Abstract

We present a filter design scheme in which we use an all-fiber lattice filter to equalize Gaussian-like spectra. With a two-step design strategy, the designed equalization filter can flatten the Gaussian-like spectra in the maximally flat sense, and the spectrum ripples can be assessed quantitatively. The equalization performance is analyzed theoretically. It is also shown that the equalization performance can be improved only with an increased odd order of the lattice filter. As an illustrative example, the proposed scheme is applied to the design of an all-fiber equalization filter to flatten the output spectrum of a superluminescence light-emitting diode. Simulation and experimental results verify the theoretical analysis.

© 2005 Optical Society of America

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  1. J. Gowar, Optical Communications Systems, 2nd ed. (Prentice-Hall, 1993).
  2. G. Keiser, Optical Fibre Communications, 3rd ed. (McGraw-Hill, 2000).
  3. R. Kashyap, R. Wyatt, and P. F. Mckee, "Wavelength flattened saturated erbium amplifier using multiple side-tap Bragg gratings," Electron. Lett. 29, 1025-1026 (1993).
    [CrossRef]
  4. P. F. Wysocki, "Broad-band erbium-doped fiber amplifier flattened beyond 40nm using long-period grating filter," IEEE Photonics Technol. Lett. 9, 1343-1345 (1997).
    [CrossRef]
  5. Y. Sun, J. B. Judkins, A. K. Strivastava, L. Garett, J. L. Zyskind, J. W. Sulhoff, C. Wolf, R. M. Derosier, A. H. Gnauck, R. W. Tkach, J. Zhou, R. P. Espindola, A. M. Vengsarkar, and A. R. Chraplyvy, "Transmission of 32-WDM 0-Gb/s channels over 640km using broad-band, gain-flattened erbium-doped silica fiber amplifiers," IEEE Photonics Technol. Lett. 9, 1652-1654 (1997).
    [CrossRef]
  6. H. S. Kim, S. H. Yun, H. K. Kim, N. Park, and B. Y. Kim, "Actively gain-flattened erbium-doped fiber amplifier over 35nm by using all-fiber acoustooptic tunable filters," IEEE Photonics Technol. Lett. 10, 790-792 (1998).
    [CrossRef]
  7. Y. P. Li, C. H. Henry, E. J. Laskowski, C. Y. Mak, H. H. Yaffe, and R. Sweatt, "A waveguide EDFA gain equalization filter," Electron. Lett. 31, 2005-2006 (1996).
    [CrossRef]
  8. C. R. Doerr, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, L. W. Stulz, and J. Gates, "Dynamic wavelength equalizer in silica using the single-filtered-arm interferometer," IEEE Photonics Technol. Lett. 11, 581-583 (1999).
    [CrossRef]
  9. B. J. Offrein, F. Horst, G. L. Bona, R. Germann, H. W. M. Salemink, and R. Beyeler, "Adaptive gain equalizer in high-index-contrast SiON technology," IEEE Photonics Technol. Lett. 12, 504-506 (2000).
    [CrossRef]
  10. W. Yang, F. Huang, M. R. Fetterman, J. C. Davis, D. Goswami, and W. S. Warren, "Real-time adaptive amplitude feedback in an AOM-based ultrafast optical pulse shaping system," IEEE Photonics Technol. Lett. 11, 1665-1667 (1999).
    [CrossRef]
  11. Q. J. Wang, Y. Zhang, and Y. C. Soh, "Design of spectrum equalization filter for SLED light source," Opt. Commun. 229, 223-231 (2003).
    [CrossRef]
  12. K. Jinguji and M. Kawachi, "Synthesis of coherent two-port lattice-form optical delay-line circuit," J. Lightwave Technol. 13, 73-82 (1995).
    [CrossRef]
  13. C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: a Signal Processing Approach (Wiley, 1999).
    [CrossRef]
  14. M. Kawachi, "Planar lightwave circuits for optical signal processing," in Proceedings of the Asia-Pacific Microwave Conference (IEEE Press, 1994), paper MS2-2, pp. 39-44.
  15. Q. J. Wang, T. Liu, Y. C. Soh, and Y. Zhang, "All-fiber F3T interleaver design with specified performance parameters," Opt. Eng. 42, 3172-3178 (2003).
    [CrossRef]

2003

Q. J. Wang, Y. Zhang, and Y. C. Soh, "Design of spectrum equalization filter for SLED light source," Opt. Commun. 229, 223-231 (2003).
[CrossRef]

Q. J. Wang, T. Liu, Y. C. Soh, and Y. Zhang, "All-fiber F3T interleaver design with specified performance parameters," Opt. Eng. 42, 3172-3178 (2003).
[CrossRef]

2000

B. J. Offrein, F. Horst, G. L. Bona, R. Germann, H. W. M. Salemink, and R. Beyeler, "Adaptive gain equalizer in high-index-contrast SiON technology," IEEE Photonics Technol. Lett. 12, 504-506 (2000).
[CrossRef]

1999

W. Yang, F. Huang, M. R. Fetterman, J. C. Davis, D. Goswami, and W. S. Warren, "Real-time adaptive amplitude feedback in an AOM-based ultrafast optical pulse shaping system," IEEE Photonics Technol. Lett. 11, 1665-1667 (1999).
[CrossRef]

