Abstract

We present the synthesis of multi-channel fiber Bragg grating (MCFBG) filters for dense wavelength-division-multiplexing (DWDM) application by using a simple optimization approach based on a Lagrange multiplier optimization (LMO) method. We demonstrate for the first time that the LMO method can be used to constrain various parameters of the designed MCFBG filters for practical application demands and fabrication requirements. The designed filters have a number of merits, i.e., flat-top and low dispersion spectral response as well as single stage. Above all, the maximum amplitude of the index modulation profiles of the designed MCFBGs can be substantially reduced under the applied constrained condition. The simulation results demonstrate that the LMO algorithm can provide a potential alternative for complex fiber grating filter design problems.

© 2006 Optical Society of America

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References

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  1. T. Erdogan, "Fiber grating spectra," J. of Lightwave Technol. 15, 1277-1294 (1997).
    [CrossRef]
  2. M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, "Sincsampled fiber Bragg gratings for identical multiple wavelength operation," IEEE Photon. Technol. Lett. 10, 842-844 (1998).
    [CrossRef]
  3. X.-F. Chen, Y. Luo, C.-C. Fan, and S.-Z. Xie, "Analytical expression of sampled Bragg gratings with chirp in the sampling period and its application in dispersion management design in a WDM system," IEEE Photon. Technol. Lett. 12, 1013-1015 (2000).
    [CrossRef]
  4. W. H. Loh, F. Q. Zhou, and J. J. Pan, "Sampled fiber grating based dispersions lope compensation," IEEE Photon. Technol. Lett. 11, 1280-1282 (1999).
    [CrossRef]
  5. H. Lee and G. P. Agrawal, "Purely phase-sampled fiber Bragg gratings for broad-band dispersion and dispersion slope compensation," IEEE Photon. Technol. Lett. 15, 1091-1093 (2003).
    [CrossRef]
  6. Q. Wu, C. Yu, K. Wang, X. Wang, Z. Yu, H. P. Chan, and P. L. Chu, "New sampling-based design of simultaneous compensation of both dispersion and dispersion slope for multichannel fiber Bragg gratings," IEEE Photon. Technol. Lett. 17, 381-383 (2005).
    [CrossRef]
  7. A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, "Optimization of refractive index sampling for multichannel fiber Bragg gratings," IEEE J. Quantum Electron. 39, 91-98 (2003).
    [CrossRef]
  8. K. Y. Kolossovski, R. A. Sammut, A. V. Buryak, and D. Y. Stepanov, "Three-step design optimization for multi-channel fiber Bragg gratings," Opt. Express 11, 1029-1038, (2003).
    [CrossRef] [PubMed]
  9. S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, and R. T. Zheng, "Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm," Opt. Commun. 260,716-722 (2006).
    [CrossRef]
  10. S. Baskar, R. T. Zheng, A. Alphones, N. Q. Ngo, and P. N. Suganthan, "Particle swarm optimization for the design of low-dispersion Fiber Bragg Gratings," IEEE Photon. Technol. Lett. 17, 615-617 (2005).
    [CrossRef]
  11. R. Feced, M. N. Zervas, and M. A. Muriel, "An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings," IEEE J. Quantum Electron. 29,1824-1834 (1993).
  12. J. Skaar, L. Wang, and T. Erdogen, "On the synthesis of fiber Bragg grating by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).
    [CrossRef]
  13. H. Li and Y. Sheng, "Direct design of multichannel fiber Bragg grating with discrete layer-peeling algorithm," IEEE Photon. Technol. Lett. 15, 1252-1254 (2003).
    [CrossRef]
  14. Q. Wu, P. L. Chu, and H. P. Chan, "General design approach to Multichannel Fiber Bragg Grating," J. of Lightwave Technol. 24, 1571-1580 (2006).
    [CrossRef]
  15. N. Wang and H. Rabitz, "Optimal control of pulse amplification without inversion," Phys. Rev. A 53, 1879-1885 (1996).
    [CrossRef] [PubMed]
  16. N. Wang and H. Rabitz, "Optimal control of population transfer in an optical dense medium," J. Chem. Phys. 104, 1173-1178 (1996).
    [CrossRef]
  17. R. Buffa, "Optimal control of population transfer through the continuum," Opt. Commun. 153, 240-244 (1998).
    [CrossRef]
  18. F. I. Lewis, Optimal Control, (Wiley, New York, 1986).
  19. S. A. Rice and M. Zhao, Optimal Control of Molecular Dynamics, (Wiley, New York, (2000).

