Abstract

We present a design scheme to achieve equalization of Gaussian-like spectra by using linear-phase optical lattice filters. The proposed scheme separates the design of the phase response from the amplitude response of the equalization filter by introducing a symmetrically folded lattice structure. With the proposed structure, the linear-phase characteristic of the equalization filter is guaranteed regardless of the other design parameters. Then the amplitude response of the equalization filter is designed through a constrained optimization problem solved by using an efficient recursive algorithm. In addition to theoretical analysis, the effectiveness of the proposed design scheme is demonstrated by simulations and experiments through the equalization of a super-luminescence light-emitting diode as an illustrative example.

© 2007 Optical Society of America

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References

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  1. G. Keiser, Optical Fibre Communications, 3rd ed. (McGraw-Hill, 2000).
  2. G. P. Agrawal, Fiber-Optic Communications Systems, 3rd ed. (Wiley, 2002).
    [CrossRef]
  3. D. Derickson, Fiber Optic Test and Measurement (Prentice Hall, 1998).
  4. H. Suzuki, N. Takachio, O. Ishida, and M. Koga, "Power excursion suppression in cascades of optical amplifiers with automatic maximum level control," IEEE Photon. Technol. Lett. 11, 1051-1053 (1999).
    [CrossRef]
  5. D. T. Reid, M. Padgett, C. McGowan, W. E. Sleat, and W. Sibbett, "Light-emitting diodes as measurement devices for femtosecond laser pulses," Opt. Lett. 22, 233-235 (1997).
    [CrossRef] [PubMed]
  6. R. H. A. Rahim and K. S. Chan, "Optical tomography system for process measurement using light-emitting diodes as a light source," Opt. Eng. 43, 1251-1257 (2004).
    [CrossRef]
  7. Y. Zhang, Q. J. Wang, and Y. C. Soh, "Equalization of Gaussian-like spectra with optical lattice filters," J. Opt. Soc. Am. B 22, 1498-1511 (2005).
    [CrossRef]
  8. Q. J. Wang, Z. G. Dong, Y. Zhang, and Y. C. Soh, "Equalization of Gaussian-like spectra via optical lattice filters with symmetric feedback structure," J. Lightwave Technol. (to be published).
  9. L. Grüner-Nielsen, B. Edvold, D. Magnussen, D. Peckham, A. Vengsarkar, D. Jacobsen, T. Veng, C. C. Larsen, and H. Damsgaard, "Large volume manufacturing of dispersion-compensating fibers," in Optical Fiber Communications Conference, Vol. 2 of OSA Proceedings Series (Optical Society of America, 1998), pp. 24-25.
  10. F. Ouellette, "Dispersion cancellation using linearly chirped Bragg grating filters in optical waveguides," Opt. Lett. 12, 847-849 (1987).
    [CrossRef] [PubMed]
  11. G. Lenz and C. K. Madsen, "General optical all-pass filter structures for dispersion control in WDM systems," J. Lightwave Technol. 17, 1248-1254 (1999).
    [CrossRef]
  12. G. Lenz, B. J. Eggleton, C. K. Madsen, C. R. Giles, and G. Nykolak, "Optimal dispersion of optical filters for WDM systems," IEEE Photon. Technol. Lett. 10, 567-569 (1998).
    [CrossRef]
  13. T. Chiba, H. Arai, K. Ohira, H. Nonen, H. Okano, and H. Uetsuka, "Novel architecture of wavelength interleaving filter with Fourier transform-based MZIs," in Optical Fiber Communications Conference, Vol. 54 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001), paper WB5.
  14. S. Kamei, M. Oguma, M. Kohtoku, T. Shibata, and Y. Inoue, "Low-loss athermal silica-based lattice-form interleave filter with silicone-filled grooves," IEEE Photon. Technol. Lett. 17, 798-800 (2005).
    [CrossRef]
  15. C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: a Signal Processing Approach (Wiley, 1999).
  16. K. Jinguji and M. Kawachi, "Synthesis of coherent two-port lattice-form optical delay-line circuit," J. Lightwave Technol. 13, 73-82 (1995).
    [CrossRef]
  17. 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]
  18. 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]
  19. J. C. Chon, A. Zeng, P. Peters, B. Jian, A. Luo, and K. Sullivan, "Integrated interleaver technology enables high performance in DWDM systems," National Fiber Optic Engineers Conference 2001 (Optical Society of America, 2001), pp. 1410-1421, 2001.
  20. M. Kawachi, "Planar lightwave circuits for optical signal processing," Proc. Asia Pacific Microwave Conference 1994, MS2-2 (IEEE, 1994), pp. 39-44, 1994.

