Abstract

Methods to produce optimal designs for multi-channel fiber Bragg gratings (FBGs) with identical or close to identical channel-to-channel spectral characteristics are discussed. The proposed approach consists of three distinct steps. The first two steps (preliminary semi-analytic minimization and subsequent fine-tuning) do not depend on the grating design details, but on the number of channels only and can be readily applied to similar problems in other fields, e.g., in radio-physics and coding theory. The third step (spectral characteristic quality improvement) is FBG field specific. A comparison with other known optimization methods shows that the proposed approach yields generally superior results for small to moderate number of channels (N<60).

© 2003 Optical Society of America

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References

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  1. A. Othonos and K. Kalli, Fiber Bragg Gratings (Boston, Artech House, 1999).
  2. H. Ishii, H. Tanobe, F. Kano, Y. Tohmori, Y. Kondo, and Y. Yoshikuni, “Quasicontinuous Wavelength Tuning in Super-Structure-Grating (SSG) DBR Lasers,” IEEE J. Quantum Electron. 32, 433–441 (1996).
    [Crossref]
  3. A. V. Buryak and D. Yu. Stepanov, “Novel multi-channel grating devices,” in proceedings of Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, vol. 60 of Top series, BThB3 (Washington DC, Optical Society of America, 2001).
  4. A. V. Buryak, K. Y. Kolossovski, and D. Yu. Stepanov, “Optimization of Refractive Index Sampling for Multi-channel Fiber Bragg Gratings,” IEEE J. Quantum Electron. 39, 91–98 (2003).
    [Crossref]
  5. J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann Fiber Bragg Gratings and Phase-Only Sampling for High Channel Counts,” IEEE Photon. Tech. Lett. 14, 1309–1311 (2002).
    [Crossref]
  6. M. Ibsen, A. Fu, H. Geiger, and R. I. Laming, “All-fibre 4×10Gbit/s WDM link with DFB fibre laser transmitters and single sinc-sampled fibre grating dispersion compensator,” Electron. Lett. 35, 982–983 (1999).
    [Crossref]
  7. Y. Painchaud, A. Mailloux, H. Chotard, E. Pelletier, and M. Guy, “Multi-channel fiber Bragg gratings for dispersion and slope compensaion,” in OSA Technical Digest of Optical Fiber Communication Conference, ThAA5, 581–582 (Washington DC, Optical Society of America, 2002).
  8. S. W. Lϕvseth and D. Yu. Stepanov, “Analysis of multiple wavelength DFB fiber lasers,” IEEE J. Quantum Electron. 37, 770–780 (2001).
    [Crossref]
  9. S. Narahashi, K. Kumagai, and T. Nojima, “Minimising peak to average power ratio of multitone signals using steepest descent method,” Electron. Lett. 31, 1552–1554 (1995).
    [Crossref]
  10. M. Friese, “Multitone signals with low crest factor,” IEEE Trans. Commun. 45, 1338–1344 (1997).
    [Crossref]
  11. A. Othonos, X. Lee, and R. M. Measures, “Superimposed multiple Bragg gratings,” Electron. Lett. 30, 1972–1974 (1994).
    [Crossref]
  12. G. Sarlet, G. Morthier, R. Baets, D. J. Robbins, and D. C. J. Reid, “Optimization of multiple exposure gratings for widely tunable laser,” IEEE Photon. Techn. Lett. 11, 21–23 (1999).
    [Crossref]
  13. V. Jayaraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor lasers with sampled grating,” IEEE J. Quantum Electron. 29, 1824–1834 (1993).
    [Crossref]
  14. B. J. Eggleton, P. A. Krug, L. Poladian, and F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30, 1620–1622 (1994).
    [Crossref]
  15. W. H. Loh, F. Q. Zhou, and J. J. Pan, “Sampled Fiber Grating Based-Dispersion Slope Compensator,” IEEE Photon. Techn. Lett. 11, 1280–1282 (1999).
    [Crossref]
  16. H. Ishii, Y. Tohmori, Y. Yoshikuni, T. Tamamura, and Y. Kondo, “Multiple-Phase-Shift Super Structure Grating DBR Lasers for Broad Wavelength Tuning,” IEEE Photon. Techn. Lett. 5, 613–615 (1993).
    [Crossref]
  17. Y. Nasu and S. Yamashita, “Multiple phase-shift superstructure fibre Bragg gratings for DWDM systems,” Electron. Lett. 37, 1471–1472 (2001).
    [Crossref]
  18. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  19. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, The Art of Scientific Computing, 2nd ed. (Cambridge England, Cambridge Univ. Press, 1992).
  20. D. R. Gimlin and C. R. Patisaul, “On minimizing the Peak-to-Average Power Ration for the Sum of N inusoids,” IEEE Trans. Commun. 41, 631–635 (1993).
    [Crossref]
  21. S. Narahashi and T. Nojima, “New phasing scheme of N-multiple carriers for reducing peak-to-average power ratio,” Electron. Lett. 30, 1382–1383 (1994).
    [Crossref]
  22. J. Schoukens, Y. Rolain, and P. Guillaume, “Design of Narrowband, High-Resolution Multisines,” IEEE Trans. Instrument. Measur. 45, 750–753 (1996).
    [Crossref]
  23. C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (New York, Wiley & Sons, 1999).
  24. J. Skaar, L. Wang, and T. Erdogan, “On the Synthesis of Fiber Bragg Gratings by Layer Peeling,” IEEE J. Quantum Electron. 37, 165–173 (2001).
    [Crossref]
  25. L. Bömer and M. Antweiler, “Polyphase Barker sequences,” Electron. Lett. 25, 1577–1579 (1989); M. Friese and H. Zottmann, “Polyphase Barker sequences up to length 31,” Electron. Lett. 30, 1930–1931 (1994); M. Friese, “Polyphase Barker sequences up to length 36,” IEEE Trans. Inform. Theory 42, 1248–1250 (1996); A. R. Brenner, “Polyphase Barker sequences up to length 45 with small alphabets,” Electron. Lett. 34, 1576–1577 (1998).
  26. E. Van der Ouderaa, J. Schoukens, and J. Renneboog, “Peak Factor Minimization using a Time-Frequency Domain Swapping Algorithm,” IEEE Trans. Instr. Measur. 37, 145–147 (1988).
    [Crossref]
  27. Y. Painchaud, H. Chotard, A. Mailloux, and Y. Vasseur, “Superposition of chirped fibre Bragg gratings for third-order dispersion compensation over 32 WDM channels,” Electron. Lett. 38, 1572–1573 (2002).
    [Crossref]
  28. A. V. Buryak, G. Edvell, A. Graf, K. Y. Kolossovski, and D. Yu. Stepanov, “Recent progress and novel directions in multi-channel FBG dispersion compensation,” in OSA Technical Digest of Conference on Lasers and Electro-Optics (Washington DC, Optical Society of America, 2003).

