Abstract

Modulation instability (MI) in a fiber Bragg grating (FBG) is investigated and reviewed analytically. The dispersion relation equation of MI obtained from the coupled-mode equation is solved exactly. The closed-form expressions of the gain of MI and the threshold condition in the normal dispersion regime are derived. The results from the closed-form expressions are well consistent with those from numerical simulations and previous literature. Based on the analytical investigation, the characteristics of MI in an FBG are analyzed.

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2005

2000

1998

1997

1996

B. J. Eggleton, C. M. de Sterke, R. E. Slusher, and J. E. Sipe, Electron. Lett. 32, 2341 (1996).
[CrossRef]

1992

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

1989

1987

Aceves, A. B.

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, Opt. Commun. 149, 267 (1998).
[CrossRef]

Agrawal, G. P.

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

G. P. Agrawal, Applications of Nonlinear Fiber Optics (Academic, 2001).

Amans, D.

Brainis, E.

Broderick, N. G. R.

Davis, G. M.

de Sterke, C. M.

C. M.de Sterke, J. Opt. Soc. Am. B 15, 2660 (1998).
[CrossRef]

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, Opt. Commun. 149, 267 (1998).
[CrossRef]

B. J. Eggleton, C. M. de Sterke, R. E. Slusher, and J. E. Sipe, Electron. Lett. 32, 2341 (1996).
[CrossRef]

Devipriya, S.

K. Porsezian, K. Senthilnathan, and S. Devipriya, IEEE J. Quantum Electron. 41, 789 (2005).
[CrossRef]

Duck, G.

Eggleton, B. J.

J. T. Mok, I. C. M. Littler, E. Tsoy, and B. J. Eggleton, Opt. Lett. 30, 2457 (2005).
[CrossRef] [PubMed]

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, Opt. Commun. 149, 267 (1998).
[CrossRef]

B. J. Eggleton, C. M. de Sterke, R. E. Slusher, and J. E. Sipe, Electron. Lett. 32, 2341 (1996).
[CrossRef]

Emplit, Ph.

Haelterman, M.

Harvey, J. D.

Ibsen, M.

Itoh, H.

Laming, R. I.

Leonhardt, R.

Littler, I. C. M.

Mok, J. T.

Murdoch, S. G.

Ohn, M. M.

Ouellette, F.

Porsezian, K.

K. Porsezian, K. Senthilnathan, and S. Devipriya, IEEE J. Quantum Electron. 41, 789 (2005).
[CrossRef]

Richardson, D. J.

Senthilnathan, K.

K. Porsezian, K. Senthilnathan, and S. Devipriya, IEEE J. Quantum Electron. 41, 789 (2005).
[CrossRef]

Sipe, J. E.

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, Opt. Commun. 149, 267 (1998).
[CrossRef]

B. J. Eggleton, C. M. de Sterke, R. E. Slusher, and J. E. Sipe, Electron. Lett. 32, 2341 (1996).
[CrossRef]

Slusher, R. E.

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, Opt. Commun. 149, 267 (1998).
[CrossRef]

B. J. Eggleton, C. M. de Sterke, R. E. Slusher, and J. E. Sipe, Electron. Lett. 32, 2341 (1996).
[CrossRef]

Strasser, T. A.

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, Opt. Commun. 149, 267 (1998).
[CrossRef]

Sudo, S.

Taverner, D.

Thomson, M. D.

Tsoy, E.

Zwillinger, D.

D. Zwillinger, Standard Mathematical Tables and Formulae, 30th ed. (CRC Press, 1996).

Electron. Lett.

B. J. Eggleton, C. M. de Sterke, R. E. Slusher, and J. E. Sipe, Electron. Lett. 32, 2341 (1996).
[CrossRef]

IEEE J. Quantum Electron.

K. Porsezian, K. Senthilnathan, and S. Devipriya, IEEE J. Quantum Electron. 41, 789 (2005).
[CrossRef]

IEEE Photon. Technol. Lett.

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

J. Opt. Soc. Am. B

Opt. Commun.

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, Opt. Commun. 149, 267 (1998).
[CrossRef]

Opt. Lett.

Other

G. P. Agrawal, Applications of Nonlinear Fiber Optics (Academic, 2001).

D. Zwillinger, Standard Mathematical Tables and Formulae, 30th ed. (CRC Press, 1996).

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Figures (2)

Fig. 1
Fig. 1

Gain spectrum for f = 2 , P 0 = 1 × 10 5 W (solid curve), P 0 = 5 × 10 5 W (dotted curve), and P 0 = 1 × 10 6 W (dashed curve).

Fig. 2
Fig. 2

Gain spectrum for f = 2 , P 0 = 1 × 10 5 W (solid curve), P 0 = 1 × 10 6 W (dotted curve), and P 0 = 1 × 10 7 W (dashed curve).

Equations (26)

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

Ω 4 A Ω 2 + B Ω + C = 0 ,
A = 2 K 2 + 2 k 2 + k 2 f 2 + k 2 f 2 + 4 k f G ,
B = 2 k 2 f 2 K 2 k 2 f 2 K ,
C = K 4 + 2 k 2 K 2 k 2 f 2 K 2 k 2 f 2 K 2 + 12 k f G K 2 ,
G = γ P 0 1 + f 2 ,
g ( K ) = 2 Im ( Ω m ) ,
B 2 = ( A + D ) ( D 2 4 C ) .
Ω 1 , 2 = A + D ± A D 2 D 2 4 C 2 ,
Ω 3 , 4 = A + D ± A D ± 2 D 2 4 C 2 ,
g ( K ) = D A + 2 D 2 4 C .
g ( K ) = A D + 1 2 D A + ( A D ) 2 4 ( D 2 4 C ) .
g ( K ) = 2 A + 2 A 2 4 C , ( A 2 4 C 0 ) ,
g ( K ) = A + 2 C , ( A 2 4 C 0 ) .
A + D 0 ,
D 2 4 C 0 ,
A D + 2 D 2 4 C 0 ,
A D 2 D 2 4 C 0 .
A 0 .
f > 0 .
A + D 4 K 2 + 4 k ( 4 k f G + k ) ,
D 2 4 C k 4 ( f 4 1 ) 2 f 4 ,
A D 2 k ( k f 4 + k 4 f 3 G ) f 2 .
P th = k ( f 3 + f ) 2 γ , ( f < 1 ) ,
P th = k ( f 3 + f 1 ) 2 γ , ( f > 1 ) .
A 2 4 C = 8 k ( 2 k 4 G ) K 2 + ( 4 k G + k 2 ) 2 .
P th = k γ .

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