Abstract

A digital concatenated grating composed of five subgratings is proposed. Essential formulas on Bragg periods of subgratings and an analytical expression for the reflection-spectrum envelope are presented, which show how to use reflection-spectrum envelopes to construct a digital concatenated grating with uniform reflection peaks. For a perfect design, the spectral center separation of adjacent Bragg gratings will be chosen as the integral times of the reflectivity peaks’ spacing. Gaussian apodization on the whole profile grating not only eliminates the sidelobes of each reflection peak but also provides a better flat reflection-spectrum envelope than that of the digital concatenated Gaussian-apodized grating.

© 2008 Optical Society of America

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References

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  1. V. Jayraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor laser with sampled gratings,” IEEE J. Quantum Electron. 29, 1824-1834 (1993).
    [CrossRef]
  2. X. He, W. Li, J. Zhang, X. Huang, J. Shan, and D. Huang, “Theoretical analysis of widely tunable external cavity semiconductor laser with sampled fiber grating,” Opt. Commun. 267, 440-446 (2006).
    [CrossRef]
  3. 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 Photonics Technol. Lett. 12, 1013-1015 (2000).
    [CrossRef]
  4. Y. Dai, X. Chen, Y. Yao, and S. Xie, “Dispersion compensation based on sampled fiber Bragg gratings fabricated with reconstruction equivalent-chip method,” IEEE Photonics Technol. Lett. 18, 941-943 (2006).
    [CrossRef]
  5. W. H. Loh, F. Q. Zhou, and J. J. Pan, “Novel designs forsampled grating based multiplexers-demultiplexers,” Opt. Lett. 24, 1457-1459 (1999).
    [CrossRef]
  6. P. Petropoulos, M. Ibsen, M. N. Zervas, and D. J. Richardson, “Generation of a 40GHZ pulse stream by pulse multiplication with a sampled fiber Bragg grating,” Opt. Lett. 25, 521-523 (2000).
    [CrossRef]
  7. J. E. Rothenberg, R. E. Caldwell, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “High-channel-count fiber Bragg gratings fabricated by phase-only sampling,” in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics (Optical Society of America, 2002), pp. 575-577.
    [CrossRef]
  8. H. Ishii, Y. Tohmori, Y. Yoshikuni, T. Tamamura, and Y. Kondo, “Multiple-phase-shift super structure grating DBR lasers for broad wavelength tuning,” IEEE Photonics Technol. Lett. 5, 613-615 (1993).
    [CrossRef]
  9. M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photonics Technol. Lett. 10, 842-845 (1998).
    [CrossRef]
  10. M. Gioannini and I. Montrosset, “Novel interleaved sampled grating mirrors for widely tunable DBR laser,” Proc. IEEE 148, 13-18 (2001).
  11. X. He, Y. Yu, D. Huang, R. Zhang, W. Liu, and S. Jiang, “Analysis and applications of reflection-spectrum envelopes for sampled gratings,” J. Lightwave Technol. 26, 720-728 (2008).
    [CrossRef]
  12. X. He, Y. Yu, W. Liu, and D. Huang, “Analytical expression of reflection-spectrum envelope for sampled gratings,” in Proceedings of the China-Ireland International Conference on Information and Communications Technologies 2007 (CIICT, 2007), pp. 637-645.
    [PubMed]

2008 (1)

2007 (1)

X. He, Y. Yu, W. Liu, and D. Huang, “Analytical expression of reflection-spectrum envelope for sampled gratings,” in Proceedings of the China-Ireland International Conference on Information and Communications Technologies 2007 (CIICT, 2007), pp. 637-645.
[PubMed]

2006 (2)

X. He, W. Li, J. Zhang, X. Huang, J. Shan, and D. Huang, “Theoretical analysis of widely tunable external cavity semiconductor laser with sampled fiber grating,” Opt. Commun. 267, 440-446 (2006).
[CrossRef]

Y. Dai, X. Chen, Y. Yao, and S. Xie, “Dispersion compensation based on sampled fiber Bragg gratings fabricated with reconstruction equivalent-chip method,” IEEE Photonics Technol. Lett. 18, 941-943 (2006).
[CrossRef]

2002 (1)

J. E. Rothenberg, R. E. Caldwell, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “High-channel-count fiber Bragg gratings fabricated by phase-only sampling,” in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics (Optical Society of America, 2002), pp. 575-577.
[CrossRef]

2001 (1)

M. Gioannini and I. Montrosset, “Novel interleaved sampled grating mirrors for widely tunable DBR laser,” Proc. IEEE 148, 13-18 (2001).

