Abstract

We have studied, both theoretically and experimentally, fiber Bragg gratings with a number of different chirp profiles. These chirp profiles can easily be achieved by a recently demonstrated technique involving a taper of desired profile etched into the cladding of a fiber. The performances of gratings with linear, quadratic, periodically modulated, and step-chirp profiles are analyzed numerically. The versatility of the technique was demonstrated when linearly and quadratically chirped gratings were made as examples of continuous chirp, and gratings with step chirps were made as examples of discontinuously chirped structures.

© 1996 Optical Society of America

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  1. J. Lauzon, S. Thibault, J. Martin, F. Oullette, “Implementation and characterization of fiber Bragg gratings linearly chirped by a temperature gradient,” Opt. Lett. 19, 2027–2029 (1994).
    [CrossRef] [PubMed]
  2. K. C. Byron, H. N. Rourke, “Fabrication of chirped fiber gratings by a novel stretch and write technique,” Electron. Lett. 31, 60–61 (1995).
    [CrossRef]
  3. P. C. Hill, B. J. Eggletton, “Strain gradient chirp of fiber Bragg gratings,” Electron. Lett. 30, 1172–1174 (1994).
    [CrossRef]
  4. M. A. Putman, G. M. Williams, E. J. Friebele, “Fabrication of tapered strain gradient chirped fiber Bragg gratings,” Electron. Lett. 31, 309–310 (1995).
    [CrossRef]
  5. M. Le Blanc, S. Y. Huang, M. M. Ohn, R. M. Measures, “Tunable chirping of a fiber Bragg grating using a tapered cantilever bed,” Electron. Lett. 30, 2163–2165 (1994).
    [CrossRef]
  6. K. C. Byron, K. Sugden, T. Bricheno, I. Bennion, “Fabrication of fiber Bragg gratings in photosensitive fiber,” Electron. Lett. 29, 1659–1660 (1993).
    [CrossRef]
  7. K. O. Hill, F. Bilodeau, B. Malo, S. Theriault, D. C. Johnson, J. Albert, “Chirped in fiber Bragg gratings for compensation of fiber dispersion,” Opt. Lett. 19, 1314–1316 (1994).
    [CrossRef] [PubMed]
  8. Y. Painchaud, A. Chandonnet, J. Lauzon, “Chirped fiber gratings produced by tilting the fiber,” Electron. Lett. 31, 171–172 (1995).
    [CrossRef]
  9. M. J. Cole, W. H. Loh, R. H. Laming, M. N. Zervas, S. Barcelos, “Moving fiber/phase mask-scanning beam technique for enhanced flexibility producing fiber gratings with uniform phase mask,” Electron. Lett. 31, 1488–1489 (1995).
    [CrossRef]
  10. R. Kashyap, P. F. McKee, R. J. Campbell, D. L. Williams, “Novel method of producing all fiber photoinduced chirped gratings,” Electron. Lett. 30, 996–997 (1994).
    [CrossRef]
  11. M. C. Farries, K. Sudgen, D. C. J. Reid, I. Bennion, A. Molony, M. J. Goodwin, “Very broad reflection bandwidth (44-nm) chirped fiber gratings and narrow bandpass filters by the use of an amplitude mask,” Electron. Lett. 30, 891–892 (1994).
    [CrossRef]
  12. K. Sugden, I. Bennion, A. Molony, N. J. Copner, “Chirped gratings produced in photosensitive optical fibers by fiber deformation during exposure,” Electron. Lett. 30, 440–442 (1994).
    [CrossRef]
  13. Q. Zhang, D. A. Brown, L. J. Reinhart, T. F. Morse, “Linearly and nonlinearly chirped Bragg gratings fabricated in curved fibers,” Opt. Lett. 20, 1122–1124 (1995).
    [CrossRef] [PubMed]
  14. L. Dong, J. L. Cruz, L. Reekie, J. A. Tocknott, “Chirped fiber Bragg gratings fabricated using etched tapers,” Opt. Fiber Technol. 1, 363–368 (1995).
    [CrossRef]
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    [CrossRef] [PubMed]
  19. A. Galvanauskas, M. E. Fermann, D. Harter, K. Sugden, I. Bennion, “All fiber femtosecond pulse amplification circuit using chirped Bragg gratings,” Appl. Phys. Lett. 66, 1053–1055 (1995).
    [CrossRef]
  20. A. R. Willians, I. Bennion, N. J. Doran, “The design of in-fiber Bragg grating systems for cubic and quadratic dispersion compensation,” Opt. Commun. 116, 62–66 (1995).
    [CrossRef]
  21. A. M. Vengsarkar, P. J. Lemaire, G. Jacobovitz, V. Bhatia, J. B. Judkins, “Long period fiber gratings as gain-flattening and laser stabilizing devices,” in Proceedings of the International Commission on Optics (ICOC-95), Hong Kong (1995), paper PD1-2, pp. 3–4.
  22. G. P. Agrawal, S. Radic, “Phase shifted fiber Bragg gratings and their application for wavelength demultiplexing,” IEEE Photon. Technol. Lett. 6, 995–997 (1994).
    [CrossRef]
  23. M. Sijka, P. Varming, J. Hubner, M. Kristensen, “Distributed feedback Er3+ doped fiber laser,” Electron. Lett. 31, 1445–1446 (1995).
    [CrossRef]
  24. B. J. Eggleton, P. A. Krug, L. Poladian, F. Oullette, “Long periodic super structure Bragg gratings in optical fibers,” Electron. Lett. 30, 1620–1622 (1944).
    [CrossRef]
  25. J. Canning, M. G. Sceats, “π-Phase shifted periodic distributed structures in optical fibers by UV postprocessing,” Electron. Lett. 30, 1344–1345 (1994).
    [CrossRef]
  26. R. Kashyap, P. F. Mackee, D. Armes, “UV written reflection grating structures in photosensitive optical fibers using phase shifted phase masks,” Electron. Lett. 30, 1977–1978 (1994).
    [CrossRef]
  27. S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. Makee, F. Sladen, B. Wojciechowicz, “High accuracy dispersion measurements of chirped fiber gratings,” Electron. Lett. 31, 1280–1282 (1995).
    [CrossRef]

