Abstract

A simultaneous dispersion and dispersion-slope compensator based on a doubly sampled fiber Bragg grating (FBG) with 153 channels has been demonstrated, which is obtained by simultaneously chirping the period of the seed grating and the periods of the two sampling functions. These two sampling functions are optimized with the simulated annealing algorithm and the Gerchberg–Saxton iterative method. Moreover, the spectral inclination (in reflection) inherently due to the different magnitudes of the channel dispersion has been successfully equalized.

© 2010 Optical Society of America

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  1. F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett. 31, 899-901(1995).
    [CrossRef]
  2. U. Peschel, T. Peschel, and F. Lederer, “A compact device for highly efficient dispersion compensation in fiber transmission,” Appl. Phys. Lett. 67, 2111-2113 (1995).
    [CrossRef]
  3. X. Chen, Y. Luo, C. Fan, T. Wu, and S. 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 Photon. Technol. Lett. 12, 1013-1015(2000).
    [CrossRef]
  4. W. H. Loh, F. Q. Zhou, and J. J. Pan, “Sampled fiber grating based--dispersion slope compensator,” IEEE Photon. Technol. Lett. 11, 1280-1282 (1999).
    [CrossRef]
  5. C. D. Chen, I. Kim, O. Mizuhara, T. V. Nguyen, K. Ogawa, R. E. Tench, L. D. Tzeng, and P. D. Yeates, “40 Gbit/s×35 ch (1.4 Tbit/s aggregate capacity) WDM transmission over 85 kmstandard singlemode fibre,” Electron. Lett. 34, 2370-2371(1998).
    [CrossRef]
  6. H. Lee and G. P. Agrawal, “Bandwidth equalization of purely phase-sampled fiber Bragg gratings for broadband dispersion and dispersion slope compensation,” Opt. Express 12, 5595-5602 (2004).
    [CrossRef] [PubMed]
  7. M. Li and H. Li, “Reflection equalization of the simultaneous dispersion and dispersion-slope compensator based on a phase-only sampled fiber Bragg grating,” Opt. Express 16, 9821-9828 (2008).
    [CrossRef] [PubMed]
  8. M. Ibsen, M. Durkin, M. Cole, and R. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10, 842-844 (1998).
    [CrossRef]
  9. Y. Painchaud, A. Mailloux, H. Chotard, E. Pelletier, and M. Guy, “Multi-channel fiber Bragg gratings for dispersion and slope compensation,” in Optical Fiber Communication (Optical Society of America, 2002), paper ThAA5.
  10. 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]
  11. H. Li, M. Li, and J. Hayashi, “Ultrahigh channel-count phase-only sampled fiber Bragg grating covering the S-, C- and L- band,” Opt. Lett. 34, 938-940 (2009).
    [CrossRef] [PubMed]
  12. M. Li, X. Chen, J. Hayashi, and H. Li, “Advanced design of the ultrahigh-channel-count fiber Bragg grating based on the double sampling method,” Opt. Express 17, 8382-8394 (2009).
    [CrossRef] [PubMed]
  13. 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).
  14. 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]
  15. J. Skaar, L. Wang, and T. Erdogan, “On the synthesis of fiber Bragg grating by layer peeling,” IEEE J. Quantum Electron. 37, 165-173 (2001).
    [CrossRef]
  16. Y. Painchaud and M. Morin, “Iterative method for the design of arbitrary multichannel fiber Bragg gratings,” in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides (Optical Society of America, 2007), paper BTuB1.
  17. A. V. BuryakK. 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]
  18. J. Bland-Hawthorn, M. Englund, and G. Edvell, “New approach to atmospheric OH suppression using an aperiodic fiber Bragg grating,” Opt. Express 12, 5902-5909 (2004).
    [CrossRef] [PubMed]
  19. A. Buryak, J. Bland-Hawthorn, and V. Steblina, “Comparison of inverse scattering algorithm for designing ultra-broadband fiber Bragg gratings,” Opt. Express 17, 1995-2004(2009).
    [CrossRef] [PubMed]

2009 (3)

2008 (1)

2007 (1)

2004 (2)

2003 (1)

A. V. BuryakK. 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]

2001 (1)

J. Skaar, L. Wang, and T. Erdogan, “On the synthesis of fiber Bragg grating 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]

X. Chen, Y. Luo, C. Fan, T. Wu, and S. 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 Photon. Technol. Lett. 12, 1013-1015(2000).
[CrossRef]

1999 (1)

W. H. Loh, F. Q. Zhou, and J. J. Pan, “Sampled fiber grating based--dispersion slope compensator,” IEEE Photon. Technol. Lett. 11, 1280-1282 (1999).
[CrossRef]

1998 (2)

C. D. Chen, I. Kim, O. Mizuhara, T. V. Nguyen, K. Ogawa, R. E. Tench, L. D. Tzeng, and P. D. Yeates, “40 Gbit/s×35 ch (1.4 Tbit/s aggregate capacity) WDM transmission over 85 kmstandard singlemode fibre,” Electron. Lett. 34, 2370-2371(1998).
[CrossRef]

M. Ibsen, M. Durkin, M. Cole, and R. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10, 842-844 (1998).
[CrossRef]

1995 (2)

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett. 31, 899-901(1995).
[CrossRef]

U. Peschel, T. Peschel, and F. Lederer, “A compact device for highly efficient dispersion compensation in fiber transmission,” Appl. Phys. Lett. 67, 2111-2113 (1995).
[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).