C. R. Doerr, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, L. W. Stulz, and J. Gates, "Dynamic wavelength equalizer in silica using the single-filtered-arm interferometer," IEEE Photonics Technol. Lett. 11, 581-583 (1999).
[CrossRef]

1998

H. S. Kim, S. H. Yun, H. K. Kim, N. Park, and B. Y. Kim, "Actively gain-flattened erbium-doped fiber amplifier over 35nm by using all-fiber acoustooptic tunable filters," IEEE Photonics Technol. Lett. 10, 790-792 (1998).
[CrossRef]

1997

P. F. Wysocki, "Broad-band erbium-doped fiber amplifier flattened beyond 40nm using long-period grating filter," IEEE Photonics Technol. Lett. 9, 1343-1345 (1997).
[CrossRef]

Y. Sun, J. B. Judkins, A. K. Strivastava, L. Garett, J. L. Zyskind, J. W. Sulhoff, C. Wolf, R. M. Derosier, A. H. Gnauck, R. W. Tkach, J. Zhou, R. P. Espindola, A. M. Vengsarkar, and A. R. Chraplyvy, "Transmission of 32-WDM 0-Gb/s channels over 640km using broad-band, gain-flattened erbium-doped silica fiber amplifiers," IEEE Photonics Technol. Lett. 9, 1652-1654 (1997).
[CrossRef]

1996

Y. P. Li, C. H. Henry, E. J. Laskowski, C. Y. Mak, H. H. Yaffe, and R. Sweatt, "A waveguide EDFA gain equalization filter," Electron. Lett. 31, 2005-2006 (1996).
[CrossRef]

1995

K. Jinguji and M. Kawachi, "Synthesis of coherent two-port lattice-form optical delay-line circuit," J. Lightwave Technol. 13, 73-82 (1995).
[CrossRef]

1993

R. Kashyap, R. Wyatt, and P. F. Mckee, "Wavelength flattened saturated erbium amplifier using multiple side-tap Bragg gratings," Electron. Lett. 29, 1025-1026 (1993).
[CrossRef]

Beyeler, R.

B. J. Offrein, F. Horst, G. L. Bona, R. Germann, H. W. M. Salemink, and R. Beyeler, "Adaptive gain equalizer in high-index-contrast SiON technology," IEEE Photonics Technol. Lett. 12, 504-506 (2000).
[CrossRef]

Bona, G. L.

B. J. Offrein, F. Horst, G. L. Bona, R. Germann, H. W. M. Salemink, and R. Beyeler, "Adaptive gain equalizer in high-index-contrast SiON technology," IEEE Photonics Technol. Lett. 12, 504-506 (2000).
[CrossRef]

Cappuzzo, M.

C. R. Doerr, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, L. W. Stulz, and J. Gates, "Dynamic wavelength equalizer in silica using the single-filtered-arm interferometer," IEEE Photonics Technol. Lett. 11, 581-583 (1999).
[CrossRef]

Chraplyvy, A. R.

Y. Sun, J. B. Judkins, A. K. Strivastava, L. Garett, J. L. Zyskind, J. W. Sulhoff, C. Wolf, R. M. Derosier, A. H. Gnauck, R. W. Tkach, J. Zhou, R. P. Espindola, A. M. Vengsarkar, and A. R. Chraplyvy, "Transmission of 32-WDM 0-Gb/s channels over 640km using broad-band, gain-flattened erbium-doped silica fiber amplifiers," IEEE Photonics Technol. Lett. 9, 1652-1654 (1997).
[CrossRef]

Davis, J. C.

W. Yang, F. Huang, M. R. Fetterman, J. C. Davis, D. Goswami, and W. S. Warren, "Real-time adaptive amplitude feedback in an AOM-based ultrafast optical pulse shaping system," IEEE Photonics Technol. Lett. 11, 1665-1667 (1999).
[CrossRef]

Derosier, R. M.

Y. Sun, J. B. Judkins, A. K. Strivastava, L. Garett, J. L. Zyskind, J. W. Sulhoff, C. Wolf, R. M. Derosier, A. H. Gnauck, R. W. Tkach, J. Zhou, R. P. Espindola, A. M. Vengsarkar, and A. R. Chraplyvy, "Transmission of 32-WDM 0-Gb/s channels over 640km using broad-band, gain-flattened erbium-doped silica fiber amplifiers," IEEE Photonics Technol. Lett. 9, 1652-1654 (1997).
[CrossRef]

Doerr, C. R.

C. R. Doerr, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, L. W. Stulz, and J. Gates, "Dynamic wavelength equalizer in silica using the single-filtered-arm interferometer," IEEE Photonics Technol. Lett. 11, 581-583 (1999).
[CrossRef]

Espindola, R. P.

Y. Sun, J. B. Judkins, A. K. Strivastava, L. Garett, J. L. Zyskind, J. W. Sulhoff, C. Wolf, R. M. Derosier, A. H. Gnauck, R. W. Tkach, J. Zhou, R. P. Espindola, A. M. Vengsarkar, and A. R. Chraplyvy, "Transmission of 32-WDM 0-Gb/s channels over 640km using broad-band, gain-flattened erbium-doped silica fiber amplifiers," IEEE Photonics Technol. Lett. 9, 1652-1654 (1997).
[CrossRef]

Fetterman, M. R.