1995 (10)

K. C. Byron, H. N. Rourke, “Fabrication of chirped fiber gratings by a novel stretch and write technique,” Electron. Lett. 31, 60–61 (1995).
[CrossRef]

M. A. Putman, G. M. Williams, E. J. Friebele, “Fabrication of tapered strain gradient chirped fiber Bragg gratings,” Electron. Lett. 31, 309–310 (1995).
[CrossRef]

Y. Painchaud, A. Chandonnet, J. Lauzon, “Chirped fiber gratings produced by tilting the fiber,” Electron. Lett. 31, 171–172 (1995).
[CrossRef]

M. J. Cole, W. H. Loh, R. H. Laming, M. N. Zervas, S. Barcelos, “Moving fiber/phase mask-scanning beam technique for enhanced flexibility producing fiber gratings with uniform phase mask,” Electron. Lett. 31, 1488–1489 (1995).
[CrossRef]

A. Galvanauskas, M. E. Fermann, D. Harter, K. Sugden, I. Bennion, “All fiber femtosecond pulse amplification circuit using chirped Bragg gratings,” Appl. Phys. Lett. 66, 1053–1055 (1995).
[CrossRef]

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

M. Sijka, P. Varming, J. Hubner, M. Kristensen, “Distributed feedback Er3+ doped fiber laser,” Electron. Lett. 31, 1445–1446 (1995).
[CrossRef]

S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. Makee, F. Sladen, B. Wojciechowicz, “High accuracy dispersion measurements of chirped fiber gratings,” Electron. Lett. 31, 1280–1282 (1995).
[CrossRef]

L. Dong, J. L. Cruz, L. Reekie, J. A. Tocknott, “Chirped fiber Bragg gratings fabricated using etched tapers,” Opt. Fiber Technol. 1, 363–368 (1995).
[CrossRef]

Q. Zhang, D. A. Brown, L. J. Reinhart, T. F. Morse, “Linearly and nonlinearly chirped Bragg gratings fabricated in curved fibers,” Opt. Lett. 20, 1122–1124 (1995).
[CrossRef] [PubMed]

1994 (11)

K. O. Hill, F. Bilodeau, B. Malo, T. Kitagawa, S. Theriault, D. C. Johnson, J. Albert, K. Takiguchi, “Chirped in fiber gratings for dispersion compensation of optical-fiber dispersion,” Opt. Lett. 19, 1314–1315 (1994).
[CrossRef] [PubMed]

K. O. Hill, F. Bilodeau, B. Malo, S. Theriault, D. C. Johnson, J. Albert, “Chirped in fiber Bragg gratings for compensation of fiber dispersion,” Opt. Lett. 19, 1314–1316 (1994).
[CrossRef] [PubMed]

J. Lauzon, S. Thibault, J. Martin, F. Oullette, “Implementation and characterization of fiber Bragg gratings linearly chirped by a temperature gradient,” Opt. Lett. 19, 2027–2029 (1994).
[CrossRef] [PubMed]

J. Canning, M. G. Sceats, “π-Phase shifted periodic distributed structures in optical fibers by UV postprocessing,” Electron. Lett. 30, 1344–1345 (1994).
[CrossRef]

R. Kashyap, P. F. Mackee, D. Armes, “UV written reflection grating structures in photosensitive optical fibers using phase shifted phase masks,” Electron. Lett. 30, 1977–1978 (1994).
[CrossRef]

G. P. Agrawal, S. Radic, “Phase shifted fiber Bragg gratings and their application for wavelength demultiplexing,” IEEE Photon. Technol. Lett. 6, 995–997 (1994).
[CrossRef]

R. Kashyap, P. F. McKee, R. J. Campbell, D. L. Williams, “Novel method of producing all fiber photoinduced chirped gratings,” Electron. Lett. 30, 996–997 (1994).
[CrossRef]