2006 (2)

S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, and R. T. Zheng, "Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm," Opt. Commun. 260,716-722 (2006).
[CrossRef]

Q. Wu, P. L. Chu, and H. P. Chan, "General design approach to Multichannel Fiber Bragg Grating," J. of Lightwave Technol. 24, 1571-1580 (2006).
[CrossRef]

2005 (2)

S. Baskar, R. T. Zheng, A. Alphones, N. Q. Ngo, and P. N. Suganthan, "Particle swarm optimization for the design of low-dispersion Fiber Bragg Gratings," IEEE Photon. Technol. Lett. 17, 615-617 (2005).
[CrossRef]

Q. Wu, C. Yu, K. Wang, X. Wang, Z. Yu, H. P. Chan, and P. L. Chu, "New sampling-based design of simultaneous compensation of both dispersion and dispersion slope for multichannel fiber Bragg gratings," IEEE Photon. Technol. Lett. 17, 381-383 (2005).
[CrossRef]

2003 (4)

A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, "Optimization of refractive index sampling for multichannel fiber Bragg gratings," IEEE J. Quantum Electron. 39, 91-98 (2003).
[CrossRef]

K. Y. Kolossovski, R. A. Sammut, A. V. Buryak, and D. Y. Stepanov, "Three-step design optimization for multi-channel fiber Bragg gratings," Opt. Express 11, 1029-1038, (2003).
[CrossRef] [PubMed]

H. Lee and G. P. Agrawal, "Purely phase-sampled fiber Bragg gratings for broad-band dispersion and dispersion slope compensation," IEEE Photon. Technol. Lett. 15, 1091-1093 (2003).
[CrossRef]

H. Li and Y. Sheng, "Direct design of multichannel fiber Bragg grating with discrete layer-peeling algorithm," IEEE Photon. Technol. Lett. 15, 1252-1254 (2003).
[CrossRef]

2001 (1)

J. Skaar, L. Wang, and T. Erdogen, "On the synthesis of fiber Bragg grating by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

2000 (1)

X.-F. Chen, Y. Luo, C.-C. Fan, and S.-Z. Xie, "Analytical expression of sampled Bragg gratings with chirp in the sampling period and its application in dispersion management design in a WDM system," IEEE Photon. Technol. Lett. 12, 1013-1015 (2000).
[CrossRef]

1999 (1)

W. H. Loh, F. Q. Zhou, and J. J. Pan, "Sampled fiber grating based dispersions lope compensation," IEEE Photon. Technol. Lett. 11, 1280-1282 (1999).
[CrossRef]

1998 (2)

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, "Sincsampled fiber Bragg gratings for identical multiple wavelength operation," IEEE Photon. Technol. Lett. 10, 842-844 (1998).
[CrossRef]

R. Buffa, "Optimal control of population transfer through the continuum," Opt. Commun. 153, 240-244 (1998).
[CrossRef]

1997 (1)

T. Erdogan, "Fiber grating spectra," J. of Lightwave Technol. 15, 1277-1294 (1997).
[CrossRef]

1996 (2)

N. Wang and H. Rabitz, "Optimal control of pulse amplification without inversion," Phys. Rev. A 53, 1879-1885 (1996).
[CrossRef] [PubMed]

N. Wang and H. Rabitz, "Optimal control of population transfer in an optical dense medium," J. Chem. Phys. 104, 1173-1178 (1996).
[CrossRef]

1993 (1)

R. Feced, M. N. Zervas, and M. A. Muriel, "An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings," IEEE J. Quantum Electron. 29,1824-1834 (1993).

Agrawal, G. P.

H. Lee and G. P. Agrawal, "Purely phase-sampled fiber Bragg gratings for broad-band dispersion and dispersion slope compensation," IEEE Photon. Technol. Lett. 15, 1091-1093 (2003).
[CrossRef]

Alphones, A.

S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, and R. T. Zheng, "Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm," Opt. Commun. 260,716-722 (2006).
[CrossRef]

S. Baskar, R. T. Zheng, A. Alphones, N. Q. Ngo, and P. N. Suganthan, "Particle swarm optimization for the design of low-dispersion Fiber Bragg Gratings," IEEE Photon. Technol. Lett. 17, 615-617 (2005).
[CrossRef]

Baskar, S.