2000 (2)

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 Photonics Technol. Lett. 12, 1013-1015 (2000).
[CrossRef]

P. Petropoulos, M. Ibsen, M. N. Zervas, and D. J. Richardson, “Generation of a 40GHZ pulse stream by pulse multiplication with a sampled fiber Bragg grating,” Opt. Lett. 25, 521-523 (2000).
[CrossRef]

1999 (1)

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 Photonics Technol. Lett. 10, 842-845 (1998).
[CrossRef]

1993 (2)

V. Jayraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor laser with sampled gratings,” IEEE J. Quantum Electron. 29, 1824-1834 (1993).
[CrossRef]

H. Ishii, Y. Tohmori, Y. Yoshikuni, T. Tamamura, and Y. Kondo, “Multiple-phase-shift super structure grating DBR lasers for broad wavelength tuning,” IEEE Photonics Technol. Lett. 5, 613-615 (1993).
[CrossRef]

Caldwell, R. E.

J. E. Rothenberg, R. E. Caldwell, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “High-channel-count fiber Bragg gratings fabricated by phase-only sampling,” in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics (Optical Society of America, 2002), pp. 575-577.
[CrossRef]

Chen, X.

Y. Dai, X. Chen, Y. Yao, and S. Xie, “Dispersion compensation based on sampled fiber Bragg gratings fabricated with reconstruction equivalent-chip method,” IEEE Photonics Technol. Lett. 18, 941-943 (2006).
[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 Photonics Technol. Lett. 12, 1013-1015 (2000).
[CrossRef]

Chuang, Z.-M.

V. Jayraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor laser with sampled gratings,” IEEE J. Quantum Electron. 29, 1824-1834 (1993).
[CrossRef]

Coldren, L. A.

V. Jayraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor laser with sampled gratings,” IEEE J. Quantum Electron. 29, 1824-1834 (1993).
[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 Photonics Technol. Lett. 10, 842-845 (1998).
[CrossRef]

Dai, Y.

Y. Dai, X. Chen, Y. Yao, and S. Xie, “Dispersion compensation based on sampled fiber Bragg gratings fabricated with reconstruction equivalent-chip method,” IEEE Photonics Technol. Lett. 18, 941-943 (2006).
[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 Photonics Technol. Lett. 10, 842-845 (1998).
[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 Photonics Technol. Lett. 12, 1013-1015 (2000).
[CrossRef]

Gioannini, M.

M. Gioannini and I. Montrosset, “Novel interleaved sampled grating mirrors for widely tunable DBR laser,” Proc. IEEE 148, 13-18 (2001).

He, X.

X. He, Y. Yu, D. Huang, R. Zhang, W. Liu, and S. Jiang, “Analysis and applications of reflection-spectrum envelopes for sampled gratings,” J. Lightwave Technol. 26, 720-728 (2008).
[CrossRef]

X. He, Y. Yu, W. Liu, and D. Huang, “Analytical expression of reflection-spectrum envelope for sampled gratings,” in Proceedings of the China-Ireland International Conference on Information and Communications Technologies 2007 (CIICT, 2007), pp. 637-645.
[PubMed]

X. He, W. Li, J. Zhang, X. Huang, J. Shan, and D. Huang, “Theoretical analysis of widely tunable external cavity semiconductor laser with sampled fiber grating,” Opt. Commun. 267, 440-446 (2006).
[CrossRef]

Huang, D.