W. Yang, F. Huang, M. R. Fetterman, J. C. Davis, D. Goswami, and W. S. Warren, "Real-time adaptive amplitude feedback in an AOM-based ultrafast optical pulse shaping system," IEEE Photonics Technol. Lett. 11, 1665-1667 (1999).
[CrossRef]

Garett, L.

Y. Sun, J. B. Judkins, A. K. Strivastava, L. Garett, J. L. Zyskind, J. W. Sulhoff, C. Wolf, R. M. Derosier, A. H. Gnauck, R. W. Tkach, J. Zhou, R. P. Espindola, A. M. Vengsarkar, and A. R. Chraplyvy, "Transmission of 32-WDM 0-Gb/s channels over 640km using broad-band, gain-flattened erbium-doped silica fiber amplifiers," IEEE Photonics Technol. Lett. 9, 1652-1654 (1997).
[CrossRef]

Gates, J.

C. R. Doerr, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, L. W. Stulz, and J. Gates, "Dynamic wavelength equalizer in silica using the single-filtered-arm interferometer," IEEE Photonics Technol. Lett. 11, 581-583 (1999).
[CrossRef]

Germann, R.

B. J. Offrein, F. Horst, G. L. Bona, R. Germann, H. W. M. Salemink, and R. Beyeler, "Adaptive gain equalizer in high-index-contrast SiON technology," IEEE Photonics Technol. Lett. 12, 504-506 (2000).
[CrossRef]

Gnauck, A. H.

Y. Sun, J. B. Judkins, A. K. Strivastava, L. Garett, J. L. Zyskind, J. W. Sulhoff, C. Wolf, R. M. Derosier, A. H. Gnauck, R. W. Tkach, J. Zhou, R. P. Espindola, A. M. Vengsarkar, and A. R. Chraplyvy, "Transmission of 32-WDM 0-Gb/s channels over 640km using broad-band, gain-flattened erbium-doped silica fiber amplifiers," IEEE Photonics Technol. Lett. 9, 1652-1654 (1997).
[CrossRef]

Gomez, L.

C. R. Doerr, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, L. W. Stulz, and J. Gates, "Dynamic wavelength equalizer in silica using the single-filtered-arm interferometer," IEEE Photonics Technol. Lett. 11, 581-583 (1999).
[CrossRef]

Goswami, D.

W. Yang, F. Huang, M. R. Fetterman, J. C. Davis, D. Goswami, and W. S. Warren, "Real-time adaptive amplitude feedback in an AOM-based ultrafast optical pulse shaping system," IEEE Photonics Technol. Lett. 11, 1665-1667 (1999).
[CrossRef]

Gowar, J.

J. Gowar, Optical Communications Systems, 2nd ed. (Prentice-Hall, 1993).

Henry, C. H.

Y. P. Li, C. H. Henry, E. J. Laskowski, C. Y. Mak, H. H. Yaffe, and R. Sweatt, "A waveguide EDFA gain equalization filter," Electron. Lett. 31, 2005-2006 (1996).
[CrossRef]

Horst, F.

B. J. Offrein, F. Horst, G. L. Bona, R. Germann, H. W. M. Salemink, and R. Beyeler, "Adaptive gain equalizer in high-index-contrast SiON technology," IEEE Photonics Technol. Lett. 12, 504-506 (2000).
[CrossRef]

Huang, F.

W. Yang, F. Huang, M. R. Fetterman, J. C. Davis, D. Goswami, and W. S. Warren, "Real-time adaptive amplitude feedback in an AOM-based ultrafast optical pulse shaping system," IEEE Photonics Technol. Lett. 11, 1665-1667 (1999).
[CrossRef]

Jinguji, K.

K. Jinguji and M. Kawachi, "Synthesis of coherent two-port lattice-form optical delay-line circuit," J. Lightwave Technol. 13, 73-82 (1995).
[CrossRef]

Judkins, J. B.

Y. Sun, J. B. Judkins, A. K. Strivastava, L. Garett, J. L. Zyskind, J. W. Sulhoff, C. Wolf, R. M. Derosier, A. H. Gnauck, R. W. Tkach, J. Zhou, R. P. Espindola, A. M. Vengsarkar, and A. R. Chraplyvy, "Transmission of 32-WDM 0-Gb/s channels over 640km using broad-band, gain-flattened erbium-doped silica fiber amplifiers," IEEE Photonics Technol. Lett. 9, 1652-1654 (1997).
[CrossRef]

Kashyap, R.

R. Kashyap, R. Wyatt, and P. F. Mckee, "Wavelength flattened saturated erbium amplifier using multiple side-tap Bragg gratings," Electron. Lett. 29, 1025-1026 (1993).
[CrossRef]

Kawachi, M.

K. Jinguji and M. Kawachi, "Synthesis of coherent two-port lattice-form optical delay-line circuit," J. Lightwave Technol. 13, 73-82 (1995).
[CrossRef]

M. Kawachi, "Planar lightwave circuits for optical signal processing," in Proceedings of the Asia-Pacific Microwave Conference (IEEE Press, 1994), paper MS2-2, pp. 39-44.

Keiser, G.

G. Keiser, Optical Fibre Communications, 3rd ed. (McGraw-Hill, 2000).

Kim, B. Y.

