Abstract

Phase-sensitive amplification (PSA), which is produced by degenerate four-wave mixing (FWM) in a randomly-birefringent fiber, has the potential to improve the performance of optical communication systems. Scalar FWM, which is driven by parallel pumps, is impaired by the generation of pump–pump and pump–signal harmonics, which limit the level, and modify the phase sensitivity, of the signal gain. In contrast, vector FWM, which is driven by perpendicular pumps, is not impaired by the generation of harmonics. Vector FWM produces PSA with the classical properties of a one-mode squeezing transformation.

© 2007 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2006 (3)

2005 (1)

2004 (2)

1993 (1)

R. D. Li, P. Kumar,W. L. Kath and J. N. Kutz, "Combating dispersion with parametric amplifiers," IEEE Photon. Technol. Lett. 5, 669-672 (1993).
[CrossRef]

1992 (3)

1985 (1)

R. Loudon, "Theory of noise accumulation in linear optical-amplifier chains," IEEE J. Quantum Electron. 21, 766-773 (1985).
[CrossRef]

Fan, J.

Inoue, K.

K. Inoue, "Polarization effect on four-wave mixing efficiency in a single-mode fiber," IEEE J. Quantum Electron. 28, 883-894 (1992).
[CrossRef]

Jopson, R. M.

Kanaev, A. V.

Kath, W. L.

R. D. Li, P. Kumar,W. L. Kath and J. N. Kutz, "Combating dispersion with parametric amplifiers," IEEE Photon. Technol. Lett. 5, 669-672 (1993).
[CrossRef]

Kogelnik, H.

Kumar, P.

R. D. Li, P. Kumar,W. L. Kath and J. N. Kutz, "Combating dispersion with parametric amplifiers," IEEE Photon. Technol. Lett. 5, 669-672 (1993).
[CrossRef]

Kutz, J. N.

R. D. Li, P. Kumar,W. L. Kath and J. N. Kutz, "Combating dispersion with parametric amplifiers," IEEE Photon. Technol. Lett. 5, 669-672 (1993).
[CrossRef]

Li, R. D.

R. D. Li, P. Kumar,W. L. Kath and J. N. Kutz, "Combating dispersion with parametric amplifiers," IEEE Photon. Technol. Lett. 5, 669-672 (1993).
[CrossRef]

Loudon, R.

R. Loudon, "Theory of noise accumulation in linear optical-amplifier chains," IEEE J. Quantum Electron. 21, 766-773 (1985).
[CrossRef]

McKinstrie, C. J.

Migdall, A.

Mu, Y.

Radic, S.

Raymer, M. G.

Savage, C. M.

Vasilyev, M. V.

C. J. McKinstrie, M. G. Raymer, S. Radic, and M. V. Vasilyev, "Quantum mechanics of phase-sensitive amplifi- cation in a fiber," Opt. Commun. 257, 146-163 (2006).
[CrossRef]

Yu, M.

Yuen, H. P.

IEEE J. Quantum Electron. (2)

R. Loudon, "Theory of noise accumulation in linear optical-amplifier chains," IEEE J. Quantum Electron. 21, 766-773 (1985).
[CrossRef]

K. Inoue, "Polarization effect on four-wave mixing efficiency in a single-mode fiber," IEEE J. Quantum Electron. 28, 883-894 (1992).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

R. D. Li, P. Kumar,W. L. Kath and J. N. Kutz, "Combating dispersion with parametric amplifiers," IEEE Photon. Technol. Lett. 5, 669-672 (1993).
[CrossRef]

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

Opt. Commun. (1)

C. J. McKinstrie, M. G. Raymer, S. Radic, and M. V. Vasilyev, "Quantum mechanics of phase-sensitive amplifi- cation in a fiber," Opt. Commun. 257, 146-163 (2006).
[CrossRef]

Opt. Express (4)

Opt. Lett. (2)

Other (3)

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

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

I. S. Gradsteyn and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic Press, 1994), pp. 987-994.

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Figures (9)

Fig. 1.
Fig. 1.

Polarization diagrams for degenerate scalar FWM (left) and degenerate vector FWM (right).

Fig. 2.
Fig. 2.

Mode powers plotted as functions of mode number for cases in which the input amplitudes ρ±= 1 and the input polarization-angle θ-=0. The other angle θ+=0 (top row), θ+=π/4 (middle row) and θ+=π/2 (bottom row), and the distance z=0 (left column) and z=2 (right column). Red (light-gray) bars represent x-components, whereas blue (dark-gray) bars represent y-components.

Fig. 3.
Fig. 3.

Normalized mode powers plotted as functions of mode number for cases in which the input amplitudes ρ=1 and ρ0=0.1, and the input phase ϕ0=0. The input polarizationangle θ0=0 (top row), θ0=π/4 (middle row) and θ0=π/2 (bottom row), and the distance z=0 (left column) and z=4 (right column). Red bars represent x-components, whereas blue bars represent y-components.

Fig. 4.
Fig. 4.

Signal gain plotted as a function of input phase and distance. Light and dark regions correspond to positive and negative gains, respectively. The solid curves show the loci of maximal and minimal gain.

Fig. 5.
Fig. 5.

Signal gain plotted as a function of input phase and distance for cases in which ρ=1 and ρ0=0.01: z=5 (left), and ϕ0=0.099 and ϕ0=1.67 (right). In the phase plot the exact and approximate results are denoted by solid and dashed curves, respectively. In the distance plot they are represented by solid and dashed curves (amplification), and dot-dashed and dotted curves (attenuation). The exact and approximate curves are nearly indistinguishable.

