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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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2007 (2)

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]

Y. Dai and X. Chen, “DFB semiconductor lasers based on reconstruction-equivalent-chirp technology,” Opt. Express,  15, 2348–2353 (2007).
[CrossRef] [PubMed]

2006 (6)

2005 (2)

M. Poulin, Y. Vasseur, F. Trepanier, M. Guy, M. Morin, Y. Painchaud, and J. Rothenberg, “Apodization of a multi-channel dispersion compensator by phase modulation coding of a phase mask,” OFC2005, paper OME17.

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 multi-channel fiber Bragg gratings,” IEEE Photon. Technol. Lett. 17, 381–383 (2005).
[CrossRef]

2004 (4)

2003 (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]

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

A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, “Optimization of refractive index sampling for multi-channel fiber Bragg gratings,” IEEE J. Quantum Electron. 39, 91–98 (2003).
[CrossRef]

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]

2002 (2)

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]

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]

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]

Buryak, A.

Buryak, A. V.

A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, “Optimization of refractive index sampling for multi-channel 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 multi-channel fiber Bragg grating,” J. Lightw. 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 multi-channel fiber Bragg gratings,” IEEE Photon. Technol. Lett. 17, 381–383 (2005).
[CrossRef]

Chen, X.

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 multi-channel fiber Bragg grating,” J. Lightw. 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 multi-channel 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]

Dai, Y.

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]

Guy, M.

Y. Painchaud, M. Poulin, M. Morin, and M. Guy, “Fiber Bragg grating based dispersion compensator slope-matched for LEAF fiber,” OFC2006, paper OThE2.

M. Poulin, Y. Vasseur, F. Trepanier, M. Guy, M. Morin, Y. Painchaud, and J. Rothenberg, “Apodization of a multi-channel dispersion compensator by phase modulation coding of a phase mask,” OFC2005, paper OME17.

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]

Jiang, D.

D. Jiang, X. Chen, Y. Dai, H. Liu, and S. Xie, “A novel distributed feedback fiber laser based on equivalent phase shift,” IEEE Photon. Technol. Lett. 16, 2598–2600 (2004).
[CrossRef]

Kao, Y.

Kolossovski, K.

Kolossovski, K. Y.

A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, “Optimization of refractive index sampling for multi-channel fiber Bragg gratings,” IEEE J. Quantum Electron. 39, 91–98 (2003).
[CrossRef]

Kristensen, M.

Kumagai, T.

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, C.

Lee, R.

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, M. Li, K. Ogusu, Y. Sheng, and J. E. Rothenberg, “Optimization of a continuous phase-only sampling for high channel-count fiber Bragg gratings,” Opt. Express 14, 3152–3160 (2006).
[CrossRef] [PubMed]

H. Li, T. Kumagai, and K. Ogusu, “Advanced design of a multi-channel fiber Bragg grating based on a layer-peeling method,” J. Opt. Soc. Am. B,  21, 1929–1938 (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. Lightw. Technol. 21, 2074–2083 (2003). 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]

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]

H. Li, M. Li, K. Ogusu, Y. Sheng, and J. E. Rothenberg, “Optimization of a continuous phase-only sampling for high channel-count fiber Bragg gratings,” Opt. Express 14, 3152–3160 (2006).
[CrossRef] [PubMed]

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. Lightw. Technol. 21, 2074–2083 (2003). 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]

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]

Liu, H.

D. Jiang, X. Chen, Y. Dai, H. Liu, and S. Xie, “A novel distributed feedback fiber laser based on equivalent phase shift,” IEEE Photon. Technol. Lett. 16, 2598–2600 (2004).
[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]

Morin, M.

Y. Painchaud, M. Poulin, M. Morin, and M. Guy, “Fiber Bragg grating based dispersion compensator slope-matched for LEAF fiber,” OFC2006, paper OThE2.

M. Poulin, Y. Vasseur, F. Trepanier, M. Guy, M. Morin, Y. Painchaud, and J. Rothenberg, “Apodization of a multi-channel dispersion compensator by phase modulation coding of a phase mask,” OFC2005, paper OME17.

Ogusu, K.

Painchaud, Y.

Y. Painchaud, M. Poulin, M. Morin, and M. Guy, “Fiber Bragg grating based dispersion compensator slope-matched for LEAF fiber,” OFC2006, paper OThE2.