H. S. Kim, S. H. Yun, H. K. Kim, N. Park, and B. Y. Kim, "Actively gain-flattened erbium-doped fiber amplifier over 35nm by using all-fiber acoustooptic tunable filters," IEEE Photonics Technol. Lett. 10, 790-792 (1998).
[CrossRef]

Kim, H. K.

H. S. Kim, S. H. Yun, H. K. Kim, N. Park, and B. Y. Kim, "Actively gain-flattened erbium-doped fiber amplifier over 35nm by using all-fiber acoustooptic tunable filters," IEEE Photonics Technol. Lett. 10, 790-792 (1998).
[CrossRef]

Kim, H. S.

H. S. Kim, S. H. Yun, H. K. Kim, N. Park, and B. Y. Kim, "Actively gain-flattened erbium-doped fiber amplifier over 35nm by using all-fiber acoustooptic tunable filters," IEEE Photonics Technol. Lett. 10, 790-792 (1998).
[CrossRef]

Laskowski, E.

C. R. Doerr, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, L. W. Stulz, and J. Gates, "Dynamic wavelength equalizer in silica using the single-filtered-arm interferometer," IEEE Photonics Technol. Lett. 11, 581-583 (1999).
[CrossRef]

Laskowski, E. J.

Y. P. Li, C. H. Henry, E. J. Laskowski, C. Y. Mak, H. H. Yaffe, and R. Sweatt, "A waveguide EDFA gain equalization filter," Electron. Lett. 31, 2005-2006 (1996).
[CrossRef]

Li, Y. P.

Y. P. Li, C. H. Henry, E. J. Laskowski, C. Y. Mak, H. H. Yaffe, and R. Sweatt, "A waveguide EDFA gain equalization filter," Electron. Lett. 31, 2005-2006 (1996).
[CrossRef]

Liu, T.

Q. J. Wang, T. Liu, Y. C. Soh, and Y. Zhang, "All-fiber F3T interleaver design with specified performance parameters," Opt. Eng. 42, 3172-3178 (2003).
[CrossRef]

Madsen, C. K.

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: a Signal Processing Approach (Wiley, 1999).
[CrossRef]

Mak, C. Y.

Y. P. Li, C. H. Henry, E. J. Laskowski, C. Y. Mak, H. H. Yaffe, and R. Sweatt, "A waveguide EDFA gain equalization filter," Electron. Lett. 31, 2005-2006 (1996).
[CrossRef]

Mckee, P. F.

R. Kashyap, R. Wyatt, and P. F. Mckee, "Wavelength flattened saturated erbium amplifier using multiple side-tap Bragg gratings," Electron. Lett. 29, 1025-1026 (1993).
[CrossRef]

Offrein, B. J.

B. J. Offrein, F. Horst, G. L. Bona, R. Germann, H. W. M. Salemink, and R. Beyeler, "Adaptive gain equalizer in high-index-contrast SiON technology," IEEE Photonics Technol. Lett. 12, 504-506 (2000).
[CrossRef]

Park, N.

H. S. Kim, S. H. Yun, H. K. Kim, N. Park, and B. Y. Kim, "Actively gain-flattened erbium-doped fiber amplifier over 35nm by using all-fiber acoustooptic tunable filters," IEEE Photonics Technol. Lett. 10, 790-792 (1998).
[CrossRef]

Paunescu, A.

C. R. Doerr, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, L. W. Stulz, and J. Gates, "Dynamic wavelength equalizer in silica using the single-filtered-arm interferometer," IEEE Photonics Technol. Lett. 11, 581-583 (1999).
[CrossRef]

Salemink, H. W.

B. J. Offrein, F. Horst, G. L. Bona, R. Germann, H. W. M. Salemink, and R. Beyeler, "Adaptive gain equalizer in high-index-contrast SiON technology," IEEE Photonics Technol. Lett. 12, 504-506 (2000).
[CrossRef]

Soh, Y. C.

Q. J. Wang, Y. Zhang, and Y. C. Soh, "Design of spectrum equalization filter for SLED light source," Opt. Commun. 229, 223-231 (2003).
[CrossRef]

Q. J. Wang, T. Liu, Y. C. Soh, and Y. Zhang, "All-fiber F3T interleaver design with specified performance parameters," Opt. Eng. 42, 3172-3178 (2003).
[CrossRef]

Strivastava, A. K.

Y. Sun, J. B. Judkins, A. K. Strivastava, L. Garett, J. L. Zyskind, J. W. Sulhoff, C. Wolf, R. M. Derosier, A. H. Gnauck, R. W. Tkach, J. Zhou, R. P. Espindola, A. M. Vengsarkar, and A. R. Chraplyvy, "Transmission of 32-WDM 0-Gb/s channels over 640km using broad-band, gain-flattened erbium-doped silica fiber amplifiers," IEEE Photonics Technol. Lett. 9, 1652-1654 (1997).
[CrossRef]

Stulz, L. W.

C. R. Doerr, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, L. W. Stulz, and J. Gates, "Dynamic wavelength equalizer in silica using the single-filtered-arm interferometer," IEEE Photonics Technol. Lett. 11, 581-583 (1999).
[CrossRef]

Sulhoff, J. W.

