Abstract

An analytical expression for calculating the reflection-peak wavelengths (RPWs) of a uniform sampled fiber Bragg grating (SFBG) with the multiple-phase-shift (MPS) technique is derived through Fourier transform of the index modulation. The new expression can accurately depict the RPWs incorporating various parameters such as the duty cycle and the DC index change. The effectiveness of the derived expression is further confirmed by comparing the RPWs estimated from the expression with the simulated reflective spectra using the piecewise uniform method. And the reflective spectrum has been well optimized by introducing the Gaussian apodization function to suppress the sidelobes without any wavelength shift on the RPWs. Then, a high-channel-count comb filter based on MPS is proposed by cascading two or more SFBGs with different Bragg periods but with the same RPWs. Noticeably, the RPWs of the new structured SFBG can also be accurately calculated through the expression. Furthermore, the number of spectral channels can be controlled by choosing gratings with specified difference Bragg periods.

© 2009 Optical Society of America

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    [CrossRef]
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  4. 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. Technol. Lett. 14, 1309-1311 (2002).
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  6. K. Y. Kolossovski, R. A. Sammut, A. V. Buryak, and D. Y. Stepanov, “Three-step design optimization for multichannel fiber Bragg gratings,” Opt. Express 11, 1029-1038 (2003).
  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. F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fiber Bragg gratings,” Electron. Lett. 31, 899-901 (1995).
    [CrossRef]
  9. X.-F. Chen, Y. Luo, C.-C. Fan, T. Wu, 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).
  10. H. Lee and G. P. Agrawal, “Purely phase-sampled fiber Bragg gratings for broadband dispersion and dispersion slope compensation,” IEEE Photon. Technol. Lett. 15, 1091-1093(2003).
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    [CrossRef]
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    [CrossRef]
  13. 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. Technol. Lett. 5, 613-615 (1993).
  14. Y. G. Han, X. Dong, J. H. Lee, and S. B. Lee, “Simultaneous measurement of bending and temperature based on a single sampled chirped fiber Bragg grating embedded on a flexible cantilever beam,” Opt. Lett. 31, 2839-2841 (2006).
    [CrossRef]
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    [CrossRef]
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  18. H. P. Li, M. Li, Y. L. Sheng, and J. E. Rothenberg, “Advances in the design and fabrication of high-channel-count fiber Bragg gratings,” J. Lightwave Technol. 25, 2739-2750 (2007).
    [CrossRef]
  19. X.-H. Zou, W. Pan, B. Luo, Z.-M. Qin, M.-Y. Wang, and W.-L. Zhang, “Periodically chirped sampled fiber Bragg gratings for multichannel comb filters,” IEEE Photon. Technol. Lett. 18, 1371-1373 (2006).
  20. J. L. Magné, J. Azaña, S. LaRochelle, and L. R. Chen, “Simple technique for eliminating the interchannel phase fluctuations in spectral Talbot-based periodic comb filters,” IEEE Photon. Technol. Lett. 18, 1958-1960 (2006).
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    [CrossRef]
  22. X. M Liu, A. X. Lin, G. Y. Sun, D. S. Moon, D. S. Hwang, and Y. J. Chung, “Identical-dual-bandpass sampled fiber Bragg grating and its application to ultranarrow filters,” Appl. Opt. 47, 5637-5643 (2008).
    [CrossRef]
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    [CrossRef]
  24. X. Y. He, Y. L. Yu, D. X. Huang, R. K. Zhang, W. Liu, and S. Jiang, “Analysis and applications of reflection-spectrum envelopes for sampled gratings,” J. Lightwave Technol. 26, 720-728 (2008).
    [CrossRef]
  25. X.-H. Zou, W. Pan, B. Luo, W.-L. Zhang, and M.-Y. Wang, “Accurate analytical expression for reflection-peak wavelengths of sampled Bragg grating,” IEEE Photon. Technol. Lett. 18, 529-531 (2006).
  26. X. J. Zhu, Y. L. Lu, G. J. Zhang, C. H. Wang, and M. F. Zhao, “Analytical determination of reflection-peak wavelengths of chirped sampled fiber Bragg gratings,” Appl. Opt. 47, 1135-1140 (2008).
    [CrossRef]
  27. C. H. Wang, L. R. Chen, and P. W. E. Smith, “Analysis of chirped-sampled and sampled-chirped fiber Bragg gratings,” Appl. Opt. 41, 1654-1660 (2002).
    [CrossRef]

