Abstract

A novel technique to implement a Bragg grating with multi-channel and high channel-count response based on nonuniform amplitude-only sampling is proposed. Thanks to the nonuniform sampling, a sophisticated phase modulation for the generation of multi-channel spectral response can be equivalently achieved, while the pitch of the Bragg grating is maintained uniform. The principle is presented. Two design examples with two Bragg gratings for multi-channel filtering and for multi-channel chromatic dispersion compensation are provided.

© 2008 Optical Society of America

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  1. H. Li, M. Li, Y. Sheng, and J. E. Rothenberg, "Advances in the design and fabrication of high-channel-count fiber Bragg gratings," J. Lightw. Technol. 25, 2739-2750 (2007).
    [CrossRef]
  2. Y. Painchaud, H. Chotard, A. Mailloux, and Y. Vasseur, "Superposition of chirped fiber Bragg grating for third-order dispersion compensation over 32 WDM channels," Electron. Lett. 38, 1572-1573 (2002).
    [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. K. Kolossovski, R. Sammut, A. Buryak, and D. Stepanov, "Three-step design optimization for multi-channel fibre Bragg gratings," Opt. Express 11, 1029-1038 (2003).
    [CrossRef] [PubMed]
  5. Q. Wu, C. Yu, K. Wang, X. Wang, Z. Pu, 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]
  6. Q. Wu, P. L. Chu, and H. P. Chan, "General design approach to multichannel fiber Bragg grating," J. Lightwave Technol. 24, 1571-1580 (2006).
    [CrossRef]
  7. 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]
  8. L. Xia, X. Li, X. Chen, and S. Xie, "A novel dispersion compensating fiber grating with a large chirp parameter and period sampled distribution," Opt. Commun. 227, 311-315 (2003).
    [CrossRef]
  9. 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]
  10. 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]
  11. 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] [PubMed]

2007

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

2006

Q. Wu, P. L. Chu, and H. P. Chan, "General design approach to multichannel fiber Bragg grating," J. Lightwave Technol. 24, 1571-1580 (2006).
[CrossRef]

2005

Q. Wu, C. Yu, K. Wang, X. Wang, Z. Pu, 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]

2003

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] [PubMed]

L. Xia, X. Li, X. Chen, and S. Xie, "A novel dispersion compensating fiber grating with a large chirp parameter and period sampled distribution," Opt. Commun. 227, 311-315 (2003).
[CrossRef]

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. Kolossovski, R. Sammut, A. Buryak, and D. Stepanov, "Three-step design optimization for multi-channel fibre Bragg gratings," Opt. Express 11, 1029-1038 (2003).
[CrossRef] [PubMed]

2002

Y. Painchaud, H. Chotard, A. Mailloux, and Y. Vasseur, "Superposition of chirped fiber Bragg grating for third-order dispersion compensation over 32 WDM channels," Electron. Lett. 38, 1572-1573 (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).
[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]

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] [PubMed]

Buryak, A.

K. Kolossovski, R. Sammut, A. Buryak, and D. Stepanov, "Three-step design optimization for multi-channel fibre Bragg gratings," Opt. Express 11, 1029-1038 (2003).
[CrossRef] [PubMed]

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]

Chan, H. P.

Q. Wu, P. L. Chu, and H. P. Chan, "General design approach to multichannel fiber Bragg grating," J. Lightwave Technol. 24, 1571-1580 (2006).
[CrossRef]

Q. Wu, C. Yu, K. Wang, X. Wang, Z. Pu, 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, X.

L. Xia, X. Li, X. Chen, and S. Xie, "A novel dispersion compensating fiber grating with a large chirp parameter and period sampled distribution," Opt. Commun. 227, 311-315 (2003).
[CrossRef]

Chotard, H.

Y. Painchaud, H. Chotard, A. Mailloux, and Y. Vasseur, "Superposition of chirped fiber Bragg grating for third-order dispersion compensation over 32 WDM channels," Electron. Lett. 38, 1572-1573 (2002).
[CrossRef]

Chu, P. L.

Q. Wu, P. L. Chu, and H. P. Chan, "General design approach to multichannel fiber Bragg grating," J. Lightwave Technol. 24, 1571-1580 (2006).
[CrossRef]

Q. Wu, C. Yu, K. Wang, X. Wang, Z. Pu, 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, and R. I. Laming, "Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation," IEEE Photon. Technol. Lett. 10, 842-844 (1998).
[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]

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.

K. Kolossovski, R. Sammut, A. Buryak, and D. Stepanov, "Three-step design optimization for multi-channel fibre Bragg gratings," Opt. Express 11, 1029-1038 (2003).
[CrossRef] [PubMed]

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]

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]

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] [PubMed]

Li, H.

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

Li, M.

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

Li, X.

L. Xia, X. Li, X. Chen, and S. Xie, "A novel dispersion compensating fiber grating with a large chirp parameter and period sampled distribution," Opt. Commun. 227, 311-315 (2003).
[CrossRef]

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]

Mailloux, A.

Y. Painchaud, H. Chotard, A. Mailloux, and Y. Vasseur, "Superposition of chirped fiber Bragg grating for third-order dispersion compensation over 32 WDM channels," Electron. Lett. 38, 1572-1573 (2002).
[CrossRef]

Painchaud, Y.