2003 (1)

A. V. Buryak, K. Y. Kolossovski, and D. Yu. Stepanov, “Optimization of Refractive Index Sampling for Multi-channel Fiber Bragg Gratings,” IEEE J. Quantum Electron. 39, 91–98 (2003).
[Crossref]

2002 (2)

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann Fiber Bragg Gratings and Phase-Only Sampling for High Channel Counts,” IEEE Photon. Tech. Lett. 14, 1309–1311 (2002).
[Crossref]

Y. Painchaud, H. Chotard, A. Mailloux, and Y. Vasseur, “Superposition of chirped fibre Bragg gratings for third-order dispersion compensation over 32 WDM channels,” Electron. Lett. 38, 1572–1573 (2002).
[Crossref]

2001 (3)

J. Skaar, L. Wang, and T. Erdogan, “On the Synthesis of Fiber Bragg Gratings by Layer Peeling,” IEEE J. Quantum Electron. 37, 165–173 (2001).
[Crossref]

S. W. Lϕvseth and D. Yu. Stepanov, “Analysis of multiple wavelength DFB fiber lasers,” IEEE J. Quantum Electron. 37, 770–780 (2001).
[Crossref]

Y. Nasu and S. Yamashita, “Multiple phase-shift superstructure fibre Bragg gratings for DWDM systems,” Electron. Lett. 37, 1471–1472 (2001).
[Crossref]

1999 (3)

W. H. Loh, F. Q. Zhou, and J. J. Pan, “Sampled Fiber Grating Based-Dispersion Slope Compensator,” IEEE Photon. Techn. Lett. 11, 1280–1282 (1999).
[Crossref]

M. Ibsen, A. Fu, H. Geiger, and R. I. Laming, “All-fibre 4×10Gbit/s WDM link with DFB fibre laser transmitters and single sinc-sampled fibre grating dispersion compensator,” Electron. Lett. 35, 982–983 (1999).
[Crossref]

G. Sarlet, G. Morthier, R. Baets, D. J. Robbins, and D. C. J. Reid, “Optimization of multiple exposure gratings for widely tunable laser,” IEEE Photon. Techn. Lett. 11, 21–23 (1999).
[Crossref]

1997 (1)

M. Friese, “Multitone signals with low crest factor,” IEEE Trans. Commun. 45, 1338–1344 (1997).
[Crossref]

1996 (2)

H. Ishii, H. Tanobe, F. Kano, Y. Tohmori, Y. Kondo, and Y. Yoshikuni, “Quasicontinuous Wavelength Tuning in Super-Structure-Grating (SSG) DBR Lasers,” IEEE J. Quantum Electron. 32, 433–441 (1996).
[Crossref]

J. Schoukens, Y. Rolain, and P. Guillaume, “Design of Narrowband, High-Resolution Multisines,” IEEE Trans. Instrument. Measur. 45, 750–753 (1996).
[Crossref]

1995 (1)

S. Narahashi, K. Kumagai, and T. Nojima, “Minimising peak to average power ratio of multitone signals using steepest descent method,” Electron. Lett. 31, 1552–1554 (1995).
[Crossref]

1994 (3)

A. Othonos, X. Lee, and R. M. Measures, “Superimposed multiple Bragg gratings,” Electron. Lett. 30, 1972–1974 (1994).
[Crossref]

B. J. Eggleton, P. A. Krug, L. Poladian, and F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30, 1620–1622 (1994).
[Crossref]

S. Narahashi and T. Nojima, “New phasing scheme of N-multiple carriers for reducing peak-to-average power ratio,” Electron. Lett. 30, 1382–1383 (1994).
[Crossref]

1993 (3)

D. R. Gimlin and C. R. Patisaul, “On minimizing the Peak-to-Average Power Ration for the Sum of N inusoids,” IEEE Trans. Commun. 41, 631–635 (1993).
[Crossref]

H. Ishii, Y. Tohmori, Y. Yoshikuni, T. Tamamura, and Y. Kondo, “Multiple-Phase-Shift Super Structure Grating DBR Lasers for Broad Wavelength Tuning,” IEEE Photon. Techn. Lett. 5, 613–615 (1993).
[Crossref]

V. Jayaraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor lasers with sampled grating,” IEEE J. Quantum Electron. 29, 1824–1834 (1993).
[Crossref]

1989 (1)

L. Bömer and M. Antweiler, “Polyphase Barker sequences,” Electron. Lett. 25, 1577–1579 (1989); M. Friese and H. Zottmann, “Polyphase Barker sequences up to length 31,” Electron. Lett. 30, 1930–1931 (1994); M. Friese, “Polyphase Barker sequences up to length 36,” IEEE Trans. Inform. Theory 42, 1248–1250 (1996); A. R. Brenner, “Polyphase Barker sequences up to length 45 with small alphabets,” Electron. Lett. 34, 1576–1577 (1998).

