Abstract

We fabricated grating-based Fabry–Perot (FP) interferometers by photowriting a pair of Bragg gratings with a spacing of a few millimeters in a germanosilicate fiber. The measured free spectral range (FSR) of the FP filters is found to vary with the frequency in the spectral range of the filters. Relative FSR variation reaches values close to 10%. An analytical model is presented and compared with a coupled-mode theory in a matrix approach. The computations and the experimental results demonstrate that the main FSR variation (10%) is due to the spectral modification of the reflection coefficients of the two gratings. The relative FSR variation that is due to the propagation effective-index modification is found to be close to 10−5. A comparison between a grating-based FP filter photowritten in a fiber and a bulk FP filter is presented.

© 1995 Optical Society of America

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  1. K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, “Photosensitivity in optical waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
    [CrossRef]
  2. G. Meltz, W. W. Morey, W. H. Glenn, “Formation of Bragg gratings in optical fibers by a transverse holographic method,” Opt. Lett. 14, 823–825 (1989).
    [CrossRef] [PubMed]
  3. K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, J. Albert, “Bragg grating fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62, 1035–1037 (1993).
    [CrossRef]
  4. C. G. Askins, T. E. Tsai, G. M. Williams, M. A. Putnam, M. Bashkansky, E. J. Friebele, “Fiber Bragg reflectors prepared by a single excimer pulse,” Opt. Lett. 17, 833–835 (1992).
    [CrossRef] [PubMed]
  5. D. Z. Anderson, V. Mizrahi, T. Erdogan, A. E. White, “Production of in-fibre gratings using a diffractive optical element,” Electron. Lett. 29, 566–568 (1993).
    [CrossRef]
  6. R. Kashyap, J. R. Armitage, R. Wyatt, S. T. Davey, D. L. Williams, “All fiber narrow-band reflection gratings at 1500 nm,” Electron. Lett. 26, 730–732 (1990).
    [CrossRef]
  7. G. A. Ball, W. W. Morey, J. P. Waters, “Nd3+fiber laser utilizing intra-core Bragg reflectors,” Electron. Lett. 26, 1829–1830 (1990).
    [CrossRef]
  8. W. W. Morey, G. Meltz, W. H. Glenn, “Bragg-grating temperature and strain sensors,” in Optical Fiber Sensors, Vol. 44 of Springer Proceedings in Physics (Springer-Verlag, Berlin, 1989), pp. 526–531.
    [CrossRef]
  9. W. W. Morey, T. J. Bailey, W. H. Glenn, G. Meltz, “Fiber Fabry–Perot interferometer using side exposed fiber Bragg gratings,” in Optical Fiber Communication, Vol. 5 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper WA2.
  10. R. T. Measures, “Fiber optic sensor considerations and developments for smart structures,” in Fiber Optic Smart Structures and Skins IV, R. O. Claus, E. Udd, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1588, 282–299 (1991).
    [CrossRef]
  11. J. Chen, P. Chang, Y. Zhao, “Cross talk of Fabry–Perot filters and its effects on the performance of optical fiber frequency-division-multiplexing/frequency-shift-keying systems,” Opt. Lett. 18, 604–606 (1993).
    [CrossRef] [PubMed]
  12. M. Yamada, K. Sakuda, “Analysis of almost-periodic distributed feedback slab waveguides via a fundamental matrix approach,” Appl. Opt. 26, 3474–3478 (1987).
    [CrossRef] [PubMed]
  13. D. K. Lam, B. K. Garside, “Characterization of single-mode optical fiber filters,” Appl. Opt. 20, 440–445 (1981).
    [CrossRef] [PubMed]
  14. A. Yariv, “Coupled mode theory for guide-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).
    [CrossRef]
  15. W. X. Xie, M. Douay, P. Bernage, P. Niay, J. F. Bayon, T. Georges, “Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres,” Opt. Commun. 101, 85–91 (1993).
    [CrossRef]
  16. W. X. Xie, P. Niay, P. Bernage, M. Douay, J. F. Bayon, T. Georges, M. Monerie, B. Poumellec, “Experimental evidence of two types of photorefractive effects occurring during photoinscriptions of Bragg gratings within germanosilicate fibres,” Opt. Commun. 104, 185–195 (1994).
    [CrossRef]
  17. J. L. Archambault, L. Reekie, P. St. J. Russel, “High reflectivity and narrow bandwidth fibre gratings written by single excimer pulse,” Electron. Lett. 21, 28–29 (1993).
    [CrossRef]
  18. K. O. Hill, “Aperiodic distributed-parameter waveguides for integrated optics,” Appl. Opt. 13, 1853–1856 (1974).
    [CrossRef] [PubMed]
  19. H. Kogelnik, “Filter response of nonuniform almost periodic structures,” Bell Syst. Tech. J. 55, 109–126 (1976).
  20. A. Empsten, I. Veretennicoff, “Optical bistability in an NL DF B device showing absorption, comparison of feedback efficiencies for different grating profiles, and study of the behavior of aperiodic and nonperfect grating profiles,” IEEE J. Quantum Electron. 26, 1089–1097 (1990).
    [CrossRef]
  21. B. G. Kim, E. Garmire, “Comparison between the matrix method and the coupled-wave method in the analysis of Bragg reflector structures,” J. Opt. Soc. Am. A 9, 132–136 (1992).
    [CrossRef]
  22. V. Mizrahi, J. E. Sipe, “Optical properties of photosensitive fiber phase gratings,” J. Lightwave Technol. 11, 1513–1517 (1993).
    [CrossRef]
  23. V. Mizrahi, T. Erdogan, D. J. DiGiovanni, P. J. Lemaire, W. M. MacDonald, S. G. Kosinski, S. Cabot, J. E. Sipe, “Four channel fibre grating demultiplexer,” Electron Lett. 30, 780–781 (1994).
    [CrossRef]

