Abstract

Employing discrete layer peeling incorporated with a traditional Gerchberg–Saxton algorithm, we demonstrate an advanced design for a complex fiber Bragg grating (FBG) with a multichannel asymmetrical triangular reflection spectrum. This type of FBG filter is designed for multiplexing wavelength interrogation in a fiber-optic measurement system. The proposed method creates a FBG with a smooth index-change profile, and should facilitate its fabrication. Moreover, under the condition of quadratic phase response of the FBG, the dependences of the reconstructed index-change profile on the phase responses of the triangular filter are numerically investigated.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. J. Rao, “In-fibre Bragg grating sensors,” Meas. Sci. Technol. 8, 355-375 (1997).
    [CrossRef]
  2. S. M. Melle, K. Liu, and R. M. Measures, “A passive wavelength demodmulation system for guided-wave Bragg grating sensors,” IEEE Photon. Technol. Lett. 4, 516-518 (1992).
    [CrossRef]
  3. S. Kim, J. Kwon, S. Kim, and B. Lee, “Multiplexed strain sensor using fiber grating-tuned fiber laser with a semiconductor optical amplifier,” IEEE Photon. Technol. Lett. 13, 350-351 (2001).
    [CrossRef]
  4. D. J. F. Cooper and P. W. E. Smith, “Limits in wavelength measurement of optical signals,” J. Opt. Soc. Am. B 21, 908-913 (2004).
    [CrossRef]
  5. R. Huang, Y. Zhou, H. Cai, R. Qu, and Z. Fang, “A fiber Bragg grating with triangular spectrum as wavelength readout in sensor systems,” Opt. Commun. 229, 197-201 (2004).
    [CrossRef]
  6. R. Feced and M. N. Zervas, “Efficient inverse scattering algorithm for the design of grating-assisted codirectional mode couplers,” J. Opt. Soc. Am. A 17, 1573-1582 (2000).
    [CrossRef]
  7. S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, and R. T. Zheng, “Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm,” Opt. Commun. 260, 716-722 (2006).
    [CrossRef]
  8. Z. L. Ran and Y. J. Rao, “A FBG sensor system with cascaded LPFGs and music algorithm for dynamic strain measurement,” Sens. Actuators, A 135, 415-419 (2007).
    [CrossRef]
  9. Y. Painchaud, H. Chotard, A. Mailloux, and Y. Vasseur, “Superposition of chirped fibre Bragg gratings for third order dispersion compensation over 32 WDM channels,” Electron. Lett. 38, 1572-1573 (2002).
    [CrossRef]
  10. H. Li, Y. Sheng, Y. Li, and J. E. Rothenberg, “Phased-only sampled fiber Bragg gratings for high channel counts chromatic dispersion compensation,” J. Lightwave Technol. 21, 2074-2083 (2003).
    [CrossRef]
  11. Y. Painchaud and M. Morin, “Iterative method for the design of arbitrary multi-channel fiber Bragg gratings,” in OSA Topical Meeting Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides (BGPP2007) (Optical Society of America, 2007), paper BTuB1.
  12. H. Li, M. Li, Y. Sheng, and J. E. Rothenberg, “Advances in the design and fabrication of high-channel-count fiber Bragg gratings,” J. Lightwave Technol. 25, 2739-2750 (2007).
    [CrossRef]
  13. R. Feced, M. N. Zervas, and M. Miguel, “An efficient inverse scattering algorithm for the design of nonuniform fibre Bragg gratings,” IEEE J. Quantum Electron. 35, 1105-1115 (1999).
    [CrossRef]
  14. J. Bland-Hawthorn, A. Buryak, and K. Kolossovski, “Optimization algorithm for ultrabroadband multichannel aperiodic fiber Bragg grating filters,” J. Opt. Soc. Am. A 25, 153-158 (2008).
    [CrossRef]
  15. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).
  16. J. Skaar, L. Wang, and T. Erdogan, “On the synthesis of fiber gratings by layer-peeling,” IEEE J. Quantum Electron. 37, 165-173 (2001).
    [CrossRef]
  17. Y. Painchaud, M. Poulin, and M. Morin, “Grating superposition encoded into a phase mask for efficient fabrication of dispersion slope compensators,” in Proceedings of the European Conference on Optical Communications (ECOC) (2006), paper Th 4.2.7.
  18. Y. Sheng, J. E. Rothenberg, H. Li, Y. Wang, and J. Zweiback, “Split of phase shifts in a phase mask for fiber Bragg grating,” IEEE Photon. Technol. Lett. 16, 1316-1318 (2004).
    [CrossRef]
  19. M. Ibsen, M. K. Durkin, M. N. Zervas, A. B. Grudinin, and R. I. Laming, “Custom design of long chirped Bragg gratings: application to gain--flattening filter with incorporated dispersion compensation,” IEEE Photon. Technol. Lett. 12, 498-500 (2000).
    [CrossRef]