1988 (1)

E. Van der Ouderaa, J. Schoukens, and J. Renneboog, “Peak Factor Minimization using a Time-Frequency Domain Swapping Algorithm,” IEEE Trans. Instr. Measur. 37, 145–147 (1988).
[Crossref]

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Antweiler, M.

L. Bömer and M. Antweiler, “Polyphase Barker sequences,” Electron. Lett. 25, 1577–1579 (1989); M. Friese and H. Zottmann, “Polyphase Barker sequences up to length 31,” Electron. Lett. 30, 1930–1931 (1994); M. Friese, “Polyphase Barker sequences up to length 36,” IEEE Trans. Inform. Theory 42, 1248–1250 (1996); A. R. Brenner, “Polyphase Barker sequences up to length 45 with small alphabets,” Electron. Lett. 34, 1576–1577 (1998).

Baets, R.

G. Sarlet, G. Morthier, R. Baets, D. J. Robbins, and D. C. J. Reid, “Optimization of multiple exposure gratings for widely tunable laser,” IEEE Photon. Techn. Lett. 11, 21–23 (1999).
[Crossref]

Bömer, L.

L. Bömer and M. Antweiler, “Polyphase Barker sequences,” Electron. Lett. 25, 1577–1579 (1989); M. Friese and H. Zottmann, “Polyphase Barker sequences up to length 31,” Electron. Lett. 30, 1930–1931 (1994); M. Friese, “Polyphase Barker sequences up to length 36,” IEEE Trans. Inform. Theory 42, 1248–1250 (1996); A. R. Brenner, “Polyphase Barker sequences up to length 45 with small alphabets,” Electron. Lett. 34, 1576–1577 (1998).

Buryak, A. V.

A. V. Buryak, K. Y. Kolossovski, and D. Yu. Stepanov, “Optimization of Refractive Index Sampling for Multi-channel Fiber Bragg Gratings,” IEEE J. Quantum Electron. 39, 91–98 (2003).
[Crossref]

A. V. Buryak and D. Yu. Stepanov, “Novel multi-channel grating devices,” in proceedings of Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, vol. 60 of Top series, BThB3 (Washington DC, Optical Society of America, 2001).

A. V. Buryak, G. Edvell, A. Graf, K. Y. Kolossovski, and D. Yu. Stepanov, “Recent progress and novel directions in multi-channel FBG dispersion compensation,” in OSA Technical Digest of Conference on Lasers and Electro-Optics (Washington DC, Optical Society of America, 2003).

Chotard, H.

Y. Painchaud, H. Chotard, A. Mailloux, and Y. Vasseur, “Superposition of chirped fibre Bragg gratings for third-order dispersion compensation over 32 WDM channels,” Electron. Lett. 38, 1572–1573 (2002).
[Crossref]

Y. Painchaud, A. Mailloux, H. Chotard, E. Pelletier, and M. Guy, “Multi-channel fiber Bragg gratings for dispersion and slope compensaion,” in OSA Technical Digest of Optical Fiber Communication Conference, ThAA5, 581–582 (Washington DC, Optical Society of America, 2002).

Chuang, Z.-M.

V. Jayaraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor lasers with sampled grating,” IEEE J. Quantum Electron. 29, 1824–1834 (1993).
[Crossref]

Coldren, L. A.

V. Jayaraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor lasers with sampled grating,” IEEE J. Quantum Electron. 29, 1824–1834 (1993).
[Crossref]

Edvell, G.

A. V. Buryak, G. Edvell, A. Graf, K. Y. Kolossovski, and D. Yu. Stepanov, “Recent progress and novel directions in multi-channel FBG dispersion compensation,” in OSA Technical Digest of Conference on Lasers and Electro-Optics (Washington DC, Optical Society of America, 2003).

Eggleton, B. J.

B. J. Eggleton, P. A. Krug, L. Poladian, and F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30, 1620–1622 (1994).
[Crossref]

Erdogan, T.

J. Skaar, L. Wang, and T. Erdogan, “On the Synthesis of Fiber Bragg Gratings by Layer Peeling,” IEEE J. Quantum Electron. 37, 165–173 (2001).
[Crossref]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, The Art of Scientific Computing, 2nd ed. (Cambridge England, Cambridge Univ. Press, 1992).

Friese, M.

M. Friese, “Multitone signals with low crest factor,” IEEE Trans. Commun. 45, 1338–1344 (1997).
[Crossref]

Fu, A.

M. Ibsen, A. Fu, H. Geiger, and R. I. Laming, “All-fibre 4×10Gbit/s WDM link with DFB fibre laser transmitters and single sinc-sampled fibre grating dispersion compensator,” Electron. Lett. 35, 982–983 (1999).
[Crossref]

Geiger, H.