S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, and R. T. Zheng, "Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm," Opt. Commun. 260,716-722 (2006).
[CrossRef]

S. Baskar, R. T. Zheng, A. Alphones, N. Q. Ngo, and P. N. Suganthan, "Particle swarm optimization for the design of low-dispersion Fiber Bragg Gratings," IEEE Photon. Technol. Lett. 17, 615-617 (2005).
[CrossRef]

Buffa, R.

R. Buffa, "Optimal control of population transfer through the continuum," Opt. Commun. 153, 240-244 (1998).
[CrossRef]

Buryak, A. V.

A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, "Optimization of refractive index sampling for multichannel fiber Bragg gratings," IEEE J. Quantum Electron. 39, 91-98 (2003).
[CrossRef]

K. Y. Kolossovski, R. A. Sammut, A. V. Buryak, and D. Y. Stepanov, "Three-step design optimization for multi-channel fiber Bragg gratings," Opt. Express 11, 1029-1038, (2003).
[CrossRef] [PubMed]

Chan, H. P.

Q. Wu, P. L. Chu, and H. P. Chan, "General design approach to Multichannel Fiber Bragg Grating," J. of Lightwave Technol. 24, 1571-1580 (2006).
[CrossRef]

Q. Wu, C. Yu, K. Wang, X. Wang, Z. Yu, H. P. Chan, and P. L. Chu, "New sampling-based design of simultaneous compensation of both dispersion and dispersion slope for multichannel fiber Bragg gratings," IEEE Photon. Technol. Lett. 17, 381-383 (2005).
[CrossRef]

Chen, X.-F.

X.-F. Chen, Y. Luo, C.-C. Fan, and S.-Z. Xie, "Analytical expression of sampled Bragg gratings with chirp in the sampling period and its application in dispersion management design in a WDM system," IEEE Photon. Technol. Lett. 12, 1013-1015 (2000).
[CrossRef]

Chu, P. L.

Q. Wu, P. L. Chu, and H. P. Chan, "General design approach to Multichannel Fiber Bragg Grating," J. of Lightwave Technol. 24, 1571-1580 (2006).
[CrossRef]

Q. Wu, C. Yu, K. Wang, X. Wang, Z. Yu, H. P. Chan, and P. L. Chu, "New sampling-based design of simultaneous compensation of both dispersion and dispersion slope for multichannel fiber Bragg gratings," IEEE Photon. Technol. Lett. 17, 381-383 (2005).
[CrossRef]

Cole, M. J.

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, "Sincsampled fiber Bragg gratings for identical multiple wavelength operation," IEEE Photon. Technol. Lett. 10, 842-844 (1998).
[CrossRef]

Durkin, M. K.

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, "Sincsampled fiber Bragg gratings for identical multiple wavelength operation," IEEE Photon. Technol. Lett. 10, 842-844 (1998).
[CrossRef]

Erdogan, T.

T. Erdogan, "Fiber grating spectra," J. of Lightwave Technol. 15, 1277-1294 (1997).
[CrossRef]

Erdogen, T.

J. Skaar, L. Wang, and T. Erdogen, "On the synthesis of fiber Bragg grating by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

Fan, C.-C.

X.-F. Chen, Y. Luo, C.-C. Fan, and S.-Z. Xie, "Analytical expression of sampled Bragg gratings with chirp in the sampling period and its application in dispersion management design in a WDM system," IEEE Photon. Technol. Lett. 12, 1013-1015 (2000).
[CrossRef]

Feced, R.

R. Feced, M. N. Zervas, and M. A. Muriel, "An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings," IEEE J. Quantum Electron. 29,1824-1834 (1993).

Ibsen, M.

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, "Sincsampled fiber Bragg gratings for identical multiple wavelength operation," IEEE Photon. Technol. Lett. 10, 842-844 (1998).
[CrossRef]

Kolossovski, K. Y.

A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, "Optimization of refractive index sampling for multichannel fiber Bragg gratings," IEEE J. Quantum Electron. 39, 91-98 (2003).
[CrossRef]

K. Y. Kolossovski, R. A. Sammut, A. V. Buryak, and D. Y. Stepanov, "Three-step design optimization for multi-channel fiber Bragg gratings," Opt. Express 11, 1029-1038, (2003).
[CrossRef] [PubMed]

Laming, R. I.

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, "Sincsampled fiber Bragg gratings for identical multiple wavelength operation," IEEE Photon. Technol. Lett. 10, 842-844 (1998).
[CrossRef]

Lee, H.

