Abstract

A novel method of generating broadband high-count-channel optical filters in phase-only sampled fiber Bragg grating based on spectral Talbot effect is presented. Integer and/or fractional Talbot effects are examined using both Dammann and multi-level discrete phase-only sampling function. It is found that very high-count channels in a wide spectral band that covers the whole C band can be obtained with very limited number of discrete phase transitions in each sampling period. It provides a novel method for making high-channel-count FBG filters that is otherwise difficult or impossible using conventional discrete phase-only sampled FBGs.

© 2008 Optical Society of America

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  1. B. Eggleton, P. A. Krug, L. Poladian, and F. Oullette, "Long periodic superstructure Bragg gratings in optical fibres," Electron. Lett. 30, 1620-1622 (1994).
    [CrossRef]
  2. 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).
    [CrossRef]
  3. 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] [PubMed]
  4. 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]
  5. 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. 11, 899-901 (1995).
    [CrossRef]
  6. 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]
  7. 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).
    [CrossRef]
  8. H. Lee and G. P. Agrawal, "Purely phase-sampled fiber Bragg gratings for broad-band dispersion and dispersion slope compensation," IEEE Photon. Technol. Lett. 15, 1091-1093 (2003).
    [CrossRef]
  9. I. Navruz and N. Fatma Guler, "Optimization of reflection spectra for phase-only sampled fiber Bragg gratings," Opt. Commun. 271, 119-123 (2007).
    [CrossRef]
  10. C. H. Wang, J. Azaña, and L. R. Chen, "Spectral Talbot-like phenomena in one-dimensional photonic bandgap structures," Opt. Lett. 29, 1590-1592 (2004).
    [CrossRef] [PubMed]
  11. J. Azaña, C. H. Wang, and L. R. Chen, "Spectral self-imaging phenomena in sampled Bragg gratings," J. Opt. Soc. Am. B 22, 1829-1841 (2005).
  12. 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).
    [CrossRef]
  13. Y. Dai, X. Chen, X. Xu, C. Fan, and S. Xie, "High channel-count comb filter based on chirped sampled fiber Bragg grating and phase shift," IEEE Photon. Technol. Lett. 17, 1040-1042 (2005).
    [CrossRef]
  14. J. Magné, P. Giaccari, S. LaRochelle, J. Azaña, and L. R. Chen, "All-fiber comb filter with tunable free spectral range," Opt. Lett. 12, 2062-2064 (2005).
    [CrossRef]
  15. C. Martijn de Sterke and Benjamin J. Eggleton, "Spectral Talbot effect: interpretation via band diagrams," Opt. Commun. 248, 117-121 (2005).
    [CrossRef]
  16. H. Li, Y. Sheng, Y. Li, and J. E. Rothenberg, "Phase-only sampled fiber Bragg gratings for high-channel-count chromatic dispersion compensation," J. Lightwave Technol. 21, 2074-2083 (2003).
    [CrossRef]
  17. J. E. Rothenberg, H. Li, Y. Sheng, J. Popelek, and J. Zweiback, "Phase-only sampled 45 channel fiber Bragg grating written with a diffraction-compensated phase mask," Opt. Lett. 31, 1199-1201 (2006).
    [CrossRef] [PubMed]
  18. H. Li, M. Li, K. Ogusu, and Y. Sheng, and J. Rothenberg, "Optimization of a continuous phase-only sampling for high channel-count fiber Bragg gratings," Opt. Express 14, 3152-3160 (2006).
    [CrossRef] [PubMed]
  19. Y. Sheng, J. E. Rothenberg, H. Li, Y. Wang, and J. Zweiback, "Split of phase-shifts in phase mask for fiber Bragg grating," IEEE Photon. Technol. Lett. 16, 1316-1318 (2004).
    [CrossRef]
  20. P. Dong, J. Azaña, and A. G. Kirk, "Synthesis of fiber Bragg grating parameters from reflectivity by means of a simulated annealing algorithm," Opt. Commun. 228, 303-308 (2003).
    [CrossRef]
  21. R. Kashyap, Fiber Bragg Grating (Academic, San Diego, 1999).
  22. S. J. Walker and J. Jahns, "Array generation with multilevel phase gratings," J. Opt. Soc. Am. A 7, 1509-1513 (1990).
    [CrossRef]