Agrawal, G. P.

Bland-Hawthorn, J.

Buryak, A.

Buryak, A. V.

A. V. BuryakK. 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]

Chen, C. D.

C. D. Chen, I. Kim, O. Mizuhara, T. V. Nguyen, K. Ogawa, R. E. Tench, L. D. Tzeng, and P. D. Yeates, “40 Gbit/s×35 ch (1.4 Tbit/s aggregate capacity) WDM transmission over 85 kmstandard singlemode fibre,” Electron. Lett. 34, 2370-2371(1998).
[CrossRef]

Chen, X.

M. Li, X. Chen, J. Hayashi, and H. Li, “Advanced design of the ultrahigh-channel-count fiber Bragg grating based on the double sampling method,” Opt. Express 17, 8382-8394 (2009).
[CrossRef] [PubMed]

X. Chen, Y. Luo, C. Fan, T. Wu, and S. 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 Photon. Technol. Lett. 12, 1013-1015(2000).
[CrossRef]

Chotard, H.

Y. Painchaud, A. Mailloux, H. Chotard, E. Pelletier, and M. Guy, “Multi-channel fiber Bragg gratings for dispersion and slope compensation,” in Optical Fiber Communication (Optical Society of America, 2002), paper ThAA5.

Cole, M.

M. Ibsen, M. Durkin, M. Cole, and R. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10, 842-844 (1998).
[CrossRef]

Dhosi, G.

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett. 31, 899-901(1995).
[CrossRef]

Durkin, M.

M. Ibsen, M. Durkin, M. Cole, and R. 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. 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]

Edvell, G.

Eggleton, B.

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett. 31, 899-901(1995).
[CrossRef]

Englund, M.

Erdogan, T.

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

Fan, C.

X. Chen, Y. Luo, C. Fan, T. Wu, and S. 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 Photon. Technol. Lett. 12, 1013-1015(2000).
[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]

Guy, M.

Y. Painchaud, A. Mailloux, H. Chotard, E. Pelletier, and M. Guy, “Multi-channel fiber Bragg gratings for dispersion and slope compensation,” in Optical Fiber Communication (Optical Society of America, 2002), paper ThAA5.

Hayashi, J.

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]

M. Ibsen, M. Durkin, M. Cole, and R. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10, 842-844 (1998).
[CrossRef]

Kim, I.

C. D. Chen, I. Kim, O. Mizuhara, T. V. Nguyen, K. Ogawa, R. E. Tench, L. D. Tzeng, and P. D. Yeates, “40 Gbit/s×35 ch (1.4 Tbit/s aggregate capacity) WDM transmission over 85 kmstandard singlemode fibre,” Electron. Lett. 34, 2370-2371(1998).
[CrossRef]

Kolossovski, K. Y.

A. V. BuryakK. 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]

Krug, P. A.

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett. 31, 899-901(1995).
[CrossRef]

Laming, R.

M. Ibsen, M. Durkin, M. Cole, and R. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10, 842-844 (1998).
[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]

Lederer, F.

U. Peschel, T. Peschel, and F. Lederer, “A compact device for highly efficient dispersion compensation in fiber transmission,” Appl. Phys. Lett. 67, 2111-2113 (1995).
[CrossRef]

Lee, H.

Li, H.

Li, M.

Loh, W. H.

W. H. Loh, F. Q. Zhou, and J. J. Pan, “Sampled fiber grating based--dispersion slope compensator,” IEEE Photon. Technol. Lett. 11, 1280-1282 (1999).
[CrossRef]

Luo, Y.

X. Chen, Y. Luo, C. Fan, T. Wu, and S. 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 Photon. Technol. Lett. 12, 1013-1015(2000).
[CrossRef]

Mailloux, A.

Y. Painchaud, A. Mailloux, H. Chotard, E. Pelletier, and M. Guy, “Multi-channel fiber Bragg gratings for dispersion and slope compensation,” in Optical Fiber Communication (Optical Society of America, 2002), paper ThAA5.

Mizuhara, O.

