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 (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]

2006 (1)

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 (1)

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 (5)

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 (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]

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 (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]

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. (1)

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. (1)

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. (4)

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. (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]

J. Lightwave Technol. (2)

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. (1)

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 (1)

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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