Abstract

We have proposed an effective method to synthesize and optimize multichannel fiber Bragg grating filters (MCFBGFs). The novel method contains two steps, i.e., the discrete layer peeling algorithm generates the excellent initial guess values and, successively, the nonlinear least squares method reconstructs and optimizes the expected fiber Bragg grating parameters from the initial guess in the previous step. Design examples demonstrate that the proposed method has unique merits to optimize the reflectivity and dispersion of MCFBGFs and effectively reduce their index modulation simultaneously.

© 2009 IEEE

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  1. X. M. Liu, Y. K. Gong, L. R. Wang, T. Wang, T. Y. Zhang, K. Q. Lu, W. Zhao, "Identical dual-wavelength fiber Bragg gratings," J. Lightw. Technol. 25, 2706-2710 (2007).
  2. A. Rosenthal, M. Horowitz, "Analysis and design of nonlinear fiber Bragg gratings and their application for optical compression of reflected pulses," Opt. Lett. 31, 1334-1336 (2006).
  3. J. H. Chow, I. C. M. Littler, G. d. Vine, D. E. McClelland, M. B. Gray, "Phase-sensitive interrogation of fiber Bragg grating resonators for sensing applications," J. Lightw. Technol. 23, 1881-1889 (2005).
  4. E. G. Turitsyna, X. Shu, S. K. Turitsyn, I. Bennion, "Design and fabrication of fiber Bragg gratings with V-shaped dispersion profile," J. Lightw. Technol. 25, 606-611 (2007).
  5. X. Shu, B. A. L. Gwandu, Y. Liu, L. Zhang, I. Bennion, "Sampled fiber Bragg grating for simultaneous refractive-index and temperature measurement," Opt. Lett. 26, 774-776 (2001).
  6. H. Li, Y. Sheng, "Direct design of multichannel fiber Bragg grating with discrete layer-peeling algorithm," IEEE Photon. Technol. Lett. 15, 1252-1254 (2003).
  7. H. Li, T. Kumagai, K. Ogusu, Y. Sheng, "Advanced design of a multichannel fiber Bragg grating based on a layer-peeling method," J. Opt. Soc. Amer. B 1929-1938 (2004).
  8. A. V. Buryak, K. Y. Kolossovski, D. Y. Stepanov, "Optimization of refractive index sampling for multichannel fiber Bragg gratings," IEEE J. Quantum Electron. 39, 91-98 (2003).
  9. Q. Wu, C. Yu, K. Wang, X. Wang, Z. Yu, H. P. Chan, 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).
  10. H. P. Li, M. Li, Y. L. Sheng, J. E. Rothenberg, "Advances in the design and fabrication of high-channel-count fiber Bragg gratings," J. Lightw. Technol. 25, 2739-2750 (2007).
  11. X. Liu, "Tunable ultranarrow dual-channel filter based on sampled FBGs," J. Lightw. Technol. 26, 1885-1890 (2008).
  12. Q. Sun, D. Liu, L. Xia, J. Wang, H. Liu, P. Shum, "Experimental demonstration of multipoint temperature warning sensor using a multichannel matched fiber Bragg grating," IEEE Photon. Technol. Lett. 20, 933-935 (2008).
  13. M. Ibsen, M. K. Durkin, M. J. Cole, R. I. Laming, "Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation," IEEE Photon. Technol. Lett. 10, 842-844 (1998).
  14. K. Kolossovski, R. Sammut, A. Buryak, D. Stepanov, "Three-step design optimization for multi-channel fibre Bragg gratings," Opt. Express. 11, 1029-1038 (2003).