M. C. Farries, K. Sudgen, D. C. J. Reid, I. Bennion, A. Molony, M. J. Goodwin, “Very broad reflection bandwidth (44-nm) chirped fiber gratings and narrow bandpass filters by the use of an amplitude mask,” Electron. Lett. 30, 891–892 (1994).
[CrossRef]

K. Sugden, I. Bennion, A. Molony, N. J. Copner, “Chirped gratings produced in photosensitive optical fibers by fiber deformation during exposure,” Electron. Lett. 30, 440–442 (1994).
[CrossRef]

M. Le Blanc, S. Y. Huang, M. M. Ohn, R. M. Measures, “Tunable chirping of a fiber Bragg grating using a tapered cantilever bed,” Electron. Lett. 30, 2163–2165 (1994).
[CrossRef]

P. C. Hill, B. J. Eggletton, “Strain gradient chirp of fiber Bragg gratings,” Electron. Lett. 30, 1172–1174 (1994).
[CrossRef]

1993 (1)

K. C. Byron, K. Sugden, T. Bricheno, I. Bennion, “Fabrication of fiber Bragg gratings in photosensitive fiber,” Electron. Lett. 29, 1659–1660 (1993).
[CrossRef]

1992 (1)

1987 (1)

1944 (1)

B. J. Eggleton, P. A. Krug, L. Poladian, F. Oullette, “Long periodic super structure Bragg gratings in optical fibers,” Electron. Lett. 30, 1620–1622 (1944).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, S. Radic, “Phase shifted fiber Bragg gratings and their application for wavelength demultiplexing,” IEEE Photon. Technol. Lett. 6, 995–997 (1994).
[CrossRef]

Albert, J.

Armes, D.

R. Kashyap, P. F. Mackee, D. Armes, “UV written reflection grating structures in photosensitive optical fibers using phase shifted phase masks,” Electron. Lett. 30, 1977–1978 (1994).
[CrossRef]

Barcelos, S.

S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. Makee, F. Sladen, B. Wojciechowicz, “High accuracy dispersion measurements of chirped fiber gratings,” Electron. Lett. 31, 1280–1282 (1995).
[CrossRef]

M. J. Cole, W. H. Loh, R. H. Laming, M. N. Zervas, S. Barcelos, “Moving fiber/phase mask-scanning beam technique for enhanced flexibility producing fiber gratings with uniform phase mask,” Electron. Lett. 31, 1488–1489 (1995).
[CrossRef]

Bennion, I.

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

A. Galvanauskas, M. E. Fermann, D. Harter, K. Sugden, I. Bennion, “All fiber femtosecond pulse amplification circuit using chirped Bragg gratings,” Appl. Phys. Lett. 66, 1053–1055 (1995).
[CrossRef]

K. Sugden, I. Bennion, A. Molony, N. J. Copner, “Chirped gratings produced in photosensitive optical fibers by fiber deformation during exposure,” Electron. Lett. 30, 440–442 (1994).
[CrossRef]

M. C. Farries, K. Sudgen, D. C. J. Reid, I. Bennion, A. Molony, M. J. Goodwin, “Very broad reflection bandwidth (44-nm) chirped fiber gratings and narrow bandpass filters by the use of an amplitude mask,” Electron. Lett. 30, 891–892 (1994).
[CrossRef]

K. C. Byron, K. Sugden, T. Bricheno, I. Bennion, “Fabrication of fiber Bragg gratings in photosensitive fiber,” Electron. Lett. 29, 1659–1660 (1993).
[CrossRef]

Bhatia, V.

A. M. Vengsarkar, P. J. Lemaire, G. Jacobovitz, V. Bhatia, J. B. Judkins, “Long period fiber gratings as gain-flattening and laser stabilizing devices,” in Proceedings of the International Commission on Optics (ICOC-95), Hong Kong (1995), paper PD1-2, pp. 3–4.

Bilodeau, F.

Bricheno, T.

K. C. Byron, K. Sugden, T. Bricheno, I. Bennion, “Fabrication of fiber Bragg gratings in photosensitive fiber,” Electron. Lett. 29, 1659–1660 (1993).
[CrossRef]

Brown, D. A.

Byron, K. C.

K. C. Byron, H. N. Rourke, “Fabrication of chirped fiber gratings by a novel stretch and write technique,” Electron. Lett. 31, 60–61 (1995).
[CrossRef]

K. C. Byron, K. Sugden, T. Bricheno, I. Bennion, “Fabrication of fiber Bragg gratings in photosensitive fiber,” Electron. Lett. 29, 1659–1660 (1993).
[CrossRef]

Campbell, R. J.

R. Kashyap, P. F. McKee, R. J. Campbell, D. L. Williams, “Novel method of producing all fiber photoinduced chirped gratings,” Electron. Lett. 30, 996–997 (1994).
[CrossRef]

Canning, J.

J. Canning, M. G. Sceats, “π-Phase shifted periodic distributed structures in optical fibers by UV postprocessing,” Electron. Lett. 30, 1344–1345 (1994).
[CrossRef]

Chandonnet, A.