Y. Sun, J. B. Judkins, A. K. Strivastava, L. Garett, J. L. Zyskind, J. W. Sulhoff, C. Wolf, R. M. Derosier, A. H. Gnauck, R. W. Tkach, J. Zhou, R. P. Espindola, A. M. Vengsarkar, and A. R. Chraplyvy, "Transmission of 32-WDM 0-Gb/s channels over 640km using broad-band, gain-flattened erbium-doped silica fiber amplifiers," IEEE Photonics Technol. Lett. 9, 1652-1654 (1997).
[CrossRef]

Sun, Y.

Y. Sun, J. B. Judkins, A. K. Strivastava, L. Garett, J. L. Zyskind, J. W. Sulhoff, C. Wolf, R. M. Derosier, A. H. Gnauck, R. W. Tkach, J. Zhou, R. P. Espindola, A. M. Vengsarkar, and A. R. Chraplyvy, "Transmission of 32-WDM 0-Gb/s channels over 640km using broad-band, gain-flattened erbium-doped silica fiber amplifiers," IEEE Photonics Technol. Lett. 9, 1652-1654 (1997).
[CrossRef]

Sweatt, R.

Y. P. Li, C. H. Henry, E. J. Laskowski, C. Y. Mak, H. H. Yaffe, and R. Sweatt, "A waveguide EDFA gain equalization filter," Electron. Lett. 31, 2005-2006 (1996).
[CrossRef]

Tkach, R. W.

Y. Sun, J. B. Judkins, A. K. Strivastava, L. Garett, J. L. Zyskind, J. W. Sulhoff, C. Wolf, R. M. Derosier, A. H. Gnauck, R. W. Tkach, J. Zhou, R. P. Espindola, A. M. Vengsarkar, and A. R. Chraplyvy, "Transmission of 32-WDM 0-Gb/s channels over 640km using broad-band, gain-flattened erbium-doped silica fiber amplifiers," IEEE Photonics Technol. Lett. 9, 1652-1654 (1997).
[CrossRef]

Vengsarkar, A. M.

Y. Sun, J. B. Judkins, A. K. Strivastava, L. Garett, J. L. Zyskind, J. W. Sulhoff, C. Wolf, R. M. Derosier, A. H. Gnauck, R. W. Tkach, J. Zhou, R. P. Espindola, A. M. Vengsarkar, and A. R. Chraplyvy, "Transmission of 32-WDM 0-Gb/s channels over 640km using broad-band, gain-flattened erbium-doped silica fiber amplifiers," IEEE Photonics Technol. Lett. 9, 1652-1654 (1997).
[CrossRef]

Wang, Q. J.

Q. J. Wang, T. Liu, Y. C. Soh, and Y. Zhang, "All-fiber F3T interleaver design with specified performance parameters," Opt. Eng. 42, 3172-3178 (2003).
[CrossRef]

Q. J. Wang, Y. Zhang, and Y. C. Soh, "Design of spectrum equalization filter for SLED light source," Opt. Commun. 229, 223-231 (2003).
[CrossRef]

Warren, W. S.

W. Yang, F. Huang, M. R. Fetterman, J. C. Davis, D. Goswami, and W. S. Warren, "Real-time adaptive amplitude feedback in an AOM-based ultrafast optical pulse shaping system," IEEE Photonics Technol. Lett. 11, 1665-1667 (1999).
[CrossRef]

Wolf, C.

Y. Sun, J. B. Judkins, A. K. Strivastava, L. Garett, J. L. Zyskind, J. W. Sulhoff, C. Wolf, R. M. Derosier, A. H. Gnauck, R. W. Tkach, J. Zhou, R. P. Espindola, A. M. Vengsarkar, and A. R. Chraplyvy, "Transmission of 32-WDM 0-Gb/s channels over 640km using broad-band, gain-flattened erbium-doped silica fiber amplifiers," IEEE Photonics Technol. Lett. 9, 1652-1654 (1997).
[CrossRef]

Wyatt, R.

R. Kashyap, R. Wyatt, and P. F. Mckee, "Wavelength flattened saturated erbium amplifier using multiple side-tap Bragg gratings," Electron. Lett. 29, 1025-1026 (1993).
[CrossRef]

Wysocki, P. F.

P. F. Wysocki, "Broad-band erbium-doped fiber amplifier flattened beyond 40nm using long-period grating filter," IEEE Photonics Technol. Lett. 9, 1343-1345 (1997).
[CrossRef]

Yaffe, H. H.

Y. P. Li, C. H. Henry, E. J. Laskowski, C. Y. Mak, H. H. Yaffe, and R. Sweatt, "A waveguide EDFA gain equalization filter," Electron. Lett. 31, 2005-2006 (1996).
[CrossRef]

Yang, W.

W. Yang, F. Huang, M. R. Fetterman, J. C. Davis, D. Goswami, and W. S. Warren, "Real-time adaptive amplitude feedback in an AOM-based ultrafast optical pulse shaping system," IEEE Photonics Technol. Lett. 11, 1665-1667 (1999).
[CrossRef]

Yun, S. H.

H. S. Kim, S. H. Yun, H. K. Kim, N. Park, and B. Y. Kim, "Actively gain-flattened erbium-doped fiber amplifier over 35nm by using all-fiber acoustooptic tunable filters," IEEE Photonics Technol. Lett. 10, 790-792 (1998).
[CrossRef]

Zhang, Y.