2008 (5)

2007 (2)

2006 (4)

Y. G. Han, X. Dong, J. H. Lee, and S. B. Lee, “Simultaneous measurement of bending and temperature based on a single sampled chirped fiber Bragg grating embedded on a flexible cantilever beam,” Opt. Lett. 31, 2839-2841 (2006).
[CrossRef]

X.-H. Zou, W. Pan, B. Luo, Z.-M. Qin, M.-Y. Wang, and W.-L. Zhang, “Periodically chirped sampled fiber Bragg gratings for multichannel comb filters,” IEEE Photon. Technol. Lett. 18, 1371-1373 (2006).

J. L. Magné, J. Azaña, S. LaRochelle, and L. R. Chen, “Simple technique for eliminating the interchannel phase fluctuations in spectral Talbot-based periodic comb filters,” IEEE Photon. Technol. Lett. 18, 1958-1960 (2006).

X.-H. Zou, W. Pan, B. Luo, W.-L. Zhang, and M.-Y. Wang, “Accurate analytical expression for reflection-peak wavelengths of sampled Bragg grating,” IEEE Photon. Technol. Lett. 18, 529-531 (2006).

2005 (2)

Y.-T. Dai, X.-F. Chen, X.-M. Xu, C.-C. Fan, and S.-Z. Xie, “High channel-count comb filter based on chirped sampled fiber Bragg grating and phase shift,” IEEE Photon. Technol. Lett. 17, 1040-1042 (2005).

Y. Nasu and S. Yamashita, “Densification of sampled fiber Bragg gratings using multiple-phase-shift (MPS) technique,” J. Lightwave Technol. 23, 1808-1817 (2005).
[CrossRef]

2004 (1)

C.-H. Wang, J. Azaña, and L. R. Chen, “Efficient technique for increasing the channel density in multiwavelength sampled fiber Bragg grating filters,” IEEE Photon. Technol. Lett. 16, 1867-1869 (2004).

2003 (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]

H. Lee and G. P. Agrawal, “Purely phase-sampled fiber Bragg gratings for broadband dispersion and dispersion slope compensation,” IEEE Photon. Technol. Lett. 15, 1091-1093(2003).

K. Y. Kolossovski, R. A. Sammut, A. V. Buryak, and D. Y. Stepanov, “Three-step design optimization for multichannel fiber Bragg gratings,” Opt. Express 11, 1029-1038 (2003).

2002 (2)

C. H. Wang, L. R. Chen, and P. W. E. Smith, “Analysis of chirped-sampled and sampled-chirped fiber Bragg gratings,” Appl. Opt. 41, 1654-1660 (2002).
[CrossRef]

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. Technol. Lett. 14, 1309-1311 (2002).

2000 (2)

X.-F. Chen, C.-C. Fan, Y. Luo, and S.-Z. Xie, “Novel flat multichannel filter based on strongly chirped sampled fiber Bragg grating,” IEEE Photon. Technol. Lett. 12, 1501-1503(2000).

X.-F. Chen, Y. Luo, C.-C. Fan, T. Wu, 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).

1998 (1)

M. Ibsen, M. K. Durkin, M. J. Cole, and 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 spectra,” J. Lightwave Technol. 15, 1277-1294 (1997).
[CrossRef]

1995 (1)

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fiber Bragg gratings,” Electron. Lett. 31, 899-901 (1995).
[CrossRef]

1994 (1)

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

1993 (2)

V. Jayaraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor lasers with sampled gratings,” IEEE J. Quantum Electron. 29, 1824-1834 (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. Technol. Lett. 5, 613-615 (1993).

Agrawal, G. P.

H. Lee and G. P. Agrawal, “Purely phase-sampled fiber Bragg gratings for broadband dispersion and dispersion slope compensation,” IEEE Photon. Technol. Lett. 15, 1091-1093(2003).

Azaña, J.