X. He, Y. Yu, D. Huang, R. Zhang, W. Liu, and S. Jiang, “Analysis and applications of reflection-spectrum envelopes for sampled gratings,” J. Lightwave Technol. 26, 720-728 (2008).
[CrossRef]

X. He, Y. Yu, W. Liu, and D. Huang, “Analytical expression of reflection-spectrum envelope for sampled gratings,” in Proceedings of the China-Ireland International Conference on Information and Communications Technologies 2007 (CIICT, 2007), pp. 637-645.
[PubMed]

X. He, W. Li, J. Zhang, X. Huang, J. Shan, and D. Huang, “Theoretical analysis of widely tunable external cavity semiconductor laser with sampled fiber grating,” Opt. Commun. 267, 440-446 (2006).
[CrossRef]

Huang, X.

X. He, W. Li, J. Zhang, X. Huang, J. Shan, and D. Huang, “Theoretical analysis of widely tunable external cavity semiconductor laser with sampled fiber grating,” Opt. Commun. 267, 440-446 (2006).
[CrossRef]

Ibsen, M.

P. Petropoulos, M. Ibsen, M. N. Zervas, and D. J. Richardson, “Generation of a 40GHZ pulse stream by pulse multiplication with a sampled fiber Bragg grating,” Opt. Lett. 25, 521-523 (2000).
[CrossRef]

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photonics Technol. Lett. 10, 842-845 (1998).
[CrossRef]

Ishii, H.

H. Ishii, Y. Tohmori, Y. Yoshikuni, T. Tamamura, and Y. Kondo, “Multiple-phase-shift super structure grating DBR lasers for broad wavelength tuning,” IEEE Photonics Technol. Lett. 5, 613-615 (1993).
[CrossRef]

Jayraman, V.

V. Jayraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor laser with sampled gratings,” IEEE J. Quantum Electron. 29, 1824-1834 (1993).
[CrossRef]

Jiang, S.

Kondo, Y.

H. Ishii, Y. Tohmori, Y. Yoshikuni, T. Tamamura, and Y. Kondo, “Multiple-phase-shift super structure grating DBR lasers for broad wavelength tuning,” IEEE Photonics Technol. Lett. 5, 613-615 (1993).
[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 Photonics Technol. Lett. 10, 842-845 (1998).
[CrossRef]

Li, H.

J. E. Rothenberg, R. E. Caldwell, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “High-channel-count fiber Bragg gratings fabricated by phase-only sampling,” in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics (Optical Society of America, 2002), pp. 575-577.
[CrossRef]

Li, W.

X. He, W. Li, J. Zhang, X. Huang, J. Shan, and D. Huang, “Theoretical analysis of widely tunable external cavity semiconductor laser with sampled fiber grating,” Opt. Commun. 267, 440-446 (2006).
[CrossRef]

Li, Y.

J. E. Rothenberg, R. E. Caldwell, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “High-channel-count fiber Bragg gratings fabricated by phase-only sampling,” in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics (Optical Society of America, 2002), pp. 575-577.
[CrossRef]

Liu, W.

X. He, Y. Yu, D. Huang, R. Zhang, W. Liu, and S. Jiang, “Analysis and applications of reflection-spectrum envelopes for sampled gratings,” J. Lightwave Technol. 26, 720-728 (2008).
[CrossRef]

X. He, Y. Yu, W. Liu, and D. Huang, “Analytical expression of reflection-spectrum envelope for sampled gratings,” in Proceedings of the China-Ireland International Conference on Information and Communications Technologies 2007 (CIICT, 2007), pp. 637-645.
[PubMed]

Loh, W. H.

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 Photonics Technol. Lett. 12, 1013-1015 (2000).
[CrossRef]

Montrosset, I.

M. Gioannini and I. Montrosset, “Novel interleaved sampled grating mirrors for widely tunable DBR laser,” Proc. IEEE 148, 13-18 (2001).

Pan, J. J.

Petropoulos, P.

Popelek, J.

J. E. Rothenberg, R. E. Caldwell, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “High-channel-count fiber Bragg gratings fabricated by phase-only sampling,” in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics (Optical Society of America, 2002), pp. 575-577.
[CrossRef]

Richardson, D. J.