2007 (1)

I. Navruz and N. Fatma Guler, "Optimization of reflection spectra for phase-only sampled fiber Bragg gratings," Opt. Commun. 271, 119-123 (2007).
[CrossRef]

2006 (2)

2005 (4)

J. Azaña, C. H. Wang, and L. R. Chen, "Spectral self-imaging phenomena in sampled Bragg gratings," J. Opt. Soc. Am. B 22, 1829-1841 (2005).

Y. Dai, X. Chen, X. Xu, C. Fan, and S. Xie, "High channel-count comb filter based on chirped sampled fiber Bragg grating and phase shift," IEEE Photon. Technol. Lett. 17, 1040-1042 (2005).
[CrossRef]

J. Magné, P. Giaccari, S. LaRochelle, J. Azaña, and L. R. Chen, "All-fiber comb filter with tunable free spectral range," Opt. Lett. 12, 2062-2064 (2005).
[CrossRef]

C. Martijn de Sterke and Benjamin J. Eggleton, "Spectral Talbot effect: interpretation via band diagrams," Opt. Commun. 248, 117-121 (2005).
[CrossRef]

C. Martijn de Sterke and Benjamin J. Eggleton, "Spectral Talbot effect: interpretation via band diagrams," Opt. Commun. 248, 117-121 (2005).
[CrossRef]

2004 (3)

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).
[CrossRef]

Y. Sheng, J. E. Rothenberg, H. Li, Y. Wang, and J. Zweiback, "Split of phase-shifts in phase mask for fiber Bragg grating," IEEE Photon. Technol. Lett. 16, 1316-1318 (2004).
[CrossRef]

C. H. Wang, J. Azaña, and L. R. Chen, "Spectral Talbot-like phenomena in one-dimensional photonic bandgap structures," Opt. Lett. 29, 1590-1592 (2004).
[CrossRef] [PubMed]

2003 (3)

P. Dong, J. Azaña, and A. G. Kirk, "Synthesis of fiber Bragg grating parameters from reflectivity by means of a simulated annealing algorithm," Opt. Commun. 228, 303-308 (2003).
[CrossRef]

H. Li, Y. Sheng, Y. Li, and J. E. Rothenberg, "Phase-only sampled fiber Bragg gratings for high-channel-count chromatic dispersion compensation," J. Lightwave Technol. 21, 2074-2083 (2003).
[CrossRef]

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

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] [PubMed]

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).
[CrossRef]

2000 (1)

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 (1)

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 (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).
[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. 11, 899-901 (1995).
[CrossRef]

1994 (1)

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

1990 (1)

Agrawal, G. P.

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

Azaña, J.

J. Azaña, C. H. Wang, and L. R. Chen, "Spectral self-imaging phenomena in sampled Bragg gratings," J. Opt. Soc. Am. B 22, 1829-1841 (2005).

J. Magné, P. Giaccari, S. LaRochelle, J. Azaña, and L. R. Chen, "All-fiber comb filter with tunable free spectral range," Opt. Lett. 12, 2062-2064 (2005).
[CrossRef]

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).
[CrossRef]

C. H. Wang, J. Azaña, and L. R. Chen, "Spectral Talbot-like phenomena in one-dimensional photonic bandgap structures," Opt. Lett. 29, 1590-1592 (2004).
[CrossRef] [PubMed]

P. Dong, J. Azaña, and A. G. Kirk, "Synthesis of fiber Bragg grating parameters from reflectivity by means of a simulated annealing algorithm," Opt. Commun. 228, 303-308 (2003).
[CrossRef]

Benjamin, C.