2008 (1)

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. Lightwave Technol. 25, 2739-2750 (2007).
[CrossRef]

Z. L. Ran and Y. J. Rao, “A FBG sensor system with cascaded LPFGs and music algorithm for dynamic strain measurement,” Sens. Actuators, A 135, 415-419 (2007).
[CrossRef]

2006 (1)

S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, and R. T. Zheng, “Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm,” Opt. Commun. 260, 716-722 (2006).
[CrossRef]

2004 (3)

R. Huang, Y. Zhou, H. Cai, R. Qu, and Z. Fang, “A fiber Bragg grating with triangular spectrum as wavelength readout in sensor systems,” Opt. Commun. 229, 197-201 (2004).
[CrossRef]

D. J. F. Cooper and P. W. E. Smith, “Limits in wavelength measurement of optical signals,” J. Opt. Soc. Am. B 21, 908-913 (2004).
[CrossRef]

Y. Sheng, J. E. Rothenberg, H. Li, Y. Wang, and J. Zweiback, “Split of phase shifts in a phase mask for fiber Bragg grating,” IEEE Photon. Technol. Lett. 16, 1316-1318 (2004).
[CrossRef]

2003 (1)

2002 (1)

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

2001 (2)

S. Kim, J. Kwon, S. Kim, and B. Lee, “Multiplexed strain sensor using fiber grating-tuned fiber laser with a semiconductor optical amplifier,” IEEE Photon. Technol. Lett. 13, 350-351 (2001).
[CrossRef]

J. Skaar, L. Wang, and T. Erdogan, “On the synthesis of fiber gratings by layer-peeling,” IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

2000 (2)

M. Ibsen, M. K. Durkin, M. N. Zervas, A. B. Grudinin, and R. I. Laming, “Custom design of long chirped Bragg gratings: application to gain--flattening filter with incorporated dispersion compensation,” IEEE Photon. Technol. Lett. 12, 498-500 (2000).
[CrossRef]

R. Feced and M. N. Zervas, “Efficient inverse scattering algorithm for the design of grating-assisted codirectional mode couplers,” J. Opt. Soc. Am. A 17, 1573-1582 (2000).
[CrossRef]

1999 (1)

R. Feced, M. N. Zervas, and M. Miguel, “An efficient inverse scattering algorithm for the design of nonuniform fibre Bragg gratings,” IEEE J. Quantum Electron. 35, 1105-1115 (1999).
[CrossRef]

1997 (1)

Y. J. Rao, “In-fibre Bragg grating sensors,” Meas. Sci. Technol. 8, 355-375 (1997).
[CrossRef]

1992 (1)

S. M. Melle, K. Liu, and R. M. Measures, “A passive wavelength demodmulation system for guided-wave Bragg grating sensors,” IEEE Photon. Technol. Lett. 4, 516-518 (1992).
[CrossRef]

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).

Alphones, A.

S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, and R. T. Zheng, “Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm,” Opt. Commun. 260, 716-722 (2006).
[CrossRef]

Baskar, S.

S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, and R. T. Zheng, “Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm,” Opt. Commun. 260, 716-722 (2006).
[CrossRef]

Bland-Hawthorn, J.

Buryak, A.

Cai, H.

R. Huang, Y. Zhou, H. Cai, R. Qu, and Z. Fang, “A fiber Bragg grating with triangular spectrum as wavelength readout in sensor systems,” Opt. Commun. 229, 197-201 (2004).
[CrossRef]

Chotard, H.

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

Cooper, D. J. F.

Durkin, M. K.

M. Ibsen, M. K. Durkin, M. N. Zervas, A. B. Grudinin, and R. I. Laming, “Custom design of long chirped Bragg gratings: application to gain--flattening filter with incorporated dispersion compensation,” IEEE Photon. Technol. Lett. 12, 498-500 (2000).
[CrossRef]

Erdogan, T.

J. Skaar, L. Wang, and T. Erdogan, “On the synthesis of fiber gratings by layer-peeling,” IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

Fang, Z.

R. Huang, Y. Zhou, H. Cai, R. Qu, and Z. Fang, “A fiber Bragg grating with triangular spectrum as wavelength readout in sensor systems,” Opt. Commun. 229, 197-201 (2004).
[CrossRef]

Feced, R.