Y. Painchaud, A. Chandonnet, J. Lauzon, “Chirped fiber gratings produced by tilting the fiber,” Electron. Lett. 31, 171–172 (1995).
[CrossRef]

Cole, M. J.

M. J. Cole, W. H. Loh, R. H. Laming, M. N. Zervas, S. Barcelos, “Moving fiber/phase mask-scanning beam technique for enhanced flexibility producing fiber gratings with uniform phase mask,” Electron. Lett. 31, 1488–1489 (1995).
[CrossRef]

Copner, N. J.

K. Sugden, I. Bennion, A. Molony, N. J. Copner, “Chirped gratings produced in photosensitive optical fibers by fiber deformation during exposure,” Electron. Lett. 30, 440–442 (1994).
[CrossRef]

Cruz, J. L.

L. Dong, J. L. Cruz, L. Reekie, J. A. Tocknott, “Chirped fiber Bragg gratings fabricated using etched tapers,” Opt. Fiber Technol. 1, 363–368 (1995).
[CrossRef]

Dong, L.

L. Dong, J. L. Cruz, L. Reekie, J. A. Tocknott, “Chirped fiber Bragg gratings fabricated using etched tapers,” Opt. Fiber Technol. 1, 363–368 (1995).
[CrossRef]

Doran, N. J.

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

Eggleton, B. J.

B. J. Eggleton, P. A. Krug, L. Poladian, F. Oullette, “Long periodic super structure Bragg gratings in optical fibers,” Electron. Lett. 30, 1620–1622 (1944).
[CrossRef]

Eggletton, B. J.

P. C. Hill, B. J. Eggletton, “Strain gradient chirp of fiber Bragg gratings,” Electron. Lett. 30, 1172–1174 (1994).
[CrossRef]

Farries, M. C.

M. C. Farries, K. Sudgen, D. C. J. Reid, I. Bennion, A. Molony, M. J. Goodwin, “Very broad reflection bandwidth (44-nm) chirped fiber gratings and narrow bandpass filters by the use of an amplitude mask,” Electron. Lett. 30, 891–892 (1994).
[CrossRef]

Fermann, M. E.

A. Galvanauskas, M. E. Fermann, D. Harter, K. Sugden, I. Bennion, “All fiber femtosecond pulse amplification circuit using chirped Bragg gratings,” Appl. Phys. Lett. 66, 1053–1055 (1995).
[CrossRef]

Friebele, E. J.

M. A. Putman, G. M. Williams, E. J. Friebele, “Fabrication of tapered strain gradient chirped fiber Bragg gratings,” Electron. Lett. 31, 309–310 (1995).
[CrossRef]

Galvanauskas, A.

A. Galvanauskas, M. E. Fermann, D. Harter, K. Sugden, I. Bennion, “All fiber femtosecond pulse amplification circuit using chirped Bragg gratings,” Appl. Phys. Lett. 66, 1053–1055 (1995).
[CrossRef]

Garmire, E.

Goodwin, M. J.

M. C. Farries, K. Sudgen, D. C. J. Reid, I. Bennion, A. Molony, M. J. Goodwin, “Very broad reflection bandwidth (44-nm) chirped fiber gratings and narrow bandpass filters by the use of an amplitude mask,” Electron. Lett. 30, 891–892 (1994).
[CrossRef]

Harter, D.

A. Galvanauskas, M. E. Fermann, D. Harter, K. Sugden, I. Bennion, “All fiber femtosecond pulse amplification circuit using chirped Bragg gratings,” Appl. Phys. Lett. 66, 1053–1055 (1995).
[CrossRef]

Hill, K. O.

Hill, P. C.

P. C. Hill, B. J. Eggletton, “Strain gradient chirp of fiber Bragg gratings,” Electron. Lett. 30, 1172–1174 (1994).
[CrossRef]

Huang, S. Y.

M. Le Blanc, S. Y. Huang, M. M. Ohn, R. M. Measures, “Tunable chirping of a fiber Bragg grating using a tapered cantilever bed,” Electron. Lett. 30, 2163–2165 (1994).
[CrossRef]

Hubner, J.

M. Sijka, P. Varming, J. Hubner, M. Kristensen, “Distributed feedback Er3+ doped fiber laser,” Electron. Lett. 31, 1445–1446 (1995).
[CrossRef]

Jacobovitz, G.

A. M. Vengsarkar, P. J. Lemaire, G. Jacobovitz, V. Bhatia, J. B. Judkins, “Long period fiber gratings as gain-flattening and laser stabilizing devices,” in Proceedings of the International Commission on Optics (ICOC-95), Hong Kong (1995), paper PD1-2, pp. 3–4.

Johnson, D. C.

Judkins, J. B.

A. M. Vengsarkar, P. J. Lemaire, G. Jacobovitz, V. Bhatia, J. B. Judkins, “Long period fiber gratings as gain-flattening and laser stabilizing devices,” in Proceedings of the International Commission on Optics (ICOC-95), Hong Kong (1995), paper PD1-2, pp. 3–4.

Kashyap, R.