1994 (2)

W. X. Xie, P. Niay, P. Bernage, M. Douay, J. F. Bayon, T. Georges, M. Monerie, B. Poumellec, “Experimental evidence of two types of photorefractive effects occurring during photoinscriptions of Bragg gratings within germanosilicate fibres,” Opt. Commun. 104, 185–195 (1994).
[CrossRef]

V. Mizrahi, T. Erdogan, D. J. DiGiovanni, P. J. Lemaire, W. M. MacDonald, S. G. Kosinski, S. Cabot, J. E. Sipe, “Four channel fibre grating demultiplexer,” Electron Lett. 30, 780–781 (1994).
[CrossRef]

1993 (6)

V. Mizrahi, J. E. Sipe, “Optical properties of photosensitive fiber phase gratings,” J. Lightwave Technol. 11, 1513–1517 (1993).
[CrossRef]

J. Chen, P. Chang, Y. Zhao, “Cross talk of Fabry–Perot filters and its effects on the performance of optical fiber frequency-division-multiplexing/frequency-shift-keying systems,” Opt. Lett. 18, 604–606 (1993).
[CrossRef] [PubMed]

J. L. Archambault, L. Reekie, P. St. J. Russel, “High reflectivity and narrow bandwidth fibre gratings written by single excimer pulse,” Electron. Lett. 21, 28–29 (1993).
[CrossRef]

W. X. Xie, M. Douay, P. Bernage, P. Niay, J. F. Bayon, T. Georges, “Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres,” Opt. Commun. 101, 85–91 (1993).
[CrossRef]

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, J. Albert, “Bragg grating fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

D. Z. Anderson, V. Mizrahi, T. Erdogan, A. E. White, “Production of in-fibre gratings using a diffractive optical element,” Electron. Lett. 29, 566–568 (1993).
[CrossRef]

1992 (2)

1990 (3)

A. Empsten, I. Veretennicoff, “Optical bistability in an NL DF B device showing absorption, comparison of feedback efficiencies for different grating profiles, and study of the behavior of aperiodic and nonperfect grating profiles,” IEEE J. Quantum Electron. 26, 1089–1097 (1990).
[CrossRef]