Rothenberg, J. E.

J. E. Rothenberg, R. E. Caldwell, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “High-channel-count fiber Bragg gratings fabricated by phase-only sampling,” in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics (Optical Society of America, 2002), pp. 575-577.
[CrossRef]

Shan, J.

X. He, W. Li, J. Zhang, X. Huang, J. Shan, and D. Huang, “Theoretical analysis of widely tunable external cavity semiconductor laser with sampled fiber grating,” Opt. Commun. 267, 440-446 (2006).
[CrossRef]

Sheng, Y.

J. E. Rothenberg, R. E. Caldwell, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “High-channel-count fiber Bragg gratings fabricated by phase-only sampling,” in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics (Optical Society of America, 2002), pp. 575-577.
[CrossRef]

Tamamura, T.

H. Ishii, Y. Tohmori, Y. Yoshikuni, T. Tamamura, and Y. Kondo, “Multiple-phase-shift super structure grating DBR lasers for broad wavelength tuning,” IEEE Photonics Technol. Lett. 5, 613-615 (1993).
[CrossRef]

Tohmori, Y.

H. Ishii, Y. Tohmori, Y. Yoshikuni, T. Tamamura, and Y. Kondo, “Multiple-phase-shift super structure grating DBR lasers for broad wavelength tuning,” IEEE Photonics Technol. Lett. 5, 613-615 (1993).
[CrossRef]

Wang, Y.

J. E. Rothenberg, R. E. Caldwell, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “High-channel-count fiber Bragg gratings fabricated by phase-only sampling,” in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics (Optical Society of America, 2002), pp. 575-577.
[CrossRef]

Wilcox, R. B.

J. E. Rothenberg, R. E. Caldwell, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “High-channel-count fiber Bragg gratings fabricated by phase-only sampling,” in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics (Optical Society of America, 2002), pp. 575-577.
[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 Photonics Technol. Lett. 12, 1013-1015 (2000).
[CrossRef]

Xie, S.

Y. Dai, X. Chen, Y. Yao, and S. Xie, “Dispersion compensation based on sampled fiber Bragg gratings fabricated with reconstruction equivalent-chip method,” IEEE Photonics Technol. Lett. 18, 941-943 (2006).
[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 Photonics Technol. Lett. 12, 1013-1015 (2000).
[CrossRef]

Yao, Y.

Y. Dai, X. Chen, Y. Yao, and S. Xie, “Dispersion compensation based on sampled fiber Bragg gratings fabricated with reconstruction equivalent-chip method,” IEEE Photonics Technol. Lett. 18, 941-943 (2006).
[CrossRef]

Yoshikuni, Y.

H. Ishii, Y. Tohmori, Y. Yoshikuni, T. Tamamura, and Y. Kondo, “Multiple-phase-shift super structure grating DBR lasers for broad wavelength tuning,” IEEE Photonics Technol. Lett. 5, 613-615 (1993).
[CrossRef]

Yu, Y.

X. He, Y. Yu, D. Huang, R. Zhang, W. Liu, and S. Jiang, “Analysis and applications of reflection-spectrum envelopes for sampled gratings,” J. Lightwave Technol. 26, 720-728 (2008).
[CrossRef]

X. He, Y. Yu, W. Liu, and D. Huang, “Analytical expression of reflection-spectrum envelope for sampled gratings,” in Proceedings of the China-Ireland International Conference on Information and Communications Technologies 2007 (CIICT, 2007), pp. 637-645.
[PubMed]

Zervas, M. N.

Zhang, J.

X. He, W. Li, J. Zhang, X. Huang, J. Shan, and D. Huang, “Theoretical analysis of widely tunable external cavity semiconductor laser with sampled fiber grating,” Opt. Commun. 267, 440-446 (2006).
[CrossRef]

Zhang, R.

Zhou, F. Q.

Zweiback, J.