S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. Makee, F. Sladen, B. Wojciechowicz, “High accuracy dispersion measurements of chirped fiber gratings,” Electron. Lett. 31, 1280–1282 (1995).
[CrossRef]

R. Kashyap, P. F. Mackee, D. Armes, “UV written reflection grating structures in photosensitive optical fibers using phase shifted phase masks,” Electron. Lett. 30, 1977–1978 (1994).
[CrossRef]

R. Kashyap, P. F. McKee, R. J. Campbell, D. L. Williams, “Novel method of producing all fiber photoinduced chirped gratings,” Electron. Lett. 30, 996–997 (1994).
[CrossRef]

Kim, B. G.

Kitagawa, T.

Kristensen, M.

M. Sijka, P. Varming, J. Hubner, M. Kristensen, “Distributed feedback Er3+ doped fiber laser,” Electron. Lett. 31, 1445–1446 (1995).
[CrossRef]

Krug, P. A.

B. J. Eggleton, P. A. Krug, L. Poladian, F. Oullette, “Long periodic super structure Bragg gratings in optical fibers,” Electron. Lett. 30, 1620–1622 (1944).
[CrossRef]

Laming, R. H.

M. J. Cole, W. H. Loh, R. H. Laming, M. N. Zervas, S. Barcelos, “Moving fiber/phase mask-scanning beam technique for enhanced flexibility producing fiber gratings with uniform phase mask,” Electron. Lett. 31, 1488–1489 (1995).
[CrossRef]

Laming, R. I.

S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. Makee, F. Sladen, B. Wojciechowicz, “High accuracy dispersion measurements of chirped fiber gratings,” Electron. Lett. 31, 1280–1282 (1995).
[CrossRef]

Lauzon, J.

Le Blanc, M.

M. Le Blanc, S. Y. Huang, M. M. Ohn, R. M. Measures, “Tunable chirping of a fiber Bragg grating using a tapered cantilever bed,” Electron. Lett. 30, 2163–2165 (1994).
[CrossRef]

Lemaire, P. J.

A. M. Vengsarkar, P. J. Lemaire, G. Jacobovitz, V. Bhatia, J. B. Judkins, “Long period fiber gratings as gain-flattening and laser stabilizing devices,” in Proceedings of the International Commission on Optics (ICOC-95), Hong Kong (1995), paper PD1-2, pp. 3–4.

Loh, W. H.

M. J. Cole, W. H. Loh, R. H. Laming, M. N. Zervas, S. Barcelos, “Moving fiber/phase mask-scanning beam technique for enhanced flexibility producing fiber gratings with uniform phase mask,” Electron. Lett. 31, 1488–1489 (1995).
[CrossRef]

Mackee, P. F.

R. Kashyap, P. F. Mackee, D. Armes, “UV written reflection grating structures in photosensitive optical fibers using phase shifted phase masks,” Electron. Lett. 30, 1977–1978 (1994).
[CrossRef]

Makee, P. F.

S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. Makee, F. Sladen, B. Wojciechowicz, “High accuracy dispersion measurements of chirped fiber gratings,” Electron. Lett. 31, 1280–1282 (1995).
[CrossRef]

Malo, B.

Martin, J.

McKee, P. F.

R. Kashyap, P. F. McKee, R. J. Campbell, D. L. Williams, “Novel method of producing all fiber photoinduced chirped gratings,” Electron. Lett. 30, 996–997 (1994).
[CrossRef]

Measures, R. M.

M. Le Blanc, S. Y. Huang, M. M. Ohn, R. M. Measures, “Tunable chirping of a fiber Bragg grating using a tapered cantilever bed,” Electron. Lett. 30, 2163–2165 (1994).
[CrossRef]

Molony, A.

M. C. Farries, K. Sudgen, D. C. J. Reid, I. Bennion, A. Molony, M. J. Goodwin, “Very broad reflection bandwidth (44-nm) chirped fiber gratings and narrow bandpass filters by the use of an amplitude mask,” Electron. Lett. 30, 891–892 (1994).
[CrossRef]

K. Sugden, I. Bennion, A. Molony, N. J. Copner, “Chirped gratings produced in photosensitive optical fibers by fiber deformation during exposure,” Electron. Lett. 30, 440–442 (1994).
[CrossRef]

Morse, T. F.

Ohn, M. M.

M. Le Blanc, S. Y. Huang, M. M. Ohn, R. M. Measures, “Tunable chirping of a fiber Bragg grating using a tapered cantilever bed,” Electron. Lett. 30, 2163–2165 (1994).
[CrossRef]

Oullette, F.

J. Lauzon, S. Thibault, J. Martin, F. Oullette, “Implementation and characterization of fiber Bragg gratings linearly chirped by a temperature gradient,” Opt. Lett. 19, 2027–2029 (1994).
[CrossRef] [PubMed]

B. J. Eggleton, P. A. Krug, L. Poladian, F. Oullette, “Long periodic super structure Bragg gratings in optical fibers,” Electron. Lett. 30, 1620–1622 (1944).
[CrossRef]

Painchaud, Y.

