Abstract

The statistics of the reflection spectrum of a short-correlated disordered fiber Bragg grating are studied. The averaged spectrum appears to be flat inside the bandgap and has significantly suppressed sidelobes compared to the uniform grating of the same bandwidth. This is due to the Anderson localization of the modes of a disordered grating. This observation prompts a new algorithm for designing passband reflection gratings. Using the stochastic invariant imbedding approach it is possible to obtain the probability distribution function for the random reflection coefficient inside the bandgap and obtain both the variance of the averaged reflectivity as well as the distribution of the time delay of the grating.

© 2008 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2007 (1)

2005 (1)

2003 (1)

E. G. Turitsyna, J. D. Ania-Castanon, S. K. Turitsyn, L. Kennedy, and K. Sugden, Electron. Lett. 39, 351 (2003).
[CrossRef]

2002 (1)

2001 (1)

J. Skaar, L. Wang, and T. Erdogan, IEEE J. Quantum Electron. 37, 165 (2001).
[CrossRef]

2000 (2)

1998 (1)

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Lamming, Electron. Lett. 34, 800 (1998).
[CrossRef]

1997 (1)

T. Erdogan, J. Lightwave Technol. 15, 1277 (1997).
[CrossRef]

1985 (1)

Ania-Castanon, J. D.

E. G. Turitsyna, J. D. Ania-Castanon, S. K. Turitsyn, L. Kennedy, and K. Sugden, Electron. Lett. 39, 351 (2003).
[CrossRef]

Belai, O. V.

Cole, M. J.

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Lamming, Electron. Lett. 34, 800 (1998).
[CrossRef]

Durkin, M. K.

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Lamming, Electron. Lett. 34, 800 (1998).
[CrossRef]

Erdogan, T.

J. Skaar, L. Wang, and T. Erdogan, IEEE J. Quantum Electron. 37, 165 (2001).
[CrossRef]

T. Erdogan, J. Lightwave Technol. 15, 1277 (1997).
[CrossRef]

Feced, R.

Frumin, L. L.

Gredescul, S. A.

I. M. Lifshitz, S. A. Gredescul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, 1988).

Horowitz, M.

Ibsen, M.

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Lamming, Electron. Lett. 34, 800 (1998).
[CrossRef]

Kalli, K.

A. Othonos and K. Kalli, Fiber Bragg Gratings (Artech House, 1999).

Kennedy, L.

E. G. Turitsyna, J. D. Ania-Castanon, S. K. Turitsyn, L. Kennedy, and K. Sugden, Electron. Lett. 39, 351 (2003).
[CrossRef]

Kogelnik, H.

H. Kogelnik, in Guided Wave Optolelectronics, T.Tamir, ed. (Springer-Verlag, 1990), pp. 7-88.

Konotop, V. V.

V. V. Konotop and L. Vazquez, Nonlinear Random Waves (World Scientific, 1994).
[CrossRef]

Lamming, R. I.

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Lamming, Electron. Lett. 34, 800 (1998).
[CrossRef]

Lifshitz, I. M.

I. M. Lifshitz, S. A. Gredescul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, 1988).

Othonos, A.

A. Othonos and K. Kalli, Fiber Bragg Gratings (Artech House, 1999).

Pastur, L. A.

I. M. Lifshitz, S. A. Gredescul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, 1988).

Podivilov, E. V.

Poladian, L.

Rosenthal, A.

Shapiro, D. A.

Shin, S. Y.

Skaar, J.

J. Skaar and R. Feced, J. Opt. Soc. Am. A 19, 2229 (2002).
[CrossRef]

J. Skaar, L. Wang, and T. Erdogan, IEEE J. Quantum Electron. 37, 165 (2001).
[CrossRef]

Song, G. H.

Sugden, K.

E. G. Turitsyna, J. D. Ania-Castanon, S. K. Turitsyn, L. Kennedy, and K. Sugden, Electron. Lett. 39, 351 (2003).
[CrossRef]

Turitsyn, S. K.

E. G. Turitsyna, J. D. Ania-Castanon, S. K. Turitsyn, L. Kennedy, and K. Sugden, Electron. Lett. 39, 351 (2003).
[CrossRef]

Turitsyna, E. G.

E. G. Turitsyna, J. D. Ania-Castanon, S. K. Turitsyn, L. Kennedy, and K. Sugden, Electron. Lett. 39, 351 (2003).
[CrossRef]

Vazquez, L.

V. V. Konotop and L. Vazquez, Nonlinear Random Waves (World Scientific, 1994).
[CrossRef]

Wang, L.

J. Skaar, L. Wang, and T. Erdogan, IEEE J. Quantum Electron. 37, 165 (2001).
[CrossRef]

Zervas, M. N.

Electron. Lett. (2)

E. G. Turitsyna, J. D. Ania-Castanon, S. K. Turitsyn, L. Kennedy, and K. Sugden, Electron. Lett. 39, 351 (2003).
[CrossRef]

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Lamming, Electron. Lett. 34, 800 (1998).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. Skaar, L. Wang, and T. Erdogan, IEEE J. Quantum Electron. 37, 165 (2001).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. A (3)

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

Opt. Lett. (1)

Other (4)

H. Kogelnik, in Guided Wave Optolelectronics, T.Tamir, ed. (Springer-Verlag, 1990), pp. 7-88.

V. V. Konotop and L. Vazquez, Nonlinear Random Waves (World Scientific, 1994).
[CrossRef]

I. M. Lifshitz, S. A. Gredescul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, 1988).

A. Othonos and K. Kalli, Fiber Bragg Gratings (Artech House, 1999).

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Figures (1)

Fig. 1
Fig. 1

Results of Monte Carlo simulation of quasi-random FBG (solid curve) compared to the uniform grating of the same bandwidth (red dashed curve) and rms strength (green dotted curve).

Equations (9)

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d ψ 1 d z = i δ ψ 1 + q * ( z ) ψ 2 ,
d ψ 2 d z = i δ ψ 2 + q ( z ) ψ 1 ,
d r d z = 2 i δ r q r 2 + q * , r ( 0 ) = 0 .
P z = 2 δ P θ + 2 D coth 2 χ 2 P θ 2 + 2 D χ [ sinh χ χ ( P sinh χ ) ] .
Y z = 2 D sinh χ χ [ sinh χ Y χ ] , Y ( χ ; 0 ) = δ ( χ ) sinh χ .
Y ( χ ; z ) = e D z 2 8 π D 3 z 3 χ χ exp ( χ 2 8 D z ) cosh χ cosh χ d χ .
R ¯ = 1 e D L 2 4 π ( D L ) 3 0 χ 2 exp [ χ 2 8 D L ] 1 + cosh χ d χ 1 π 5 2 32 ( D L ) 3 e D L 2 , D L 1 .
η = ( R R ¯ ) 2 R ¯ π 5 4 ( 512 ( D L ) 3 ) 1 4 exp [ D L 4 ] .
P ( θ δ ) = 1 D θ δ 2 exp [ 1 D θ δ ] , θ δ > 0 .

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