C. Martijn de Sterke and Benjamin J. Eggleton, "Spectral Talbot effect: interpretation via band diagrams," Opt. Commun. 248, 117-121 (2005).
[CrossRef]

Chen, L. R.

J. Azaña, C. H. Wang, and L. R. Chen, "Spectral self-imaging phenomena in sampled Bragg gratings," J. Opt. Soc. Am. B 22, 1829-1841 (2005).

J. Magné, P. Giaccari, S. LaRochelle, J. Azaña, and L. R. Chen, "All-fiber comb filter with tunable free spectral range," Opt. Lett. 12, 2062-2064 (2005).
[CrossRef]

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).
[CrossRef]

C. H. Wang, J. Azaña, and L. R. Chen, "Spectral Talbot-like phenomena in one-dimensional photonic bandgap structures," Opt. Lett. 29, 1590-1592 (2004).
[CrossRef] [PubMed]

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] [PubMed]

Chen, X.

Y. Dai, X. Chen, X. Xu, C. Fan, and S. Xie, "High channel-count comb filter based on chirped sampled fiber Bragg grating and phase shift," IEEE Photon. Technol. Lett. 17, 1040-1042 (2005).
[CrossRef]

Chen, X.-F.

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]

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).
[CrossRef]

Dai, Y.

Y. Dai, X. Chen, X. Xu, C. Fan, and S. Xie, "High channel-count comb filter based on chirped sampled fiber Bragg grating and phase shift," IEEE Photon. Technol. Lett. 17, 1040-1042 (2005).
[CrossRef]

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. 11, 899-901 (1995).
[CrossRef]

Dong, P.

P. Dong, J. Azaña, and A. G. Kirk, "Synthesis of fiber Bragg grating parameters from reflectivity by means of a simulated annealing algorithm," Opt. Commun. 228, 303-308 (2003).
[CrossRef]

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).
[CrossRef]

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. 11, 899-901 (1995).
[CrossRef]

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

Fan, C.

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

Fatma Guler, N.

I. Navruz and N. Fatma Guler, "Optimization of reflection spectra for phase-only sampled fiber Bragg gratings," Opt. Commun. 271, 119-123 (2007).
[CrossRef]

Giaccari, P.

J. Magné, P. Giaccari, S. LaRochelle, J. Azaña, and L. R. Chen, "All-fiber comb filter with tunable free spectral range," Opt. Lett. 12, 2062-2064 (2005).
[CrossRef]

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).
[CrossRef]

Jahns, J.

Kirk, A. G.

P. Dong, J. Azaña, and A. G. Kirk, "Synthesis of fiber Bragg grating parameters from reflectivity by means of a simulated annealing algorithm," Opt. Commun. 228, 303-308 (2003).
[CrossRef]

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. 11, 899-901 (1995).
[CrossRef]

B. Eggleton, P. A. Krug, L. Poladian, and F. Oullette, "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).
[CrossRef]

LaRochelle, S.

J. Magné, P. Giaccari, S. LaRochelle, J. Azaña, and L. R. Chen, "All-fiber comb filter with tunable free spectral range," Opt. Lett. 12, 2062-2064 (2005).
[CrossRef]

Lee, H.

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

Li, H.

Li, M.

Li, Y.

H. Li, Y. Sheng, Y. Li, and J. E. Rothenberg, "Phase-only sampled fiber Bragg gratings for high-channel-count chromatic dispersion compensation," J. Lightwave Technol. 21, 2074-2083 (2003).
[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).
[CrossRef]

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]

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]

Magné, J.

J. Magné, P. Giaccari, S. LaRochelle, J. Azaña, and L. R. Chen, "All-fiber comb filter with tunable free spectral range," Opt. Lett. 12, 2062-2064 (2005).
[CrossRef]

Martijn de Sterke, C.

C. Martijn de Sterke and Benjamin J. Eggleton, "Spectral Talbot effect: interpretation via band diagrams," Opt. Commun. 248, 117-121 (2005).
[CrossRef]

Navruz, I.