Q. J. Wang, Y. Zhang, and Y. C. Soh, "Design of spectrum equalization filter for SLED light source," Opt. Commun. 229, 223-231 (2003).
[CrossRef]

Q. J. Wang, T. Liu, Y. C. Soh, and Y. Zhang, "All-fiber F3T interleaver design with specified performance parameters," Opt. Eng. 42, 3172-3178 (2003).
[CrossRef]

Zhao, J. H.

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: a Signal Processing Approach (Wiley, 1999).
[CrossRef]

Zhou, J.

Y. Sun, J. B. Judkins, A. K. Strivastava, L. Garett, J. L. Zyskind, J. W. Sulhoff, C. Wolf, R. M. Derosier, A. H. Gnauck, R. W. Tkach, J. Zhou, R. P. Espindola, A. M. Vengsarkar, and A. R. Chraplyvy, "Transmission of 32-WDM 0-Gb/s channels over 640km using broad-band, gain-flattened erbium-doped silica fiber amplifiers," IEEE Photonics Technol. Lett. 9, 1652-1654 (1997).
[CrossRef]

Zyskind, J. L.

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Figures (10)

Fig. 1
Fig. 1

Scheme of Gaussian-like spectrum equalization.

Fig. 2
Fig. 2

Configuration of an M th -order optical lattice filter.

Fig. 3
Fig. 3

Flow chart illustrating the design algorithm.

Fig. 4
Fig. 4

Block diagram illustrating the tunability of the proposed scheme implemented with waveguide couplers.

Fig. 5
Fig. 5

Tuning algorithm for equalization of varying Gaussian spectra.

Fig. 6
Fig. 6

Performance of the overall spectrum responses with respect to the parameters of the input Gaussian spectrum bearing up to ± 5 % variations where the designed equalization lattice filter is fixed.

Fig. 7
Fig. 7

Original spectrum of the SLED measured from an OSA.

Fig. 8
Fig. 8

Overall SLED spectrum responses with a maximally flat transmission.

Fig. 9
Fig. 9

Comparisons of the overall spectra of SLED designed by lattice filters with different orders.

Fig. 10
Fig. 10

Experimental SLED spectrum responses with a maximally flat transmission.

Tables (2)

Tables Icon

Table 1 ϵ - dB Bandwidth of the Equalized Spectrum Obtained with the Proposed Equalization Scheme a

Tables Icon

Table 2 Design Parameters of Optical Lattice Filters with Different Orders for the Maximally Flat Spectrum of SLED

Equations (46)

