Abstract

We propose and analyze a first-order optical differentiator based on a fiber Bragg grating (FBG) in transmission. It is shown in the examples that a simple uniform-period FBG in a very strong coupling regime (maximum reflectivity very close to 100%) can perform close to ideal temporal differentiation of the complex envelope of an arbitrary-input optical signal.

© 2008 Optical Society of America

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References

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  1. N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, Opt. Commun. 230, 115 (2004).
    [CrossRef]
  2. H. Chen, M. Chen, C. Qiu, and S. Xie, IEEE Photonics Technol. Lett. 19, 2021 (2007).
    [CrossRef]
  3. J. A. Ney da Silva and M. L. R. de Campos, IEEE Trans. Commun. 55, 313 (2007).
    [CrossRef]
  4. G. R. Aiello and G. D. Rogerson, IEEE Microw. Mag. 4, 36 (2003).
    [CrossRef]
  5. H. J. A. da Silva and J. J. O'Reilly, Opt. Lett. 14, 526 (1989).
    [CrossRef] [PubMed]
  6. R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, Opt. Express 14, 10699 (2006).
    [CrossRef] [PubMed]
  7. N. K. Berger, B. Levit, B. Fischer, M. Kulishov, D. V. Plant, and J. Azaña, Opt. Express 15, 371 (2007).
    [CrossRef] [PubMed]
  8. L.-M. Rivas, K. Singh, A. Carballar, and J. Azaña, IEEE Photon. Technol. Lett. 19, 1209 (2007).
    [CrossRef]
  9. M. A. Preciado, V. Garcia-Muñoz, and M. A. Muriel, Opt. Express 15, 7196 (2007).
    [CrossRef] [PubMed]
  10. M. A. Preciado and M. A. Muriel, Opt. Express 15, 12102 (2007).
    [CrossRef] [PubMed]
  11. Y. Park, R. Slavik, and J. Azaña, Opt. Lett. 32, 710 (2007).
    [CrossRef] [PubMed]
  12. J. Skaar, J. Opt. Soc. Am. A 18, 557 (2001).
    [CrossRef]
  13. K. Hinton, J. Lightwave Technol. 16, 2336 (1998).
    [CrossRef]
  14. A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, 1962).
  15. A. D. Poularikas, The Handbook of Formulas and Tables for Signal Processing (IEEE Press, 1998).
    [CrossRef]
  16. N. Quoc Ngo, Opt. Lett. 32, 3020 (2007).
    [CrossRef] [PubMed]
  17. R. Feced, M. N. Zervas, and M. A. Muriel, IEEE J. Quantum Electron. 35, 1105 (1999).
    [CrossRef]

2007

2006

2004

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, Opt. Commun. 230, 115 (2004).
[CrossRef]

2003

G. R. Aiello and G. D. Rogerson, IEEE Microw. Mag. 4, 36 (2003).
[CrossRef]

2001

1999

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

1998

1989

Aiello, G. R.

G. R. Aiello and G. D. Rogerson, IEEE Microw. Mag. 4, 36 (2003).
[CrossRef]

Azaña, J.

Berger, N. K.

Carballar, A.

L.-M. Rivas, K. Singh, A. Carballar, and J. Azaña, IEEE Photon. Technol. Lett. 19, 1209 (2007).
[CrossRef]

Chen, H.

H. Chen, M. Chen, C. Qiu, and S. Xie, IEEE Photonics Technol. Lett. 19, 2021 (2007).
[CrossRef]

Chen, M.

H. Chen, M. Chen, C. Qiu, and S. Xie, IEEE Photonics Technol. Lett. 19, 2021 (2007).
[CrossRef]

da Silva, H. J. A.

de Campos, M. L. R.

J. A. Ney da Silva and M. L. R. de Campos, IEEE Trans. Commun. 55, 313 (2007).
[CrossRef]

Feced, R.

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

Fischer, B.

Garcia-Muñoz, V.

Hinton, K.

Kam, C. H.

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, Opt. Commun. 230, 115 (2004).
[CrossRef]

Kulishov, M.

Levit, B.

Morandotti, R.

Muriel, M. A.

Ney da Silva, J. A.

J. A. Ney da Silva and M. L. R. de Campos, IEEE Trans. Commun. 55, 313 (2007).
[CrossRef]

Ngo, N. Q.

