Abstract

The design of integrated optics filters by use of refinement software based on the Abelès thin-film computation method and the film mode matching method is studied. The results obtained with the two computation methods are compared. Good agreement is obtained provided that the fill factor of the guided mode in the component is high and that modal losses between waveguide sections are simulated by absorption with the Abelès computation method. Integrated optics devices that manage either the amplitude of guided waves such as a dense wavelength division multiplexing narrow-bandpass filter and a gain-flattening filter or the phase of guided waves such as a broadband dispersion compensator are presented and their optical performance is discussed.

© 2002 Optical Society of America

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  1. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University, Cambridge, England, 1999), Chaps. 8 and 11.
  2. E. Rosencher, B. Vinter, Optoélectronique (Masson, Paris, 1998), Chap. 9.
  3. F. Bilodeau, K. O. Hill, B. Malo, D. C. Johnson, J. Albert, “High-return-loss narrowband all-fibre bandpass Bragg transmission filter,” IEEE Photon. Technol. Lett. 6, 80–82 (1994).
    [CrossRef]
  4. C. Narayanan, H. M. Presby, A. M. Vengsarkar, “Band-rejection fibre filter using periodic core deformation,” Electron. Lett. 33, 280–281 (1997).
    [CrossRef]
  5. A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
    [CrossRef]
  6. G. A. Ball, W. W. Morey, “Tunable Bragg grating fiber filters and their applications,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 108–109.
  7. M. Okai, I. F. Lealman, L. J. Rivers, C. Dix, M. J. Robertson, “In-line Fabry-Perot optical waveguide filter with quasi-chirped gratings,” Electron. Lett. 32, 108–109 (1996).
    [CrossRef]
  8. M. Wilkinson, A. Bebbington, S. A. Cassidy, P. McKee, “D-fibre filter for erbium gain spectrum flattening,” Electron. Lett. 28, 131–132 (1992).
    [CrossRef]
  9. A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
    [CrossRef]
  10. M. Fujimaki, Y. Ohki, “Fabrication of long-period optical fiber gratings by use of ion implantation,” Opt. Lett. 25, 88–89 (2000).
    [CrossRef]
  11. M. Janos, J. Canning, “Permanent and transient resonances thermally induced in optical fibre Bragg gratings,” Electron. Lett. 31, 1007–1009 (1995).
    [CrossRef]
  12. F. Ouellette, J. F. Cliché, S. Gagnon, “All-fiber devices for chromatic dispersion compensation based on chirped distributed resonant coupling,” J. Lightwave Technol. 12, 1728–1738 (1994).
    [CrossRef]
  13. J. A. R. Williams, I. Bennion, N. J. Doran, “The design of in-fiber Bragg gratings systems for cubic and quadratic dispersion compensation,” Opt. Commun. 116, 62–66 (1995).
    [CrossRef]
  14. M. J. Cole, H. Geiger, R. I. Laming, S. Y. Set, M. N. Zervas, W. H. Loh, V. Gusmeroli, “Broadband dispersion-compensating chirped fiber Bragg gratings in 10 Gbit/s NRZ 110 km non-dispersion-shifted fibre link operating at 1.55 µm,” Electron. Lett. 33, 70–71 (1997).
    [CrossRef]
  15. J.-C. Dung, S. Chi, “Dispersion compensation and gain flattened for a wavelength division multiplexing system by using chirped fiber gratings in an erbium-doped fiber amplifier,” Opt. Commun. 162, 219–222 (1999).
    [CrossRef]
  16. A. Inoue, “Great gratings,” Photonics Spectra, August2000, pp. 98–100.
  17. M. Das, K. Thyagarajan, “Dispersion compensation in transmission using uniform long period fiber gratings,” Opt. Commun. 190, 159–163 (2001).
    [CrossRef]
  18. H. A. Macleod, Thin Film Optical Filters (Hilger, Bristol, UK, 1986).
  19. A. S. Sudbo, “Film mode matching: a versatile numerical method for vector mode field calculations in dielectric waveguides,” Pure Appl. Opt. 2, 211–233 (1993).
    [CrossRef]
  20. J. Čtyroký, “Photonic bandgap structures in planar waveguides,” J. Opt. Soc. Am. A 18, 435–441 (2001).
    [CrossRef]
  21. L. Escoubas, E. Drouard, F. Flory, “Designing waveguide filters with optical thin-film computational tools,” Opt. Commun. 197, 309–316 (2001).
    [CrossRef]
  22. F. Abelès, “Recherche sur la propagation des ondes électromagnétiques sinusoïdales dans les milieux stratifiés,” Ann. Phys. (Paris) 5, 596–640 (1950).
  23. Ref. 22, pp. 706–782.
  24. K. Lefebvre, “Techniques take differing measures of chromatic dispersion,” WDM Solutions, May2001, pp. 79–82.
  25. D. C. McCarthy, “Chirped Bragg gratings covers the C-band,” Photonics Spectra, May2001, p. 34.
  26. J. F. Brennan, “Dispersion compensation gratings for the C-band,” Photonics Spectra, June2001, pp. 159–165.
  27. M. Ibsen, M. K. Durkin, K. Ennser, M. J. Cole, R. I. Laming, “Long continuously chirped fiber Bragg gratings for compensation of linear and 3rd order dispersion,” Technical note of Southampton Photonics available at www.southamptonphotonics.com .