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[ E 3 E 4 ] = S M + 1 i = M 1 ( S i ϕ S i ) [ E 1 E 2 ] ,
S i = [ c i j s i j s i c i ] for i = 1 , 2 , , M + 1 ,
S i ϕ = [ exp ( j w ) 0 0 exp ( j w ) ] for i = 1 , 2 , M ,
T bar M = exp [ j M w ]0 { k = 1 M + 1 b k , M + 1 exp [ 2 j ( k 1 ) w ] } ,
P bar M = T bar M T bar M * = { k = 1 M + 1 b k , M + 1 exp [ 2 j ( k 1 ) w ] } { k = 1 M + 1 b k , M + 1 exp [ 2 j ( k 1 ) w ] } = k = 1 M + 1 a k , M + 1 cos 2 ( k 1 ) w ,
d q ( P bar M F ) d q w w = 0 = l = 0 q [ C q l ] d q l ( P bar M ) d w q l d l ( F ) d w l w = 0
f ( 2 p ) ( w ) = f ( 2 p ) ( w ) ,
f ( 2 p 1 ) ( w ) = f ( 2 p 1 ) ( w ) ,
d 2 p ( P bar M F ) d 2 p w w = 0 = l = 0 p [ C 2 q 2 l ] d 2 p 2 l ( P bar M ) d w 2 p 2 l d 2 l ( F ) d w 2 l w = 0 = k = 1 M + 1 { l = 0 p [ C 2 q 2 l ] ( 1 ) p ( 2 k 2 ) ( 2 p 2 l ) i = 1 l ( 2 i 1 ) δ 2 l } a k , M + 1 = 0 ,
[ 1 δ 2 2 2 + 1 δ 2 ( 2 M ) 2 + 1 δ 2 3 δ 4 2 4 + 6 2 2 δ 2 + 3 δ 4 ( 2 M ) 4 + 6 ( 2 M ) 2 1 δ 2 + 3 δ 4 i = 1 M + 1 ( 2 i 1 ) δ 2 M + 2 , l = 0 M + 1 C 2 M + 2 2 l ( 4 2 ) ( 2 M + 2 2 l ) i = 1 l ( 2 i 1 ) δ 2 l , , l = 0 M + 1 C 2 M + 2 2 l ( 2 M ) ( 2 M + 2 2 l ) i = 1 l ( 2 i 1 ) δ 2 l ] v = 0 .
max { a 1 , M + 1 , a 2 , M + 1 , , a M + 1 , M + 1 } [ ( P bar M F ) w = 0 ] .
max { a 1 , M + 1 , a 2 , M + 1 , , a M + 1 , M + 1 } [ k = 1 M + 1 a k , M + 1 ] .
{ max [ g ( v ) ] = max [ k = 1 M + 1 a k , M + 1 ] s.t. A v = 0 } ,
A = [ 1 δ 2 2 2 + 1 δ 2 ( 2 M ) 2 + 1 δ 2 3 δ 4 2 4 + 6 2 2 δ 2 + 3 δ 4 ( 2 M ) 4 + 6 ( 2 M ) 2 1 δ 2 + 3 δ 4 i = 1 M ( 2 i 1 ) δ 2 M , l = 0 M C 2 M 2 l 2 2 ( M l ) i = 1 l ( 2 i 1 ) δ 2 l , , l = 0 M C 2 M 2 l ( 2 M ) 2 ( M l ) i = 1 l ( 2 i 1 ) δ 2 l ] .
A 1 v 1 + a 1 v 2 = 0 .
{ max [ e T v 1 + v 2 ] = max [ ( 1 e T A 1 1 a 1 ) v 2 ] s.t. 1 2 v 2 0 } ,
[ I 0 e T A 1 1 I ] [ A 1 a 1 e T 1 ] [ I A 1 1 a 1 0 I ] = [ A 1 0 0 1 e T A 1 1 a 1 ] .
det [ A 1 a 1 e T 1 ] = det ( A 1 ) det ( 1 e T A 1 a 1 ) .
1 e T A 1 a 1 = det [ A 1 a 1 e T 1 ] det ( A 1 ) .
v 1 = 1 2 A 1 1 a 1
θ n = arctan ( c n , n b n , n ) ,
b k , n 1 = ( b k + 1 , n cos θ n c k + 1 , n sin θ n ) ,
c k , n 1 = ( b k , n sin θ n + c k , n cos θ n )
( P ̂ bar M F ) ( 2 M + 2 ) w = 0 = [ i = 1 M + 1 ( 2 i 1 ) δ 2 M + 2 , l = 0 M + 1 C 2 M + 2 2 l ( 4 2 ) ( 2 M + 2 2 l ) i = 1 l ( 2 i 1 ) δ 2 l , , l = 0 M + 1 C 2 M + 2 2 l ( 2 M ) ( 2 M + 2 2 l ) i = 1 l ( 2 i 1 ) δ 2 l ] v ̂ .
P ¯ bar M F e T v ̂ + u ( δ ) T v ̂ ( 2 M + 2 ) ! w 2 M + 2 .
BW ϵ = 2 ( λ b λ c ) = 2 ( λ c Δ L π n ref Δ L π n ref 2 w b λ c λ c ) ,
max [ P bar 1 F w = 0 ]
d ( P bar 1 F ) d w w = 0 = d 2 ( P bar 1 F ) d w 2 w = 0 = d 3 ( P bar 1 F ) d w 3 w = 0 = 0 .
[ 1 δ 2 , 2 2 + 1 δ 2 ] [ a 1 , 2 a 2 , 2 ] = 0 .
[ 1 δ 2 , 2 2 + 1 δ 2 , 4 2 + 1 δ 2 3 δ 4 , 2 4 + 6 2 2 δ 2 + 3 δ 4 , 4 4 + 6 4 2 δ 2 + 3 δ 4 ] [ a 1 , 3 a 2 , 3 a 3 , 3 ] = 0 .