2005 (2)

Y. Zhang, Q. J. Wang, and Y. C. Soh, "Equalization of Gaussian-like spectra with optical lattice filters," J. Opt. Soc. Am. B 22, 1498-1511 (2005).
[CrossRef]

S. Kamei, M. Oguma, M. Kohtoku, T. Shibata, and Y. Inoue, "Low-loss athermal silica-based lattice-form interleave filter with silicone-filled grooves," IEEE Photon. Technol. Lett. 17, 798-800 (2005).
[CrossRef]

2004 (1)

R. H. A. Rahim and K. S. Chan, "Optical tomography system for process measurement using light-emitting diodes as a light source," Opt. Eng. 43, 1251-1257 (2004).
[CrossRef]

2003 (2)

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]

1999 (2)

G. Lenz and C. K. Madsen, "General optical all-pass filter structures for dispersion control in WDM systems," J. Lightwave Technol. 17, 1248-1254 (1999).
[CrossRef]

H. Suzuki, N. Takachio, O. Ishida, and M. Koga, "Power excursion suppression in cascades of optical amplifiers with automatic maximum level control," IEEE Photon. Technol. Lett. 11, 1051-1053 (1999).
[CrossRef]

1998 (1)

G. Lenz, B. J. Eggleton, C. K. Madsen, C. R. Giles, and G. Nykolak, "Optimal dispersion of optical filters for WDM systems," IEEE Photon. Technol. Lett. 10, 567-569 (1998).
[CrossRef]

1997 (1)

1995 (1)

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

1987 (1)

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communications Systems, 3rd ed. (Wiley, 2002).
[CrossRef]

Arai, H.

T. Chiba, H. Arai, K. Ohira, H. Nonen, H. Okano, and H. Uetsuka, "Novel architecture of wavelength interleaving filter with Fourier transform-based MZIs," in Optical Fiber Communications Conference, Vol. 54 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001), paper WB5.

Chan, K. S.

R. H. A. Rahim and K. S. Chan, "Optical tomography system for process measurement using light-emitting diodes as a light source," Opt. Eng. 43, 1251-1257 (2004).
[CrossRef]

Chiba, T.

T. Chiba, H. Arai, K. Ohira, H. Nonen, H. Okano, and H. Uetsuka, "Novel architecture of wavelength interleaving filter with Fourier transform-based MZIs," in Optical Fiber Communications Conference, Vol. 54 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001), paper WB5.

Chon, J. C.

J. C. Chon, A. Zeng, P. Peters, B. Jian, A. Luo, and K. Sullivan, "Integrated interleaver technology enables high performance in DWDM systems," National Fiber Optic Engineers Conference 2001 (Optical Society of America, 2001), pp. 1410-1421, 2001.

Damsgaard, H.

L. Grüner-Nielsen, B. Edvold, D. Magnussen, D. Peckham, A. Vengsarkar, D. Jacobsen, T. Veng, C. C. Larsen, and H. Damsgaard, "Large volume manufacturing of dispersion-compensating fibers," in Optical Fiber Communications Conference, Vol. 2 of OSA Proceedings Series (Optical Society of America, 1998), pp. 24-25.

Derickson, D.

D. Derickson, Fiber Optic Test and Measurement (Prentice Hall, 1998).

Dong, Z. G.