H. Lee and G. P. Agrawal, "Purely phase-sampled fiber Bragg gratings for broad-band dispersion and dispersion slope compensation," IEEE Photon. Technol. Lett. 15, 1091-1093 (2003).
[CrossRef]

Li, H.

H. Li and Y. Sheng, "Direct design of multichannel fiber Bragg grating with discrete layer-peeling algorithm," IEEE Photon. Technol. Lett. 15, 1252-1254 (2003).
[CrossRef]

Loh, W. H.

W. H. Loh, F. Q. Zhou, and J. J. Pan, "Sampled fiber grating based dispersions lope compensation," IEEE Photon. Technol. Lett. 11, 1280-1282 (1999).
[CrossRef]

Luo, Y.

X.-F. Chen, Y. Luo, C.-C. Fan, and S.-Z. Xie, "Analytical expression of sampled Bragg gratings with chirp in the sampling period and its application in dispersion management design in a WDM system," IEEE Photon. Technol. Lett. 12, 1013-1015 (2000).
[CrossRef]

Muriel, M. A.

R. Feced, M. N. Zervas, and M. A. Muriel, "An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings," IEEE J. Quantum Electron. 29,1824-1834 (1993).

Ngo, N. Q.

S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, and R. T. Zheng, "Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm," Opt. Commun. 260,716-722 (2006).
[CrossRef]

S. Baskar, R. T. Zheng, A. Alphones, N. Q. Ngo, and P. N. Suganthan, "Particle swarm optimization for the design of low-dispersion Fiber Bragg Gratings," IEEE Photon. Technol. Lett. 17, 615-617 (2005).
[CrossRef]

Pan, J. J.

W. H. Loh, F. Q. Zhou, and J. J. Pan, "Sampled fiber grating based dispersions lope compensation," IEEE Photon. Technol. Lett. 11, 1280-1282 (1999).
[CrossRef]

Rabitz, H.

N. Wang and H. Rabitz, "Optimal control of pulse amplification without inversion," Phys. Rev. A 53, 1879-1885 (1996).
[CrossRef] [PubMed]

N. Wang and H. Rabitz, "Optimal control of population transfer in an optical dense medium," J. Chem. Phys. 104, 1173-1178 (1996).
[CrossRef]

Sammut, R. A.

Sheng, Y.

H. Li and Y. Sheng, "Direct design of multichannel fiber Bragg grating with discrete layer-peeling algorithm," IEEE Photon. Technol. Lett. 15, 1252-1254 (2003).
[CrossRef]

Skaar, J.

J. Skaar, L. Wang, and T. Erdogen, "On the synthesis of fiber Bragg grating by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

Stepanov, D. Y.

K. Y. Kolossovski, R. A. Sammut, A. V. Buryak, and D. Y. Stepanov, "Three-step design optimization for multi-channel fiber Bragg gratings," Opt. Express 11, 1029-1038, (2003).
[CrossRef] [PubMed]

A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, "Optimization of refractive index sampling for multichannel fiber Bragg gratings," IEEE J. Quantum Electron. 39, 91-98 (2003).
[CrossRef]

Suganthan, P. N.

S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, and R. T. Zheng, "Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm," Opt. Commun. 260,716-722 (2006).
[CrossRef]

S. Baskar, R. T. Zheng, A. Alphones, N. Q. Ngo, and P. N. Suganthan, "Particle swarm optimization for the design of low-dispersion Fiber Bragg Gratings," IEEE Photon. Technol. Lett. 17, 615-617 (2005).
[CrossRef]

Wang, K.

Q. Wu, C. Yu, K. Wang, X. Wang, Z. Yu, H. P. Chan, and P. L. Chu, "New sampling-based design of simultaneous compensation of both dispersion and dispersion slope for multichannel fiber Bragg gratings," IEEE Photon. Technol. Lett. 17, 381-383 (2005).
[CrossRef]

Wang, L.

J. Skaar, L. Wang, and T. Erdogen, "On the synthesis of fiber Bragg grating by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

Wang, N.

N. Wang and H. Rabitz, "Optimal control of pulse amplification without inversion," Phys. Rev. A 53, 1879-1885 (1996).
[CrossRef] [PubMed]

N. Wang and H. Rabitz, "Optimal control of population transfer in an optical dense medium," J. Chem. Phys. 104, 1173-1178 (1996).
[CrossRef]

Wang, X.