I. Navruz and N. Fatma Guler, "Optimization of reflection spectra for phase-only sampled fiber Bragg gratings," Opt. Commun. 271, 119-123 (2007).
[CrossRef]

Ogusu, K.

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. 11, 899-901 (1995).
[CrossRef]

Oullette, F.

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

Poladian, L.

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

Popelek, J.

J. E. Rothenberg, H. Li, Y. Sheng, J. Popelek, and J. Zweiback, "Phase-only sampled 45 channel fiber Bragg grating written with a diffraction-compensated phase mask," Opt. Lett. 31, 1199-1201 (2006).
[CrossRef] [PubMed]

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).
[CrossRef]

Rothenberg, J.

Rothenberg, J. E.

J. E. Rothenberg, H. Li, Y. Sheng, J. Popelek, and J. Zweiback, "Phase-only sampled 45 channel fiber Bragg grating written with a diffraction-compensated phase mask," Opt. Lett. 31, 1199-1201 (2006).
[CrossRef] [PubMed]

Y. Sheng, J. E. Rothenberg, H. Li, Y. Wang, and J. Zweiback, "Split of phase-shifts in phase mask for fiber Bragg grating," IEEE Photon. Technol. Lett. 16, 1316-1318 (2004).
[CrossRef]

H. Li, Y. Sheng, Y. Li, and J. E. Rothenberg, "Phase-only sampled fiber Bragg gratings for high-channel-count chromatic dispersion compensation," J. Lightwave Technol. 21, 2074-2083 (2003).
[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).
[CrossRef]

Sheng, Y.

Smith, P. W. E.

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. 11, 899-901 (1995).
[CrossRef]

Walker, S. J.

Wang, C. H.

Wang, Y.

Y. Sheng, J. E. Rothenberg, H. Li, Y. Wang, and J. Zweiback, "Split of phase-shifts in phase mask for fiber Bragg grating," IEEE Photon. Technol. Lett. 16, 1316-1318 (2004).
[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).
[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. Technol. Lett. 14, 1309-1311(2002).
[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.

Y. Dai, X. Chen, X. Xu, C. Fan, and S. Xie, "High channel-count comb filter based on chirped sampled fiber Bragg grating and phase shift," IEEE Photon. Technol. Lett. 17, 1040-1042 (2005).
[CrossRef]

Xie, S.-Z.

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]

Xu, X.

Y. Dai, X. Chen, X. Xu, C. Fan, and S. Xie, "High channel-count comb filter based on chirped sampled fiber Bragg grating and phase shift," IEEE Photon. Technol. Lett. 17, 1040-1042 (2005).
[CrossRef]

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]

Zweiback, J.

J. E. Rothenberg, H. Li, Y. Sheng, J. Popelek, and J. Zweiback, "Phase-only sampled 45 channel fiber Bragg grating written with a diffraction-compensated phase mask," Opt. Lett. 31, 1199-1201 (2006).
[CrossRef] [PubMed]

Y. Sheng, J. E. Rothenberg, H. Li, Y. Wang, and J. Zweiback, "Split of phase-shifts in phase mask for fiber Bragg grating," IEEE Photon. Technol. Lett. 16, 1316-1318 (2004).
[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).
[CrossRef]

Appl. Opt. (1)

Electron. Lett. (2)

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Opt. Express (1)

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Figures (6)

Fig. 1.
Fig. 1.

(a). Distribution of the phase transition at different positions with binary phase values (0 or π) of a Dammann PSFBG; (b). Distribution of the phase transition with optimized values at equally distributed positions (0.1mm) of a multi-level PSFBG.

Fig. 2.
Fig. 2.

Talbot effect observed in a Dammann binary PSFBG with different Talbot conditions. Figures 2(a), 2(b), 2(c) and (2d) show the spectral reflectivity and Figs. 2(e), 2(f), 2(g), 2(h) show the corresponding group delay of Figs. 2(a), 2(b), 2(c) and 2(d), respectively, in which two or three channels are zoomed with dashed lines for clarity purpose. (a) s=0, m=1(c g =0, i.e., uniform PSFBG); (b) s=1, m=1 (c g =5.2188×10-4 1/mm); (c) s=1, m=2 (c g =2.6094×10-4 1/mm); and (d) s=2, m=3 (c g =3.4792×10-4 1/mm).

