Abstract

The reflection-peak wavelengths (RPWs) in the spectra of sampled fiber Bragg gratings with large chirp (SFBGs-LC) are theoretically investigated. Such RPWs are divided into two parts, the RPWs of equivalent uniform SFBGs (U-SFBGs) and the wavelength shift caused by the large chirp in the grating period (CGP). We propose a quasi-equivalent transform to deal with the CGP. That is, the CGP is transferred into quasi-equivalent phase shifts to directly derive the Fourier transform of the refractive index modulation. Then, in the case of both the direct and the inverse Talbot effect, the wavelength shift is obtained from the Fourier transform. Finally, the RPWs of SFBGs-LC can be achieved by combining the wavelength shift and the RPWs of equivalent U-SFBGs. Several simulations are shown to numerically confirm these predicted RPWs of SFBGs-LC.

© 2008 Optical Society of America

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References

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  1. F. Ouellette, P. A. Krug, T. Stephens, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fiber Bragg gratings,” Electron. Lett. 31, 899-901(1995).
    [CrossRef]
  2. 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).
    [CrossRef]
  3. W. H. Loh, F. Q. Zhou, and J. J. Pan, “Sampled fiber grating based dispersion slope compensator,” IEEE Photon. Technol. Lett. 11, 1280-1282 (1999).
    [CrossRef]
  4. H. Lee and G. P. Agrawal, “Bandwidth equalization of purely phase-sampled fiber Bragg gratings for broadband dispersion and dispersion slope compensation,” Opt. Express 12, 5595-5602 (2004).
    [CrossRef] [PubMed]
  5. Y. Nasu and S. Yamashita, “Densification of sampled fiber Bragg gratings using multiple phase shift (MPS) technique,” J. Lightwave Technol. 231808-1817 (2005).
    [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]
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    [CrossRef]
  10. C. 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).
    [CrossRef]
  11. J. Azaña, C. Wang, and L. R. Chen, “Spectral self-imaging phenomena in sampled Bragg gratings,” J. Opt. Soc. Am. B 221829-1841 (2005).
    [CrossRef]
  12. 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 filter,” IEEE Photon. Technol. Lett. 18, 1371-1373 (2006).
    [CrossRef]
  13. Y. T. Dai, X. F. Chen, J. Sun, and S. Z. Xie, “Wideband multichannel dispersion compensation based on a strongly chirped sampled Bragg grating and phase shifts,” Opt. Lett. 31, 311-313 (2006).
    [CrossRef] [PubMed]
  14. 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]
  15. 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]
  16. 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).
    [CrossRef]
  17. X. Zhu, Y. Lu, G. Zhang, C. Wang, M. Zhao, “Analytical determination of reflection-peak wavelengths of chirped sampled fiber Bragg gratings,” Appl. Opt. 47, 1135-1140 (2008).
    [CrossRef] [PubMed]
  18. S. Yamashita and M. Yokooji, “Channel spacing-tunable sampled fiber Bragg grating by linear chirp and its application to multiwavelength fiber laser,” Opt. Commun. 263, 42-46(2006).
    [CrossRef]
  19. 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, 393-395 (1993).
    [CrossRef]
  20. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277-1294 (1997).
    [CrossRef]

2008

2007

2006

S. Yamashita and M. Yokooji, “Channel spacing-tunable sampled fiber Bragg grating by linear chirp and its application to multiwavelength fiber laser,” Opt. Commun. 263, 42-46(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 filter,” IEEE Photon. Technol. Lett. 18, 1371-1373 (2006).
[CrossRef]

Y. T. Dai, X. F. Chen, J. Sun, and S. Z. Xie, “Wideband multichannel dispersion compensation based on a strongly chirped sampled Bragg grating and phase shifts,” Opt. Lett. 31, 311-313 (2006).
[CrossRef] [PubMed]

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).
[CrossRef]

2005

J. Azaña, C. Wang, and L. R. Chen, “Spectral self-imaging phenomena in sampled Bragg gratings,” J. Opt. Soc. Am. B 221829-1841 (2005).
[CrossRef]

Y. Nasu and S. Yamashita, “Densification of sampled fiber Bragg gratings using multiple phase shift (MPS) technique,” J. Lightwave Technol. 231808-1817 (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]

2004

H. Lee and G. P. Agrawal, “Bandwidth equalization of purely phase-sampled fiber Bragg gratings for broadband dispersion and dispersion slope compensation,” Opt. Express 12, 5595-5602 (2004).
[CrossRef] [PubMed]

C. 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).
[CrossRef]

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]

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]

2002

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).
[CrossRef]

1999

W. H. Loh, F. Q. Zhou, and J. J. Pan, “Sampled fiber grating based dispersion slope compensator,” IEEE Photon. Technol. Lett. 11, 1280-1282 (1999).
[CrossRef]

1998

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).
[CrossRef]

1997

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

1995

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

1993

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, 393-395 (1993).
[CrossRef]

Agrawal, G. P.