[ 1 0 0 1 δ 2 0 1 0 3 δ 4 0 0 1 i = 1 M ( 2 i 1 ) δ 2 M 0 0 0 1 ] × [ 1 δ 2 2 2 + 1 δ 2 ( 2 M ) 2 + 1 δ 2 3 δ 4 2 4 + 6 2 2 δ 2 + 3 δ 4 ( 2 M ) 4 + 6 ( 2 M ) 2 1 δ 2 + 3 δ 4 i = 1 M ( 2 i 1 ) δ 2 M , l = 0 M C 2 M 2 l 2 2 ( M 1 ) i = 1 l ( 2 i 1 ) δ 2 l , , l = 0 M C 2 M 2 l ( 2 M ) 2 ( M l ) i = 1 l ( 2 i 1 ) δ 2 l 1 , 1 , , 1 ]
= [ 0 2 2 ( 2 M ) 2 0 2 4 + 6 2 2 δ 2 ( 2 M ) 4 + 6 ( 2 M ) 2 1 δ 2 0 , l = 0 M 1 C 2 M 2 l 2 2 ( M l ) i = 1 l ( 2 i 1 ) δ 2 l , , l = 0 M 1 C 2 M 2 l ( 2 M ) 2 ( M l ) i = 1 l ( 2 i 1 ) δ 2 l 1 , 1 , , 1 ] .
det [ A 1 a 1 e T 1 ] = ( 1 ) M + 2 det ( B 1 ) ,
[ 2 2 4 2 ( 2 M ) 2 2 4 4 4 ( 2 M ) 4 2 2 ( M 1 ) 4 2 ( M 1 ) , ( 2 M ) 2 ( M 1 ) 2 2 M 4 2 M , ( 2 M ) 2 M ] .
A 1 = [ 1 δ 2 2 2 + 1 δ 2 ( 2 M 2 ) 2 + 1 δ 2 3 δ 4 2 4 + 6 2 2 δ 2 + 3 δ 4 ( 2 M 2 ) 4 + 6 ( 2 M 2 ) 2 1 δ 2 + 3 δ 4 i = 1 M ( 2 i 1 ) δ 2 M , l = 0 M 1 C 2 M 2 l 2 2 ( M l ) i = 1 l ( 2 i 1 ) δ 2 l , , l = 0 M 1 C 2 M 2 l ( 2 M 2 ) 2 ( M l ) i = 1 l ( 2 i 1 ) δ 2 l ] .
[ 1 δ 2 2 2 ( 2 M 2 ) 2 3 δ 4 2 4 ( 2 M 2 ) 4 ( 1 ) p 1 i = 1 p ( 2 i 1 ) δ 2 p 2 2 p ( 2 M 2 ) 2 p ( 1 ) M 1 i = 1 M ( 2 i 1 ) δ 2 M , 2 2 M ( 2 M 2 ) 2 M ] .
[ 1 δ 2 2 2 ( 2 M 2 ) 2 3 δ 4 2 4 ( 2 M 2 ) 4 ( 1 ) p 1 i = 1 p ( 2 i 1 ) δ 2 p , 2 2 p ( 2 M 2 ) 2 p ] .
E 1 A 1 ( k ) E 2 = [ 1 δ 2 2 2 ( 2 M 2 ) 2 3 δ 4 2 4 ( 2 M 2 ) 4 ( 1 ) k 2 i = 1 k 1 ( 2 i 1 ) δ 2 ( k 1 ) , 2 2 ( k 1 ) ( 2 M 2 ) 2 ( k 1 ) ] .
A 1 ( k ) = [ A 1 ( k 1 ) i = 1 k ( 2 i 1 ) δ 2 k , l = 0 k 1 C 2 k 2 l 2 ( 2 k 2 l ) i = 1 l ( 2 i 1 ) δ 2 l , , l = 0 k 1 C 2 k 2 l ( 2 M 2 ) ( 2 k 2 l ) i = 1 l ( 2 i 1 ) δ 2 l ] .
[ E 1 0 0 1 ] A 1 ( k + 1 ) [ E 2 0 0 1 ] = [ E 1 A 1 ( k ) E 2 i = 1 k ( 2 i 1 ) δ 2 k , l = 0 k 1 C 2 k 2 l 2 ( 2 k 2 l ) i = 1 l ( 2 i 1 ) δ 2 l , , l = 0 k 1 C 2 k 2 l ( 2 M 2 ) ( 2 k 2 l ) i = 1 l ( 2 i 1 ) δ 2 l ]
= [ 1 δ 2 2 2 ( 2 M 2 ) 2 3 δ 4 2 4 ( 2 M 2 ) 4 ( 1 ) k 2 i = 1 k 1 ( 2 i 1 ) δ 2 k , 2 2 ( k 1 ) ( 2 M 2 ) 2 ( k 1 ) i = 1 k ( 2 i 1 ) δ 2 k , l = 0 k 1 C 2 k 2 l 2 ( 2 k 2 l ) i = 1 l ( 2 i 1 ) δ 2 l , , l = 0 k 1 C 2 k 2 l ( 2 M 2 ) ( 2 k 2 l ) i = 1 l ( 2 i 1 ) δ 2 l ] .
[ 1 δ 2 2 2 ( 2 M 2 ) 2 3 δ 4 2 4 ( 2 M 2 ) 4 ( 1 ) ( k 1 ) 1 i = 1 k 1 ( 2 i 1 ) δ 2 ( k 1 ) , 2 2 ( k 1 ) ( 2 M 2 ) 2 ( k 1 ) h 2 2 k ( 2 M 2 ) 2 k ] ,
h = [ 1 δ 2 C 2 k 2 ( k 1 ) ( 2 k 3 ) ! 2 k 2 ( k 2 ) ! δ 2 ( k 1 ) + 3 δ 4 C 2 k 2 ( k 2 ) ( 2 k 5 ) ! 2 k 3 ( k 3 ) ! δ 2 ( k 2 ) + + ( 1 ) k 1 ( 2 k 3 ) ! 2 k 2 ( k 2 ) ! δ 2 ( k 1 ) C 2 k 2 1 δ 2 ] + ( 2 k 1 ) ! 2 k 1 ( k 1 ) ! δ 2 k .
h = i = 1 k ( 2 i 1 ) δ 2 k
h = 2 × 4 n ( 4 n 1 ) ! 2 2 n 1 ( 2 n 1 ) ! δ 2 k [ i = 1 2 n 1 ( 1 ) i ( 2 i 1 ) ! 2 2 n 1 ( 2 n 1 ) ! 2 i 1 ( i 1 ) ! 2 2 n i ( 2 n i ) ! ( 2 i ) ! ] + i = 1 k ( 2 i 1 ) δ 2 k = 2 × 4 n ( 4 n 1 ) ! 2 2 n 1 ( 2 n 1 ) ! δ 2 k [ 2 8 n + 1 8 n i = 0 2 n ( 1 ) i C 2 n i ] + i = 1 k ( 2 i 1 ) δ 2 k = i = 1 k ( 2 i 1 ) δ 2 k
det ( A 1 ) = p = 1 M ( 1 ) p + 1 ( 1 ) p 1 i = 1 p ( 2 i 1 ) δ 2 p det ( A p , 1 ) > 0 ,

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