R. Feced and M. N. Zervas, “Efficient inverse scattering algorithm for the design of grating-assisted codirectional mode couplers,” J. Opt. Soc. Am. A 17, 1573-1582 (2000).
[CrossRef]

R. Feced, M. N. Zervas, and M. Miguel, “An efficient inverse scattering algorithm for the design of nonuniform fibre Bragg gratings,” IEEE J. Quantum Electron. 35, 1105-1115 (1999).
[CrossRef]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).

Grudinin, A. B.

M. Ibsen, M. K. Durkin, M. N. Zervas, A. B. Grudinin, and R. I. Laming, “Custom design of long chirped Bragg gratings: application to gain--flattening filter with incorporated dispersion compensation,” IEEE Photon. Technol. Lett. 12, 498-500 (2000).
[CrossRef]

Huang, R.

R. Huang, Y. Zhou, H. Cai, R. Qu, and Z. Fang, “A fiber Bragg grating with triangular spectrum as wavelength readout in sensor systems,” Opt. Commun. 229, 197-201 (2004).
[CrossRef]

Ibsen, M.

M. Ibsen, M. K. Durkin, M. N. Zervas, A. B. Grudinin, and R. I. Laming, “Custom design of long chirped Bragg gratings: application to gain--flattening filter with incorporated dispersion compensation,” IEEE Photon. Technol. Lett. 12, 498-500 (2000).
[CrossRef]

Kim, S.

S. Kim, J. Kwon, S. Kim, and B. Lee, “Multiplexed strain sensor using fiber grating-tuned fiber laser with a semiconductor optical amplifier,” IEEE Photon. Technol. Lett. 13, 350-351 (2001).
[CrossRef]

S. Kim, J. Kwon, S. Kim, and B. Lee, “Multiplexed strain sensor using fiber grating-tuned fiber laser with a semiconductor optical amplifier,” IEEE Photon. Technol. Lett. 13, 350-351 (2001).
[CrossRef]

Kolossovski, K.

Kwon, J.

S. Kim, J. Kwon, S. Kim, and B. Lee, “Multiplexed strain sensor using fiber grating-tuned fiber laser with a semiconductor optical amplifier,” IEEE Photon. Technol. Lett. 13, 350-351 (2001).
[CrossRef]

Laming, R. I.

M. Ibsen, M. K. Durkin, M. N. Zervas, A. B. Grudinin, and R. I. Laming, “Custom design of long chirped Bragg gratings: application to gain--flattening filter with incorporated dispersion compensation,” IEEE Photon. Technol. Lett. 12, 498-500 (2000).
[CrossRef]

Lee, B.

S. Kim, J. Kwon, S. Kim, and B. Lee, “Multiplexed strain sensor using fiber grating-tuned fiber laser with a semiconductor optical amplifier,” IEEE Photon. Technol. Lett. 13, 350-351 (2001).
[CrossRef]

Li, H.

Li, M.

Li, Y.

Liu, K.

S. M. Melle, K. Liu, and R. M. Measures, “A passive wavelength demodmulation system for guided-wave Bragg grating sensors,” IEEE Photon. Technol. Lett. 4, 516-518 (1992).
[CrossRef]

Mailloux, A.

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

Measures, R. M.

S. M. Melle, K. Liu, and R. M. Measures, “A passive wavelength demodmulation system for guided-wave Bragg grating sensors,” IEEE Photon. Technol. Lett. 4, 516-518 (1992).
[CrossRef]

Melle, S. M.

S. M. Melle, K. Liu, and R. M. Measures, “A passive wavelength demodmulation system for guided-wave Bragg grating sensors,” IEEE Photon. Technol. Lett. 4, 516-518 (1992).
[CrossRef]

Miguel, M.

R. Feced, M. N. Zervas, and M. Miguel, “An efficient inverse scattering algorithm for the design of nonuniform fibre Bragg gratings,” IEEE J. Quantum Electron. 35, 1105-1115 (1999).
[CrossRef]

Morin, M.

Y. Painchaud and M. Morin, “Iterative method for the design of arbitrary multi-channel fiber Bragg gratings,” in OSA Topical Meeting Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides (BGPP2007) (Optical Society of America, 2007), paper BTuB1.

Y. Painchaud, M. Poulin, and M. Morin, “Grating superposition encoded into a phase mask for efficient fabrication of dispersion slope compensators,” in Proceedings of the European Conference on Optical Communications (ECOC) (2006), paper Th 4.2.7.

Ngo, N. Q.

S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, and R. T. Zheng, “Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm,” Opt. Commun. 260, 716-722 (2006).
[CrossRef]

Painchaud, Y.