Q. J. Wang, Z. G. Dong, Y. Zhang, and Y. C. Soh, "Equalization of Gaussian-like spectra via optical lattice filters with symmetric feedback structure," J. Lightwave Technol. (to be published).

Edvold, B.

L. Grüner-Nielsen, B. Edvold, D. Magnussen, D. Peckham, A. Vengsarkar, D. Jacobsen, T. Veng, C. C. Larsen, and H. Damsgaard, "Large volume manufacturing of dispersion-compensating fibers," in Optical Fiber Communications Conference, Vol. 2 of OSA Proceedings Series (Optical Society of America, 1998), pp. 24-25.

Eggleton, B. J.

G. Lenz, B. J. Eggleton, C. K. Madsen, C. R. Giles, and G. Nykolak, "Optimal dispersion of optical filters for WDM systems," IEEE Photon. Technol. Lett. 10, 567-569 (1998).
[CrossRef]

Giles, C. R.

G. Lenz, B. J. Eggleton, C. K. Madsen, C. R. Giles, and G. Nykolak, "Optimal dispersion of optical filters for WDM systems," IEEE Photon. Technol. Lett. 10, 567-569 (1998).
[CrossRef]

Grüner-Nielsen, L.

L. Grüner-Nielsen, B. Edvold, D. Magnussen, D. Peckham, A. Vengsarkar, D. Jacobsen, T. Veng, C. C. Larsen, and H. Damsgaard, "Large volume manufacturing of dispersion-compensating fibers," in Optical Fiber Communications Conference, Vol. 2 of OSA Proceedings Series (Optical Society of America, 1998), pp. 24-25.

Inoue, Y.

S. Kamei, M. Oguma, M. Kohtoku, T. Shibata, and Y. Inoue, "Low-loss athermal silica-based lattice-form interleave filter with silicone-filled grooves," IEEE Photon. Technol. Lett. 17, 798-800 (2005).
[CrossRef]

Ishida, O.

H. Suzuki, N. Takachio, O. Ishida, and M. Koga, "Power excursion suppression in cascades of optical amplifiers with automatic maximum level control," IEEE Photon. Technol. Lett. 11, 1051-1053 (1999).
[CrossRef]

Jacobsen, D.

L. Grüner-Nielsen, B. Edvold, D. Magnussen, D. Peckham, A. Vengsarkar, D. Jacobsen, T. Veng, C. C. Larsen, and H. Damsgaard, "Large volume manufacturing of dispersion-compensating fibers," in Optical Fiber Communications Conference, Vol. 2 of OSA Proceedings Series (Optical Society of America, 1998), pp. 24-25.

Jian, B.

J. C. Chon, A. Zeng, P. Peters, B. Jian, A. Luo, and K. Sullivan, "Integrated interleaver technology enables high performance in DWDM systems," National Fiber Optic Engineers Conference 2001 (Optical Society of America, 2001), pp. 1410-1421, 2001.

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]

Kamei, S.

S. Kamei, M. Oguma, M. Kohtoku, T. Shibata, and Y. Inoue, "Low-loss athermal silica-based lattice-form interleave filter with silicone-filled grooves," IEEE Photon. Technol. Lett. 17, 798-800 (2005).
[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," Proc. Asia Pacific Microwave Conference 1994, MS2-2 (IEEE, 1994), pp. 39-44, 1994.

Keiser, G.

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

Koga, M.

H. Suzuki, N. Takachio, O. Ishida, and M. Koga, "Power excursion suppression in cascades of optical amplifiers with automatic maximum level control," IEEE Photon. Technol. Lett. 11, 1051-1053 (1999).
[CrossRef]

Kohtoku, M.

S. Kamei, M. Oguma, M. Kohtoku, T. Shibata, and Y. Inoue, "Low-loss athermal silica-based lattice-form interleave filter with silicone-filled grooves," IEEE Photon. Technol. Lett. 17, 798-800 (2005).
[CrossRef]

Larsen, C. C.