  15. N. Plougmann, M. Kristensen, "Efficient iterative technique for designing Bragg gratings," Opt. Lett. 29, 23-25 (2004).
  16. Q. Wu, P. L. Chu, H. P. Chan, "General design approach to multichannel fiber Bragg grating," J. Lightw. Technol. 24, 1571-1580 (2006).
  17. J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, J. Zweiback, "Dammann fiber Bragg gratings and phase-only sampling for high channel counts," IEEE Photon. Technol. Lett. 14, 1309-1311 (2002).
  18. H. Li, Y. Sheng, Y. Li, J. E. Rothenberg, "Phased-only sampled fiber Bragg gratings for high-channel-count chromatic dispersion compensation," J. Lightw. Technol. 21, 2074-2083 (2003).
  19. H. Lee, G. Agrawal, "Bandwidth equalization of purely phase-sampled fiber Bragg gratings for broadband dispersion and dispersion slope compensation," Opt. Express. 12, 5595-5602 (2004).
  20. S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, R. T. Zheng, "Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm," Opt. Commun. 260, 716-722 (2006).
  21. C. Lee, R. Lee, Y. Kao, "Design of multichannel DWDM fiber Bragg grating filters by Lagrange multiplier constrained optimization," Opt. Express. 14, 11002-11011 (2006).
  22. T. Erdogan, "Fiber grating spectrum," J. Lightw. Technol. 15, 1277-1293 (1997).
  23. K. Madsen, H. B. Nielsen, O. Tingleff, Infomatics and Mathematical Modeling (Technical Univ. Demark, DTU, 2004).
  24. http://en.wikipedia.org/wiki/Gauss–Newton_algorithm.
  25. J. Skaar, L. Wang, T. Erdogan, "On the synthesis of fiber Bragg gratings by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).
  26. L. Wang, T. Erdogan, "Layer peeling algorithm for reconstruction of long-period fibre gratings," Electron. Lett. 37, 154-156 (2001).
  27. K. Aksnes, J. Skaar, "Design of short fiber Bragg gratings by use of optimization," Appl. Opt. 43, 2226-2230 (2004).
  28. J. Skaar, Synthesis and Characterization of Fiber Bragg Gratings Ph.D. dissertation Norwegian Univ. Sci. and Technol.TrondheimNorway (2000).
  29. Y. Painchaud, M. Poulin, M. Morin, "Grating superposition encoded into a phase mask for efficient fabrication of dispersion slope compensators," Proc. Opt. Commun. ECOC 2005. 31st Eur. Conf. (2005) pp. 419-420.
  30. S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, R. T. Zheng, "Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm," Opt. Commun. 260, 716-722 (2006).
  31. J. C. C. Carvalho, M. J. Sousa, C. S. S. Junior, J. C. W. A. Costa, C. R. L. Frances, M. E. V. Segatto, "A new acceleration technique for the design of fibre gratings," Opt. Express. 14, 10715-10725 (2006).
  32. S. Baskar, R. T. Zheng, A. Alphones, N. Q. Ngo, P. N. Suganthan, "Particle swarm optimization for the design of low-dispersion fiber Bragg gratings," IEEE Photon. Technol. Lett. 17, 615-617 (2005).
  33. M. Li, H. Li, "Advanced design of complex fiber Bragg grating for multi-channel asymmetrical triangular filter," Proc. Opto-Electron.Commun. Conf, 2008 and the 2008 Austral. Conf. Opt. Fibre Technol. OECC/ACOFT 2008 (2008) pp. 1-2.