Y. Painchaud, A. Chandonnet, J. Lauzon, “Chirped fiber gratings produced by tilting the fiber,” Electron. Lett. 31, 171–172 (1995).
[CrossRef]

Payne, D. N.

S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. Makee, F. Sladen, B. Wojciechowicz, “High accuracy dispersion measurements of chirped fiber gratings,” Electron. Lett. 31, 1280–1282 (1995).
[CrossRef]

Poladian, L.

B. J. Eggleton, P. A. Krug, L. Poladian, F. Oullette, “Long periodic super structure Bragg gratings in optical fibers,” Electron. Lett. 30, 1620–1622 (1944).
[CrossRef]

Putman, M. A.

M. A. Putman, G. M. Williams, E. J. Friebele, “Fabrication of tapered strain gradient chirped fiber Bragg gratings,” Electron. Lett. 31, 309–310 (1995).
[CrossRef]

Radic, S.

G. P. Agrawal, S. Radic, “Phase shifted fiber Bragg gratings and their application for wavelength demultiplexing,” IEEE Photon. Technol. Lett. 6, 995–997 (1994).
[CrossRef]

Reekie, L.

S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. Makee, F. Sladen, B. Wojciechowicz, “High accuracy dispersion measurements of chirped fiber gratings,” Electron. Lett. 31, 1280–1282 (1995).
[CrossRef]

L. Dong, J. L. Cruz, L. Reekie, J. A. Tocknott, “Chirped fiber Bragg gratings fabricated using etched tapers,” Opt. Fiber Technol. 1, 363–368 (1995).
[CrossRef]

Reid, D. C. J.

M. C. Farries, K. Sudgen, D. C. J. Reid, I. Bennion, A. Molony, M. J. Goodwin, “Very broad reflection bandwidth (44-nm) chirped fiber gratings and narrow bandpass filters by the use of an amplitude mask,” Electron. Lett. 30, 891–892 (1994).
[CrossRef]

Reinhart, L. J.

Rourke, H. N.

K. C. Byron, H. N. Rourke, “Fabrication of chirped fiber gratings by a novel stretch and write technique,” Electron. Lett. 31, 60–61 (1995).
[CrossRef]

Sakuda, K.

Sceats, M. G.

J. Canning, M. G. Sceats, “π-Phase shifted periodic distributed structures in optical fibers by UV postprocessing,” Electron. Lett. 30, 1344–1345 (1994).
[CrossRef]

Sijka, M.

M. Sijka, P. Varming, J. Hubner, M. Kristensen, “Distributed feedback Er3+ doped fiber laser,” Electron. Lett. 31, 1445–1446 (1995).
[CrossRef]

Sladen, F.

S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. Makee, F. Sladen, B. Wojciechowicz, “High accuracy dispersion measurements of chirped fiber gratings,” Electron. Lett. 31, 1280–1282 (1995).
[CrossRef]

Sudgen, K.

M. C. Farries, K. Sudgen, D. C. J. Reid, I. Bennion, A. Molony, M. J. Goodwin, “Very broad reflection bandwidth (44-nm) chirped fiber gratings and narrow bandpass filters by the use of an amplitude mask,” Electron. Lett. 30, 891–892 (1994).
[CrossRef]

Sugden, K.

A. Galvanauskas, M. E. Fermann, D. Harter, K. Sugden, I. Bennion, “All fiber femtosecond pulse amplification circuit using chirped Bragg gratings,” Appl. Phys. Lett. 66, 1053–1055 (1995).
[CrossRef]

K. Sugden, I. Bennion, A. Molony, N. J. Copner, “Chirped gratings produced in photosensitive optical fibers by fiber deformation during exposure,” Electron. Lett. 30, 440–442 (1994).
[CrossRef]

K. C. Byron, K. Sugden, T. Bricheno, I. Bennion, “Fabrication of fiber Bragg gratings in photosensitive fiber,” Electron. Lett. 29, 1659–1660 (1993).
[CrossRef]

Takiguchi, K.

Theriault, S.

Thibault, S.

Tocknott, J. A.

L. Dong, J. L. Cruz, L. Reekie, J. A. Tocknott, “Chirped fiber Bragg gratings fabricated using etched tapers,” Opt. Fiber Technol. 1, 363–368 (1995).
[CrossRef]

Tucknott, J. A.

S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. Makee, F. Sladen, B. Wojciechowicz, “High accuracy dispersion measurements of chirped fiber gratings,” Electron. Lett. 31, 1280–1282 (1995).
[CrossRef]

Varming, P.

M. Sijka, P. Varming, J. Hubner, M. Kristensen, “Distributed feedback Er3+ doped fiber laser,” Electron. Lett. 31, 1445–1446 (1995).
[CrossRef]

Vengsarkar, A. M.

A. M. Vengsarkar, P. J. Lemaire, G. Jacobovitz, V. Bhatia, J. B. Judkins, “Long period fiber gratings as gain-flattening and laser stabilizing devices,” in Proceedings of the International Commission on Optics (ICOC-95), Hong Kong (1995), paper PD1-2, pp. 3–4.

Williams, D. L.