Y. Painchaud, H. Chotard, A. Mailloux, and Y. Vasseur, "Superposition of chirped fiber Bragg grating for third-order dispersion compensation over 32 WDM channels," Electron. Lett. 38, 1572-1573 (2002).
[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).
[CrossRef]

Pu, Z.

Q. Wu, C. Yu, K. Wang, X. Wang, Z. Pu, 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]

Rothenberg, J. E.

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

Sammut, R.

K. Kolossovski, R. Sammut, A. Buryak, and D. Stepanov, "Three-step design optimization for multi-channel fibre Bragg gratings," Opt. Express 11, 1029-1038 (2003).
[CrossRef] [PubMed]

Sheng, Y.

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

Stepanov, D.

K. Kolossovski, R. Sammut, A. Buryak, and D. Stepanov, "Three-step design optimization for multi-channel fibre Bragg gratings," Opt. Express 11, 1029-1038 (2003).
[CrossRef] [PubMed]

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]

Vasseur, Y.

Y. Painchaud, H. Chotard, A. Mailloux, and Y. Vasseur, "Superposition of chirped fiber Bragg grating for third-order dispersion compensation over 32 WDM channels," Electron. Lett. 38, 1572-1573 (2002).
[CrossRef]

Wang, K.

Q. Wu, C. Yu, K. Wang, X. Wang, Z. Pu, 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, X.

Q. Wu, C. Yu, K. Wang, X. Wang, Z. Pu, 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, 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).
[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, Q.

Q. Wu, P. L. Chu, and H. P. Chan, "General design approach to multichannel fiber Bragg grating," J. Lightwave Technol. 24, 1571-1580 (2006).
[CrossRef]

Q. Wu, C. Yu, K. Wang, X. Wang, Z. Pu, 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]

Xia, L.

L. Xia, X. Li, X. Chen, and S. Xie, "A novel dispersion compensating fiber grating with a large chirp parameter and period sampled distribution," Opt. Commun. 227, 311-315 (2003).
[CrossRef]

Xie, S.

L. Xia, X. Li, X. Chen, and S. Xie, "A novel dispersion compensating fiber grating with a large chirp parameter and period sampled distribution," Opt. Commun. 227, 311-315 (2003).
[CrossRef]

Yu, C.

Q. Wu, C. Yu, K. Wang, X. Wang, Z. Pu, 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]

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).
[CrossRef]

Electron. Lett.

Y. Painchaud, H. Chotard, A. Mailloux, and Y. Vasseur, "Superposition of chirped fiber Bragg grating for third-order dispersion compensation over 32 WDM channels," Electron. Lett. 38, 1572-1573 (2002).
[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.

Q. Wu, C. Yu, K. Wang, X. Wang, Z. Pu, 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]

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]

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]

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] [PubMed]

J. Lightw. Technol.

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

J. Lightwave Technol.

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]

Q. Wu, P. L. Chu, and H. P. Chan, "General design approach to multichannel fiber Bragg grating," J. Lightwave Technol. 24, 1571-1580 (2006).
[CrossRef]

Opt. Commun.

L. Xia, X. Li, X. Chen, and S. Xie, "A novel dispersion compensating fiber grating with a large chirp parameter and period sampled distribution," Opt. Commun. 227, 311-315 (2003).
[CrossRef]

Opt. Express

K. Kolossovski, R. Sammut, A. Buryak, and D. Stepanov, "Three-step design optimization for multi-channel fibre Bragg gratings," Opt. Express 11, 1029-1038 (2003).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1.
Fig. 1.

The principle of a multi-channel Bragg grating implemented based on the nonuniform sampling technology. (a) Conventional sampling (FSR ≈ 40 nm). (b) If the nonuniform sampling is used, the desired multi-channel response is realized in the m=-1 channel (marked in the dashed box).

Fig. 2.
Fig. 2.

(a). The phase-only sampling function, π0(z), within one sample. (b) The reflection spectrum of the phase-only sampled grating. The transmission loss in each channel is -20 dB.

Fig. 3.
Fig. 3.

The amplitude-only sampling function for multi-channel filtering within one sample.

Fig. 4.
Fig. 4.

(a). The reflection spectrum of the amplitude-only sampled grating for multi-channel filtering. (b). The spectral response in the m=-1 channel. A 45-channel response is achieved without any true phase modulation. The transmission loss in each channel is -20 dB.

Fig. 5.
Fig. 5.

Spectral response of the 45-channel dispersion compensating grating with amplitude-only sampling. The chromatic dispersion in each channel is -1020 ps/nm. The transmission loss in each channel is -20 dB. (a). The whole band spectrum; (b) and (c) the channels at the left side and at the center,respectively.

Equations (10)

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

s ( z ) = A ( z ) s 0 [ z + f ( z ) ]
Δ n ( z ) = 1 2 s ( z ) exp ( j 2 π z Λ ) + c . c
s 0 ( z ) = m F m exp ( j 2 π m P z )
Δ n ( z ) = m 1 2 F m A ( z ) exp [ j 2 π m P f ( z ) ] × exp ( j 2 π z Λ m ) + c . c
Λ m = Λ P + P Λ m Λ 2 P
f ( z ) = φ ps ( z ) 2 π P
P < 4 n eff Λ 2 B
φ PS ( z ) = k = 0 N 1 φ 0 ( z kP 0 )
P 0 = λ 2 2 n eff Δλ
φ PS ( z ) = k = 0 N 1 φ 0 ( z kP 0 ) 4 n neff 2 π C λ 2 ( z NP 0 2 ) 2

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