M. Ibsen, A. Fu, H. Geiger, and R. I. Laming, “All-fibre 4×10Gbit/s WDM link with DFB fibre laser transmitters and single sinc-sampled fibre grating dispersion compensator,” Electron. Lett. 35, 982–983 (1999).
[Crossref]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Gimlin, D. R.

D. R. Gimlin and C. R. Patisaul, “On minimizing the Peak-to-Average Power Ration for the Sum of N inusoids,” IEEE Trans. Commun. 41, 631–635 (1993).
[Crossref]

Graf, A.

A. V. Buryak, G. Edvell, A. Graf, K. Y. Kolossovski, and D. Yu. Stepanov, “Recent progress and novel directions in multi-channel FBG dispersion compensation,” in OSA Technical Digest of Conference on Lasers and Electro-Optics (Washington DC, Optical Society of America, 2003).

Guillaume, P.

J. Schoukens, Y. Rolain, and P. Guillaume, “Design of Narrowband, High-Resolution Multisines,” IEEE Trans. Instrument. Measur. 45, 750–753 (1996).
[Crossref]

Guy, M.

Y. Painchaud, A. Mailloux, H. Chotard, E. Pelletier, and M. Guy, “Multi-channel fiber Bragg gratings for dispersion and slope compensaion,” in OSA Technical Digest of Optical Fiber Communication Conference, ThAA5, 581–582 (Washington DC, Optical Society of America, 2002).

Ibsen, M.

M. Ibsen, A. Fu, H. Geiger, and R. I. Laming, “All-fibre 4×10Gbit/s WDM link with DFB fibre laser transmitters and single sinc-sampled fibre grating dispersion compensator,” Electron. Lett. 35, 982–983 (1999).
[Crossref]

Ishii, H.

H. Ishii, H. Tanobe, F. Kano, Y. Tohmori, Y. Kondo, and Y. Yoshikuni, “Quasicontinuous Wavelength Tuning in Super-Structure-Grating (SSG) DBR Lasers,” IEEE J. Quantum Electron. 32, 433–441 (1996).
[Crossref]

H. Ishii, Y. Tohmori, Y. Yoshikuni, T. Tamamura, and Y. Kondo, “Multiple-Phase-Shift Super Structure Grating DBR Lasers for Broad Wavelength Tuning,” IEEE Photon. Techn. Lett. 5, 613–615 (1993).
[Crossref]

Jayaraman, V.

V. Jayaraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor lasers with sampled grating,” IEEE J. Quantum Electron. 29, 1824–1834 (1993).
[Crossref]

Kalli, K.

A. Othonos and K. Kalli, Fiber Bragg Gratings (Boston, Artech House, 1999).

Kano, F.

H. Ishii, H. Tanobe, F. Kano, Y. Tohmori, Y. Kondo, and Y. Yoshikuni, “Quasicontinuous Wavelength Tuning in Super-Structure-Grating (SSG) DBR Lasers,” IEEE J. Quantum Electron. 32, 433–441 (1996).
[Crossref]

Kolossovski, K. Y.

A. V. Buryak, K. Y. Kolossovski, and D. Yu. Stepanov, “Optimization of Refractive Index Sampling for Multi-channel Fiber Bragg Gratings,” IEEE J. Quantum Electron. 39, 91–98 (2003).
[Crossref]

A. V. Buryak, G. Edvell, A. Graf, K. Y. Kolossovski, and D. Yu. Stepanov, “Recent progress and novel directions in multi-channel FBG dispersion compensation,” in OSA Technical Digest of Conference on Lasers and Electro-Optics (Washington DC, Optical Society of America, 2003).

Kondo, Y.

H. Ishii, H. Tanobe, F. Kano, Y. Tohmori, Y. Kondo, and Y. Yoshikuni, “Quasicontinuous Wavelength Tuning in Super-Structure-Grating (SSG) DBR Lasers,” IEEE J. Quantum Electron. 32, 433–441 (1996).
[Crossref]

H. Ishii, Y. Tohmori, Y. Yoshikuni, T. Tamamura, and Y. Kondo, “Multiple-Phase-Shift Super Structure Grating DBR Lasers for Broad Wavelength Tuning,” IEEE Photon. Techn. Lett. 5, 613–615 (1993).
[Crossref]

Krug, P. A.

B. J. Eggleton, P. A. Krug, L. Poladian, and F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30, 1620–1622 (1994).
[Crossref]

Kumagai, K.

S. Narahashi, K. Kumagai, and T. Nojima, “Minimising peak to average power ratio of multitone signals using steepest descent method,” Electron. Lett. 31, 1552–1554 (1995).
[Crossref]

L?vseth, S. W.

S. W. Lϕvseth and D. Yu. Stepanov, “Analysis of multiple wavelength DFB fiber lasers,” IEEE J. Quantum Electron. 37, 770–780 (2001).
[Crossref]

Laming, R. I.

M. Ibsen, A. Fu, H. Geiger, and R. I. Laming, “All-fibre 4×10Gbit/s WDM link with DFB fibre laser transmitters and single sinc-sampled fibre grating dispersion compensator,” Electron. Lett. 35, 982–983 (1999).
[Crossref]

Lee, X.

A. Othonos, X. Lee, and R. M. Measures, “Superimposed multiple Bragg gratings,” Electron. Lett. 30, 1972–1974 (1994).
[Crossref]

Li, H.

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann Fiber Bragg Gratings and Phase-Only Sampling for High Channel Counts,” IEEE Photon. Tech. Lett. 14, 1309–1311 (2002).
[Crossref]

Li, Y.