J. L. Magné, J. Azaña, S. LaRochelle, and L. R. Chen, “Simple technique for eliminating the interchannel phase fluctuations in spectral Talbot-based periodic comb filters,” IEEE Photon. Technol. Lett. 18, 1958-1960 (2006).

C.-H. Wang, J. Azaña, and L. R. Chen, “Efficient technique for increasing the channel density in multiwavelength sampled fiber Bragg grating filters,” IEEE Photon. Technol. Lett. 16, 1867-1869 (2004).

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 multichannel fiber Bragg gratings,” Opt. Express 11, 1029-1038 (2003).

Chen, L. R.

J. L. Magné, J. Azaña, S. LaRochelle, and L. R. Chen, “Simple technique for eliminating the interchannel phase fluctuations in spectral Talbot-based periodic comb filters,” IEEE Photon. Technol. Lett. 18, 1958-1960 (2006).

C.-H. Wang, J. Azaña, and L. R. Chen, “Efficient technique for increasing the channel density in multiwavelength sampled fiber Bragg grating filters,” IEEE Photon. Technol. Lett. 16, 1867-1869 (2004).

C. H. Wang, L. R. Chen, and P. W. E. Smith, “Analysis of chirped-sampled and sampled-chirped fiber Bragg gratings,” Appl. Opt. 41, 1654-1660 (2002).
[CrossRef]

Chen, X.-F.

Y.-T. Dai, X.-F. Chen, X.-M. Xu, C.-C. Fan, and S.-Z. Xie, “High channel-count comb filter based on chirped sampled fiber Bragg grating and phase shift,” IEEE Photon. Technol. Lett. 17, 1040-1042 (2005).

X.-F. Chen, Y. Luo, C.-C. Fan, T. Wu, 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).

X.-F. Chen, C.-C. Fan, Y. Luo, and S.-Z. Xie, “Novel flat multichannel filter based on strongly chirped sampled fiber Bragg grating,” IEEE Photon. Technol. Lett. 12, 1501-1503(2000).

Chuang, Z.-M.

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

Chung, Y. J.

Coldren, L. A.

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

Cole, M. J.

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

Dai, Y.-T.

Y.-T. Dai, X.-F. Chen, X.-M. Xu, C.-C. Fan, and S.-Z. Xie, “High channel-count comb filter based on chirped sampled fiber Bragg grating and phase shift,” IEEE Photon. Technol. Lett. 17, 1040-1042 (2005).

Dhosi, G.

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fiber Bragg gratings,” Electron. Lett. 31, 899-901 (1995).
[CrossRef]

Dong, X.

Durkin, M. K.

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

Eggleton, B.

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fiber Bragg gratings,” Electron. Lett. 31, 899-901 (1995).
[CrossRef]

Eggleton, B. J.

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

Erdogan, T.

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

Fan, C.-C.

Y.-T. Dai, X.-F. Chen, X.-M. Xu, C.-C. Fan, and S.-Z. Xie, “High channel-count comb filter based on chirped sampled fiber Bragg grating and phase shift,” IEEE Photon. Technol. Lett. 17, 1040-1042 (2005).

X.-F. Chen, Y. Luo, C.-C. Fan, T. Wu, 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).

X.-F. Chen, C.-C. Fan, Y. Luo, and S.-Z. Xie, “Novel flat multichannel filter based on strongly chirped sampled fiber Bragg grating,” IEEE Photon. Technol. Lett. 12, 1501-1503(2000).

Han, Y. G.

He, X. Y.

Huang, D. X.

Hwang, D. S.

Ibsen, M.

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

Ishii, H.

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. Technol. Lett. 5, 613-615 (1993).

Jayaraman, V.

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

Jiang, S.

Kolossovski, K. Y.

K. Y. Kolossovski, R. A. Sammut, A. V. Buryak, and D. Y. Stepanov, “Three-step design optimization for multichannel fiber Bragg gratings,” Opt. Express 11, 1029-1038 (2003).

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]

Kondo, Y.

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. Technol. Lett. 5, 613-615 (1993).

Krug, P. A.

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fiber Bragg gratings,” Electron. Lett. 31, 899-901 (1995).
[CrossRef]

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

Laming, R. I.