2001

M. Das, K. Thyagarajan, “Dispersion compensation in transmission using uniform long period fiber gratings,” Opt. Commun. 190, 159–163 (2001).
[CrossRef]

J. Čtyroký, “Photonic bandgap structures in planar waveguides,” J. Opt. Soc. Am. A 18, 435–441 (2001).
[CrossRef]

L. Escoubas, E. Drouard, F. Flory, “Designing waveguide filters with optical thin-film computational tools,” Opt. Commun. 197, 309–316 (2001).
[CrossRef]

K. Lefebvre, “Techniques take differing measures of chromatic dispersion,” WDM Solutions, May2001, pp. 79–82.

D. C. McCarthy, “Chirped Bragg gratings covers the C-band,” Photonics Spectra, May2001, p. 34.

J. F. Brennan, “Dispersion compensation gratings for the C-band,” Photonics Spectra, June2001, pp. 159–165.

2000

1999

J.-C. Dung, S. Chi, “Dispersion compensation and gain flattened for a wavelength division multiplexing system by using chirped fiber gratings in an erbium-doped fiber amplifier,” Opt. Commun. 162, 219–222 (1999).
[CrossRef]

1997

M. J. Cole, H. Geiger, R. I. Laming, S. Y. Set, M. N. Zervas, W. H. Loh, V. Gusmeroli, “Broadband dispersion-compensating chirped fiber Bragg gratings in 10 Gbit/s NRZ 110 km non-dispersion-shifted fibre link operating at 1.55 µm,” Electron. Lett. 33, 70–71 (1997).
[CrossRef]

C. Narayanan, H. M. Presby, A. M. Vengsarkar, “Band-rejection fibre filter using periodic core deformation,” Electron. Lett. 33, 280–281 (1997).
[CrossRef]

1996

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

M. Okai, I. F. Lealman, L. J. Rivers, C. Dix, M. J. Robertson, “In-line Fabry-Perot optical waveguide filter with quasi-chirped gratings,” Electron. Lett. 32, 108–109 (1996).
[CrossRef]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

1995

M. Janos, J. Canning, “Permanent and transient resonances thermally induced in optical fibre Bragg gratings,” Electron. Lett. 31, 1007–1009 (1995).
[CrossRef]

J. A. R. Williams, I. Bennion, N. J. Doran, “The design of in-fiber Bragg gratings systems for cubic and quadratic dispersion compensation,” Opt. Commun. 116, 62–66 (1995).
[CrossRef]

1994

F. Ouellette, J. F. Cliché, S. Gagnon, “All-fiber devices for chromatic dispersion compensation based on chirped distributed resonant coupling,” J. Lightwave Technol. 12, 1728–1738 (1994).
[CrossRef]