Fig. 3.
Fig. 3.

Talbot effect observed in a multi-level PSFBG with different Talbot conditions. Figures 3(a), 3(b), 3(c) and 3(d) show the spectral reflectivity and Figs. 3(e), 3(f), 3(g), 3(h) show the corresponding group delay of Figs. 3(a), 3(b), 3(c), 3(d) respectively, in which two channels are zoomed with dashed lines for clarity purpose. (a) s=0, m=1(cg=0, i.e., uniform PSFBG); (b) s=1, m=1 (c g =5.2188×10-4 1/mm); (c) s=1, m=2 (c g =2.6094×10-4 1/mm); and (d) s=2, m=3 (c g =3.4792×10-4 1/mm).

Fig. 4.
Fig. 4.

The detailed comparison spectrum with and without Talbot effect for both Dammann and multi-level type of PSFBGs. In the plots, the channel spacing(FSR) is all ~0.4nm, P is the sampling period, T is the total number of sampling period, s and m decide the chirp coefficient c g , i.e., different Talbot conditions. (a) and (b): The total grating length is 8mm with (a) No Talbot effect, and (b) Talbot condition at s=1, m=2(c) and (d): The total grating length is 4mm with (c) no Talbot effect, and (d) Talbot condition at s=1, m=2; (e) and (f): The phase distribution of the Dammann and multi-level PSFBGs.

Fig. 5.
Fig. 5.

High-count-channel generation using PSFBG based on the fractional Talbot effect. (a): no Talbot effect; (b) fractional Talbot effect, s=1, m=2, and the number of multi-levels is six, total 44 channels; (c) fractional Talbot effect, s=1, m=2, and the number of multi-levels is ten, total 80 channels; (d), (e) and (f) are the phase distribution of the multi-lever PSFBGs corresponding to (a), (b) and (c).

Fig. 6.
Fig. 6.

The amplitude of reflection coefficient from a sequence of decomposed individual gratings (the first three, the 15th, and 60th shown in the graph with chirp coefficient s=1, m=2) of a PSFBG. The grating parameters are the same as those given in the Fig. 2.

Equations (13)

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Δ n 0 ( z ) = Δ n D C ( z ) + Δ n 0 G ( z ) s ( z ) Re ( exp { i [ 2 π z Λ ( z ) + ϕ 0 ] } )
s ( z ) = s p ( z ) * Σ n = + δ ( z n P )
Δ λ = λ B 2 ( 2 n 0 P )
s p ( z ) = Σ m = 0 K exp ( i θ m ) rect [ z ( z m + 1 z m ) 2 ( z m + 1 z m ) ]
S n = ( 1 2 i n π ) Σ m = 0 K ( 1 ) m [ exp ( 2 i π n z m + 1 ) exp ( 2 i π n z m ) ] , for n 0
S 0 = Σ m = 0 K ( 1 ) m ( z m + 1 z m ) , for n = 0
S n = ( 1 2 i n π ) Σ m = 0 K ( 2 i π n m P K ) [ exp ( i θ m + 1 ) exp ( 2 i θ m ) ] , for n 0
S 0 = ( P K ) Σ m = 0 K exp ( i θ m ) , for n = 0
κ n = S n π Δ n 0 λ B
r n = tanh 2 ( κ n L )
C = 1 M [ Σ n = N N W n 1 ( r 0 r n 2 ) + Σ n = ( N + 1 ) W n 2 ( r 1 r n 2 ) + Σ n = N + 1 + W n 2 ( r 1 r n 2 )
Λ ( z ) = Λ 0 ( 1 + c g z ) ( L 2 < z < L 2 )
c g = s m ( Λ 0 P 2 )

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