R. Kashyap, J. R. Armitage, R. Wyatt, S. T. Davey, D. L. Williams, “All fiber narrow-band reflection gratings at 1500 nm,” Electron. Lett. 26, 730–732 (1990).
[CrossRef]

G. A. Ball, W. W. Morey, J. P. Waters, “Nd3+fiber laser utilizing intra-core Bragg reflectors,” Electron. Lett. 26, 1829–1830 (1990).
[CrossRef]

1989 (1)

1987 (1)

1981 (1)

1978 (1)

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, “Photosensitivity in optical waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

1976 (1)

H. Kogelnik, “Filter response of nonuniform almost periodic structures,” Bell Syst. Tech. J. 55, 109–126 (1976).

1974 (1)

1973 (1)

A. Yariv, “Coupled mode theory for guide-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).
[CrossRef]

Albert, J.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, J. Albert, “Bragg grating fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

Anderson, D. Z.

D. Z. Anderson, V. Mizrahi, T. Erdogan, A. E. White, “Production of in-fibre gratings using a diffractive optical element,” Electron. Lett. 29, 566–568 (1993).
[CrossRef]

Archambault, J. L.

J. L. Archambault, L. Reekie, P. St. J. Russel, “High reflectivity and narrow bandwidth fibre gratings written by single excimer pulse,” Electron. Lett. 21, 28–29 (1993).
[CrossRef]

Armitage, J. R.

R. Kashyap, J. R. Armitage, R. Wyatt, S. T. Davey, D. L. Williams, “All fiber narrow-band reflection gratings at 1500 nm,” Electron. Lett. 26, 730–732 (1990).
[CrossRef]

Askins, C. G.

Bailey, T. J.

W. W. Morey, T. J. Bailey, W. H. Glenn, G. Meltz, “Fiber Fabry–Perot interferometer using side exposed fiber Bragg gratings,” in Optical Fiber Communication, Vol. 5 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper WA2.

Ball, G. A.

G. A. Ball, W. W. Morey, J. P. Waters, “Nd3+fiber laser utilizing intra-core Bragg reflectors,” Electron. Lett. 26, 1829–1830 (1990).
[CrossRef]

Bashkansky, M.

Bayon, J. F.

W. X. Xie, P. Niay, P. Bernage, M. Douay, J. F. Bayon, T. Georges, M. Monerie, B. Poumellec, “Experimental evidence of two types of photorefractive effects occurring during photoinscriptions of Bragg gratings within germanosilicate fibres,” Opt. Commun. 104, 185–195 (1994).
[CrossRef]

W. X. Xie, M. Douay, P. Bernage, P. Niay, J. F. Bayon, T. Georges, “Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres,” Opt. Commun. 101, 85–91 (1993).
[CrossRef]

Bernage, P.

W. X. Xie, P. Niay, P. Bernage, M. Douay, J. F. Bayon, T. Georges, M. Monerie, B. Poumellec, “Experimental evidence of two types of photorefractive effects occurring during photoinscriptions of Bragg gratings within germanosilicate fibres,” Opt. Commun. 104, 185–195 (1994).
[CrossRef]

W. X. Xie, M. Douay, P. Bernage, P. Niay, J. F. Bayon, T. Georges, “Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres,” Opt. Commun. 101, 85–91 (1993).
[CrossRef]

Bilodeau, F.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, J. Albert, “Bragg grating fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

Cabot, S.

V. Mizrahi, T. Erdogan, D. J. DiGiovanni, P. J. Lemaire, W. M. MacDonald, S. G. Kosinski, S. Cabot, J. E. Sipe, “Four channel fibre grating demultiplexer,” Electron Lett. 30, 780–781 (1994).
[CrossRef]

Chang, P.

Chen, J.

Davey, S. T.

R. Kashyap, J. R. Armitage, R. Wyatt, S. T. Davey, D. L. Williams, “All fiber narrow-band reflection gratings at 1500 nm,” Electron. Lett. 26, 730–732 (1990).
[CrossRef]

DiGiovanni, D. J.