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann Fiber Bragg Gratings and Phase-Only Sampling for High Channel Counts,” IEEE Photon. Tech. Lett. 14, 1309–1311 (2002).
[Crossref]

Loh, W. H.

W. H. Loh, F. Q. Zhou, and J. J. Pan, “Sampled Fiber Grating Based-Dispersion Slope Compensator,” IEEE Photon. Techn. Lett. 11, 1280–1282 (1999).
[Crossref]

Madsen, C. K.

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (New York, Wiley & Sons, 1999).

Mailloux, A.

Y. Painchaud, H. Chotard, A. Mailloux, and Y. Vasseur, “Superposition of chirped fibre Bragg gratings for third-order dispersion compensation over 32 WDM channels,” Electron. Lett. 38, 1572–1573 (2002).
[Crossref]

Y. Painchaud, A. Mailloux, H. Chotard, E. Pelletier, and M. Guy, “Multi-channel fiber Bragg gratings for dispersion and slope compensaion,” in OSA Technical Digest of Optical Fiber Communication Conference, ThAA5, 581–582 (Washington DC, Optical Society of America, 2002).

Measures, R. M.

A. Othonos, X. Lee, and R. M. Measures, “Superimposed multiple Bragg gratings,” Electron. Lett. 30, 1972–1974 (1994).
[Crossref]

Morthier, G.

G. Sarlet, G. Morthier, R. Baets, D. J. Robbins, and D. C. J. Reid, “Optimization of multiple exposure gratings for widely tunable laser,” IEEE Photon. Techn. Lett. 11, 21–23 (1999).
[Crossref]

Narahashi, S.

S. Narahashi, K. Kumagai, and T. Nojima, “Minimising peak to average power ratio of multitone signals using steepest descent method,” Electron. Lett. 31, 1552–1554 (1995).
[Crossref]

S. Narahashi and T. Nojima, “New phasing scheme of N-multiple carriers for reducing peak-to-average power ratio,” Electron. Lett. 30, 1382–1383 (1994).
[Crossref]

Nasu, Y.

Y. Nasu and S. Yamashita, “Multiple phase-shift superstructure fibre Bragg gratings for DWDM systems,” Electron. Lett. 37, 1471–1472 (2001).
[Crossref]

Nojima, T.

S. Narahashi, K. Kumagai, and T. Nojima, “Minimising peak to average power ratio of multitone signals using steepest descent method,” Electron. Lett. 31, 1552–1554 (1995).
[Crossref]

S. Narahashi and T. Nojima, “New phasing scheme of N-multiple carriers for reducing peak-to-average power ratio,” Electron. Lett. 30, 1382–1383 (1994).
[Crossref]

Othonos, A.

A. Othonos, X. Lee, and R. M. Measures, “Superimposed multiple Bragg gratings,” Electron. Lett. 30, 1972–1974 (1994).
[Crossref]

A. Othonos and K. Kalli, Fiber Bragg Gratings (Boston, Artech House, 1999).

Ouellette, F.

B. J. Eggleton, P. A. Krug, L. Poladian, and F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30, 1620–1622 (1994).
[Crossref]

Painchaud, Y.

Y. Painchaud, H. Chotard, A. Mailloux, and Y. Vasseur, “Superposition of chirped fibre Bragg gratings for third-order dispersion compensation over 32 WDM channels,” Electron. Lett. 38, 1572–1573 (2002).
[Crossref]

Y. Painchaud, A. Mailloux, H. Chotard, E. Pelletier, and M. Guy, “Multi-channel fiber Bragg gratings for dispersion and slope compensaion,” in OSA Technical Digest of Optical Fiber Communication Conference, ThAA5, 581–582 (Washington DC, Optical Society of America, 2002).

Pan, J. J.

W. H. Loh, F. Q. Zhou, and J. J. Pan, “Sampled Fiber Grating Based-Dispersion Slope Compensator,” IEEE Photon. Techn. Lett. 11, 1280–1282 (1999).
[Crossref]

Patisaul, C. R.

D. R. Gimlin and C. R. Patisaul, “On minimizing the Peak-to-Average Power Ration for the Sum of N inusoids,” IEEE Trans. Commun. 41, 631–635 (1993).
[Crossref]

Pelletier, E.

Y. Painchaud, A. Mailloux, H. Chotard, E. Pelletier, and M. Guy, “Multi-channel fiber Bragg gratings for dispersion and slope compensaion,” in OSA Technical Digest of Optical Fiber Communication Conference, ThAA5, 581–582 (Washington DC, Optical Society of America, 2002).

Poladian, L.

B. J. Eggleton, P. A. Krug, L. Poladian, and F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30, 1620–1622 (1994).
[Crossref]

Popelek, J.

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann Fiber Bragg Gratings and Phase-Only Sampling for High Channel Counts,” IEEE Photon. Tech. Lett. 14, 1309–1311 (2002).
[Crossref]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, The Art of Scientific Computing, 2nd ed. (Cambridge England, Cambridge Univ. Press, 1992).

Reid, D. C. J.

G. Sarlet, G. Morthier, R. Baets, D. J. Robbins, and D. C. J. Reid, “Optimization of multiple exposure gratings for widely tunable laser,” IEEE Photon. Techn. Lett. 11, 21–23 (1999).
[Crossref]

Renneboog, J.

E. Van der Ouderaa, J. Schoukens, and J. Renneboog, “Peak Factor Minimization using a Time-Frequency Domain Swapping Algorithm,” IEEE Trans. Instr. Measur. 37, 145–147 (1988).
[Crossref]

Robbins, D. J.