F. Bilodeau, K. O. Hill, B. Malo, D. C. Johnson, J. Albert, “High-return-loss narrowband all-fibre bandpass Bragg transmission filter,” IEEE Photon. Technol. Lett. 6, 80–82 (1994).
[CrossRef]

1993

A. S. Sudbo, “Film mode matching: a versatile numerical method for vector mode field calculations in dielectric waveguides,” Pure Appl. Opt. 2, 211–233 (1993).
[CrossRef]

1992

M. Wilkinson, A. Bebbington, S. A. Cassidy, P. McKee, “D-fibre filter for erbium gain spectrum flattening,” Electron. Lett. 28, 131–132 (1992).
[CrossRef]

1950

F. Abelès, “Recherche sur la propagation des ondes électromagnétiques sinusoïdales dans les milieux stratifiés,” Ann. Phys. (Paris) 5, 596–640 (1950).

Abelès, F.

F. Abelès, “Recherche sur la propagation des ondes électromagnétiques sinusoïdales dans les milieux stratifiés,” Ann. Phys. (Paris) 5, 596–640 (1950).

Albert, J.

F. Bilodeau, K. O. Hill, B. Malo, D. C. Johnson, J. Albert, “High-return-loss narrowband all-fibre bandpass Bragg transmission filter,” IEEE Photon. Technol. Lett. 6, 80–82 (1994).
[CrossRef]

Ball, G. A.

G. A. Ball, W. W. Morey, “Tunable Bragg grating fiber filters and their applications,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 108–109.

Bebbington, A.

M. Wilkinson, A. Bebbington, S. A. Cassidy, P. McKee, “D-fibre filter for erbium gain spectrum flattening,” Electron. Lett. 28, 131–132 (1992).
[CrossRef]

Bennion, I.

J. A. R. Williams, I. Bennion, N. J. Doran, “The design of in-fiber Bragg gratings systems for cubic and quadratic dispersion compensation,” Opt. Commun. 116, 62–66 (1995).
[CrossRef]

Bhatia, V.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

Bilodeau, F.

F. Bilodeau, K. O. Hill, B. Malo, D. C. Johnson, J. Albert, “High-return-loss narrowband all-fibre bandpass Bragg transmission filter,” IEEE Photon. Technol. Lett. 6, 80–82 (1994).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University, Cambridge, England, 1999), Chaps. 8 and 11.

Brennan, J. F.

J. F. Brennan, “Dispersion compensation gratings for the C-band,” Photonics Spectra, June2001, pp. 159–165.

Canning, J.

M. Janos, J. Canning, “Permanent and transient resonances thermally induced in optical fibre Bragg gratings,” Electron. Lett. 31, 1007–1009 (1995).
[CrossRef]

Cassidy, S. A.

M. Wilkinson, A. Bebbington, S. A. Cassidy, P. McKee, “D-fibre filter for erbium gain spectrum flattening,” Electron. Lett. 28, 131–132 (1992).
[CrossRef]

Chi, S.

J.-C. Dung, S. Chi, “Dispersion compensation and gain flattened for a wavelength division multiplexing system by using chirped fiber gratings in an erbium-doped fiber amplifier,” Opt. Commun. 162, 219–222 (1999).
[CrossRef]

Cliché, J. F.

F. Ouellette, J. F. Cliché, S. Gagnon, “All-fiber devices for chromatic dispersion compensation based on chirped distributed resonant coupling,” J. Lightwave Technol. 12, 1728–1738 (1994).
[CrossRef]

Cole, M. J.

M. J. Cole, H. Geiger, R. I. Laming, S. Y. Set, M. N. Zervas, W. H. Loh, V. Gusmeroli, “Broadband dispersion-compensating chirped fiber Bragg gratings in 10 Gbit/s NRZ 110 km non-dispersion-shifted fibre link operating at 1.55 µm,” Electron. Lett. 33, 70–71 (1997).
[CrossRef]

M. Ibsen, M. K. Durkin, K. Ennser, M. J. Cole, R. I. Laming, “Long continuously chirped fiber Bragg gratings for compensation of linear and 3rd order dispersion,” Technical note of Southampton Photonics available at www.southamptonphotonics.com .

