Abstract

We demonstrate a simple technique for the implementation of an all-optical integrator based on a uniform-period fiber Bragg grating (FBG) in reflection that is designed to present a decreasing exponential impulse response. The proposed FBG integrator is readily feasible and can perform close to ideal integration of few-picosecond and subpicosecond pulses.

© 2008 Optical Society of America

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References

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  1. N. Q. Ngo and L. N. Binh, Opt. Commun. 119, 390 (1995).
    [CrossRef]
  2. N. Q. Ngo and L. N. Binh, J. Lightwave Technol. 24, 563 (2006).
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  3. N. Q. Ngo, Appl. Opt. 45, 6785 (2006).
    [CrossRef] [PubMed]
  4. N. Q. Ngo and L. N. Binh, Appl. Opt. 46, 3546 (2007).
    [CrossRef] [PubMed]
  5. G. S. Pandian and F. E. Seraji, IEE Proc.-J: Optoelectron. 138, 235 (1991).
    [CrossRef]
  6. N. Q. Ngo, Opt. Lett. 32, 3020 (2007).
    [CrossRef]
  7. J. Azaña, Opt. Lett. 33, 4 (2008).
    [CrossRef]
  8. A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, 1962).
  9. R. Feced, M. N. Zervas, and M. A. Muriel, IEEE J. Quantum Electron. 35, 1105 (1999).
    [CrossRef]
  10. J. Capmany, M. A. Muriel, and S. Sales, Opt. Lett. 32, 2312 (2007).
    [CrossRef] [PubMed]
  11. S. Longhi, M. Marano, P. Laporta, O. Svelto, M. Belmonte, B. Agogliati, L. Arcangeli, V. Pruneri, M. N. Zervas, and M. Ibsen, Opt. Lett. 25, 1481 (2000).
    [CrossRef]
  12. J. T. Mok, M. Ibsen, C. Martijn De Sterke, and B. J. Eggleton, Electron. Lett. 43, 1418 (2007).
    [CrossRef]

2008 (1)

2007 (4)

2006 (2)

2000 (1)

1999 (1)

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

1995 (1)

N. Q. Ngo and L. N. Binh, Opt. Commun. 119, 390 (1995).
[CrossRef]

1991 (1)

G. S. Pandian and F. E. Seraji, IEE Proc.-J: Optoelectron. 138, 235 (1991).
[CrossRef]

Agogliati, B.

Arcangeli, L.

Azaña, J.

Belmonte, M.

Binh, L. N.

Capmany, J.

Eggleton, B. J.

J. T. Mok, M. Ibsen, C. Martijn De Sterke, and B. J. Eggleton, Electron. Lett. 43, 1418 (2007).
[CrossRef]

Feced, R.

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

Ibsen, M.

Laporta, P.

Longhi, S.

Marano, M.

Martijn De Sterke, C.

J. T. Mok, M. Ibsen, C. Martijn De Sterke, and B. J. Eggleton, Electron. Lett. 43, 1418 (2007).
[CrossRef]

Mok, J. T.

J. T. Mok, M. Ibsen, C. Martijn De Sterke, and B. J. Eggleton, Electron. Lett. 43, 1418 (2007).
[CrossRef]

Muriel, M. A.

J. Capmany, M. A. Muriel, and S. Sales, Opt. Lett. 32, 2312 (2007).
[CrossRef] [PubMed]

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

Ngo, N. Q.

Pandian, G. S.

G. S. Pandian and F. E. Seraji, IEE Proc.-J: Optoelectron. 138, 235 (1991).
[CrossRef]

Papoulis, A.

A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, 1962).

Pruneri, V.

Sales, S.

Seraji, F. E.

G. S. Pandian and F. E. Seraji, IEE Proc.-J: Optoelectron. 138, 235 (1991).
[CrossRef]

Svelto, O.

Zervas, M. N.

Appl. Opt. (2)

Electron. Lett. (1)

J. T. Mok, M. Ibsen, C. Martijn De Sterke, and B. J. Eggleton, Electron. Lett. 43, 1418 (2007).
[CrossRef]

IEE Proc.-J: Optoelectron. (1)

G. S. Pandian and F. E. Seraji, IEE Proc.-J: Optoelectron. 138, 235 (1991).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

J. Lightwave Technol. (1)

Opt. Commun. (1)

N. Q. Ngo and L. N. Binh, Opt. Commun. 119, 390 (1995).
[CrossRef]

Opt. Lett. (4)

Other (1)

A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, 1962).

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Figures (4)

Fig. 1
Fig. 1

Coupling coefficient function of the FBG integrator, obtained by an inverse scattering algorithm.

Fig. 2
Fig. 2

Magnitude and phase of the spectral response corresponding to the designed FBG (solid curve), and to an ideal integrator (dotted line).

Fig. 3
Fig. 3

Numerical simulations results, where input pulses of plots (a)–(c), respectively, are the first-time derivative of a 1 ps Gaussian pulse, a 1 ps Gaussian pulse, and the first-time derivative of a 100 ps Gaussian pulse (too long to be correctly processed). Plots show the temporal waveforms of the input pulse (dashed curves), and output pulse corresponding to FBG (solid curves) and ideal (dotted curves) integrators, which are hardly distinguishable in plots (a) and (b).

Fig. 4
Fig. 4

Measures of energy efficiency (squares, dotted curve) and normalized cross correlation coefficient (circles, dashed curve) that estimate the similarity between the output pulse and the ideal integrated pulse and represent the integration accuracy. Eight FBG integrators applied to the first derivative of a 10 s Gaussian pulse are represented, with lengths of 24, 12, 6, 3, 1.5, 0.75, 0.375, and 0.1875 cm and a maximum reflectivity of 80%.

Equations (5)

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H ideal ( ω ) = F out ( ω ) F in ( ω ) = 1 ( j ω ) ,
h ideal ( t ) = u ( t ) ,
H aprx ( ω ) = A ( j ω + τ 1 ) ,
h aprx ( t ) = A exp ( t τ ) u ( t ) ,
C = max ( f out , FBG ( t ) f out , ideal * ( t ) d t ( f out , FBG ( t ) 2 d t f out , ideal ( t ) 2 d t ) 1 2 ) ,

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