G. Sarlet, G. Morthier, R. Baets, D. J. Robbins, and D. C. J. Reid, “Optimization of multiple exposure gratings for widely tunable laser,” IEEE Photon. Techn. Lett. 11, 21–23 (1999).
[Crossref]

Rolain, Y.

J. Schoukens, Y. Rolain, and P. Guillaume, “Design of Narrowband, High-Resolution Multisines,” IEEE Trans. Instrument. Measur. 45, 750–753 (1996).
[Crossref]

Rothenberg, J. E.

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann Fiber Bragg Gratings and Phase-Only Sampling for High Channel Counts,” IEEE Photon. Tech. Lett. 14, 1309–1311 (2002).
[Crossref]

Sarlet, G.

G. Sarlet, G. Morthier, R. Baets, D. J. Robbins, and D. C. J. Reid, “Optimization of multiple exposure gratings for widely tunable laser,” IEEE Photon. Techn. Lett. 11, 21–23 (1999).
[Crossref]

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Schoukens, J.

J. Schoukens, Y. Rolain, and P. Guillaume, “Design of Narrowband, High-Resolution Multisines,” IEEE Trans. Instrument. Measur. 45, 750–753 (1996).
[Crossref]

E. Van der Ouderaa, J. Schoukens, and J. Renneboog, “Peak Factor Minimization using a Time-Frequency Domain Swapping Algorithm,” IEEE Trans. Instr. Measur. 37, 145–147 (1988).
[Crossref]

Sheng, Y.

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann Fiber Bragg Gratings and Phase-Only Sampling for High Channel Counts,” IEEE Photon. Tech. Lett. 14, 1309–1311 (2002).
[Crossref]

Skaar, J.

J. Skaar, L. Wang, and T. Erdogan, “On the Synthesis of Fiber Bragg Gratings by Layer Peeling,” IEEE J. Quantum Electron. 37, 165–173 (2001).
[Crossref]

Stepanov, D. Yu.

A. V. Buryak, K. Y. Kolossovski, and D. Yu. Stepanov, “Optimization of Refractive Index Sampling for Multi-channel Fiber Bragg Gratings,” IEEE J. Quantum Electron. 39, 91–98 (2003).
[Crossref]

S. W. Lϕvseth and D. Yu. Stepanov, “Analysis of multiple wavelength DFB fiber lasers,” IEEE J. Quantum Electron. 37, 770–780 (2001).
[Crossref]

A. V. Buryak and D. Yu. Stepanov, “Novel multi-channel grating devices,” in proceedings of Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, vol. 60 of Top series, BThB3 (Washington DC, Optical Society of America, 2001).

A. V. Buryak, G. Edvell, A. Graf, K. Y. Kolossovski, and D. Yu. Stepanov, “Recent progress and novel directions in multi-channel FBG dispersion compensation,” in OSA Technical Digest of Conference on Lasers and Electro-Optics (Washington DC, Optical Society of America, 2003).

Tamamura, T.

H. Ishii, Y. Tohmori, Y. Yoshikuni, T. Tamamura, and Y. Kondo, “Multiple-Phase-Shift Super Structure Grating DBR Lasers for Broad Wavelength Tuning,” IEEE Photon. Techn. Lett. 5, 613–615 (1993).
[Crossref]

Tanobe, H.

H. Ishii, H. Tanobe, F. Kano, Y. Tohmori, Y. Kondo, and Y. Yoshikuni, “Quasicontinuous Wavelength Tuning in Super-Structure-Grating (SSG) DBR Lasers,” IEEE J. Quantum Electron. 32, 433–441 (1996).
[Crossref]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, The Art of Scientific Computing, 2nd ed. (Cambridge England, Cambridge Univ. Press, 1992).

Tohmori, Y.

H. Ishii, H. Tanobe, F. Kano, Y. Tohmori, Y. Kondo, and Y. Yoshikuni, “Quasicontinuous Wavelength Tuning in Super-Structure-Grating (SSG) DBR Lasers,” IEEE J. Quantum Electron. 32, 433–441 (1996).
[Crossref]

H. Ishii, Y. Tohmori, Y. Yoshikuni, T. Tamamura, and Y. Kondo, “Multiple-Phase-Shift Super Structure Grating DBR Lasers for Broad Wavelength Tuning,” IEEE Photon. Techn. Lett. 5, 613–615 (1993).
[Crossref]

Van der Ouderaa, E.

E. Van der Ouderaa, J. Schoukens, and J. Renneboog, “Peak Factor Minimization using a Time-Frequency Domain Swapping Algorithm,” IEEE Trans. Instr. Measur. 37, 145–147 (1988).
[Crossref]

Vasseur, Y.

Y. Painchaud, H. Chotard, A. Mailloux, and Y. Vasseur, “Superposition of chirped fibre Bragg gratings for third-order dispersion compensation over 32 WDM channels,” Electron. Lett. 38, 1572–1573 (2002).
[Crossref]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, The Art of Scientific Computing, 2nd ed. (Cambridge England, Cambridge Univ. Press, 1992).

Wang, L.

J. Skaar, L. Wang, and T. Erdogan, “On the Synthesis of Fiber Bragg Gratings by Layer Peeling,” IEEE J. Quantum Electron. 37, 165–173 (2001).
[Crossref]

Wang, Y.

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann Fiber Bragg Gratings and Phase-Only Sampling for High Channel Counts,” IEEE Photon. Tech. Lett. 14, 1309–1311 (2002).
[Crossref]

Wilcox, R. B.