R. Kashyap, P. F. McKee, R. J. Campbell, D. L. Williams, “Novel method of producing all fiber photoinduced chirped gratings,” Electron. Lett. 30, 996–997 (1994).
[CrossRef]

Williams, G. M.

M. A. Putman, G. M. Williams, E. J. Friebele, “Fabrication of tapered strain gradient chirped fiber Bragg gratings,” Electron. Lett. 31, 309–310 (1995).
[CrossRef]

Willians, A. R.

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

Wojciechowicz, B.

S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. Makee, F. Sladen, B. Wojciechowicz, “High accuracy dispersion measurements of chirped fiber gratings,” Electron. Lett. 31, 1280–1282 (1995).
[CrossRef]

Xu, M. G.

M. G. Xu, “The measurement of physical fields using optical fibers and fiber gratings,” Ph.D. dissertation (Department of Electronics and Computer Science, University of Southampton, UK, 1995).

Yamada, M.

Zervas, M. N.

S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. Makee, F. Sladen, B. Wojciechowicz, “High accuracy dispersion measurements of chirped fiber gratings,” Electron. Lett. 31, 1280–1282 (1995).
[CrossRef]

M. J. Cole, W. H. Loh, R. H. Laming, M. N. Zervas, S. Barcelos, “Moving fiber/phase mask-scanning beam technique for enhanced flexibility producing fiber gratings with uniform phase mask,” Electron. Lett. 31, 1488–1489 (1995).
[CrossRef]

Zhang, Q.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

A. Galvanauskas, M. E. Fermann, D. Harter, K. Sugden, I. Bennion, “All fiber femtosecond pulse amplification circuit using chirped Bragg gratings,” Appl. Phys. Lett. 66, 1053–1055 (1995).
[CrossRef]

Electron. Lett. (15)

K. C. Byron, H. N. Rourke, “Fabrication of chirped fiber gratings by a novel stretch and write technique,” Electron. Lett. 31, 60–61 (1995).
[CrossRef]

P. C. Hill, B. J. Eggletton, “Strain gradient chirp of fiber Bragg gratings,” Electron. Lett. 30, 1172–1174 (1994).
[CrossRef]

M. A. Putman, G. M. Williams, E. J. Friebele, “Fabrication of tapered strain gradient chirped fiber Bragg gratings,” Electron. Lett. 31, 309–310 (1995).
[CrossRef]

M. Le Blanc, S. Y. Huang, M. M. Ohn, R. M. Measures, “Tunable chirping of a fiber Bragg grating using a tapered cantilever bed,” Electron. Lett. 30, 2163–2165 (1994).
[CrossRef]

K. C. Byron, K. Sugden, T. Bricheno, I. Bennion, “Fabrication of fiber Bragg gratings in photosensitive fiber,” Electron. Lett. 29, 1659–1660 (1993).
[CrossRef]

Y. Painchaud, A. Chandonnet, J. Lauzon, “Chirped fiber gratings produced by tilting the fiber,” Electron. Lett. 31, 171–172 (1995).
[CrossRef]

M. J. Cole, W. H. Loh, R. H. Laming, M. N. Zervas, S. Barcelos, “Moving fiber/phase mask-scanning beam technique for enhanced flexibility producing fiber gratings with uniform phase mask,” Electron. Lett. 31, 1488–1489 (1995).
[CrossRef]

R. Kashyap, P. F. McKee, R. J. Campbell, D. L. Williams, “Novel method of producing all fiber photoinduced chirped gratings,” Electron. Lett. 30, 996–997 (1994).
[CrossRef]

M. C. Farries, K. Sudgen, D. C. J. Reid, I. Bennion, A. Molony, M. J. Goodwin, “Very broad reflection bandwidth (44-nm) chirped fiber gratings and narrow bandpass filters by the use of an amplitude mask,” Electron. Lett. 30, 891–892 (1994).
[CrossRef]

K. Sugden, I. Bennion, A. Molony, N. J. Copner, “Chirped gratings produced in photosensitive optical fibers by fiber deformation during exposure,” Electron. Lett. 30, 440–442 (1994).
[CrossRef]

M. Sijka, P. Varming, J. Hubner, M. Kristensen, “Distributed feedback Er3+ doped fiber laser,” Electron. Lett. 31, 1445–1446 (1995).
[CrossRef]

B. J. Eggleton, P. A. Krug, L. Poladian, F. Oullette, “Long periodic super structure Bragg gratings in optical fibers,” Electron. Lett. 30, 1620–1622 (1944).
[CrossRef]

J. Canning, M. G. Sceats, “π-Phase shifted periodic distributed structures in optical fibers by UV postprocessing,” Electron. Lett. 30, 1344–1345 (1994).
[CrossRef]

R. Kashyap, P. F. Mackee, D. Armes, “UV written reflection grating structures in photosensitive optical fibers using phase shifted phase masks,” Electron. Lett. 30, 1977–1978 (1994).
[CrossRef]

S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. Makee, F. Sladen, B. Wojciechowicz, “High accuracy dispersion measurements of chirped fiber gratings,” Electron. Lett. 31, 1280–1282 (1995).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