Ctyroký, J.

Das, M.

M. Das, K. Thyagarajan, “Dispersion compensation in transmission using uniform long period fiber gratings,” Opt. Commun. 190, 159–163 (2001).
[CrossRef]

Dix, C.

M. Okai, I. F. Lealman, L. J. Rivers, C. Dix, M. J. Robertson, “In-line Fabry-Perot optical waveguide filter with quasi-chirped gratings,” Electron. Lett. 32, 108–109 (1996).
[CrossRef]

Doran, N. J.

J. A. R. Williams, I. Bennion, N. J. Doran, “The design of in-fiber Bragg gratings systems for cubic and quadratic dispersion compensation,” Opt. Commun. 116, 62–66 (1995).
[CrossRef]

Drouard, E.

L. Escoubas, E. Drouard, F. Flory, “Designing waveguide filters with optical thin-film computational tools,” Opt. Commun. 197, 309–316 (2001).
[CrossRef]

Dung, J.-C.

J.-C. Dung, S. Chi, “Dispersion compensation and gain flattened for a wavelength division multiplexing system by using chirped fiber gratings in an erbium-doped fiber amplifier,” Opt. Commun. 162, 219–222 (1999).
[CrossRef]

Durkin, M. K.

M. Ibsen, M. K. Durkin, K. Ennser, M. J. Cole, R. I. Laming, “Long continuously chirped fiber Bragg gratings for compensation of linear and 3rd order dispersion,” Technical note of Southampton Photonics available at www.southamptonphotonics.com .

Ennser, K.

M. Ibsen, M. K. Durkin, K. Ennser, M. J. Cole, R. I. Laming, “Long continuously chirped fiber Bragg gratings for compensation of linear and 3rd order dispersion,” Technical note of Southampton Photonics available at www.southamptonphotonics.com .

Erdogan, T.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

Escoubas, L.

L. Escoubas, E. Drouard, F. Flory, “Designing waveguide filters with optical thin-film computational tools,” Opt. Commun. 197, 309–316 (2001).
[CrossRef]

Flory, F.

L. Escoubas, E. Drouard, F. Flory, “Designing waveguide filters with optical thin-film computational tools,” Opt. Commun. 197, 309–316 (2001).
[CrossRef]

Fujimaki, M.

Gagnon, S.

F. Ouellette, J. F. Cliché, S. Gagnon, “All-fiber devices for chromatic dispersion compensation based on chirped distributed resonant coupling,” J. Lightwave Technol. 12, 1728–1738 (1994).
[CrossRef]

Geiger, H.

M. J. Cole, H. Geiger, R. I. Laming, S. Y. Set, M. N. Zervas, W. H. Loh, V. Gusmeroli, “Broadband dispersion-compensating chirped fiber Bragg gratings in 10 Gbit/s NRZ 110 km non-dispersion-shifted fibre link operating at 1.55 µm,” Electron. Lett. 33, 70–71 (1997).
[CrossRef]

Gusmeroli, V.

M. J. Cole, H. Geiger, R. I. Laming, S. Y. Set, M. N. Zervas, W. H. Loh, V. Gusmeroli, “Broadband dispersion-compensating chirped fiber Bragg gratings in 10 Gbit/s NRZ 110 km non-dispersion-shifted fibre link operating at 1.55 µm,” Electron. Lett. 33, 70–71 (1997).
[CrossRef]

Hill, K. O.

F. Bilodeau, K. O. Hill, B. Malo, D. C. Johnson, J. Albert, “High-return-loss narrowband all-fibre bandpass Bragg transmission filter,” IEEE Photon. Technol. Lett. 6, 80–82 (1994).
[CrossRef]

Ibsen, M.