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

Y. Painchaud, M. Poulin, and M. Morin, “Grating superposition encoded into a phase mask for efficient fabrication of dispersion slope compensators,” in Proceedings of the European Conference on Optical Communications (ECOC) (2006), paper Th 4.2.7.

Y. Painchaud and M. Morin, “Iterative method for the design of arbitrary multi-channel fiber Bragg gratings,” in OSA Topical Meeting Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides (BGPP2007) (Optical Society of America, 2007), paper BTuB1.

Poulin, M.

Y. Painchaud, M. Poulin, and M. Morin, “Grating superposition encoded into a phase mask for efficient fabrication of dispersion slope compensators,” in Proceedings of the European Conference on Optical Communications (ECOC) (2006), paper Th 4.2.7.

Qu, R.

R. Huang, Y. Zhou, H. Cai, R. Qu, and Z. Fang, “A fiber Bragg grating with triangular spectrum as wavelength readout in sensor systems,” Opt. Commun. 229, 197-201 (2004).
[CrossRef]

Ran, Z. L.

Z. L. Ran and Y. J. Rao, “A FBG sensor system with cascaded LPFGs and music algorithm for dynamic strain measurement,” Sens. Actuators, A 135, 415-419 (2007).
[CrossRef]

Rao, Y. J.

Z. L. Ran and Y. J. Rao, “A FBG sensor system with cascaded LPFGs and music algorithm for dynamic strain measurement,” Sens. Actuators, A 135, 415-419 (2007).
[CrossRef]

Y. J. Rao, “In-fibre Bragg grating sensors,” Meas. Sci. Technol. 8, 355-375 (1997).
[CrossRef]

Rothenberg, J. E.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).

Sheng, Y.

Skaar, J.

J. Skaar, L. Wang, and T. Erdogan, “On the synthesis of fiber gratings by layer-peeling,” IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

Smith, P. W. E.

Suganthan, P. N.

S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, and R. T. Zheng, “Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm,” Opt. Commun. 260, 716-722 (2006).
[CrossRef]

Vasseur, Y.

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

Wang, L.

J. Skaar, L. Wang, and T. Erdogan, “On the synthesis of fiber gratings by layer-peeling,” IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

Wang, Y.

Y. Sheng, J. E. Rothenberg, H. Li, Y. Wang, and J. Zweiback, “Split of phase shifts in a phase mask for fiber Bragg grating,” IEEE Photon. Technol. Lett. 16, 1316-1318 (2004).
[CrossRef]

Zervas, M. N.

M. Ibsen, M. K. Durkin, M. N. Zervas, A. B. Grudinin, and R. I. Laming, “Custom design of long chirped Bragg gratings: application to gain--flattening filter with incorporated dispersion compensation,” IEEE Photon. Technol. Lett. 12, 498-500 (2000).
[CrossRef]

R. Feced and M. N. Zervas, “Efficient inverse scattering algorithm for the design of grating-assisted codirectional mode couplers,” J. Opt. Soc. Am. A 17, 1573-1582 (2000).
[CrossRef]

R. Feced, M. N. Zervas, and M. Miguel, “An efficient inverse scattering algorithm for the design of nonuniform fibre Bragg gratings,” IEEE J. Quantum Electron. 35, 1105-1115 (1999).
[CrossRef]

Zheng, R. T.

S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, and R. T. Zheng, “Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm,” Opt. Commun. 260, 716-722 (2006).
[CrossRef]

Zhou, Y.

R. Huang, Y. Zhou, H. Cai, R. Qu, and Z. Fang, “A fiber Bragg grating with triangular spectrum as wavelength readout in sensor systems,” Opt. Commun. 229, 197-201 (2004).
[CrossRef]

Zweiback, J.

Y. Sheng, J. E. Rothenberg, H. Li, Y. Wang, and J. Zweiback, “Split of phase shifts in a phase mask for fiber Bragg grating,” IEEE Photon. Technol. Lett. 16, 1316-1318 (2004).
[CrossRef]

Electron. Lett. (1)

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

IEEE J. Quantum Electron. (2)

J. Skaar, L. Wang, and T. Erdogan, “On the synthesis of fiber gratings by layer-peeling,” IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

R. Feced, M. N. Zervas, and M. Miguel, “An efficient inverse scattering algorithm for the design of nonuniform fibre Bragg gratings,” IEEE J. Quantum Electron. 35, 1105-1115 (1999).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

Y. Sheng, J. E. Rothenberg, H. Li, Y. Wang, and J. Zweiback, “Split of phase shifts in a phase mask for fiber Bragg grating,” IEEE Photon. Technol. Lett. 16, 1316-1318 (2004).
[CrossRef]