Azaña, J.

J. Azaña, C. Wang, and L. R. Chen, “Spectral self-imaging phenomena in sampled Bragg gratings,” J. Opt. Soc. Am. B 221829-1841 (2005).
[CrossRef]

C. 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).
[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, 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, L. R.

Chen, X. F.

Y. T. Dai, X. F. Chen, J. Sun, and S. Z. Xie, “Wideband multichannel dispersion compensation based on a strongly chirped sampled Bragg grating and phase shifts,” Opt. Lett. 31, 311-313 (2006).
[CrossRef] [PubMed]

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).
[CrossRef]

Chu, P. L.

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, R. I. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10, 842-844(1998).
[CrossRef]

Dai, Y. T.

Durkin, M. K.

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).
[CrossRef]

Eggleton, B.

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

Erdogan, T.

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

Fan, C. C.

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).
[CrossRef]

Ibsen, M.

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).
[CrossRef]

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, 393-395 (1993).
[CrossRef]

Kolossovski, K. 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]

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, 393-395 (1993).
[CrossRef]

Krug, P. A.

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

Laming, R. I.

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).
[CrossRef]

Lee, H.

Li, H.

Li, M.

Loh, W. H.

W. H. Loh, F. Q. Zhou, and J. J. Pan, “Sampled fiber grating based dispersion slope compensator,” IEEE Photon. Technol. Lett. 11, 1280-1282 (1999).
[CrossRef]

Lu, Y.

Luo, B.

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 filter,” IEEE Photon. Technol. Lett. 18, 1371-1373 (2006).
[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).
[CrossRef]

Luo, Y.

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).
[CrossRef]

Nasu, Y.

Ouellette, F.

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

Pan, J. J.

W. H. Loh, F. Q. Zhou, and J. J. Pan, “Sampled fiber grating based dispersion slope compensator,” IEEE Photon. Technol. Lett. 11, 1280-1282 (1999).
[CrossRef]

Pan, W.

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 filter,” IEEE Photon. Technol. Lett. 18, 1371-1373 (2006).
[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).
[CrossRef]

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 filter,” IEEE Photon. Technol. Lett. 18, 1371-1373 (2006).
[CrossRef]

Rothenberg, J. E.

Sammut, R. A.

Sheng, Y.

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 multi-channel fiber Bragg gratings,” Opt. Express 11, 1029-1038 (2003).
[CrossRef] [PubMed]

Stephens, T.

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

Sun, J.

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, 393-395 (1993).
[CrossRef]

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, 393-395 (1993).
[CrossRef]

Wang, C.

Wang, C. H.

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, M. Y.

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).
[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 filter,” IEEE Photon. Technol. Lett. 18, 1371-1373 (2006).
[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, 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, 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).
[CrossRef]

Xie, S. Z.

Y. T. Dai, X. F. Chen, J. Sun, and S. Z. Xie, “Wideband multichannel dispersion compensation based on a strongly chirped sampled Bragg grating and phase shifts,” Opt. Lett. 31, 311-313 (2006).
[CrossRef] [PubMed]

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).
[CrossRef]

Yamashita, S.

S. Yamashita and M. Yokooji, “Channel spacing-tunable sampled fiber Bragg grating by linear chirp and its application to multiwavelength fiber laser,” Opt. Commun. 263, 42-46(2006).
[CrossRef]

Y. Nasu and S. Yamashita, “Densification of sampled fiber Bragg gratings using multiple phase shift (MPS) technique,” J. Lightwave Technol. 231808-1817 (2005).
[CrossRef]

Yokooji, M.

S. Yamashita and M. Yokooji, “Channel spacing-tunable sampled fiber Bragg grating by linear chirp and its application to multiwavelength fiber laser,” Opt. Commun. 263, 42-46(2006).
[CrossRef]

Yoshikuni, 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, 393-395 (1993).
[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]

Zhang, G.