M. Ibsen, M. K. Durkin, K. Ennser, M. J. Cole, R. I. Laming, “Long continuously chirped fiber Bragg gratings for compensation of linear and 3rd order dispersion,” Technical note of Southampton Photonics available at www.southamptonphotonics.com .

Inoue, A.

A. Inoue, “Great gratings,” Photonics Spectra, August2000, pp. 98–100.

Janos, M.

M. Janos, J. Canning, “Permanent and transient resonances thermally induced in optical fibre Bragg gratings,” Electron. Lett. 31, 1007–1009 (1995).
[CrossRef]

Johnson, D. C.

F. Bilodeau, K. O. Hill, B. Malo, D. C. Johnson, J. Albert, “High-return-loss narrowband all-fibre bandpass Bragg transmission filter,” IEEE Photon. Technol. Lett. 6, 80–82 (1994).
[CrossRef]

Judkins, J. B.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

Laming, R. I.

M. J. Cole, H. Geiger, R. I. Laming, S. Y. Set, M. N. Zervas, W. H. Loh, V. Gusmeroli, “Broadband dispersion-compensating chirped fiber Bragg gratings in 10 Gbit/s NRZ 110 km non-dispersion-shifted fibre link operating at 1.55 µm,” Electron. Lett. 33, 70–71 (1997).
[CrossRef]

M. Ibsen, M. K. Durkin, K. Ennser, M. J. Cole, R. I. Laming, “Long continuously chirped fiber Bragg gratings for compensation of linear and 3rd order dispersion,” Technical note of Southampton Photonics available at www.southamptonphotonics.com .

Lealman, I. F.

M. Okai, I. F. Lealman, L. J. Rivers, C. Dix, M. J. Robertson, “In-line Fabry-Perot optical waveguide filter with quasi-chirped gratings,” Electron. Lett. 32, 108–109 (1996).
[CrossRef]

Lefebvre, K.

K. Lefebvre, “Techniques take differing measures of chromatic dispersion,” WDM Solutions, May2001, pp. 79–82.

Lemaire, P. J.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

Loh, W. H.

M. J. Cole, H. Geiger, R. I. Laming, S. Y. Set, M. N. Zervas, W. H. Loh, V. Gusmeroli, “Broadband dispersion-compensating chirped fiber Bragg gratings in 10 Gbit/s NRZ 110 km non-dispersion-shifted fibre link operating at 1.55 µm,” Electron. Lett. 33, 70–71 (1997).
[CrossRef]

Macleod, H. A.

H. A. Macleod, Thin Film Optical Filters (Hilger, Bristol, UK, 1986).

Malo, B.

F. Bilodeau, K. O. Hill, B. Malo, D. C. Johnson, J. Albert, “High-return-loss narrowband all-fibre bandpass Bragg transmission filter,” IEEE Photon. Technol. Lett. 6, 80–82 (1994).
[CrossRef]

McCarthy, D. C.

D. C. McCarthy, “Chirped Bragg gratings covers the C-band,” Photonics Spectra, May2001, p. 34.

McKee, P.

M. Wilkinson, A. Bebbington, S. A. Cassidy, P. McKee, “D-fibre filter for erbium gain spectrum flattening,” Electron. Lett. 28, 131–132 (1992).
[CrossRef]

Morey, W. W.

G. A. Ball, W. W. Morey, “Tunable Bragg grating fiber filters and their applications,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 108–109.

Narayanan, C.

C. Narayanan, H. M. Presby, A. M. Vengsarkar, “Band-rejection fibre filter using periodic core deformation,” Electron. Lett. 33, 280–281 (1997).
[CrossRef]

Ohki, Y.

Okai, M.

M. Okai, I. F. Lealman, L. J. Rivers, C. Dix, M. J. Robertson, “In-line Fabry-Perot optical waveguide filter with quasi-chirped gratings,” Electron. Lett. 32, 108–109 (1996).
[CrossRef]

Ouellette, F.

F. Ouellette, J. F. Cliché, S. Gagnon, “All-fiber devices for chromatic dispersion compensation based on chirped distributed resonant coupling,” J. Lightwave Technol. 12, 1728–1738 (1994).
[CrossRef]

Presby, H. M.

