Abstract

Due to the equivalence between an integral multiple of 2π and zero in the phase space, a general configuration of sampled fiber Bragg gratings (SFBGs) with super-periodic structures has been introduced and investigated. These super-periodic structures can be used to implement spectral Talbot effect with a large degree of freedom, as long as any one of the three parameters involved in quadratic phase profile is an even number. Then the phase profiles of such SFBGs are analyzed in detail. Although their phase increments are constant or non-constant periodic functions in different cases, theoretical analysis and simulations show that the obtained filtering characteristics are the same. In contrast to uniform SFBGs with identical sampling period, multiplied filtering channels and similar group-delay characteristic are achieved for these SFBGs with super-periodic structures.

© 2007 Optical Society of America

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  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]
  2. X. F. Chen, C. C. Fan, Y. Luo, S. Z. Xie, and S. Hu, "Novel flat multichannel filter based on strongly chirped sampled fiber Bragg grating," IEEE Photon. Technol. Lett. 12, 1501-1503 (2000).
    [CrossRef]
  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]
  4. C. 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]
  5. L. R. Chen and J. Azaña, "Spectral Talbot phenomena in sampled arbitrarily chirped Bragg gratings," Opt. Commun. 250, 302-308 (2005).
    [CrossRef]
  6. J. Azaña, C. Wang, and L. R. Chen, "Spectral self-imaging phenomena in sampled Bragg gratings," J. Opt. Soc. Am. B 22, 1829-1841 (2005).
    [CrossRef]
  7. Y. T. Dai, X. F. Chen, X. Xu, 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).
    [CrossRef]
  8. 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]
  9. 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]
  10. H. Li, Y. Sheng, Y. Li, and J. E. Rothenberg, "Phased-only sampled fiber Bragg gratings for high-channel-count chromatic dispersion compensation," J. Lightwave Technol. 21, 2074-2083 (2003).
    [CrossRef]
  11. 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]
  12. 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]
  13. J. Azaña and M. A. Muriel, "Temporal self-imaging effects: theory and application for multiplying pulse repetition rates," IEEE J. Sel. Top. Quantum Electron. 7, 728-744 (2001).
    [CrossRef]
  14. J. Azaña and S. Gupta, "Complete family of periodic Talbot filter for pulse repetition rate multiplication," Opt. Express 14, 4270-4279 (2006).
    [CrossRef] [PubMed]
  15. T. Erdogan, "Fiber grating spectra," J. Lightwave Technol. 15, 1277-1294 (1997).
    [CrossRef]

2006

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]

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

L. R. Chen and J. Azaña, "Spectral Talbot phenomena in sampled arbitrarily chirped Bragg gratings," Opt. Commun. 250, 302-308 (2005).
[CrossRef]

Y. T. Dai, X. F. Chen, X. Xu, 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).
[CrossRef]

2004

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]

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

2001

J. Azaña and M. A. Muriel, "Temporal self-imaging effects: theory and application for multiplying pulse repetition rates," IEEE J. Sel. Top. Quantum Electron. 7, 728-744 (2001).
[CrossRef]

2000

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

1998

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]

1997

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

1995

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]

Azaña, J.

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]

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]

Y. T. Dai, X. F. Chen, X. Xu, 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).
[CrossRef]

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

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]

Y. T. Dai, X. F. Chen, X. Xu, 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).
[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. 31, 899-901 (1995).
[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. 31, 899-901 (1995).
[CrossRef]

Erdogan, T.

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

Fan, C.

Y. T. Dai, X. F. Chen, X. Xu, 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).
[CrossRef]

Fan, C. C.

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

Gupta, S.

Hu, S.

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

Kolossovski, K. 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]

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]

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]

Li, H.

Li, 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]

Luo, Y.

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

Muriel, M. A.

J. Azaña and M. A. Muriel, "Temporal self-imaging effects: theory and application for multiplying pulse repetition rates," IEEE J. Sel. Top. Quantum Electron. 7, 728-744 (2001).
[CrossRef]

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, 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]

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.

Sheng, Y.

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]

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, J.

Wang, C.

Wang, M. Y.

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]

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]

Y. T. Dai, X. F. Chen, X. Xu, 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).
[CrossRef]

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

Xu, X.

Y. T. Dai, X. F. Chen, X. Xu, 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).
[CrossRef]

Yamashita, S.

Zhang, W. L.

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]

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]

Electron. Lett.

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]

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 J. Sel. Top. Quantum Electron.

J. Azaña and M. A. Muriel, "Temporal self-imaging effects: theory and application for multiplying pulse repetition rates," IEEE J. Sel. Top. Quantum Electron. 7, 728-744 (2001).
[CrossRef]

IEEE Photon. Technol. Lett.

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]

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

Y. T. Dai, X. F. Chen, X. Xu, 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).
[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.

L. R. Chen and J. Azaña, "Spectral Talbot phenomena in sampled arbitrarily chirped Bragg gratings," Opt. Commun. 250, 302-308 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

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Figures (4)

Fig. 1.
Fig. 1.

Phase profiles of (a) conventional chirped-SFBG, (b) proposed SFBG with and “θ(k) = 0, and (c) proposed SFBG with “θ(k) = mN k,2 ́ π; (d) chirp effect corresponding to phase profile (a).

Fig. 2.
Fig. 2.

Filtering characteristics of SFBGs with super-periodic structures (s =1, N k,2 ́ =1, m = 2)

Fig. 3.
Fig. 3.

Schematic diagram of (a) phase profile and (b) phase condition (phase increment) for SFBGs with super-periodic structures when s > 1.

Fig. 4.
Fig. 4.

Filtering characteristics of proposed SFBGs with different parameters: (a) s=2, N k,2 ́ =1, m =3, (b) s = 3, N k,2 ́ =1, m = 2.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

Δ n ( z ) = Δ n k = + u ( z kP ) Re { 1 + exp j [ β 0 z + θ ( z ) ] } ,
θ ( z ) = θ 2 z 2 2 + θ 3 z 3 6 + θ 4 z 4 24 + = r = 2 + θ r z r ( r ! ) ,
Δ θ ( k ) = θ [ z = ( k + m ) P ] θ ( z = kP ) = N k π ,
N k , r π = θ r r ! × m i = 0 r 1 k i ( k + m ) ( r 1 i ) , θ r = π ( r ! ) P r m × N k , r i = 0 r 1 k i ( k + m ) ( r 1 i ) = π ( r ! ) P r m × N k , r ,
θ ( z = tP ) = 2 ,
θ [ z = ( s × m ) P ] = ( s 2 m N k , 2 ) π = 2 .
Δ θ ( k ) = N k , 2 ( 2 k + m ) π .

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