G. P. Agrawal, S. Radic, “Phase shifted fiber Bragg gratings and their application for wavelength demultiplexing,” IEEE Photon. Technol. Lett. 6, 995–997 (1994).
[CrossRef]

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

Opt. Commun. (1)

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

Opt. Fiber Technol. (1)

L. Dong, J. L. Cruz, L. Reekie, J. A. Tocknott, “Chirped fiber Bragg gratings fabricated using etched tapers,” Opt. Fiber Technol. 1, 363–368 (1995).
[CrossRef]

Opt. Lett. (4)

Other (2)

A. M. Vengsarkar, P. J. Lemaire, G. Jacobovitz, V. Bhatia, J. B. Judkins, “Long period fiber gratings as gain-flattening and laser stabilizing devices,” in Proceedings of the International Commission on Optics (ICOC-95), Hong Kong (1995), paper PD1-2, pp. 3–4.

M. G. Xu, “The measurement of physical fields using optical fibers and fiber gratings,” Ph.D. dissertation (Department of Electronics and Computer Science, University of Southampton, UK, 1995).

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Figures (11)

Fig. 1
Fig. 1

Tapers for different chirp profiles: (a) linear chirp, (b) quadratic chirp, (c) phase-modulated grating, (d) phase-mismatched grating.

Fig. 2
Fig. 2

Reflectivity of a linearly chirped grating as a function of the normalized detuning Δβ · L = −(β − π/Λ) · L for different strains in the 125-μm fiber. Normalized coupling coefficient, |κ|L = πΔnL B = 8: (a) original grating, no strain; (b) strain 0.02%; (c) strain 0.04%; (d) strain 0.08%.

Fig. 3
Fig. 3

Normalized group delay in the reflection as one looks from the large end of a taper for the linear chirp as a function of the normalized detuning for different applied strains in the 125-μm fiber, |κ|L = 8. Time normalization factor, τ0 = 2nL/c: (a) original grating, no strain; (b) strain 0.02%; (c) strain 0.04%; (d) strain 0.08%.

Fig. 4
Fig. 4

Reflectivity of a quadratic grating as a function of the normalized detuning for different applied strains in the 125-μm fiber, κL = 8: (a) original grating, no strain; (b) strain 0.02%, (c) strain 0.08%.

Fig. 5
Fig. 5

Normalized group delay in the reflection looking from the large end of a taper for the quadratic chirp as a function of normalized detuning for different applied strains in the 125-μm fiber, |κ|L = 8: (a) original grating, no strain; (b) strain 0.02%, (c) strain 0.08%.

Fig. 6
Fig. 6

Reflectivity of a phase-modulated grating as a function of normalized detuning for different strains in the 125-μm fiber, κL = 8: (A) original grating [curve (a)] and response under a strain of 0.02% [curve (b)]; (B) original grating [curve (a)] and response under a strain of 0.08% [curve (b)].

Fig. 7
Fig. 7

Reflectivity of a phase-mismatched grating as a function of the normalized detuning for different strains in the 125-μm fiber, |κ|L = 8: (a) original grating, no strain; (b) strain 0.04%; (c) strain 0.08%.

Fig. 8
Fig. 8

Measured diameter profile of three tapers etched in fibers: (a) linear, (b) quadratic, (c) phase mismatched.

Fig. 9
Fig. 9

Measured response of a linear grating written under a load of 53.3 g. The fiber is in a relaxed state when being measured: (A) reflectivity, (B) group delay.

Fig. 10
Fig. 10

Measured transmission coefficient of a quadratically chirped grating under different loads: (a) 0 g, (b) 10.2 g, (c) 25.7 g.

Fig. 11
Fig. 11

Measured transmission coefficient of a phase-mismatched grating under different loads: (a) 0 g, (b) 55.3 g, (c) 93.8 g.

Equations (7)

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Δ λ B λ B = F π E r 2 x F π E r 2 ,
r ( z ) = r ( 0 ) r ( L ) { [ r ( 0 ) 2 r ( L ) 2 ] f ( z / L ) + r ( L ) 2 } 1 / 2 ,
[ b i ( 2 ) a i ( 2 ) ] = ( T 11 i T 12 i T 21 i T 22 i ) [ a i ( 1 ) b i ( 1 ) ] ,
T = i = 1 N T ( i ) .
T 11 i = S 21 i S 22 i S 11 i / S 12 i , T 12 i = S 22 i / S 12 i , T 21 i = S 11 i / S 12 i , T 22 i = 1 / S 12 i ,
[ b i ( 1 ) b i ( 2 ) ] = ( S 11 i S 12 i S 21 i S 22 i ) [ a i ( 1 ) a i ( 2 ) ] ,
S 11 = S 22 = κ exp ( μ L ) exp ( + μ L ) ( μ j Δ β ) exp ( μ L ) + ( μ + j Δ β ) exp ( + μ L ) , S 12 = S 21 = 2 μ ( μ j Δ β ) exp ( μ L ) + ( μ + j Δ β ) exp ( + μ L ) ,

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