2008 (2)

X. Liu, "Tunable ultranarrow dual-channel filter based on sampled FBGs," J. Lightw. Technol. 26, 1885-1890 (2008).

Q. Sun, D. Liu, L. Xia, J. Wang, H. Liu, P. Shum, "Experimental demonstration of multipoint temperature warning sensor using a multichannel matched fiber Bragg grating," IEEE Photon. Technol. Lett. 20, 933-935 (2008).

2007 (3)

H. P. Li, M. Li, Y. L. Sheng, J. E. Rothenberg, "Advances in the design and fabrication of high-channel-count fiber Bragg gratings," J. Lightw. Technol. 25, 2739-2750 (2007).

X. M. Liu, Y. K. Gong, L. R. Wang, T. Wang, T. Y. Zhang, K. Q. Lu, W. Zhao, "Identical dual-wavelength fiber Bragg gratings," J. Lightw. Technol. 25, 2706-2710 (2007).

E. G. Turitsyna, X. Shu, S. K. Turitsyn, I. Bennion, "Design and fabrication of fiber Bragg gratings with V-shaped dispersion profile," J. Lightw. Technol. 25, 606-611 (2007).

2006 (6)

A. Rosenthal, M. Horowitz, "Analysis and design of nonlinear fiber Bragg gratings and their application for optical compression of reflected pulses," Opt. Lett. 31, 1334-1336 (2006).

Q. Wu, P. L. Chu, H. P. Chan, "General design approach to multichannel fiber Bragg grating," J. Lightw. Technol. 24, 1571-1580 (2006).

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

C. Lee, R. Lee, Y. Kao, "Design of multichannel DWDM fiber Bragg grating filters by Lagrange multiplier constrained optimization," Opt. Express. 14, 11002-11011 (2006).

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

J. C. C. Carvalho, M. J. Sousa, C. S. S. Junior, J. C. W. A. Costa, C. R. L. Frances, M. E. V. Segatto, "A new acceleration technique for the design of fibre gratings," Opt. Express. 14, 10715-10725 (2006).

2005 (3)

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

J. H. Chow, I. C. M. Littler, G. d. Vine, D. E. McClelland, M. B. Gray, "Phase-sensitive interrogation of fiber Bragg grating resonators for sensing applications," J. Lightw. Technol. 23, 1881-1889 (2005).

Q. Wu, C. Yu, K. Wang, X. Wang, Z. Yu, H. P. Chan, 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).

2004 (4)

H. Li, T. Kumagai, K. Ogusu, Y. Sheng, "Advanced design of a multichannel fiber Bragg grating based on a layer-peeling method," J. Opt. Soc. Amer. B 1929-1938 (2004).

N. Plougmann, M. Kristensen, "Efficient iterative technique for designing Bragg gratings," Opt. Lett. 29, 23-25 (2004).

H. Lee, G. Agrawal, "Bandwidth equalization of purely phase-sampled fiber Bragg gratings for broadband dispersion and dispersion slope compensation," Opt. Express. 12, 5595-5602 (2004).

K. Aksnes, J. Skaar, "Design of short fiber Bragg gratings by use of optimization," Appl. Opt. 43, 2226-2230 (2004).

2003 (4)

H. Li, Y. Sheng, Y. Li, J. E. Rothenberg, "Phased-only sampled fiber Bragg gratings for high-channel-count chromatic dispersion compensation," J. Lightw. Technol. 21, 2074-2083 (2003).

K. Kolossovski, R. Sammut, A. Buryak, D. Stepanov, "Three-step design optimization for multi-channel fibre Bragg gratings," Opt. Express. 11, 1029-1038 (2003).

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

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

2002 (1)

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, J. Zweiback, "Dammann fiber Bragg gratings and phase-only sampling for high channel counts," IEEE Photon. Technol. Lett. 14, 1309-1311 (2002).

2001 (3)

X. Shu, B. A. L. Gwandu, Y. Liu, L. Zhang, I. Bennion, "Sampled fiber Bragg grating for simultaneous refractive-index and temperature measurement," Opt. Lett. 26, 774-776 (2001).

J. Skaar, L. Wang, T. Erdogan, "On the synthesis of fiber Bragg gratings by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).

L. Wang, T. Erdogan, "Layer peeling algorithm for reconstruction of long-period fibre gratings," Electron. Lett. 37, 154-156 (2001).

1998 (1)

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

1997 (1)

T. Erdogan, "Fiber grating spectrum," J. Lightw. Technol. 15, 1277-1293 (1997).

Appl. Opt. (1)

Electron. Lett. (1)

L. Wang, T. Erdogan, "Layer peeling algorithm for reconstruction of long-period fibre gratings," Electron. Lett. 37, 154-156 (2001).

IEEE J. Quantum Electron. (2)

J. Skaar, L. Wang, T. Erdogan, "On the synthesis of fiber Bragg gratings by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).

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

IEEE Photon. Technol. Lett. (6)

Q. Wu, C. Yu, K. Wang, X. Wang, Z. Yu, H. P. Chan, 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).

Q. Sun, D. Liu, L. Xia, J. Wang, H. Liu, P. Shum, "Experimental demonstration of multipoint temperature warning sensor using a multichannel matched fiber Bragg grating," IEEE Photon. Technol. Lett. 20, 933-935 (2008).

