Abstract

We present what we believe to be a novel method for the synthesis of complex 1D (fiber and waveguide) Bragg gratings, which is based on an impedance reconstruction layer aggregation technique. The main advantage brought by the method is the possibility of synthesizing structures containing defects or discontinuities of the size of the local period, a feature that is not possible with prior reported methods. In addition, this enhanced spatial resolution allows the synthesis of very strong fiber Bragg grating devices providing convergent solutions. The method directly renders the refractive index profile n(z) as it does not rely on the coupled-mode theory.

© 2007 Optical Society of America

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References

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    [CrossRef]

2004 (1)

2003 (2)

2001 (1)

J. Skaar, L. Wang, and T. Erdogan, J. Lightwave Technol. 37, 165 (2001).

2000 (1)

1999 (1)

R. Feced, M. N. Zervas, and M. A. Muriel, IEEE J. Quantum Electron. 35, 1105 (1999).
[CrossRef]

1997 (1)

C. R. Giles, J. Lightwave Technol. 15, 1391 (1997).
[CrossRef]

1985 (1)

A. Bruckstein, B. Levy, and T. Kailath, SIAM J. Appl. Math. 45, 312 (1985).
[CrossRef]

Bruckstein, A.

A. Bruckstein, B. Levy, and T. Kailath, SIAM J. Appl. Math. 45, 312 (1985).
[CrossRef]

Capmany, J.

Erdogan, T.

J. Skaar, L. Wang, and T. Erdogan, J. Lightwave Technol. 37, 165 (2001).

Feced, R.

R. Feced, M. N. Zervas, and M. A. Muriel, IEEE J. Quantum Electron. 35, 1105 (1999).
[CrossRef]

Giles, C. R.

C. R. Giles, J. Lightwave Technol. 15, 1391 (1997).
[CrossRef]

Horowitz, M.

A. Rosenthal and M. Horowitz, J. Opt. Soc. Am. A 21, 552 (2004).
[CrossRef]

A. Rosenthal and M. Horowitz, IEEE J. Quantum Electron. 39, 1018 (2003).
[CrossRef]

Kailath, T.

A. Bruckstein, B. Levy, and T. Kailath, SIAM J. Appl. Math. 45, 312 (1985).
[CrossRef]

Levy, B.

A. Bruckstein, B. Levy, and T. Kailath, SIAM J. Appl. Math. 45, 312 (1985).
[CrossRef]

Muriel, M. A.

J. Capmany, M. A. Muriel, S. Sales, J. J. Rubio, and D. Pastor, J. Lightwave Technol. 21, 3125 (2003).
[CrossRef]

R. Feced, M. N. Zervas, and M. A. Muriel, IEEE J. Quantum Electron. 35, 1105 (1999).
[CrossRef]

Pastor, D.

Poladian, L.

Rosenthal, A.

A. Rosenthal and M. Horowitz, J. Opt. Soc. Am. A 21, 552 (2004).
[CrossRef]

A. Rosenthal and M. Horowitz, IEEE J. Quantum Electron. 39, 1018 (2003).
[CrossRef]

Rubio, J. J.

Sales, S.

Skaar, J.

J. Skaar, L. Wang, and T. Erdogan, J. Lightwave Technol. 37, 165 (2001).

Wang, L.

J. Skaar, L. Wang, and T. Erdogan, J. Lightwave Technol. 37, 165 (2001).

Zervas, M. N.

R. Feced, M. N. Zervas, and M. A. Muriel, IEEE J. Quantum Electron. 35, 1105 (1999).
[CrossRef]

IEEE J. Quantum Electron. (2)

R. Feced, M. N. Zervas, and M. A. Muriel, IEEE J. Quantum Electron. 35, 1105 (1999).
[CrossRef]

A. Rosenthal and M. Horowitz, IEEE J. Quantum Electron. 39, 1018 (2003).
[CrossRef]

J. Lightwave Technol. (3)

J. Capmany, M. A. Muriel, S. Sales, J. J. Rubio, and D. Pastor, J. Lightwave Technol. 21, 3125 (2003).
[CrossRef]

J. Skaar, L. Wang, and T. Erdogan, J. Lightwave Technol. 37, 165 (2001).

C. R. Giles, J. Lightwave Technol. 15, 1391 (1997).
[CrossRef]

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

Opt. Lett. (1)

SIAM J. Appl. Math. (1)

A. Bruckstein, B. Levy, and T. Kailath, SIAM J. Appl. Math. 45, 312 (1985).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Layout of the decomposition of the FBGs in slabs and the contributions to the total impulse response.

Fig. 2
Fig. 2

Layout for the calculation of the value of the refractive index in the third slab.

Fig. 3
Fig. 3

(a) Target transfer function (obscured black trace) and synthesized (gray or blue trace) of a superimposed grating formed by two 1 cm Cauchy-apodized FBGs. (b) Synthesized refractive index profiles of one of the two gratings.

Fig. 4
Fig. 4

(a) Target transfer function (inner gray or blue trace) of the FBGs given by Eq. (12) and transfer function (outer gray or red trace) of the synthesized FBGs. (b) Synthesized refractive index profile.

Equations (12)

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n e f f ( z ) = n e f f + δ n e f f D C ( z ) + δ n e f f A C ( z ) cos ( 2 π Λ 0 z + φ ( z ) ) ,
h ( t ) = k = 0 h R ( k ) δ ( t 2 k Δ t ) .
Δ t = n e f f Δ z c = n i Δ z i c .
n 1 = n 0 [ 1 h R ( 0 ) 1 + h R ( 0 ) ] .
h R ( 1 ) = t 01 r 12 t 10 ,
r 12 = h R ( 1 ) t 01 t 10 = ( n 0 + n 1 ) 2 h R ( 1 ) 4 n 0 n 1 ,
n 2 = n 1 [ 1 r 12 1 + r 12 ] .
h R n r ( 2 ) = t 01 t 12 r 23 t 21 t 10 = r 23 i = 0 1 ( 4 n i n i + 1 ( n i + n i + 1 ) 2 ) ,
n 3 = n 2 [ 1 r 23 1 + r 23 ] .
r 23 = h R n r ( 2 ) i = 0 1 4 n i n i + 1 ( n i + n i + 1 ) 2 = h R ( 2 ) h R r ( 2 ) i = 0 1 4 n i n i + 1 ( n i + n i + 1 ) 2 ,
δ n e f f A C ( z ) = δ n e f f A C M A X [ 1 ( 2 z L ) 2 1 ( 2 B z L ) 2 ] ,
H ( ω ) = 0.99999 exp [ ( ω 2 π × 193.5 × 10 12 2 π × 25 × 10 9 ) 20 ] .

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