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann Fiber Bragg Gratings and Phase-Only Sampling for High Channel Counts,” IEEE Photon. Tech. Lett. 14, 1309–1311 (2002).
[Crossref]

Yamashita, S.

Y. Nasu and S. Yamashita, “Multiple phase-shift superstructure fibre Bragg gratings for DWDM systems,” Electron. Lett. 37, 1471–1472 (2001).
[Crossref]

Yoshikuni, Y.

H. Ishii, H. Tanobe, F. Kano, Y. Tohmori, Y. Kondo, and Y. Yoshikuni, “Quasicontinuous Wavelength Tuning in Super-Structure-Grating (SSG) DBR Lasers,” IEEE J. Quantum Electron. 32, 433–441 (1996).
[Crossref]

H. Ishii, Y. Tohmori, Y. Yoshikuni, T. Tamamura, and Y. Kondo, “Multiple-Phase-Shift Super Structure Grating DBR Lasers for Broad Wavelength Tuning,” IEEE Photon. Techn. Lett. 5, 613–615 (1993).
[Crossref]

Zhao, J. H.

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (New York, Wiley & Sons, 1999).

Zhou, F. Q.

W. H. Loh, F. Q. Zhou, and J. J. Pan, “Sampled Fiber Grating Based-Dispersion Slope Compensator,” IEEE Photon. Techn. Lett. 11, 1280–1282 (1999).
[Crossref]

Zweiback, J.

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann Fiber Bragg Gratings and Phase-Only Sampling for High Channel Counts,” IEEE Photon. Tech. Lett. 14, 1309–1311 (2002).
[Crossref]

Electron. Lett. (8)

M. Ibsen, A. Fu, H. Geiger, and R. I. Laming, “All-fibre 4×10Gbit/s WDM link with DFB fibre laser transmitters and single sinc-sampled fibre grating dispersion compensator,” Electron. Lett. 35, 982–983 (1999).
[Crossref]

S. Narahashi, K. Kumagai, and T. Nojima, “Minimising peak to average power ratio of multitone signals using steepest descent method,” Electron. Lett. 31, 1552–1554 (1995).
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A. Othonos, X. Lee, and R. M. Measures, “Superimposed multiple Bragg gratings,” Electron. Lett. 30, 1972–1974 (1994).
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B. J. Eggleton, P. A. Krug, L. Poladian, and F. Ouellette, “Long periodic superstructure Bragg gratings in optical fibres,” Electron. Lett. 30, 1620–1622 (1994).
[Crossref]

Y. Nasu and S. Yamashita, “Multiple phase-shift superstructure fibre Bragg gratings for DWDM systems,” Electron. Lett. 37, 1471–1472 (2001).
[Crossref]

S. Narahashi and T. Nojima, “New phasing scheme of N-multiple carriers for reducing peak-to-average power ratio,” Electron. Lett. 30, 1382–1383 (1994).
[Crossref]

L. Bömer and M. Antweiler, “Polyphase Barker sequences,” Electron. Lett. 25, 1577–1579 (1989); M. Friese and H. Zottmann, “Polyphase Barker sequences up to length 31,” Electron. Lett. 30, 1930–1931 (1994); M. Friese, “Polyphase Barker sequences up to length 36,” IEEE Trans. Inform. Theory 42, 1248–1250 (1996); A. R. Brenner, “Polyphase Barker sequences up to length 45 with small alphabets,” Electron. Lett. 34, 1576–1577 (1998).

Y. Painchaud, H. Chotard, A. Mailloux, and Y. Vasseur, “Superposition of chirped fibre Bragg gratings for third-order dispersion compensation over 32 WDM channels,” Electron. Lett. 38, 1572–1573 (2002).
[Crossref]

IEEE J. Quantum Electron. (5)

V. Jayaraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor lasers with sampled grating,” IEEE J. Quantum Electron. 29, 1824–1834 (1993).
[Crossref]

J. Skaar, L. Wang, and T. Erdogan, “On the Synthesis of Fiber Bragg Gratings by Layer Peeling,” IEEE J. Quantum Electron. 37, 165–173 (2001).
[Crossref]

S. W. Lϕvseth and D. Yu. Stepanov, “Analysis of multiple wavelength DFB fiber lasers,” IEEE J. Quantum Electron. 37, 770–780 (2001).
[Crossref]

H. Ishii, H. Tanobe, F. Kano, Y. Tohmori, Y. Kondo, and Y. Yoshikuni, “Quasicontinuous Wavelength Tuning in Super-Structure-Grating (SSG) DBR Lasers,” IEEE J. Quantum Electron. 32, 433–441 (1996).
[Crossref]

A. V. Buryak, K. Y. Kolossovski, and D. Yu. Stepanov, “Optimization of Refractive Index Sampling for Multi-channel Fiber Bragg Gratings,” IEEE J. Quantum Electron. 39, 91–98 (2003).
[Crossref]

IEEE Photon. Tech. Lett. (1)

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann Fiber Bragg Gratings and Phase-Only Sampling for High Channel Counts,” IEEE Photon. Tech. Lett. 14, 1309–1311 (2002).
[Crossref]

IEEE Photon. Techn. Lett. (3)

W. H. Loh, F. Q. Zhou, and J. J. Pan, “Sampled Fiber Grating Based-Dispersion Slope Compensator,” IEEE Photon. Techn. Lett. 11, 1280–1282 (1999).
[Crossref]

