Abstract

The modulation instability (MI) in optical fiber amplifiers and lasers with anomalous dispersion leads to cw radiation breakup. This can be both a detrimental effect limiting the performance of amplifiers and an underlying physical mechanism in the operation of MI-based devices. Here we revisit the analytical theory of MI in fiber optical amplifiers. The results of the exact theory are compared with the previously used adiabatic approximation model, and the range of applicability of the latter is determined.

© 2010 Optical Society of America

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References

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2010 (1)

2009 (1)

V. E. Zakharov and L. A. Ostrovsky, Physica D (Amsterdam) 238, 540 (2009).
[CrossRef]

2003 (1)

2002 (1)

1995 (1)

1992 (1)

G. P. Agrawal, IEEE Photonics Technol. Lett. 4, 562 (1992).
[CrossRef]

1990 (1)

1989 (1)

M. Nakazawa, K. Suzuki, and H. A. Haus, IEEE J. Quantum Electron. 25, 2036 (1989).
[CrossRef]

1986 (1)

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

1980 (1)

N. N. Rozanov and V. A. Smirnov, Sov. J. Quantum Electron. 10, 232 (1980).
[CrossRef]

1966 (1)

V. I. Bespalov and V. I. Talanov, JETP Lett. 3, 307 (1966).

Agrawal, G. P.

G. P. Agrawal, IEEE Photonics Technol. Lett. 4, 562 (1992).
[CrossRef]

Bespalov, V. I.

V. I. Bespalov and V. I. Talanov, JETP Lett. 3, 307 (1966).

Chernikov, S. V.

Chestnut, D. A.

de Matos, C. J. S.

Dianov, E. M.

Fedoruk, M. P.

Gong, Y.

Guo, X.

Hasegawa, A.

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

Haus, H. A.

M. Nakazawa, K. Suzuki, and H. A. Haus, IEEE J. Quantum Electron. 25, 2036 (1989).
[CrossRef]

Ince, E. L.

E. L. Ince, Ordinary Differential Equations (Dover, 1956).

Jewell, J. L.

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

Karlsson, M.

Lu, C.

Mamyshev, P. V.

Nakazawa, M.

M. Nakazawa, K. Suzuki, and H. A. Haus, IEEE J. Quantum Electron. 25, 2036 (1989).
[CrossRef]

Ostrovsky, L. A.

V. E. Zakharov and L. A. Ostrovsky, Physica D (Amsterdam) 238, 540 (2009).
[CrossRef]

Prokhorov, A. M.

Rozanov, N. N.

N. N. Rozanov and V. A. Smirnov, Sov. J. Quantum Electron. 10, 232 (1980).
[CrossRef]

Rubenchik, A. M.

Shum, P.

Smirnov, V. A.

N. N. Rozanov and V. A. Smirnov, Sov. J. Quantum Electron. 10, 232 (1980).
[CrossRef]

Suzuki, K.

M. Nakazawa, K. Suzuki, and H. A. Haus, IEEE J. Quantum Electron. 25, 2036 (1989).
[CrossRef]

Tai, K.

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

Talanov, V. I.

V. I. Bespalov and V. I. Talanov, JETP Lett. 3, 307 (1966).

Tang, D.

Taylor, J. R.

Tomita, A.

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

Turitsyn, S. K.

Zakharov, V. E.

V. E. Zakharov and L. A. Ostrovsky, Physica D (Amsterdam) 238, 540 (2009).
[CrossRef]

Appl. Phys. Lett. (1)

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Nakazawa, K. Suzuki, and H. A. Haus, IEEE J. Quantum Electron. 25, 2036 (1989).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

G. P. Agrawal, IEEE Photonics Technol. Lett. 4, 562 (1992).
[CrossRef]

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

JETP Lett. (1)

V. I. Bespalov and V. I. Talanov, JETP Lett. 3, 307 (1966).

Opt. Express (2)

Opt. Lett. (2)

Physica D (Amsterdam) (1)

V. E. Zakharov and L. A. Ostrovsky, Physica D (Amsterdam) 238, 540 (2009).
[CrossRef]

Sov. J. Quantum Electron. (1)

N. N. Rozanov and V. A. Smirnov, Sov. J. Quantum Electron. 10, 232 (1980).
[CrossRef]

Other (1)

E. L. Ince, Ordinary Differential Equations (Dover, 1956).

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Figures (4)

Fig. 1
Fig. 1

Counterplot of the coefficient A = [ a ( 0 ) η K i μ ( η ) + b ( 0 ) μ K i μ ( η ) ] before the growing solution in the plane ( η , ϕ ) with μ = 1 .

Fig. 2
Fig. 2

Gain Γ ( ν ) for L = 100 m , G = 30 dB . Here P 0 = | Ψ 0 | 2 : 50 (lower red curves), 100 (central green curves) and 200 mW (top blue curves). Solid curves, exact solutions; dashed curves, adiabatic approximation [3].

Fig. 3
Fig. 3

Integrated gain Γ (log scale) versus propagation distance for a ( z * ) = 1 and b ( z * ) = 0 (red curve), b ( z * ) = 1 (green curve), b ( z * ) = 2 (blue curve); black curve, I i μ , P 0 = 50 mW . Inset, normal scale.

Fig. 4
Fig. 4

Counterplot Γ in the plane ( p , G ) , η 2 / μ = 0.03 . The white zone corresponds to the oscillating solutions. The border between stable and unstable regimes is given by the condition G > μ 2 / η 2 .

Equations (5)

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i Ψ z β 2 2 Ψ t t + γ | Ψ | 2 Ψ = i g 0 2 Ψ + i g 0 T 2 2 2 Ψ t t .
d a d z = g 0 μ 2 b ( z ) s a ( z ) , d b d z = η 2 g 0 2 μ ( p 2 + exp [ g 0 z ] ) a ( z ) s b ( z ) .
a ( z ) = A I i μ ( η e g 0 z / 2 ) + B K i μ ( η e g 0 z / 2 ) , b ( z ) = η e g 0 z / 2 2 μ { C ( I i μ 1 + I i μ + 1 ) + D ( K i μ 1 + K i μ + 1 ) } .
I i μ ( η e g 0 z / 2 ) exp [ η 2 e g 0 z μ 2 + μ arcsin ( μ e g 0 z / 2 η ) ] 2 π ( η 2 e g 0 z μ 2 ) 4 + , K i μ ( η e g 0 z / 2 ) π × exp [ η 2 e g 0 z μ 2 μ arcsin ( μ e g 0 z / 2 η ) ] 4 ( η 2 e g 0 z μ 2 ) 4 + .
f = ( η 2 e g 0 L μ 2 ) 1 / 2 η 2 μ 2 + μ arcsin ( μ e g 0 z / 2 η ) μ arcsin ( μ η ) , μ η < 1 , f = ( η 2 e g 0 L μ 2 ) 1 / 2 + μ arcsin ( μ e g 0 L / 2 η ) , μ η > 1.

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