Q. Wu, C. Yu, K. Wang, X. Wang, Z. Yu, H. P. Chan, and P. L. Chu, "New sampling-based design of simultaneous compensation of both dispersion and dispersion slope for multichannel fiber Bragg gratings," IEEE Photon. Technol. Lett. 17, 381-383 (2005).
[CrossRef]

Wu, Q.

Q. Wu, P. L. Chu, and H. P. Chan, "General design approach to Multichannel Fiber Bragg Grating," J. of Lightwave Technol. 24, 1571-1580 (2006).
[CrossRef]

Q. Wu, C. Yu, K. Wang, X. Wang, Z. Yu, H. P. Chan, and P. L. Chu, "New sampling-based design of simultaneous compensation of both dispersion and dispersion slope for multichannel fiber Bragg gratings," IEEE Photon. Technol. Lett. 17, 381-383 (2005).
[CrossRef]

Xie, S.-Z.

X.-F. Chen, Y. Luo, C.-C. Fan, and S.-Z. Xie, "Analytical expression of sampled Bragg gratings with chirp in the sampling period and its application in dispersion management design in a WDM system," IEEE Photon. Technol. Lett. 12, 1013-1015 (2000).
[CrossRef]

Yu, C.

Q. Wu, C. Yu, K. Wang, X. Wang, Z. Yu, H. P. Chan, and P. L. Chu, "New sampling-based design of simultaneous compensation of both dispersion and dispersion slope for multichannel fiber Bragg gratings," IEEE Photon. Technol. Lett. 17, 381-383 (2005).
[CrossRef]

Yu, Z.

Q. Wu, C. Yu, K. Wang, X. Wang, Z. Yu, H. P. Chan, and P. L. Chu, "New sampling-based design of simultaneous compensation of both dispersion and dispersion slope for multichannel fiber Bragg gratings," IEEE Photon. Technol. Lett. 17, 381-383 (2005).
[CrossRef]

Zervas, M. N.

R. Feced, M. N. Zervas, and M. A. Muriel, "An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings," IEEE J. Quantum Electron. 29,1824-1834 (1993).

Zheng, R. T.

S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, and R. T. Zheng, "Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm," Opt. Commun. 260,716-722 (2006).
[CrossRef]

S. Baskar, R. T. Zheng, A. Alphones, N. Q. Ngo, and P. N. Suganthan, "Particle swarm optimization for the design of low-dispersion Fiber Bragg Gratings," IEEE Photon. Technol. Lett. 17, 615-617 (2005).
[CrossRef]

Zhou, F. Q.

W. H. Loh, F. Q. Zhou, and J. J. Pan, "Sampled fiber grating based dispersions lope compensation," IEEE Photon. Technol. Lett. 11, 1280-1282 (1999).
[CrossRef]

IEEE J. Quantum Electron. (3)

A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, "Optimization of refractive index sampling for multichannel fiber Bragg gratings," IEEE J. Quantum Electron. 39, 91-98 (2003).
[CrossRef]

R. Feced, M. N. Zervas, and M. A. Muriel, "An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings," IEEE J. Quantum Electron. 29,1824-1834 (1993).

J. Skaar, L. Wang, and T. Erdogen, "On the synthesis of fiber Bragg grating by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

IEEE Photon. Technol. Lett. (7)

H. Li and Y. Sheng, "Direct design of multichannel fiber Bragg grating with discrete layer-peeling algorithm," IEEE Photon. Technol. Lett. 15, 1252-1254 (2003).
[CrossRef]

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, "Sincsampled fiber Bragg gratings for identical multiple wavelength operation," IEEE Photon. Technol. Lett. 10, 842-844 (1998).
[CrossRef]

X.-F. Chen, Y. Luo, C.-C. Fan, and S.-Z. Xie, "Analytical expression of sampled Bragg gratings with chirp in the sampling period and its application in dispersion management design in a WDM system," IEEE Photon. Technol. Lett. 12, 1013-1015 (2000).
[CrossRef]

W. H. Loh, F. Q. Zhou, and J. J. Pan, "Sampled fiber grating based dispersions lope compensation," IEEE Photon. Technol. Lett. 11, 1280-1282 (1999).
[CrossRef]

H. Lee and G. P. Agrawal, "Purely phase-sampled fiber Bragg gratings for broad-band dispersion and dispersion slope compensation," IEEE Photon. Technol. Lett. 15, 1091-1093 (2003).
[CrossRef]

