Raman transmission: applications and fiber issues,�?? in Raman Amplifiers in Telecommunications 2: Sub-Systems and Systems, ed. by M. N. Islam, Springer, New York, 2004, pp. 383�??412.
[CrossRef]

Other

Here, conventional fiber is assumed to be averaging the nonlinear interaction over the signal states of polarization while preserving the relative orientation of the pump and signal. Coefficients a, b, ε, and εp are straightforwardly derived from Eq. (4.2.10) of [33], as done, for example, in [34].

R. W. Boyd, Nonlinear Optics (Academic Press, San Diego, 2003), Chap. 4.2.

M. Vasilyev, lecture notes for Nonlinear Optics course (University of Texas at Arlington, 2004).

G. P. Agrawal, Nonlinear fiber optics (Academic Press, San Diego, 1995).

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Figures (4)

Fig. 1.
Fig. 1.

Optical amplifier evolution quantified by the net NF limits of a fiber span. Numbers next to arrows show the signal-to-noise-ratio improvement for a 100-km-long span, accounting for signal-power adjustment by (ln G)/(1–1/G) between lumped and distributed amplifiers due to their difference in nonlinear path integrals. Dashed box shows focus of this paper.

Fig. 2.
Fig. 2.

Example of wideband square-law optical detector. The local oscillator LO with phase φ and cw wave are assumed to be separated by more than 2∆ω=ωS- ω I , i.e. WDM coupler can be used for their multiplexing. The output optical spectrum is related to the spectrum of fictitious homodyne photocurrent.

Fig. 3.
Fig. 3.

Left: comparison of the quantum limit 2-1/G for PIA NF (dashed) and direct-detected PSA NF of Eq. (7) increased by 3 dB to account for effective input SNR based on total power of signal and idler (solid). Right: comparison of overall link NF limits for different amplifiers (α=0.25 dB/km, span length between lumped amplifiers is L=100 km). Direct-detected distributed PSA is close to the distributed PSA limit for z >100 km. Lumped-case NFs have been adjusted by a ratio (1-e L )/(αL) to account for the difference between lumped and distributed path-averaged powers responsible for nonlinear penalties.

Fig. 4.
Fig. 4.

Transmission link with cascaded distributed PSAs. OPLL-optical phase-locked loop. PIA/BS-PIA or nonlinear beam splitter (BS). DSF-dispersion-shifted fiber. WDM-wavelength-division-multiplexing coupler for signal and Raman-pump bands. Inset diagrams show relative polarizations of the signal and idler with respect to the parametric and Raman pumps.

Equations (14)

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d A S , I dz = i γε [ 2 a ( P 1 + P 2 ) A S , I + 2 b A 1 A 2 A I , S + e i Δβz ] ,
d A 1 , 2 dz = i γε ( P 1,2 + 2 ε P P 2,1 ) A 1,2 .
A S ( z ) = μ A S ( 0 ) + v A I + ( 0 ) ,
A I ( z ) = μ A I ( 0 ) + v A S + ( 0 ) ,
μ = e i [ κ 2 + 2 γε a ( P 1 + P 2 ) ] z [ cosh gz i κ 2 g sinh gz ] ,
v = i e i [ κ 2 + 2 γε a ( P 1 + P 2 ) ] z 2 γε b g P 1 P 2 e i ( θ 1 + θ 2 ) sinh gz ,
A + = A S + A I 2 , A = A S A I 2 ,
X ± ( z ) = A ± ( z ) + A ± + ( z ) 2 = ( μ ± v ) X ± ( 0 ) ,
Y ± ( z ) = A ± ( z ) A ± + ( z ) 2 i = ( μ v ) Y ± ( 0 ) .
G PSA = ( μ + v ) 2 = ( G PIA + G PIA 1 ) 2 = exp ( 2 gz )
1 / G PSA = ( μ + v ) 2 = ( G PIA G PIA 1 ) 2 = exp ( 2 gz )
NF SIG PSA = 2 G PIA 1 ( G PIA + G PIA 1 ) 2 1 2
A S , I ( z ) = e αz / 2 [ μ A I , S ( 0 ) + v A I , S + ( 0 ) ] +
+ α 0 z e α ( z ' z ) / 2 { μ ( z ) [ μ * ( z ' ) c S ( z ' ) v ( z ' ) c I + ( z ' ) ] v ( z ) [ v * ( z ' ) c S ( z ' ) μ ( z ' ) c I + ( z ' ) ] } dz ' ,

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