L. Grüner-Nielsen, B. Edvold, D. Magnussen, D. Peckham, A. Vengsarkar, D. Jacobsen, T. Veng, C. C. Larsen, and H. Damsgaard, "Large volume manufacturing of dispersion-compensating fibers," in Optical Fiber Communications Conference, Vol. 2 of OSA Proceedings Series (Optical Society of America, 1998), pp. 24-25.

Lenz, G.

G. Lenz and C. K. Madsen, "General optical all-pass filter structures for dispersion control in WDM systems," J. Lightwave Technol. 17, 1248-1254 (1999).
[CrossRef]

G. Lenz, B. J. Eggleton, C. K. Madsen, C. R. Giles, and G. Nykolak, "Optimal dispersion of optical filters for WDM systems," IEEE Photon. Technol. Lett. 10, 567-569 (1998).
[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]

Luo, A.

J. C. Chon, A. Zeng, P. Peters, B. Jian, A. Luo, and K. Sullivan, "Integrated interleaver technology enables high performance in DWDM systems," National Fiber Optic Engineers Conference 2001 (Optical Society of America, 2001), pp. 1410-1421, 2001.

Madsen, C. K.

G. Lenz and C. K. Madsen, "General optical all-pass filter structures for dispersion control in WDM systems," J. Lightwave Technol. 17, 1248-1254 (1999).
[CrossRef]

G. Lenz, B. J. Eggleton, C. K. Madsen, C. R. Giles, and G. Nykolak, "Optimal dispersion of optical filters for WDM systems," IEEE Photon. Technol. Lett. 10, 567-569 (1998).
[CrossRef]

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

Magnussen, D.

L. Grüner-Nielsen, B. Edvold, D. Magnussen, D. Peckham, A. Vengsarkar, D. Jacobsen, T. Veng, C. C. Larsen, and H. Damsgaard, "Large volume manufacturing of dispersion-compensating fibers," in Optical Fiber Communications Conference, Vol. 2 of OSA Proceedings Series (Optical Society of America, 1998), pp. 24-25.

McGowan, C.

Nonen, H.

T. Chiba, H. Arai, K. Ohira, H. Nonen, H. Okano, and H. Uetsuka, "Novel architecture of wavelength interleaving filter with Fourier transform-based MZIs," in Optical Fiber Communications Conference, Vol. 54 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001), paper WB5.

Nykolak, G.

G. Lenz, B. J. Eggleton, C. K. Madsen, C. R. Giles, and G. Nykolak, "Optimal dispersion of optical filters for WDM systems," IEEE Photon. Technol. Lett. 10, 567-569 (1998).
[CrossRef]

Oguma, M.

S. Kamei, M. Oguma, M. Kohtoku, T. Shibata, and Y. Inoue, "Low-loss athermal silica-based lattice-form interleave filter with silicone-filled grooves," IEEE Photon. Technol. Lett. 17, 798-800 (2005).
[CrossRef]

Ohira, K.

T. Chiba, H. Arai, K. Ohira, H. Nonen, H. Okano, and H. Uetsuka, "Novel architecture of wavelength interleaving filter with Fourier transform-based MZIs," in Optical Fiber Communications Conference, Vol. 54 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001), paper WB5.

Okano, H.

T. Chiba, H. Arai, K. Ohira, H. Nonen, H. Okano, and H. Uetsuka, "Novel architecture of wavelength interleaving filter with Fourier transform-based MZIs," in Optical Fiber Communications Conference, Vol. 54 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001), paper WB5.

Ouellette, F.

Padgett, M.

Peckham, D.

L. Grüner-Nielsen, B. Edvold, D. Magnussen, D. Peckham, A. Vengsarkar, D. Jacobsen, T. Veng, C. C. Larsen, and H. Damsgaard, "Large volume manufacturing of dispersion-compensating fibers," in Optical Fiber Communications Conference, Vol. 2 of OSA Proceedings Series (Optical Society of America, 1998), pp. 24-25.

Peters, P.