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

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

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, J. Zweiback, "Dammann fiber Bragg gratings and phase-only sampling for high channel counts," IEEE Photon. Technol. Lett. 14, 1309-1311 (2002).

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

J. Lightw. Technol. (8)

Q. Wu, P. L. Chu, H. P. Chan, "General design approach to multichannel fiber Bragg grating," J. Lightw. Technol. 24, 1571-1580 (2006).

T. Erdogan, "Fiber grating spectrum," J. Lightw. Technol. 15, 1277-1293 (1997).

H. Li, Y. Sheng, Y. Li, J. E. Rothenberg, "Phased-only sampled fiber Bragg gratings for high-channel-count chromatic dispersion compensation," J. Lightw. Technol. 21, 2074-2083 (2003).

H. P. Li, M. Li, Y. L. Sheng, J. E. Rothenberg, "Advances in the design and fabrication of high-channel-count fiber Bragg gratings," J. Lightw. Technol. 25, 2739-2750 (2007).

X. Liu, "Tunable ultranarrow dual-channel filter based on sampled FBGs," J. Lightw. Technol. 26, 1885-1890 (2008).

X. M. Liu, Y. K. Gong, L. R. Wang, T. Wang, T. Y. Zhang, K. Q. Lu, W. Zhao, "Identical dual-wavelength fiber Bragg gratings," J. Lightw. Technol. 25, 2706-2710 (2007).

J. H. Chow, I. C. M. Littler, G. d. Vine, D. E. McClelland, M. B. Gray, "Phase-sensitive interrogation of fiber Bragg grating resonators for sensing applications," J. Lightw. Technol. 23, 1881-1889 (2005).

E. G. Turitsyna, X. Shu, S. K. Turitsyn, I. Bennion, "Design and fabrication of fiber Bragg gratings with V-shaped dispersion profile," J. Lightw. Technol. 25, 606-611 (2007).

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

H. Li, T. Kumagai, K. Ogusu, Y. Sheng, "Advanced design of a multichannel fiber Bragg grating based on a layer-peeling method," J. Opt. Soc. Amer. B 1929-1938 (2004).

Opt. Commun. (2)

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

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

Opt. Express. (4)

J. C. C. Carvalho, M. J. Sousa, C. S. S. Junior, J. C. W. A. Costa, C. R. L. Frances, M. E. V. Segatto, "A new acceleration technique for the design of fibre gratings," Opt. Express. 14, 10715-10725 (2006).

C. Lee, R. Lee, Y. Kao, "Design of multichannel DWDM fiber Bragg grating filters by Lagrange multiplier constrained optimization," Opt. Express. 14, 11002-11011 (2006).

H. Lee, G. Agrawal, "Bandwidth equalization of purely phase-sampled fiber Bragg gratings for broadband dispersion and dispersion slope compensation," Opt. Express. 12, 5595-5602 (2004).

K. Kolossovski, R. Sammut, A. Buryak, D. Stepanov, "Three-step design optimization for multi-channel fibre Bragg gratings," Opt. Express. 11, 1029-1038 (2003).

Opt. Lett. (3)

Other (5)

K. Madsen, H. B. Nielsen, O. Tingleff, Infomatics and Mathematical Modeling (Technical Univ. Demark, DTU, 2004).

http://en.wikipedia.org/wiki/Gauss–Newton_algorithm.

J. Skaar, Synthesis and Characterization of Fiber Bragg Gratings Ph.D. dissertation Norwegian Univ. Sci. and Technol.TrondheimNorway (2000).

Y. Painchaud, M. Poulin, M. Morin, "Grating superposition encoded into a phase mask for efficient fabrication of dispersion slope compensators," Proc. Opt. Commun. ECOC 2005. 31st Eur. Conf. (2005) pp. 419-420.

M. Li, H. Li, "Advanced design of complex fiber Bragg grating for multi-channel asymmetrical triangular filter," Proc. Opto-Electron.Commun. Conf, 2008 and the 2008 Austral. Conf. Opt. Fibre Technol. OECC/ACOFT 2008 (2008) pp. 1-2.

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