V. Mizrahi, T. Erdogan, D. J. DiGiovanni, P. J. Lemaire, W. M. MacDonald, S. G. Kosinski, S. Cabot, J. E. Sipe, “Four channel fibre grating demultiplexer,” Electron Lett. 30, 780–781 (1994).
[CrossRef]

Douay, M.

W. X. Xie, P. Niay, P. Bernage, M. Douay, J. F. Bayon, T. Georges, M. Monerie, B. Poumellec, “Experimental evidence of two types of photorefractive effects occurring during photoinscriptions of Bragg gratings within germanosilicate fibres,” Opt. Commun. 104, 185–195 (1994).
[CrossRef]

W. X. Xie, M. Douay, P. Bernage, P. Niay, J. F. Bayon, T. Georges, “Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres,” Opt. Commun. 101, 85–91 (1993).
[CrossRef]

Empsten, A.

A. Empsten, I. Veretennicoff, “Optical bistability in an NL DF B device showing absorption, comparison of feedback efficiencies for different grating profiles, and study of the behavior of aperiodic and nonperfect grating profiles,” IEEE J. Quantum Electron. 26, 1089–1097 (1990).
[CrossRef]

Erdogan, T.

V. Mizrahi, T. Erdogan, D. J. DiGiovanni, P. J. Lemaire, W. M. MacDonald, S. G. Kosinski, S. Cabot, J. E. Sipe, “Four channel fibre grating demultiplexer,” Electron Lett. 30, 780–781 (1994).
[CrossRef]

D. Z. Anderson, V. Mizrahi, T. Erdogan, A. E. White, “Production of in-fibre gratings using a diffractive optical element,” Electron. Lett. 29, 566–568 (1993).
[CrossRef]

Friebele, E. J.

Fujii, Y.

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, “Photosensitivity in optical waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Garmire, E.

Garside, B. K.

Georges, T.

W. X. Xie, P. Niay, P. Bernage, M. Douay, J. F. Bayon, T. Georges, M. Monerie, B. Poumellec, “Experimental evidence of two types of photorefractive effects occurring during photoinscriptions of Bragg gratings within germanosilicate fibres,” Opt. Commun. 104, 185–195 (1994).
[CrossRef]

W. X. Xie, M. Douay, P. Bernage, P. Niay, J. F. Bayon, T. Georges, “Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres,” Opt. Commun. 101, 85–91 (1993).
[CrossRef]

Glenn, W. H.

G. Meltz, W. W. Morey, W. H. Glenn, “Formation of Bragg gratings in optical fibers by a transverse holographic method,” Opt. Lett. 14, 823–825 (1989).
[CrossRef] [PubMed]

W. W. Morey, T. J. Bailey, W. H. Glenn, G. Meltz, “Fiber Fabry–Perot interferometer using side exposed fiber Bragg gratings,” in Optical Fiber Communication, Vol. 5 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper WA2.

W. W. Morey, G. Meltz, W. H. Glenn, “Bragg-grating temperature and strain sensors,” in Optical Fiber Sensors, Vol. 44 of Springer Proceedings in Physics (Springer-Verlag, Berlin, 1989), pp. 526–531.
[CrossRef]

Hill, K. O.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, J. Albert, “Bragg grating fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, “Photosensitivity in optical waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

K. O. Hill, “Aperiodic distributed-parameter waveguides for integrated optics,” Appl. Opt. 13, 1853–1856 (1974).
[CrossRef] [PubMed]

Johnson, D. C.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, J. Albert, “Bragg grating fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, “Photosensitivity in optical waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Kashyap, R.

R. Kashyap, J. R. Armitage, R. Wyatt, S. T. Davey, D. L. Williams, “All fiber narrow-band reflection gratings at 1500 nm,” Electron. Lett. 26, 730–732 (1990).
[CrossRef]

Kawasaki, B. S.

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, “Photosensitivity in optical waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Kim, B. G.

Kogelnik, H.

H. Kogelnik, “Filter response of nonuniform almost periodic structures,” Bell Syst. Tech. J. 55, 109–126 (1976).

Kosinski, S. G.