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

LaRochelle, S.

J. L. Magné, J. Azaña, S. LaRochelle, and L. R. Chen, “Simple technique for eliminating the interchannel phase fluctuations in spectral Talbot-based periodic comb filters,” IEEE Photon. Technol. Lett. 18, 1958-1960 (2006).

Lee, H.

H. Lee and G. P. Agrawal, “Purely phase-sampled fiber Bragg gratings for broadband dispersion and dispersion slope compensation,” IEEE Photon. Technol. Lett. 15, 1091-1093(2003).

Lee, J. H.

Lee, S. B.

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. Technol. Lett. 14, 1309-1311 (2002).

Li, H. P.

Li, M.

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. Technol. Lett. 14, 1309-1311 (2002).

Lin, A. X.

Liu, W.

Lu, Y. L.

Luo, B.

X.-H. Zou, W. Pan, B. Luo, M.-Y. Wang, and W.-L. Zhang, “Spectral Talbot effect in sampled fiber Bragg gratings with superperiodic structures,” Opt. Express 15, 8812-8815 (2007).
[CrossRef]

X.-H. Zou, W. Pan, B. Luo, W.-L. Zhang, and M.-Y. Wang, “Accurate analytical expression for reflection-peak wavelengths of sampled Bragg grating,” IEEE Photon. Technol. Lett. 18, 529-531 (2006).

X.-H. Zou, W. Pan, B. Luo, Z.-M. Qin, M.-Y. Wang, and W.-L. Zhang, “Periodically chirped sampled fiber Bragg gratings for multichannel comb filters,” IEEE Photon. Technol. Lett. 18, 1371-1373 (2006).

Luo, Y.

X.-F. Chen, C.-C. Fan, Y. Luo, and S.-Z. Xie, “Novel flat multichannel filter based on strongly chirped sampled fiber Bragg grating,” IEEE Photon. Technol. Lett. 12, 1501-1503(2000).

X.-F. Chen, Y. Luo, C.-C. Fan, T. Wu, 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).

M, X.

Magné, J. L.

J. L. Magné, J. Azaña, S. LaRochelle, and L. R. Chen, “Simple technique for eliminating the interchannel phase fluctuations in spectral Talbot-based periodic comb filters,” IEEE Photon. Technol. Lett. 18, 1958-1960 (2006).

Moon, D. S.

Nasu, Y.

Ouellette, F.

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fiber Bragg gratings,” Electron. Lett. 31, 899-901 (1995).
[CrossRef]

Pan, W.

X.-H. Zou, W. Pan, B. Luo, M.-Y. Wang, and W.-L. Zhang, “Spectral Talbot effect in sampled fiber Bragg gratings with superperiodic structures,” Opt. Express 15, 8812-8815 (2007).
[CrossRef]

X.-H. Zou, W. Pan, B. Luo, W.-L. Zhang, and M.-Y. Wang, “Accurate analytical expression for reflection-peak wavelengths of sampled Bragg grating,” IEEE Photon. Technol. Lett. 18, 529-531 (2006).

X.-H. Zou, W. Pan, B. Luo, Z.-M. Qin, M.-Y. Wang, and W.-L. Zhang, “Periodically chirped sampled fiber Bragg gratings for multichannel comb filters,” IEEE Photon. Technol. Lett. 18, 1371-1373 (2006).

Poladian, L.

B. J. Eggleton, P. A. Krug, and L. Poladian, “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. Technol. Lett. 14, 1309-1311 (2002).

Qin, Z.-M.

X.-H. Zou, W. Pan, B. Luo, Z.-M. Qin, M.-Y. Wang, and W.-L. Zhang, “Periodically chirped sampled fiber Bragg gratings for multichannel comb filters,” IEEE Photon. Technol. Lett. 18, 1371-1373 (2006).

Rothenberg, J. E.

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

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. Technol. Lett. 14, 1309-1311 (2002).

Sammut, R. A.

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. Technol. Lett. 14, 1309-1311 (2002).

Sheng, Y. L.

Smith, P. W. E.

Stepanov, D. 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 multichannel fiber Bragg gratings,” Opt. Express 11, 1029-1038 (2003).