H. Ishii, Y. Tohmori, Y. Yoshikuni, T. Tamamura, and Y. Kondo, “Multiple-Phase-Shift Super Structure Grating DBR Lasers for Broad Wavelength Tuning,” IEEE Photon. Techn. Lett. 5, 613–615 (1993).
[Crossref]

G. Sarlet, G. Morthier, R. Baets, D. J. Robbins, and D. C. J. Reid, “Optimization of multiple exposure gratings for widely tunable laser,” IEEE Photon. Techn. Lett. 11, 21–23 (1999).
[Crossref]

IEEE Trans. Commun. (2)

M. Friese, “Multitone signals with low crest factor,” IEEE Trans. Commun. 45, 1338–1344 (1997).
[Crossref]

D. R. Gimlin and C. R. Patisaul, “On minimizing the Peak-to-Average Power Ration for the Sum of N inusoids,” IEEE Trans. Commun. 41, 631–635 (1993).
[Crossref]

IEEE Trans. Instr. Measur. (1)

E. Van der Ouderaa, J. Schoukens, and J. Renneboog, “Peak Factor Minimization using a Time-Frequency Domain Swapping Algorithm,” IEEE Trans. Instr. Measur. 37, 145–147 (1988).
[Crossref]

IEEE Trans. Instrument. Measur. (1)

J. Schoukens, Y. Rolain, and P. Guillaume, “Design of Narrowband, High-Resolution Multisines,” IEEE Trans. Instrument. Measur. 45, 750–753 (1996).
[Crossref]

Optik (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Other (6)

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, The Art of Scientific Computing, 2nd ed. (Cambridge England, Cambridge Univ. Press, 1992).

A. V. Buryak and D. Yu. Stepanov, “Novel multi-channel grating devices,” in proceedings of Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, vol. 60 of Top series, BThB3 (Washington DC, Optical Society of America, 2001).

A. Othonos and K. Kalli, Fiber Bragg Gratings (Boston, Artech House, 1999).

Y. Painchaud, A. Mailloux, H. Chotard, E. Pelletier, and M. Guy, “Multi-channel fiber Bragg gratings for dispersion and slope compensaion,” in OSA Technical Digest of Optical Fiber Communication Conference, ThAA5, 581–582 (Washington DC, Optical Society of America, 2002).

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (New York, Wiley & Sons, 1999).

A. V. Buryak, G. Edvell, A. Graf, K. Y. Kolossovski, and D. Yu. Stepanov, “Recent progress and novel directions in multi-channel FBG dispersion compensation,” in OSA Technical Digest of Conference on Lasers and Electro-Optics (Washington DC, Optical Society of America, 2003).

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Figures (3)

Fig. 1.
Fig. 1.

Normalized peak index change as a result of the first two steps in the three-step optimization process. Solid curve shows the analytic estimate (Eq. (7)).

Fig. 2.
Fig. 2.

An illustration of three-stage optimization of a 9-channel dispersion compensator design. Non-trivially modulated phase profile and group delay characteristics are not shown. (a), (b) the amplitude profile and the transmission spectrum obtained after the first step of optimization; (c), (d) the same as (a), (b) but after the second step; (e), (f) result of the third step. The final result is presented in more detail in Fig. 3.

Fig. 3.
Fig. 3.

Details of the 9-channel dispersion compensator design shown in Figs. 2(e,f). (a) amplitude and phase profiles; (b) enlarged (a); (c) central part of the reflection spectrum; (d) group delay. We note that, all fast oscillations of κ(z) profile in the vicinity of the main peak (z≈2.6) were completely eliminated after 30 iterations, though some unimportant weak modulation of the profile in the region z≈3.8 still presents.

Equations (15)

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E b z + i δ E b q ( z ) E f = 0 ,
E f z i δ E f q * ( z ) E b = 0 ,
[ E b ( 0 ) E f ( 0 ) ] = [ 1 t * r 1 t r 2 t 1 t ] [ E b ( L ) E f ( L ) ] ,
q ( z ) = l = 1 N κ ( z ) e i θ ( z ) e i [ ( 2 l N 1 ) Δ k z 2 + ϕ l ] = κ ( z ) e i θ ( z ) S ( z ) ,
arg { S ( z ) } = arctan [ l = 1 N sin ( [ 2 l N 1 ] Δ k z 2 + ϕ l ) l = 1 N cos ( [ 2 l N 1 ] Δ k z 2 + ϕ l ) ] .
S ( z ) = N ( 1 + 2 N Re p = 1 N 1 C p e i p Δ k z ) 1 2 ,
C P = l = 1 N p m l + p m l * , p = 1 , 2 , , N 1 ,
Δ n N = max z S ( z ) Δ n 1 = N + 2 Δ n 1 ,
Δ ( ϕ ) = [ s ( z ) s ( z ) ] 2 = 1 s ( z ) 2 ,
s ( z ) = 1 1 4 N 2 p = 1 N 1 C p 2 + O ( x 3 ) .
Δ n env ( av ) = N ( 1 1 4 N 2 ) Δ n 1 .
F = 1 2 N + O ( 1 N 2 ) .
Δ ( ϕ ) = 1 2 N p = 1 N 1 C p 2 + O ( x 3 x 2 ) ,
Δ ( ϕ ) ϕ l = Im { p = 1 l 1 C p m l p m l * + p = 1 N l C p * m l + p m l * } 2 N 2 Δ ( ϕ ) + O ( x 3 x 2 ) ,
1 2 q ( z 2 ) = + r ( δ ) exp ( i δ z ) d δ .

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