V. Mizrahi, T. Erdogan, D. J. DiGiovanni, P. J. Lemaire, W. M. MacDonald, S. G. Kosinski, S. Cabot, J. E. Sipe, “Four channel fibre grating demultiplexer,” Electron Lett. 30, 780–781 (1994).
[CrossRef]

Lam, D. K.

Lemaire, P. J.

V. Mizrahi, T. Erdogan, D. J. DiGiovanni, P. J. Lemaire, W. M. MacDonald, S. G. Kosinski, S. Cabot, J. E. Sipe, “Four channel fibre grating demultiplexer,” Electron Lett. 30, 780–781 (1994).
[CrossRef]

MacDonald, W. M.

V. Mizrahi, T. Erdogan, D. J. DiGiovanni, P. J. Lemaire, W. M. MacDonald, S. G. Kosinski, S. Cabot, J. E. Sipe, “Four channel fibre grating demultiplexer,” Electron Lett. 30, 780–781 (1994).
[CrossRef]

Malo, B.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, J. Albert, “Bragg grating fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

Measures, R. T.

R. T. Measures, “Fiber optic sensor considerations and developments for smart structures,” in Fiber Optic Smart Structures and Skins IV, R. O. Claus, E. Udd, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1588, 282–299 (1991).
[CrossRef]

Meltz, G.

G. Meltz, W. W. Morey, W. H. Glenn, “Formation of Bragg gratings in optical fibers by a transverse holographic method,” Opt. Lett. 14, 823–825 (1989).
[CrossRef] [PubMed]

W. W. Morey, G. Meltz, W. H. Glenn, “Bragg-grating temperature and strain sensors,” in Optical Fiber Sensors, Vol. 44 of Springer Proceedings in Physics (Springer-Verlag, Berlin, 1989), pp. 526–531.
[CrossRef]

W. W. Morey, T. J. Bailey, W. H. Glenn, G. Meltz, “Fiber Fabry–Perot interferometer using side exposed fiber Bragg gratings,” in Optical Fiber Communication, Vol. 5 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper WA2.

Mizrahi, V.

V. Mizrahi, T. Erdogan, D. J. DiGiovanni, P. J. Lemaire, W. M. MacDonald, S. G. Kosinski, S. Cabot, J. E. Sipe, “Four channel fibre grating demultiplexer,” Electron Lett. 30, 780–781 (1994).
[CrossRef]

V. Mizrahi, J. E. Sipe, “Optical properties of photosensitive fiber phase gratings,” J. Lightwave Technol. 11, 1513–1517 (1993).
[CrossRef]

D. Z. Anderson, V. Mizrahi, T. Erdogan, A. E. White, “Production of in-fibre gratings using a diffractive optical element,” Electron. Lett. 29, 566–568 (1993).
[CrossRef]

Monerie, M.

W. X. Xie, P. Niay, P. Bernage, M. Douay, J. F. Bayon, T. Georges, M. Monerie, B. Poumellec, “Experimental evidence of two types of photorefractive effects occurring during photoinscriptions of Bragg gratings within germanosilicate fibres,” Opt. Commun. 104, 185–195 (1994).
[CrossRef]

Morey, W. W.

G. A. Ball, W. W. Morey, J. P. Waters, “Nd3+fiber laser utilizing intra-core Bragg reflectors,” Electron. Lett. 26, 1829–1830 (1990).
[CrossRef]

G. Meltz, W. W. Morey, W. H. Glenn, “Formation of Bragg gratings in optical fibers by a transverse holographic method,” Opt. Lett. 14, 823–825 (1989).
[CrossRef] [PubMed]

W. W. Morey, G. Meltz, W. H. Glenn, “Bragg-grating temperature and strain sensors,” in Optical Fiber Sensors, Vol. 44 of Springer Proceedings in Physics (Springer-Verlag, Berlin, 1989), pp. 526–531.
[CrossRef]

W. W. Morey, T. J. Bailey, W. H. Glenn, G. Meltz, “Fiber Fabry–Perot interferometer using side exposed fiber Bragg gratings,” in Optical Fiber Communication, Vol. 5 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper WA2.