C. D. Chen, I. Kim, O. Mizuhara, T. V. Nguyen, K. Ogawa, R. E. Tench, L. D. Tzeng, and P. D. Yeates, “40 Gbit/s×35 ch (1.4 Tbit/s aggregate capacity) WDM transmission over 85 kmstandard singlemode fibre,” Electron. Lett. 34, 2370-2371(1998).
[CrossRef]

Morin, M.

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

Nguyen, T. V.

C. D. Chen, I. Kim, O. Mizuhara, T. V. Nguyen, K. Ogawa, R. E. Tench, L. D. Tzeng, and P. D. Yeates, “40 Gbit/s×35 ch (1.4 Tbit/s aggregate capacity) WDM transmission over 85 kmstandard singlemode fibre,” Electron. Lett. 34, 2370-2371(1998).
[CrossRef]

Ogawa, K.

C. D. Chen, I. Kim, O. Mizuhara, T. V. Nguyen, K. Ogawa, R. E. Tench, L. D. Tzeng, and P. D. Yeates, “40 Gbit/s×35 ch (1.4 Tbit/s aggregate capacity) WDM transmission over 85 kmstandard singlemode fibre,” Electron. Lett. 34, 2370-2371(1998).
[CrossRef]

Ouellette, F.

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett. 31, 899-901(1995).
[CrossRef]

Painchaud, Y.

Y. Painchaud, A. Mailloux, H. Chotard, E. Pelletier, and M. Guy, “Multi-channel fiber Bragg gratings for dispersion and slope compensation,” in Optical Fiber Communication (Optical Society of America, 2002), paper ThAA5.

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

Pan, J. J.

W. H. Loh, F. Q. Zhou, and J. J. Pan, “Sampled fiber grating based--dispersion slope compensator,” IEEE Photon. Technol. Lett. 11, 1280-1282 (1999).
[CrossRef]

Pelletier, E.

Y. Painchaud, A. Mailloux, H. Chotard, E. Pelletier, and M. Guy, “Multi-channel fiber Bragg gratings for dispersion and slope compensation,” in Optical Fiber Communication (Optical Society of America, 2002), paper ThAA5.

Peschel, T.

U. Peschel, T. Peschel, and F. Lederer, “A compact device for highly efficient dispersion compensation in fiber transmission,” Appl. Phys. Lett. 67, 2111-2113 (1995).
[CrossRef]

Peschel, U.

U. Peschel, T. Peschel, and F. Lederer, “A compact device for highly efficient dispersion compensation in fiber transmission,” Appl. Phys. Lett. 67, 2111-2113 (1995).
[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 Bragg grating by layer peeling,” IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

Steblina, V.

Stepanov, D. Y.

A. V. BuryakK. 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]

Stephens, T.

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett. 31, 899-901(1995).
[CrossRef]

Tench, R. E.

C. D. Chen, I. Kim, O. Mizuhara, T. V. Nguyen, K. Ogawa, R. E. Tench, L. D. Tzeng, and P. D. Yeates, “40 Gbit/s×35 ch (1.4 Tbit/s aggregate capacity) WDM transmission over 85 kmstandard singlemode fibre,” Electron. Lett. 34, 2370-2371(1998).
[CrossRef]

Tzeng, L. D.

C. D. Chen, I. Kim, O. Mizuhara, T. V. Nguyen, K. Ogawa, R. E. Tench, L. D. Tzeng, and P. D. Yeates, “40 Gbit/s×35 ch (1.4 Tbit/s aggregate capacity) WDM transmission over 85 kmstandard singlemode fibre,” Electron. Lett. 34, 2370-2371(1998).
[CrossRef]

Wang, L.

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

Wu, T.

X. Chen, Y. Luo, C. Fan, T. Wu, and S. 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 Photon. Technol. Lett. 12, 1013-1015(2000).
[CrossRef]

Xie, S.

X. Chen, Y. Luo, C. Fan, T. Wu, and S. 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 Photon. Technol. Lett. 12, 1013-1015(2000).
[CrossRef]

Yeates, P. D.

C. D. Chen, I. Kim, O. Mizuhara, T. V. Nguyen, K. Ogawa, R. E. Tench, L. D. Tzeng, and P. D. Yeates, “40 Gbit/s×35 ch (1.4 Tbit/s aggregate capacity) WDM transmission over 85 kmstandard singlemode fibre,” Electron. Lett. 34, 2370-2371(1998).
[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]

Zhou, F. Q.