M. Poulin, Y. Vasseur, F. Trepanier, M. Guy, M. Morin, Y. Painchaud, and J. Rothenberg, “Apodization of a multi-channel dispersion compensator by phase modulation coding of a phase mask,” OFC2005, paper OME17.

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]

Plougmann, N.

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]

Poulin, M.

Y. Painchaud, M. Poulin, M. Morin, and M. Guy, “Fiber Bragg grating based dispersion compensator slope-matched for LEAF fiber,” OFC2006, paper OThE2.

M. Poulin, Y. Vasseur, F. Trepanier, M. Guy, M. Morin, Y. Painchaud, and J. Rothenberg, “Apodization of a multi-channel dispersion compensator by phase modulation coding of a phase mask,” OFC2005, paper OME17.

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 multi-channel fiber Bragg gratings,” IEEE Photon. Technol. Lett. 17, 381–383 (2005).
[CrossRef]

Rothenberg, J.

M. Poulin, Y. Vasseur, F. Trepanier, M. Guy, M. Morin, Y. Painchaud, and J. Rothenberg, “Apodization of a multi-channel dispersion compensator by phase modulation coding of a phase mask,” OFC2005, paper OME17.

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, M. Li, K. Ogusu, Y. Sheng, and J. E. Rothenberg, “Optimization of a continuous phase-only sampling for high channel-count fiber Bragg gratings,” Opt. Express 14, 3152–3160 (2006).
[CrossRef] [PubMed]

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

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.

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, M. Li, K. Ogusu, Y. Sheng, and J. E. Rothenberg, “Optimization of a continuous phase-only sampling for high channel-count fiber Bragg gratings,” Opt. Express 14, 3152–3160 (2006).
[CrossRef] [PubMed]

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

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.

Stepanov, D. Y.

A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, “Optimization of refractive index sampling for multi-channel fiber Bragg gratings,” IEEE J. Quantum Electron. 39, 91–98 (2003).
[CrossRef]

Sun, J.

Trepanier, F.

M. Poulin, Y. Vasseur, F. Trepanier, M. Guy, M. Morin, Y. Painchaud, and J. Rothenberg, “Apodization of a multi-channel dispersion compensator by phase modulation coding of a phase mask,” OFC2005, paper OME17.

Vasseur, Y.

M. Poulin, Y. Vasseur, F. Trepanier, M. Guy, M. Morin, Y. Painchaud, and J. Rothenberg, “Apodization of a multi-channel dispersion compensator by phase modulation coding of a phase mask,” OFC2005, paper OME17.

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 multi-channel 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 multi-channel 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 multi-channel fiber Bragg grating,” J. Lightw. 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 multi-channel fiber Bragg gratings,” IEEE Photon. Technol. Lett. 17, 381–383 (2005).
[CrossRef]

Xia, L.

Y. Dai, X. Chen, L. Xia, Y. Zhang, and S. Xie, “Sampled Bragg grating with desired response in one channel by use of a reconstruction algorithm and equivalent chirp,” Opt. Lett. 29, 1333–1335 (2004).
[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]

Xie, S.

Yao, Y.

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 multi-channel fiber Bragg gratings,” IEEE Photon. Technol. Lett. 17, 381–383 (2005).
[CrossRef]

Zhang, Y.

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 multi-channel 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 multi-channel fiber Bragg gratings,” IEEE Photon. Technol. Lett. 17, 381–383 (2005).
[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]

D. Jiang, X. Chen, Y. Dai, H. Liu, and S. Xie, “A novel distributed feedback fiber laser based on equivalent phase shift,” IEEE Photon. Technol. Lett. 16, 2598–2600 (2004).
[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. Lightw. Technol. (3)

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. Lightw. Technol. 21, 2074–2083 (2003). 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]

Q. Wu, P. L. Chu, and H. P. Chan, “General design approach to multi-channel fiber Bragg grating,” J. Lightw. Technol. 24, 1571–1580 (2006).
[CrossRef]

J. Opt. Soc. Am. B (1)

OFC (2)

M. Poulin, Y. Vasseur, F. Trepanier, M. Guy, M. Morin, Y. Painchaud, and J. Rothenberg, “Apodization of a multi-channel dispersion compensator by phase modulation coding of a phase mask,” OFC2005, paper OME17.

Y. Painchaud, M. Poulin, M. Morin, and M. Guy, “Fiber Bragg grating based dispersion compensator slope-matched for LEAF fiber,” OFC2006, paper OThE2.

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 (5)

Opt. Lett. (3)

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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)

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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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