J. C. Chon, A. Zeng, P. Peters, B. Jian, A. Luo, and K. Sullivan, "Integrated interleaver technology enables high performance in DWDM systems," National Fiber Optic Engineers Conference 2001 (Optical Society of America, 2001), pp. 1410-1421, 2001.

Rahim, R. H. A.

R. H. A. Rahim and K. S. Chan, "Optical tomography system for process measurement using light-emitting diodes as a light source," Opt. Eng. 43, 1251-1257 (2004).
[CrossRef]

Reid, D. T.

Shibata, T.

S. Kamei, M. Oguma, M. Kohtoku, T. Shibata, and Y. Inoue, "Low-loss athermal silica-based lattice-form interleave filter with silicone-filled grooves," IEEE Photon. Technol. Lett. 17, 798-800 (2005).
[CrossRef]

Sibbett, W.

Sleat, W. E.

Soh, Y. C.

Y. Zhang, Q. J. Wang, and Y. C. Soh, "Equalization of Gaussian-like spectra with optical lattice filters," J. Opt. Soc. Am. B 22, 1498-1511 (2005).
[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]

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, Z. G. Dong, Y. Zhang, and Y. C. Soh, "Equalization of Gaussian-like spectra via optical lattice filters with symmetric feedback structure," J. Lightwave Technol. (to be published).

Sullivan, K.

J. C. Chon, A. Zeng, P. Peters, B. Jian, A. Luo, and K. Sullivan, "Integrated interleaver technology enables high performance in DWDM systems," National Fiber Optic Engineers Conference 2001 (Optical Society of America, 2001), pp. 1410-1421, 2001.

Suzuki, H.

H. Suzuki, N. Takachio, O. Ishida, and M. Koga, "Power excursion suppression in cascades of optical amplifiers with automatic maximum level control," IEEE Photon. Technol. Lett. 11, 1051-1053 (1999).
[CrossRef]

Takachio, N.

H. Suzuki, N. Takachio, O. Ishida, and M. Koga, "Power excursion suppression in cascades of optical amplifiers with automatic maximum level control," IEEE Photon. Technol. Lett. 11, 1051-1053 (1999).
[CrossRef]

Uetsuka, H.

T. Chiba, H. Arai, K. Ohira, H. Nonen, H. Okano, and H. Uetsuka, "Novel architecture of wavelength interleaving filter with Fourier transform-based MZIs," in Optical Fiber Communications Conference, Vol. 54 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001), paper WB5.

Veng, T.

L. Grüner-Nielsen, B. Edvold, D. Magnussen, D. Peckham, A. Vengsarkar, D. Jacobsen, T. Veng, C. C. Larsen, and H. Damsgaard, "Large volume manufacturing of dispersion-compensating fibers," in Optical Fiber Communications Conference, Vol. 2 of OSA Proceedings Series (Optical Society of America, 1998), pp. 24-25.

Vengsarkar, A.

L. Grüner-Nielsen, B. Edvold, D. Magnussen, D. Peckham, A. Vengsarkar, D. Jacobsen, T. Veng, C. C. Larsen, and H. Damsgaard, "Large volume manufacturing of dispersion-compensating fibers," in Optical Fiber Communications Conference, Vol. 2 of OSA Proceedings Series (Optical Society of America, 1998), pp. 24-25.

Wang, Q. J.

Y. Zhang, Q. J. Wang, and Y. C. Soh, "Equalization of Gaussian-like spectra with optical lattice filters," J. Opt. Soc. Am. B 22, 1498-1511 (2005).
[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]

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, Z. G. Dong, Y. Zhang, and Y. C. Soh, "Equalization of Gaussian-like spectra via optical lattice filters with symmetric feedback structure," J. Lightwave Technol. (to be published).

Zeng, A.

J. C. Chon, A. Zeng, P. Peters, B. Jian, A. Luo, and K. Sullivan, "Integrated interleaver technology enables high performance in DWDM systems," National Fiber Optic Engineers Conference 2001 (Optical Society of America, 2001), pp. 1410-1421, 2001.