Stephens, T.

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fiber Bragg gratings,” Electron. Lett. 31, 899-901 (1995).
[CrossRef]

Sun, G. Y.

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. Technol. Lett. 5, 613-615 (1993).

Tohmori, Y.

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. Technol. Lett. 5, 613-615 (1993).

Wang, C. H.

Wang, C.-H.

C.-H. Wang, J. Azaña, and L. R. Chen, “Efficient technique for increasing the channel density in multiwavelength sampled fiber Bragg grating filters,” IEEE Photon. Technol. Lett. 16, 1867-1869 (2004).

Wang, M.-Y.

X.-H. Zou, W. Pan, B. Luo, M.-Y. Wang, and W.-L. Zhang, “Spectral Talbot effect in sampled fiber Bragg gratings with superperiodic structures,” Opt. Express 15, 8812-8815 (2007).
[CrossRef]

X.-H. Zou, W. Pan, B. Luo, W.-L. Zhang, and M.-Y. Wang, “Accurate analytical expression for reflection-peak wavelengths of sampled Bragg grating,” IEEE Photon. Technol. Lett. 18, 529-531 (2006).

X.-H. Zou, W. Pan, B. Luo, Z.-M. Qin, M.-Y. Wang, and W.-L. Zhang, “Periodically chirped sampled fiber Bragg gratings for multichannel comb filters,” IEEE Photon. Technol. Lett. 18, 1371-1373 (2006).

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. Technol. Lett. 14, 1309-1311 (2002).

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. Technol. Lett. 14, 1309-1311 (2002).

Wu, T.

X.-F. Chen, Y. Luo, C.-C. Fan, T. Wu, 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).

Xia, L.

M. Yan, M. Y. Yao, H. M. Zhang, L. Xia, and Y. Zhang, “En/Decoder for spectral phase-code OCDMA system based on amplitude sampled FBG,” IEEE Photon. Technol. Lett. 20, 788-790 (2008).

Xie, S.-Z.

Y.-T. Dai, X.-F. Chen, X.-M. Xu, C.-C. Fan, and S.-Z. Xie, “High channel-count comb filter based on chirped sampled fiber Bragg grating and phase shift,” IEEE Photon. Technol. Lett. 17, 1040-1042 (2005).

X.-F. Chen, Y. Luo, C.-C. Fan, T. Wu, 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).

X.-F. Chen, C.-C. Fan, Y. Luo, and S.-Z. Xie, “Novel flat multichannel filter based on strongly chirped sampled fiber Bragg grating,” IEEE Photon. Technol. Lett. 12, 1501-1503(2000).

Xu, X.-M.

Y.-T. Dai, X.-F. Chen, X.-M. Xu, C.-C. Fan, and S.-Z. Xie, “High channel-count comb filter based on chirped sampled fiber Bragg grating and phase shift,” IEEE Photon. Technol. Lett. 17, 1040-1042 (2005).

Yamashita, S.

Yan, M.

M. Yan, M. Y. Yao, H. M. Zhang, L. Xia, and Y. Zhang, “En/Decoder for spectral phase-code OCDMA system based on amplitude sampled FBG,” IEEE Photon. Technol. Lett. 20, 788-790 (2008).

Yao, M. Y.

M. Yan, M. Y. Yao, H. M. Zhang, L. Xia, and Y. Zhang, “En/Decoder for spectral phase-code OCDMA system based on amplitude sampled FBG,” IEEE Photon. Technol. Lett. 20, 788-790 (2008).

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Zhang, G. J.

Zhang, H. M.

M. Yan, M. Y. Yao, H. M. Zhang, L. Xia, and Y. Zhang, “En/Decoder for spectral phase-code OCDMA system based on amplitude sampled FBG,” IEEE Photon. Technol. Lett. 20, 788-790 (2008).

Zhang, R. K.

Zhang, W.-L.