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, Opt. Commun. 230, 115 (2004).
[CrossRef]

O'Reilly, J. J.

Papoulis, A.

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

Park, Y.

Plant, D. V.

Poularikas, A. D.

A. D. Poularikas, The Handbook of Formulas and Tables for Signal Processing (IEEE Press, 1998).
[CrossRef]

Preciado, M. A.

Qiu, C.

H. Chen, M. Chen, C. Qiu, and S. Xie, IEEE Photonics Technol. Lett. 19, 2021 (2007).
[CrossRef]

Quoc Ngo, N.

Rivas, L.-M.

L.-M. Rivas, K. Singh, A. Carballar, and J. Azaña, IEEE Photon. Technol. Lett. 19, 1209 (2007).
[CrossRef]

Rogerson, G. D.

G. R. Aiello and G. D. Rogerson, IEEE Microw. Mag. 4, 36 (2003).
[CrossRef]

Singh, K.

L.-M. Rivas, K. Singh, A. Carballar, and J. Azaña, IEEE Photon. Technol. Lett. 19, 1209 (2007).
[CrossRef]

Skaar, J.

Slavik, R.

Slavík, R.

Tjin, S. C.

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, Opt. Commun. 230, 115 (2004).
[CrossRef]

Xie, S.

H. Chen, M. Chen, C. Qiu, and S. Xie, IEEE Photonics Technol. Lett. 19, 2021 (2007).
[CrossRef]

Yu, S. F.

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, Opt. Commun. 230, 115 (2004).
[CrossRef]

Zervas, M. N.

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

IEEE J. Quantum Electron.

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

IEEE Microw. Mag.

G. R. Aiello and G. D. Rogerson, IEEE Microw. Mag. 4, 36 (2003).
[CrossRef]

IEEE Photon. Technol. Lett.

L.-M. Rivas, K. Singh, A. Carballar, and J. Azaña, IEEE Photon. Technol. Lett. 19, 1209 (2007).
[CrossRef]

IEEE Photonics Technol. Lett.

H. Chen, M. Chen, C. Qiu, and S. Xie, IEEE Photonics Technol. Lett. 19, 2021 (2007).
[CrossRef]

IEEE Trans. Commun.

J. A. Ney da Silva and M. L. R. de Campos, IEEE Trans. Commun. 55, 313 (2007).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. A

Opt. Commun.

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, Opt. Commun. 230, 115 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

Other

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

A. D. Poularikas, The Handbook of Formulas and Tables for Signal Processing (IEEE Press, 1998).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

FBG differentiator SR amplitude in (a) reflection and (b) transmission, corresponding to ideal bandwidth-limited (solid curve), Gaussian approximation (dotted curve), and Lorentzian approximation (dashed curve) functions.

Fig. 2
Fig. 2

Grating profile obtained by inverse scattering in different scales.

Fig. 3
Fig. 3

Spectral response in transmission of the designed FBG (solid curve) and the ideal differentiator (dotted curve).

Fig. 4
Fig. 4

Temporal waveforms of the input pulse (dashed curve) and output pulse corresponding to FBG (solid curve) and the ideal differentiator (dotted curve), which are hardly distinguishable in both plots. Input pulses of plots (a) and (b) respectively are a 7 ps Gaussian pulse and the first-order derivative of a 7 ps Gaussian pulse.

Fig. 5
Fig. 5

Grating length (squares, dotted curve) and cross-correlation coefficient, Corr (circles, dashed curve), which represents the operation accuracy. Thirteen FBG differentiators are designed assuming the same operation bandwidth to obtain transmission dip values from 20 to 80 dB and are applied to a 7 ps Gaussian pulse.

Equations (3)

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arg H T ( ω ) = HT { ln H T ( ω ) } , ln H T ( ω ) = C 0 + HT 1 { arg H T ( ω ) } ,
ln H T ( ω ε ) = C 0 + 1 π arg ( H T ( Ω ) ) Ω ω ε d Ω = C 0 + 1 π arg ( H T ( Ω + ω ε ) ) Ω d Ω C 0 + 1 π ( I ± W W ( π 2 ) sign ( Ω + ω ε ) Ω d Ω ) = C 0 + I π ln ( ω ε W ) = ln ( C 1 ω ε ) ,
Corr = 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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