C. Narayanan, H. M. Presby, A. M. Vengsarkar, “Band-rejection fibre filter using periodic core deformation,” Electron. Lett. 33, 280–281 (1997).
[CrossRef]

Rivers, L. J.

M. Okai, I. F. Lealman, L. J. Rivers, C. Dix, M. J. Robertson, “In-line Fabry-Perot optical waveguide filter with quasi-chirped gratings,” Electron. Lett. 32, 108–109 (1996).
[CrossRef]

Robertson, M. J.

M. Okai, I. F. Lealman, L. J. Rivers, C. Dix, M. J. Robertson, “In-line Fabry-Perot optical waveguide filter with quasi-chirped gratings,” Electron. Lett. 32, 108–109 (1996).
[CrossRef]

Rosencher, E.

E. Rosencher, B. Vinter, Optoélectronique (Masson, Paris, 1998), Chap. 9.

Set, S. Y.

M. J. Cole, H. Geiger, R. I. Laming, S. Y. Set, M. N. Zervas, W. H. Loh, V. Gusmeroli, “Broadband dispersion-compensating chirped fiber Bragg gratings in 10 Gbit/s NRZ 110 km non-dispersion-shifted fibre link operating at 1.55 µm,” Electron. Lett. 33, 70–71 (1997).
[CrossRef]

Sipe, J. E.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

Sudbo, A. S.

A. S. Sudbo, “Film mode matching: a versatile numerical method for vector mode field calculations in dielectric waveguides,” Pure Appl. Opt. 2, 211–233 (1993).
[CrossRef]

Thyagarajan, K.

M. Das, K. Thyagarajan, “Dispersion compensation in transmission using uniform long period fiber gratings,” Opt. Commun. 190, 159–163 (2001).
[CrossRef]

Vengsarkar, A. M.

C. Narayanan, H. M. Presby, A. M. Vengsarkar, “Band-rejection fibre filter using periodic core deformation,” Electron. Lett. 33, 280–281 (1997).
[CrossRef]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

Vinter, B.

E. Rosencher, B. Vinter, Optoélectronique (Masson, Paris, 1998), Chap. 9.

Wilkinson, M.

M. Wilkinson, A. Bebbington, S. A. Cassidy, P. McKee, “D-fibre filter for erbium gain spectrum flattening,” Electron. Lett. 28, 131–132 (1992).
[CrossRef]

Williams, J. A. R.

J. A. R. Williams, I. Bennion, N. J. Doran, “The design of in-fiber Bragg gratings systems for cubic and quadratic dispersion compensation,” Opt. Commun. 116, 62–66 (1995).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University, Cambridge, England, 1999), Chaps. 8 and 11.

Zervas, M. N.

M. J. Cole, H. Geiger, R. I. Laming, S. Y. Set, M. N. Zervas, W. H. Loh, V. Gusmeroli, “Broadband dispersion-compensating chirped fiber Bragg gratings in 10 Gbit/s NRZ 110 km non-dispersion-shifted fibre link operating at 1.55 µm,” Electron. Lett. 33, 70–71 (1997).
[CrossRef]

Ann. Phys. (Paris)

F. Abelès, “Recherche sur la propagation des ondes électromagnétiques sinusoïdales dans les milieux stratifiés,” Ann. Phys. (Paris) 5, 596–640 (1950).

Electron. Lett.