Zhang, W. L.

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).
[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 filter,” IEEE Photon. Technol. Lett. 18, 1371-1373 (2006).
[CrossRef]

Zhao, M.

Zhou, F. Q.

W. H. Loh, F. Q. Zhou, and J. J. Pan, “Sampled fiber grating based dispersion slope compensator,” IEEE Photon. Technol. Lett. 11, 1280-1282 (1999).
[CrossRef]

Zhu, X.

Zou, X. H.

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 filter,” IEEE Photon. Technol. Lett. 18, 1371-1373 (2006).
[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).
[CrossRef]

Appl. Opt.

Electron. Lett.

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

IEEE J. Quantum Electron.

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]

IEEE Photon. Technol. Lett.

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).
[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, 393-395 (1993).
[CrossRef]

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).
[CrossRef]

W. H. Loh, F. Q. Zhou, and J. J. Pan, “Sampled fiber grating based dispersion slope compensator,” IEEE Photon. Technol. Lett. 11, 1280-1282 (1999).
[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]

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).
[CrossRef]

C. 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).
[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 filter,” IEEE Photon. Technol. Lett. 18, 1371-1373 (2006).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Opt. Commun.

S. Yamashita and M. Yokooji, “Channel spacing-tunable sampled fiber Bragg grating by linear chirp and its application to multiwavelength fiber laser,” Opt. Commun. 263, 42-46(2006).
[CrossRef]

Opt. Express

Opt. Lett.

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Figures (4)

Fig. 1
Fig. 1

Schematic of (a) equivalent transform from MPS to CGP [18] and (b) quasi-equivalent transform from CGP to MPS. Solid curves, variation of real parameters; and dotted curves, variation of equivalent (or quasi-equivalent) parameters.

Fig. 2
Fig. 2

RPWs of C-SFBGs with integer Talbot effect: (a) equivalent U-SFBG; (b)  m = 1 , s = 1 ; (c)  m = 1 , s = 2 .

Fig. 3
Fig. 3

RPWs of C-SFBGs with fractional Talbot effect: (a) equivalent U-SFBG; (b)  m = 2 , s = 1 .

Fig. 4
Fig. 4

RPWs of C-SFBGs with fractional Talbot effect: (a) equivalent U-SFBG; (b)  m = 3 , s = 1 ; (c)  m = 3 , s = 2 .

Tables (2)

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Table 1 Detailed Equivalent (or Quasi-Equivalent) Parameters for Mutual Transformation between Linear CGP and MPS

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Table 2 Comparison between Calculated and Simulated RPWs

Equations (10)

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Δ n ( z ) = Δ n k = + u ( z k P ) + Δ n k = + u ( z k P ) exp j [ β 0 z + θ ( z ) ] ,
θ ( z ) C π Λ 0 2 z 2 ,
C = s Λ 0 2 / m P 2 ,
θ ( z ) s π m P 2 z 2 .
θ k s π m k 2 .
φ k = s π m ( 2 k 1 ) ,
Δ N ( β ) = Δ n U ( β β 0 ) × k = + exp j [ ( β β 0 ) P + s π m k ] k ,
Δ N ( β ) = Δ n U ( β β 0 ) k = 1 2 m M = + exp j [ ( β β 0 ) P + s π m ( 2 m M + k ) ] ( 2 m M + k ) = Δ n π m P U ( β β 0 ) k = 1 2 m exp j [ ( β β 0 ) P + s π m k ] k M = + δ ( β β 0 + π m P M ) = Δ n π m P U ( β β 0 ) M = + Q ( s , m , M ) δ ( β β 0 + π m P M ) ,
Q ( s , m , M ) = k = 1 2 m exp j [ π m ( M + s k ) k ] = { 1 + exp j [ π ( M + s m ) ] } k = 1 m exp j [ π m ( M + s k ) k ] = { 0 M + s m is odd 2 k = 1 m exp j [ π m ( M + s k ) k ] M + s m is even ,
Δ N ( β ) = { 2 Δ n π m P U ( β β 0 ) M = + { k = 1 m exp j [ π m ( 2 M + s k ) k ] } δ ( β β 0 + 2 π m P M ) s m is even 2 Δ n π m P U ( β β 0 ) M = + { k = 1 m exp j [ π m ( 2 M + 1 + s k ) k ] } δ ( β β 0 + 2 π m P M + π m P ) s m is odd .

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