Q. Wu, C. Yu, K. Wang, X. Wang, Z. Yu, H. P. Chan, and P. L. Chu, "New sampling-based design of simultaneous compensation of both dispersion and dispersion slope for multichannel fiber Bragg gratings," IEEE Photon. Technol. Lett. 17, 381-383 (2005).
[CrossRef]

S. Baskar, R. T. Zheng, A. Alphones, N. Q. Ngo, and P. N. Suganthan, "Particle swarm optimization for the design of low-dispersion Fiber Bragg Gratings," IEEE Photon. Technol. Lett. 17, 615-617 (2005).
[CrossRef]

J. Chem. Phys. (1)

N. Wang and H. Rabitz, "Optimal control of population transfer in an optical dense medium," J. Chem. Phys. 104, 1173-1178 (1996).
[CrossRef]

J. of Lightwave Technol. (2)

Q. Wu, P. L. Chu, and H. P. Chan, "General design approach to Multichannel Fiber Bragg Grating," J. of Lightwave Technol. 24, 1571-1580 (2006).
[CrossRef]

T. Erdogan, "Fiber grating spectra," J. of Lightwave Technol. 15, 1277-1294 (1997).
[CrossRef]

Opt. Commun. (2)

S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, and R. T. Zheng, "Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm," Opt. Commun. 260,716-722 (2006).
[CrossRef]

R. Buffa, "Optimal control of population transfer through the continuum," Opt. Commun. 153, 240-244 (1998).
[CrossRef]

Opt. Express (1)

Phys. Rev. A (1)

N. Wang and H. Rabitz, "Optimal control of pulse amplification without inversion," Phys. Rev. A 53, 1879-1885 (1996).
[CrossRef] [PubMed]

Other (2)

F. I. Lewis, Optimal Control, (Wiley, New York, 1986).

S. A. Rice and M. Zhao, Optimal Control of Molecular Dynamics, (Wiley, New York, (2000).

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Figures (4)

Fig. 1.
Fig. 1.

Two-channel low dispersion FBG filter with channel spacing 50GHz synthesized by the LMO method. (a) Reflection spectrum and dispersion profile, (b) transmission and target spectra, (c) the detailed dispersion profile in one channel, (d) designed apodization profile of the index modulation.

Fig. 2.
Fig. 2.

Eight-channel low dispersion FBG filter with channel spacing 25GHz synthesized by the LMO method. (a) Reflection spectrum and dispersion profile, (b) transmission and target spectra, (c) the detailed dispersion profile in one channel, (d) designed apodization profile of the index modulation.

Fig. 3.
Fig. 3.

Typical evolution curves of the average error for the designed MCFBGs in the LMO method.

Fig. 4.
Fig. 4.

Reflection spectra and the apodization index profiles for (a), (b) two-channel FBG and (c), (d) eight-channel FBG with the weighting parameter β=0 and 1×10-7 for unconstrained and constrained coupling coefficient designs, respectively.

Equations (14)

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d R ( δ , z ) dz = i δ · R ( δ , z ) + i κ ( z ) S ( δ , z )
d S ( δ , z ) dz = i δ · S ( δ , z ) i κ * ( z ) R ( δ , z )
J = 1 2 [ r ( λ ) r d ( λ ) ] 2 d λ + β 2 0 L [ κ ( z ) ] 2 d z
+ 0 L μ R , R · Re [ d R d z i δ R i κ S ] d λ d z
+ 0 L μ R , I · Im [ d R d z i δ R i κ S ] d λ d z
+ 0 L μ S , R · Re [ d S d z + i δ S + i κ * R ] d λ d z
+ 0 L μ S , I · Im [ d S d z + i δ S + i κ * R ] d λ d z
μ R z = i δ · μ R i κ μ S
μ S z = i δ · μ S + i κ * μ R
μ R ( 0 ) = R ( 0 ) 2 r Δ r R R 2 + R I 2
μ S ( 0 ) = S ( 0 ) 2 Δ r R R 2 + R I 2
δ J δ κ * = β · κ + i ( μ R S * μ S * R ) d λ
κ new ( z ) = κ old ( z ) α δ J δ κ *
r = m = N 2 N 2 1 r 0 · exp { [ λ ( λ c + ( 2 m + 1 2 ) · Δ CS ) Δ λ ] } 20

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