J. E. Rothenberg, R. E. Caldwell, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “High-channel-count fiber Bragg gratings fabricated by phase-only sampling,” in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics (Optical Society of America, 2002), pp. 575-577.
[CrossRef]

IEEE J. Quantum Electron. (1)

V. Jayraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor laser with sampled gratings,” IEEE J. Quantum Electron. 29, 1824-1834 (1993).
[CrossRef]

IEEE Photonics Technol. Lett. (4)

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 Photonics Technol. Lett. 12, 1013-1015 (2000).
[CrossRef]

Y. Dai, X. Chen, Y. Yao, and S. Xie, “Dispersion compensation based on sampled fiber Bragg gratings fabricated with reconstruction equivalent-chip method,” IEEE Photonics Technol. Lett. 18, 941-943 (2006).
[CrossRef]

H. Ishii, Y. Tohmori, Y. Yoshikuni, T. Tamamura, and Y. Kondo, “Multiple-phase-shift super structure grating DBR lasers for broad wavelength tuning,” IEEE Photonics Technol. Lett. 5, 613-615 (1993).
[CrossRef]

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photonics Technol. Lett. 10, 842-845 (1998).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Commun. (1)

X. He, W. Li, J. Zhang, X. Huang, J. Shan, and D. Huang, “Theoretical analysis of widely tunable external cavity semiconductor laser with sampled fiber grating,” Opt. Commun. 267, 440-446 (2006).
[CrossRef]

Opt. Lett. (2)

Proc. IEEE (1)

M. Gioannini and I. Montrosset, “Novel interleaved sampled grating mirrors for widely tunable DBR laser,” Proc. IEEE 148, 13-18 (2001).

Other (2)

X. He, Y. Yu, W. Liu, and D. Huang, “Analytical expression of reflection-spectrum envelope for sampled gratings,” in Proceedings of the China-Ireland International Conference on Information and Communications Technologies 2007 (CIICT, 2007), pp. 637-645.
[PubMed]

J. E. Rothenberg, R. E. Caldwell, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “High-channel-count fiber Bragg gratings fabricated by phase-only sampling,” in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics (Optical Society of America, 2002), pp. 575-577.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

DCG based on the multiple reflection-spectrum envelope concatenation technology. (a) Reflection-spectrum envelopes of conventional sampled gratings, (c) resultant reflection-spectrum envelope. (b) Structure profiles of subgratings, (d) structure profile of the DCG.

Fig. 2
Fig. 2

Reflection spectrum and reflection-spectrum envelope of the digital concatenated grating with five subgratings.

Fig. 3
Fig. 3

Reflection-spectrum envelopes of DCGs with different spectral center separations.

Fig. 4
Fig. 4

Reflection spectra of DCGs with different spectral center separations.

Fig. 5
Fig. 5

DCG with Gaussian apodization on the sampling function. (a) Refractive-index profile, (b) reflection spectrum.

Fig. 6
Fig. 6

DCG with Gaussian apodization on the whole grating profile. (a) Refractive-index profile, (b) reflection spectrum.

Tables (1)

Tables Icon

Table 1 Design Parameters of Each Subgrating in the DCG in Fig. 2

Equations (6)

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

κ ( n ) = κ 0 Z g Z 0 sinc ( π n Z g Z 0 ) e i π n Z g Z 0 ,
κ ( λ ) = κ 0 Z g Z 0 sinc [ π Z g Z 0 Z 0 ( 2 n 0 , e f f λ 1 Λ ) ] exp [ i π Z g Z 0 Z 0 ( 2 n 0 , e f f λ 1 Λ ) ] .
κ i ( λ ) = κ 0 Z g Z 0 sinc [ π Z g Z 0 Z 0 ( 2 n 0 , e f f λ 1 Λ i ) ] exp [ i π ( Z g 2 d ) ( 2 n 0 , e f f λ 1 Λ i ) ] , i = 1 , 2 , , M ,
Λ ( i ) = λ c 2 n e f f + [ H Z 0 ( λ c 2 n e f f ) 2 ] ,
H = m × ( i M + 1 2 ) , i = 1 , 2 , , M .
R e n v ( λ ) = tanh 2 ( κ 1 ( λ ) + κ 2 ( λ ) + + κ i ( λ ) + + κ M ( λ ) L ) .

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