M. J. Cole, H. Geiger, R. I. Laming, S. Y. Set, M. N. Zervas, W. H. Loh, V. Gusmeroli, “Broadband dispersion-compensating chirped fiber Bragg gratings in 10 Gbit/s NRZ 110 km non-dispersion-shifted fibre link operating at 1.55 µm,” Electron. Lett. 33, 70–71 (1997).
[CrossRef]

C. Narayanan, H. M. Presby, A. M. Vengsarkar, “Band-rejection fibre filter using periodic core deformation,” Electron. Lett. 33, 280–281 (1997).
[CrossRef]

M. Okai, I. F. Lealman, L. J. Rivers, C. Dix, M. J. Robertson, “In-line Fabry-Perot optical waveguide filter with quasi-chirped gratings,” Electron. Lett. 32, 108–109 (1996).
[CrossRef]

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Figures (15)

Fig. 1
Fig. 1

Deeply etched waveguide including a Bragg reflector that was recently proposed by Čtyroký.20

Fig. 2
Fig. 2

Integrated Bragg reflector composed of a periodic alternation of 31 TiO2 and Ta2O5 waveguide sections surrounded by SiO2 and deposited on a silica substrate.

Fig. 3
Fig. 3

Computed TE00 mode spectral reflectance of the integrated Bragg reflector in Fig. 2 for three different fill factors.

Fig. 4
Fig. 4

Modal losses of the integrated Bragg reflector in Fig. 2 for three different fill factors.

Fig. 5
Fig. 5

Dependence of modal losses of the integrated Bragg reflector, with 31 sections, at 1.55-µm wavelength versus the average fill factor (average of TiO2 and Ta2O5 waveguide fill factors).

Fig. 6
Fig. 6

Transmittance (in decibels) of the M48 2L M48 L M48 2L M48 DWDM narrow-bandpass filter calculated with the FMM method for three different fill factors.

Fig. 7
Fig. 7

Transmittance (in decibels) of the M48 2L M48 L M48 2L M48 DWDM narrow-bandpass filter calculated with the FMM method, with the ACM including extinction coefficients to simulate radiative losses between waveguide sections, and with the ACM without taking losses into account.

Fig. 8
Fig. 8

FMM and ACM computed transmission phase of the M48 2L M48 L M48 2L M48 DWDM narrow-bandpass filter.

Fig. 9
Fig. 9

FMM and ACM computed group delay in transmission of the M48 2L M48 L M48 2L M48 DWDM narrow-bandpass filter.

Fig. 10
Fig. 10

FMM and ACM computed group delay dispersion in transmission of the M48 2L M48 L M48 2L M48 DWDM narrow-bandpass filter.

Fig. 11
Fig. 11

Calculated reflectance of an IGFF obtained by use of the thin-film synthesis software. The target curve is also shown for comparison with the ACM and the FMM computed curves.

Fig. 12
Fig. 12

Computed losses of the gain-flattening filter.

Fig. 13
Fig. 13

Setup of the differential phase-shift method. The amplitude of the input signal is modulated by a reference signal and applied to the fiber under test. The wavelength is also modulated around a central wavelength where the group delay is to be measured. The transmitted signal is detected at the output of the fiber, and the phase of the transmitted signal is compared with the reference signal that is used to modulate the input signal. The detected signal not only has a phase difference but also varies with frequency. To obtain the dispersion curve, we repeated the measurement for several wavelengths.

Fig. 14
Fig. 14

(a) Transmission phase of an 18.5-km-long single-mode fiber measured at 1.55 µm with the differential phase-shift method. The modulation frequency is 40 MHz. The chromatic dispersion can easily be obtained from the slope of the linear part of the curve. (b) Group delay τ (in femtoseconds) of the 18.5-km-long single-mode fiber computed from the value of dϕ/dλ by use of the formula τ = (λ2 dϕ)/(2πc dλ).

Fig. 15
Fig. 15

(a) Reflectance (in percent) of the broadband dispersion compensator (59 sections and 13.1 µm long) computed with the FMM method and the ACM. Reflectance values are in good agreement and, because of the refractive-index contrast between TiO2 and Ta2O5 waveguide sections, these values are higher than 95% over the whole spectral range. (b) Reflectance group delay (in femtoseconds) of the broadband dispersion compensator computed with the FMM method and the ACM. Only a slight difference of approximately 1 fs can be observed. (c) Fiber plus broadband dispersion compensator reflectance group delay (in femtoseconds). The filter can be used to compensate the fiber group delay with a ±1.5-fs tolerance over the 1530–1565-nm spectral range.

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