X.-H. Zou, W. Pan, B. Luo, M.-Y. Wang, and W.-L. Zhang, “Spectral Talbot effect in sampled fiber Bragg gratings with superperiodic structures,” Opt. Express 15, 8812-8815 (2007).
[CrossRef]

X.-H. Zou, W. Pan, B. Luo, W.-L. Zhang, and M.-Y. Wang, “Accurate analytical expression for reflection-peak wavelengths of sampled Bragg grating,” IEEE Photon. Technol. Lett. 18, 529-531 (2006).

X.-H. Zou, W. Pan, B. Luo, Z.-M. Qin, M.-Y. Wang, and W.-L. Zhang, “Periodically chirped sampled fiber Bragg gratings for multichannel comb filters,” IEEE Photon. Technol. Lett. 18, 1371-1373 (2006).

Zhang, Y.

M. Yan, M. Y. Yao, H. M. Zhang, L. Xia, and Y. Zhang, “En/Decoder for spectral phase-code OCDMA system based on amplitude sampled FBG,” IEEE Photon. Technol. Lett. 20, 788-790 (2008).

Zhao, M. F.

Zhu, X. J.

Zou, X.-H.

X.-H. Zou, W. Pan, B. Luo, M.-Y. Wang, and W.-L. Zhang, “Spectral Talbot effect in sampled fiber Bragg gratings with superperiodic structures,” Opt. Express 15, 8812-8815 (2007).
[CrossRef]

X.-H. Zou, W. Pan, B. Luo, W.-L. Zhang, and M.-Y. Wang, “Accurate analytical expression for reflection-peak wavelengths of sampled Bragg grating,” IEEE Photon. Technol. Lett. 18, 529-531 (2006).

X.-H. Zou, W. Pan, B. Luo, Z.-M. Qin, M.-Y. Wang, and W.-L. Zhang, “Periodically chirped sampled fiber Bragg gratings for multichannel comb filters,” IEEE Photon. Technol. Lett. 18, 1371-1373 (2006).

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. Technol. Lett. 14, 1309-1311 (2002).

Appl. Opt. (3)

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[CrossRef]

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X.-H. Zou, W. Pan, B. Luo, W.-L. Zhang, and M.-Y. Wang, “Accurate analytical expression for reflection-peak wavelengths of sampled Bragg grating,” IEEE Photon. Technol. Lett. 18, 529-531 (2006).

X.-F. Chen, Y. Luo, C.-C. Fan, T. Wu, 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).

H. Lee and G. P. Agrawal, “Purely phase-sampled fiber Bragg gratings for broadband dispersion and dispersion slope compensation,” IEEE Photon. Technol. Lett. 15, 1091-1093(2003).

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. Technol. Lett. 5, 613-615 (1993).

M. Yan, M. Y. Yao, H. M. Zhang, L. Xia, and Y. Zhang, “En/Decoder for spectral phase-code OCDMA system based on amplitude sampled FBG,” IEEE Photon. Technol. Lett. 20, 788-790 (2008).

X.-H. Zou, W. Pan, B. Luo, Z.-M. Qin, M.-Y. Wang, and W.-L. Zhang, “Periodically chirped sampled fiber Bragg gratings for multichannel comb filters,” IEEE Photon. Technol. Lett. 18, 1371-1373 (2006).

J. L. Magné, J. Azaña, S. LaRochelle, and L. R. Chen, “Simple technique for eliminating the interchannel phase fluctuations in spectral Talbot-based periodic comb filters,” IEEE Photon. Technol. Lett. 18, 1958-1960 (2006).

Y.-T. Dai, X.-F. Chen, X.-M. Xu, C.-C. Fan, and S.-Z. Xie, “High channel-count comb filter based on chirped sampled fiber Bragg grating and phase shift,” IEEE Photon. Technol. Lett. 17, 1040-1042 (2005).

C.-H. Wang, J. Azaña, and L. R. Chen, “Efficient technique for increasing the channel density in multiwavelength sampled fiber Bragg grating filters,” IEEE Photon. Technol. Lett. 16, 1867-1869 (2004).

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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. Technol. Lett. 14, 1309-1311 (2002).

X.-F. Chen, C.-C. Fan, Y. Luo, and S.-Z. Xie, “Novel flat multichannel filter based on strongly chirped sampled fiber Bragg grating,” IEEE Photon. Technol. Lett. 12, 1501-1503(2000).