M. Ibsen, M. K. Durkin, M. N. Zervas, A. B. Grudinin, and R. I. Laming, “Custom design of long chirped Bragg gratings: application to gain--flattening filter with incorporated dispersion compensation,” IEEE Photon. Technol. Lett. 12, 498-500 (2000).
[CrossRef]

S. M. Melle, K. Liu, and R. M. Measures, “A passive wavelength demodmulation system for guided-wave Bragg grating sensors,” IEEE Photon. Technol. Lett. 4, 516-518 (1992).
[CrossRef]

S. Kim, J. Kwon, S. Kim, and B. Lee, “Multiplexed strain sensor using fiber grating-tuned fiber laser with a semiconductor optical amplifier,” IEEE Photon. Technol. Lett. 13, 350-351 (2001).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. A (2)

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

Meas. Sci. Technol. (1)

Y. J. Rao, “In-fibre Bragg grating sensors,” Meas. Sci. Technol. 8, 355-375 (1997).
[CrossRef]

Opt. Commun. (2)

R. Huang, Y. Zhou, H. Cai, R. Qu, and Z. Fang, “A fiber Bragg grating with triangular spectrum as wavelength readout in sensor systems,” Opt. Commun. 229, 197-201 (2004).
[CrossRef]

S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, and R. T. Zheng, “Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm,” Opt. Commun. 260, 716-722 (2006).
[CrossRef]

Optik (Jena) (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).

Sens. Actuators, A (1)

Z. L. Ran and Y. J. Rao, “A FBG sensor system with cascaded LPFGs and music algorithm for dynamic strain measurement,” Sens. Actuators, A 135, 415-419 (2007).
[CrossRef]

Other (2)

Y. Painchaud and M. Morin, “Iterative method for the design of arbitrary multi-channel fiber Bragg gratings,” in OSA Topical Meeting Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides (BGPP2007) (Optical Society of America, 2007), paper BTuB1.

Y. Painchaud, M. Poulin, and M. Morin, “Grating superposition encoded into a phase mask for efficient fabrication of dispersion slope compensators,” in Proceedings of the European Conference on Optical Communications (ECOC) (2006), paper Th 4.2.7.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Reflection spectrum of a single-channel FBG where λ a and λ c are the minimum and maximum wavelengths in the interest region, respectively. λ b is the wavelength where the reflection is maximized. R max and R min are the maximum and minimum reflections of the triangular filter, respectively.

Fig. 2
Fig. 2

Target spectrum and the synthesized index-change profile of the MFBG. (a) Spectrum for a 41-channel triangular filter with λ w = 1 nm , R max = 80 % , and R min = 0 where λ l l and λ u l are the minimum and maximum wavelengths in the region of interest, respectively. (b) Synthesized index-change profile.

Fig. 3
Fig. 3

Flow chart of the proposed design algorithm.

Fig. 4
Fig. 4

Reconstructed FBG after the smoothing processes. (a) Index-change profile and (b) wrapped phase distribution.

Fig. 5
Fig. 5

Design results of the reflection spectrum and its ripples. (a) Reflection spectrum of the synthesized grating and (b) reflection ripples for the inset of Fig. 5a.

Fig. 6
Fig. 6

Design results for the triangular filters with different bandwidths and channel spacings: (a) bandwidth = 1 nm , channel spacing = 1 nm ; (b) bandwidth = 1 nm , channel spacing = 2 nm ; and (c) bandwidth = 2 nm , channel spacing = 2 nm .

Fig. 7
Fig. 7

Influences of the initial spectral phase ϕ ( λ ) (a) the index-change profile, (b) the reflection spectrum, and (c) the initial and the obtained group delay spectra for D 2 = 500 ps nm

Equations (6)

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

r ( λ ) = r s ( λ ) m = N = 1 N + 1 δ ( λ m Δ λ 0 ) = ( R exp ( i Φ ( λ ) ) ) m = N 1 N + 1 δ ( λ m Δ λ 0 ) ,
q ( z ) = j π Δ n 1 ( z ) n 0 Λ e i Ψ ( z ) ,
q ( z ) = q ( z ) e i ψ ( z ) .
CF = λ = λ l l λ u l r ( λ ) r ( λ ) 2 .
ϕ ( λ ) = υ 0 λ a λ ( 2 π λ 2 ) D 2 ( λ λ 0 ) d λ ,
TL = ( η × Δ n 1 ) 2 × D 2 65.447 [ dB ] ,

Metrics