W. H. Loh, F. Q. Zhou, and J. J. Pan, “Sampled fiber grating based--dispersion slope compensator,” IEEE Photon. Technol. Lett. 11, 1280-1282 (1999).
[CrossRef]

Appl. Phys. Lett. (1)

U. Peschel, T. Peschel, and F. Lederer, “A compact device for highly efficient dispersion compensation in fiber transmission,” Appl. Phys. Lett. 67, 2111-2113 (1995).
[CrossRef]

Electron. Lett. (2)

C. D. Chen, I. Kim, O. Mizuhara, T. V. Nguyen, K. Ogawa, R. E. Tench, L. D. Tzeng, and P. D. Yeates, “40 Gbit/s×35 ch (1.4 Tbit/s aggregate capacity) WDM transmission over 85 kmstandard singlemode fibre,” Electron. Lett. 34, 2370-2371(1998).
[CrossRef]

F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fibre Bragg gratings,” Electron. Lett. 31, 899-901(1995).
[CrossRef]

IEEE J. Quantum Electron. (2)

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

A. V. BuryakK. 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)

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]

X. Chen, Y. Luo, C. Fan, T. Wu, and S. 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 Photon. Technol. Lett. 12, 1013-1015(2000).
[CrossRef]

W. H. Loh, F. Q. Zhou, and J. J. Pan, “Sampled fiber grating based--dispersion slope compensator,” IEEE Photon. Technol. Lett. 11, 1280-1282 (1999).
[CrossRef]

M. Ibsen, M. Durkin, M. Cole, and R. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10, 842-844 (1998).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Express (5)

Opt. Lett. (1)

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).

Other (2)

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

Y. Painchaud, A. Mailloux, H. Chotard, E. Pelletier, and M. Guy, “Multi-channel fiber Bragg gratings for dispersion and slope compensation,” in Optical Fiber Communication (Optical Society of America, 2002), paper ThAA5.

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Figures (8)

Fig. 1
Fig. 1

Fourier analysis of the chirped doubly sampled FBG for simultaneous dispersion and dispersion-slope compensation. See text for description of (a)–(d).

Fig. 2
Fig. 2

(a) Reflection spectrum of the 153-channel FBG and (b) reflection and group-delay spectra of the central 3 channels.

Fig. 3
Fig. 3

Dispersion spectra of the target and the designed 153-channel FBG.

Fig. 4
Fig. 4

Designed FBG recovered from the spectral target (shown in Fig. 2) by using the inverse scattering method. (a) Index-change profile, (b) phase profile of the FBG. The inset of (a) shows the index-change profile within a length of 0.05 cm .

Fig. 5
Fig. 5

Modified Fourier coefficients of (a) 51 channels and (b) 3 channels.

Fig. 6
Fig. 6

(a) Equalized reflection spectrum for the 153 channels and (b) reflection spectrum of the central 3 channels.

Fig. 7
Fig. 7

Reflection through all the 153 channels with and without reflection equalization. R_E: reflection equalization.

Fig. 8
Fig. 8

Dispersion spectrum with and without reflection equalization.

Equations (14)

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

Δ n = Re { Δ n s g · s 1 ( z ) · s 2 ( z ) } = Re { Δ n 1 ( z ) 2 exp [ i 2 π z Λ + i ϕ g ( z ) ] · s 1 ( z ) · s ( z ) 2 } .
s 1 ( z ) = a 1 ( z ) · exp [ i θ 1 ( z ) ] = n = N 1 N 1 S 1 n exp [ i 2 n π z P 1 ] ,
s 2 ( z ) = exp [ i θ 2 ( z ) ] m = N 2 N 2 S 2 m exp [ i 2 m π z P 2 ] ,
Δ n s g ( z ) = Re { Δ n 1 ( z ) 2 exp [ i 2 π z Λ ( z ) ] } .
Λ ( z ) = Λ 0 ( 1 + C g · z ) ,
s 1 ( z ) = n = N 1 N 1 S 1 n exp [ i 2 n π z P 1 ( 1 + C 1 z ) ] ,
s 2 ( z ) = m = N 2 N 2 S 2 m exp [ i 2 m π z P 2 ( 1 + C 2 z ) ] ,
Δ n = Re { Δ n s g · s 1 ( z ) · s 2 ( z ) } Re { Δ n 1 ( z ) 2 n = N 1 N 1 m = N 2 N 2 S 1 n exp [ i 2 π n z P 1 ] × S 2 m exp [ i 2 π m z P 2 ] × exp [ i 2 π z Λ 0 ( 1 + C m n · z ) ] } ,
C m n = C g + C 2 m Λ 0 P 2 + C 1 n Λ 0 P 1 .
D i = D 2 + D 3 · Δ λ · i
( 2 N 1 + 1 ) ( 2 N 2 + 1 ) 1 2 i ( 2 N 1 + 1 ) ( 2 N 2 + 1 ) 1 2 ,
R | Δ n | 2 × | D | ,
| Δ n | 2 | S 1 n | 2 · | S 2 m | 2 .
CF = m = N 2 N 2 [ | S 2 m | 2 η 2 N 2 + 1 | D 0 | | D m | ] 2 ,

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