Zhang, Y.

Y. Zhang, Q. J. Wang, and Y. C. Soh, "Equalization of Gaussian-like spectra with optical lattice filters," J. Opt. Soc. Am. B 22, 1498-1511 (2005).
[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]

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, Z. G. Dong, Y. Zhang, and Y. C. Soh, "Equalization of Gaussian-like spectra via optical lattice filters with symmetric feedback structure," J. Lightwave Technol. (to be published).

Zhao, J. H.

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

IEEE Photon. Technol. Lett. (3)

H. Suzuki, N. Takachio, O. Ishida, and M. Koga, "Power excursion suppression in cascades of optical amplifiers with automatic maximum level control," IEEE Photon. Technol. Lett. 11, 1051-1053 (1999).
[CrossRef]

G. Lenz, B. J. Eggleton, C. K. Madsen, C. R. Giles, and G. Nykolak, "Optimal dispersion of optical filters for WDM systems," IEEE Photon. Technol. Lett. 10, 567-569 (1998).
[CrossRef]

S. Kamei, M. Oguma, M. Kohtoku, T. Shibata, and Y. Inoue, "Low-loss athermal silica-based lattice-form interleave filter with silicone-filled grooves," IEEE Photon. Technol. Lett. 17, 798-800 (2005).
[CrossRef]

J. Lightwave Technol. (2)

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

G. Lenz and C. K. Madsen, "General optical all-pass filter structures for dispersion control in WDM systems," J. Lightwave Technol. 17, 1248-1254 (1999).
[CrossRef]

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

Opt. Commun. (1)

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]

Opt. Eng. (2)

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]

R. H. A. Rahim and K. S. Chan, "Optical tomography system for process measurement using light-emitting diodes as a light source," Opt. Eng. 43, 1251-1257 (2004).
[CrossRef]

Opt. Lett. (2)

Other (9)

J. C. Chon, A. Zeng, P. Peters, B. Jian, A. Luo, and K. Sullivan, "Integrated interleaver technology enables high performance in DWDM systems," National Fiber Optic Engineers Conference 2001 (Optical Society of America, 2001), pp. 1410-1421, 2001.

M. Kawachi, "Planar lightwave circuits for optical signal processing," Proc. Asia Pacific Microwave Conference 1994, MS2-2 (IEEE, 1994), pp. 39-44, 1994.

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

T. Chiba, H. Arai, K. Ohira, H. Nonen, H. Okano, and H. Uetsuka, "Novel architecture of wavelength interleaving filter with Fourier transform-based MZIs," in Optical Fiber Communications Conference, Vol. 54 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001), paper WB5.

Q. J. Wang, Z. G. Dong, Y. Zhang, and Y. C. Soh, "Equalization of Gaussian-like spectra via optical lattice filters with symmetric feedback structure," J. Lightwave Technol. (to be published).

L. Grüner-Nielsen, B. Edvold, D. Magnussen, D. Peckham, A. Vengsarkar, D. Jacobsen, T. Veng, C. C. Larsen, and H. Damsgaard, "Large volume manufacturing of dispersion-compensating fibers," in Optical Fiber Communications Conference, Vol. 2 of OSA Proceedings Series (Optical Society of America, 1998), pp. 24-25.

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

G. P. Agrawal, Fiber-Optic Communications Systems, 3rd ed. (Wiley, 2002).
[CrossRef]

D. Derickson, Fiber Optic Test and Measurement (Prentice Hall, 1998).

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Figures (6)

Fig. 1
Fig. 1

Gaussian-like spectrum equalization scheme.

Fig. 2
Fig. 2

Proposed equalization filter with symmetric-mirror structure.

Fig. 3
Fig. 3

Flow chart illustrating the design algorithm.

Fig. 4
Fig. 4

Comparisons of the overall spectra and group delay responses, respectively, between the proposed method and the design method of Ref. [7].

Fig. 5
Fig. 5

Trade-offs among passband ripple, attenuation, and passband bandwidth.