J. Lightwave Technol. (4)

Opt. Express (3)

Opt. Lett. (1)

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Figures (11)

Fig. 1
Fig. 1

Schematic diagram of a MPS technique based SFBG.

Fig. 2
Fig. 2

Schematic diagram of a new MPS based SFBG structure.

Fig. 3
Fig. 3

Comparison of RPWs between simulated reflective spectra using the piecewise-uniform (PU) method and our calculated results (dashed): (a)  p = 0.2 , m = 2 ; (b) details of enlarged comparison of RPWs in (a).

Fig. 4
Fig. 4

Comparison of RPWs between simulated reflective spectra using the piecewise-uniform (PU) method and our calculated results (dashed): (a)  p = 0.2 , m = 3 ; (b) details of enlarged comparison of RPWs in (a).

Fig. 5
Fig. 5

Reflective spectrum of Gaussian-apodized SFBG.

Fig. 6
Fig. 6

Calculated RPWs with different multiplication factors.

Fig. 7
Fig. 7

Channel-spacing comparison between our analytical calculation and the conventional simulation method with different multiplication factors.

Fig. 8
Fig. 8

Comparison of reflective spectra: (a) SFBG1 with the Bragg period Λ 1 = 521.4 nm and the duty cycle p 1 = 0.2 ; (b) SFBG2 with the Bragg period Λ 2 = 523.308 nm and the duty cycle p 2 = 0.2 ; (c) the new SFBG with the duty cycle p = 0.4 .

Fig. 9
Fig. 9

Reflective spectra of the new SFBG with different multiplication factors: (a)  m = 2 , (b)  m = 3 , (c)  m = 4 .

Fig. 10
Fig. 10

Details of enlarged RPW comparison for the new SFBG between simulated reflective spectra (solid line) and our calculated results (dashed) of Figs. 9a, 9b, 9c, respectively.

Fig. 11
Fig. 11

Reflective spectra of (a) uniform MPS based SFBG with Λ = 521.81 nm , (b) cascaded MPS-based SFBG with Λ 1 = 521.4 nm and Λ 2 = 522 . 262 nm , (c) cascaded MPS-based SFBG with Λ 1 = 521.4 nm and Λ 2 = 523 . 173 nm .

Tables (1)

Tables Icon

Table 1 Calculated RPWs for Different m and p = 0.2

Equations (10)

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ν ( z ) = { Δ n k = k = rect ( z k L p L a ) exp [ j β 0 z + j π m k ( k 1 ) ] } rect ( z L ) ,
F ( β ) = { 2 π m Δ n L a L p k = sinc [ k L a / m L p ] exp j [ π m ( k 1 2 ) 2 + π 4 ] × L sinc [ ( β 2 π Λ 1 ( k ) ) L / π ] ( m : odd ) 2 π m Δ n L a L p k = sinc [ k L a / m L p ] exp j [ π m k 2 + π 4 ] × L sinc [ ( β 2 π Λ 2 ( k ) ) L / π ] ( m : even ) ,
Λ ( k ) = { Λ 1 ( k ) = Λ m L p ( m L p k Λ ) ( m : odd ) Λ 2 ( k ) = Λ m L p [ m L p ( k + 0.5 ) Λ ] ( m : even ) .
δ n 1 ¯ = p Δ n .
Λ ( k ) = 2 n eff Λ ( k ) ( 1 + δ n 1 ¯ n eff ) ,
G ( z ) = exp [ 8 ( z L / 2 ) 2 L 2 ] .
Δ λ ( k ) = { Δ λ 1 ( k ) = 2 n eff ( 1 + δ n 1 ¯ n eff ) Λ 2 L p m ( L p k Λ / m ) [ L p ( k + 1 ) Λ / m ] ( m : odd ) Δ λ 2 ( k ) = 2 n eff ( 1 + δ n 1 ¯ n eff ) Λ 2 L p m [ L p ( k + 0.5 ) Λ / m ] [ L p ( k + 1.5 ) Λ / m ] ( m : even ) .
Δ λ = 2 n eff Λ 2 m L p .
N u δ λ Δ λ = 2 m L p L a .
N u < N c < N N u ,

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