Fig. 6.
Fig. 6.

Normalized mode powers plotted as functions of mode number for the case in which ρ = 1, ρ0=0.01 and ϕ0=0.099: z=0 (left) and z=5 (right). Red bars represent x-components, whereas blue bars represent y-components.

Fig. 7.
Fig. 7.

Normalized mode powers plotted as functions of mode number for cases in which ρ = 1, ρ0 = 0.01 and z=5: ϕ0=1.57 (left) and ϕ0= 1.67 (right). Red bars represent x-components, whereas blue bars represent y-components.

Fig. 8.
Fig. 8.

Normalized mode powers plotted as functions of mode number for cases in which ρ±=1, θ-=0 and z=2: θ+ =0 (left) and θ+=π/2 (right). Light- and dark-gray bars correspond to frequency spacings of 50 and 200 GHz, respectively.

Fig. 9.
Fig. 9.

Normalized mode powers plotted as functions of mode number for cases in which ρ=1, ρ0=0.01 and z=5: ϕ0=0.099 (left) and ϕ0=1.67 (right). Light- and dark-gray bars correspond to frequency spacings of 50 and 200 GHz, respectively.

Equations (28)

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i z X = β ( i τ ) X + γ ( X 2 + Y 2 ) X ,
i z Y = β ( i τ ) Y + γ ( X 2 + Y 2 ) Y ,
z X = i γ ( X 2 + Y 2 ) X ,
z Y = i γ ( X 2 + Y 2 ) Y ,
X ( τ , z ) = X ( τ , 0 ) exp ( i γ [ X ( τ , 0 ) 2 + Y ( τ , 0 ) 2 ] z ) ,
Y ( τ , z ) = Y ( τ , 0 ) exp ( i γ [ X ( τ , 0 ) 2 + Y ( τ , 0 ) 2 ] z ) .
X ( τ , 0 ) = ρ cos θ exp ( i ϕ ) + ρ + cos θ + exp ( i ϕ + ) ,
Y ( τ , 0 ) = ρ sin θ exp ( i ϕ ) + ρ + sin θ + exp ( i ϕ + ) ,
X ( τ , 0 ) = ρ cos θ exp ( i ϕ ) + ρ + cos θ + exp ( i ϕ ) ,
Y ( τ , 0 ) = ρ sin θ exp ( i ϕ ) + ρ + sin θ + exp ( i ϕ ) ,
X n ( ζ ) = ρ cos θ i ( n + 1 ) 2 J ( n + 1 ) 2 ( ζ ) + ρ + cos θ + i ( n 1 ) 2 J ( n 1 ) 2 ( ζ ) ,
Y n ( ζ ) = ρ sin θ i ( n + 1 ) 2 J ( n + 1 ) 2 ( ζ ) + ρ + sin θ + i ( n 1 ) 2 J ( n 1 ) 2 ( ζ ) ,
n X ( ζ ) 2 = ρ 2 cos 2 θ + ρ + 2 cos 2 θ + ,
n [ X n ( ζ ) 2 X n ( ζ ) 2 ] = ( ρ + 2 cos 2 θ + ρ 2 cos 2 θ ) J 0 2 ( ζ ) ,
X ( τ , 0 ) = ρ exp ( i ϕ ) + ρ 0 cos θ 0 exp ( i ϕ 0 ) ,
Y ( τ , 0 ) = ρ 0 sin θ 0 exp ( i ϕ 0 ) + ρ exp ( i ϕ ) ,
ρ e = ρ 0 [ 1 + sin ( 2 θ 0 ) cos ( 2 ϕ 0 ) ] 1 2 ,
ϕ e = tan 1 [ tan ϕ 0 ( 1 tan θ 0 ) ( 1 + tan θ 0 ) ] .
X n ( ζ ) = i n + 1 J n + 1 ( ζ ) ρ exp ( e ) + i n J n ( ζ ) ρ 0 cos θ 0 exp ( 0 ) ,
Y n ( ζ ) = i n 1 J n 1 ( ζ ) ρ exp ( e ) + i n J n ( ζ ) ρ 0 sin θ 0 exp ( 0 ) ,
X n ( ζ ) = i n + 1 J n + 1 ( ζ ) ρ + i n J n ( ζ ) ρ 0 cos θ 0 ,
Y n ( ζ ) = i n 1 J n 1 ( ζ ) ρ + i n J n ( ζ ) ρ 0 sin θ 0 ,
X n ( ζ ) = i n + 1 J n + 1 ( ζ ) ρ + i n J n ( ζ ) ρ̂ 0 exp ( 0 ) ,
Y n ( ζ ) = i n 1 J n 1 ( ζ ) ρ + i n J n ( ζ ) ρ̂ 0 exp ( 0 ) ,
X 0 ( ζ ) = i J 1 ( ζ ) ρ + J 0 ( ζ ) ρ̂ 0 exp ( 0 ) ,
X 0 ( z ) ( 1 + 2 z ) ρ̂ 0 exp ( 0 ) + 2 z ρ̂ 0 exp ( i ϕ 0 ) .
P 0 ( z ) ρ 0 2 [ 1 + 2 ( ρ 2 z ) 2 + 2 ( ρ 2 z ) sin ( 2 ϕ 0 ) + 2 ( ρ 2 z ) 2 cos ( 2 ϕ 0 ) ] .
X 2 ( z ) = i 2 ρ 2 zρ̂ 0 cos ϕ 0 .

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