Fig. 6
Fig. 6

Experimental SLED responses of the proposed method compared with that without linear-phase design.[7] (a) Amplitude responses with maximally flat transmissions. (b) Group delay responses of the equalizers.

Tables (2)

Tables Icon

Table 1 Design Parameters of Optical Lattice Filter for Fourth-Order Maximal Flatness

Tables Icon

Table 2 Passband Ripple and Bandwidth of the Equalized Spectrum When Considering Even-Order Unflatness a

Equations (31)

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

( E 3 ( w ) E 4 ( w ) ) = [ T bar M T cross M * T cross M T bar M * ] ( E 1 ( w ) E 2 ( w ) ) ,
( E 1 ( w ) E 2 ( w ) ) = [ T bar M T cross M T cross M * T bar M * ] ( E 3 ( w ) E 4 ( w ) ) .
S = [ Q bar M Q cross M * Q cross M Q bar M * ] = [ T bar M T cross M T cross M * T bar M * ] [ e j w 0 0 e j w ] [ T bar M T cross M * T cross M T bar M * ] .
Q cross M = T bar M * T cross M e j w T bar M T cross M * e j w = j ( k = 1 2 M + 2 f k , 2 M + 2 M e j ( 2 k 2 ) w ) e j ( 2 M + 1 ) w = j k = 1 M + 1 f M + 2 k , 2 M + 2 M cos ( 2 k 1 ) w ,
P LF M = Q cross M 2 = ( Q cross M ) 2 .
d q ( P LF M × F ) d q w w = 0 = l = 0 q ( q l ) d q 1 ( Q cross M ) 2 d w q l d l ( F ) d w l w = 0
d 2 p ( P LF M F ) d 2 p w w = 0 = l = 0 p q = 0 p l ( 2 p 2 l ) ( 2 p 2 l 2 q ) d 2 p 2 l 2 q ( Q cross M ) d w 2 p 2 l 2 q d 2 q ( Q cross M ) d w 2 q d 2 l ( F ) d w 2 l w = 0
= { ϵ when p = 1 , 0 , p = 2 , 4 , , M + 1 } .
v = [ f M + 1 , 2 M + 2 , f M , 2 M + 2 , , f 1 , 2 M + 2 ] T ,
v T A p v = { ϵ when p = 1 , 0 , p = 2 , 4 , , M + 1 } ,
a k , n p = l = 0 p q = 0 p l ( 2 p 2 l ) ( 2 p 2 l 2 q ) ( 1 ) q m = 1 l ( 2 m 1 ) δ 2 p k = 1 M + 1 n = 1 M + 1 ( 2 k 1 ) 2 p 2 l 2 q ( 2 n 1 ) 2 q ,
{ max { g ( v ) } s.t. v T A 1 v = ϵ v T A 2 v = 0 v T A M v = 0 } ,
P LF M F C 0 + C 2 w 2 + C 2 M + 2 w 2 M + 2 ,
ϵ = 10 log ( C 0 + C 2 w h 2 + v ̂ T A M + 1 v ̂ ( 2 M + 2 ) ! w h 2 M + 2 C 0 ) .
B W ϵ = 2 ( λ b λ c ) = 2 ( λ c Δ L π n eff Δ L π n eff 2 w b λ c λ c ) ,
Q bar M ( e j w ) Q bar M * ( e j w ) = 1 Q cross M ( e j w ) Q cross M * ( e j w ) = a 0 a 0 * k = 1 M + 1 ( z α k ) ( z 1 α k * ) ,
S M = [ Q bar M Q cross M * Q cross M Q bar M * ] = S M + 1 S M ϕ S M 1 S M ϕ S M + 1 ,
[ Q bar M 1 Q cross M 1 Q cross M 1 Q bar M 1 * ] = [ e j w 0 0 e j w ] [ cos θ M + 1 j sin θ M + 1 j sin θ M + 1 cos θ M + 1 ] [ Q bar M Q cross M Q cross M Q bar M * ] × [ cos θ M + 1 j sin θ M + 1 j sin θ M + 1 cos θ M + 1 ] [ e j w 0 0 e j w ]
Q bar M 1 = cos 2 θ M + 1 e 2 j w Q bar M sin 2 θ M + 1 e 2 j w Q bar M * + 2 j sin θ M + 1 cos θ M + 1 e 2 j w Q cross M ,
Q cross M 1 = ( cos 2 θ M + 1 sin 2 θ M + 1 ) Q cross M + j sin θ M + 1 cos θ M + 1 ( Q bar M + Q bar M * ) .
e 2 j M w Q bar M = e 2 j M w ( ( T bar M ) 2 e j w + ( T cross M ) 2 e j w ) = ( k = 1 2 M + 2 g k , 2 M + 2 M e j ( 2 k 2 ) w ) e j ( 2 M + 1 ) w ,
Q bar M 1 = ( k = 1 2 M g k , 2 M M 1 e j ( 2 k 2 ) w ) e j ( 2 M 1 ) w ,
Q cross M 1 = j ( k = 1 2 M f k , 2 M M 1 e j ( 2 k 2 ) w ) e j ( 2 M 1 ) w ,
Q bar M 1 = ( k = 1 2 M ( 2 sin θ M + 1 cos θ M + 1 f k + 2 , 2 M + 2 M + cos 2 θ M + 1 g k + 2 , 2 M + 2 M sin 2 θ M + 1 g 2 M + 1 k , 2 M + 2 M ) e 2 j ( k 1 ) w ) e j ( 2 M 1 ) w + ( 2 sin θ M + 1 cos θ M + 1 f 1 , 2 M + 2 M + cos 2 θ M + 1 g 1 , 2 M + 2 M sin 2 θ M + 1 g 2 M + 2 , 2 M + 2 M ) e j ( 2 M + 3 ) w + ( 2 sin θ M + 1 cos θ M + 1 f 2 , 2 M + 2 M + cos 2 θ M + 1 g 2 , 2 M + 2 M sin 2 θ M + 1 g 2 M + 1 , 2 M + 2 M ) e j ( 2 M + 1 ) w ,
Q cross M 1 = j { k = 1 2 M [ ( cos 2 θ M + 1 sin 2 θ M + 1 ) f k + 1 , 2 M + 2 M sin θ M + 1 cos θ M + 1 ( g k + 1 , 2 M + 2 M + g 2 M + 2 k , 2 M + 2 M ) ] e 2 j ( k 1 ) w } e j ( 2 M 1 ) w j [ 2 cos 2 θ M + 1 f 1 , 2 M + 2 M sin 2 θ M + 1 ( g 1 , 2 M + 2 M + g 2 M + 2 , 2 M + 2 M ) ] cos ( 2 M + 1 ) .
θ M + 1 = arctan ( g 1 , 2 M + 2 M f 1 , 2 M + 2 M ) = arctan ( f 1 , 2 M + 2 M g 2 M + 2 , 2 M + 2 M ) .
θ n + 1 = arctan ( g 1 , 2 n + 2 n f 1 , 2 n + 2 n ) ,
g k , 2 n n 1 = 2 sin θ n + 1 cos θ n + 1 f k + 2 , 2 n + 2 n + cos 2 θ n + 1 g k + 2 , 2 n + 2 n sin 2 θ n + 1 g 2 n + 1 k , 2 n + 2 n ,
f k , 2 n n 1 = ( cos 2 θ n + 1 sin 2 θ n + 1 ) f k + 1 , 2 n + 2 n sin θ n + 1 cos θ n + 1 ( g k + 1 , 2 n + 2 n + g 2 n + 2 k , 2 n + 2 n ) ,
max { P LF ( 2 ) × F w = 0 } ,
d 2 ( P LF ( 2 ) F ) d w 2 w = 0 = d 4 ( P LF ( 2 ) F ) d w 4 w = 0 = 0 .

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