Niay, P.

W. X. Xie, P. Niay, P. Bernage, M. Douay, J. F. Bayon, T. Georges, M. Monerie, B. Poumellec, “Experimental evidence of two types of photorefractive effects occurring during photoinscriptions of Bragg gratings within germanosilicate fibres,” Opt. Commun. 104, 185–195 (1994).
[CrossRef]

W. X. Xie, M. Douay, P. Bernage, P. Niay, J. F. Bayon, T. Georges, “Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres,” Opt. Commun. 101, 85–91 (1993).
[CrossRef]

Poumellec, B.

W. X. Xie, P. Niay, P. Bernage, M. Douay, J. F. Bayon, T. Georges, M. Monerie, B. Poumellec, “Experimental evidence of two types of photorefractive effects occurring during photoinscriptions of Bragg gratings within germanosilicate fibres,” Opt. Commun. 104, 185–195 (1994).
[CrossRef]

Putnam, M. A.

Reekie, L.

J. L. Archambault, L. Reekie, P. St. J. Russel, “High reflectivity and narrow bandwidth fibre gratings written by single excimer pulse,” Electron. Lett. 21, 28–29 (1993).
[CrossRef]

Russel, P. St. J.

J. L. Archambault, L. Reekie, P. St. J. Russel, “High reflectivity and narrow bandwidth fibre gratings written by single excimer pulse,” Electron. Lett. 21, 28–29 (1993).
[CrossRef]

Sakuda, K.

Sipe, J. E.

V. Mizrahi, T. Erdogan, D. J. DiGiovanni, P. J. Lemaire, W. M. MacDonald, S. G. Kosinski, S. Cabot, J. E. Sipe, “Four channel fibre grating demultiplexer,” Electron Lett. 30, 780–781 (1994).
[CrossRef]

V. Mizrahi, J. E. Sipe, “Optical properties of photosensitive fiber phase gratings,” J. Lightwave Technol. 11, 1513–1517 (1993).
[CrossRef]

Tsai, T. E.

Veretennicoff, I.

A. Empsten, I. Veretennicoff, “Optical bistability in an NL DF B device showing absorption, comparison of feedback efficiencies for different grating profiles, and study of the behavior of aperiodic and nonperfect grating profiles,” IEEE J. Quantum Electron. 26, 1089–1097 (1990).
[CrossRef]

Waters, J. P.

G. A. Ball, W. W. Morey, J. P. Waters, “Nd3+fiber laser utilizing intra-core Bragg reflectors,” Electron. Lett. 26, 1829–1830 (1990).
[CrossRef]

White, A. E.

D. Z. Anderson, V. Mizrahi, T. Erdogan, A. E. White, “Production of in-fibre gratings using a diffractive optical element,” Electron. Lett. 29, 566–568 (1993).
[CrossRef]

Williams, D. L.

R. Kashyap, J. R. Armitage, R. Wyatt, S. T. Davey, D. L. Williams, “All fiber narrow-band reflection gratings at 1500 nm,” Electron. Lett. 26, 730–732 (1990).
[CrossRef]

Williams, G. M.

Wyatt, R.

R. Kashyap, J. R. Armitage, R. Wyatt, S. T. Davey, D. L. Williams, “All fiber narrow-band reflection gratings at 1500 nm,” Electron. Lett. 26, 730–732 (1990).
[CrossRef]

Xie, W. X.

W. X. Xie, P. Niay, P. Bernage, M. Douay, J. F. Bayon, T. Georges, M. Monerie, B. Poumellec, “Experimental evidence of two types of photorefractive effects occurring during photoinscriptions of Bragg gratings within germanosilicate fibres,” Opt. Commun. 104, 185–195 (1994).
[CrossRef]

W. X. Xie, M. Douay, P. Bernage, P. Niay, J. F. Bayon, T. Georges, “Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres,” Opt. Commun. 101, 85–91 (1993).
[CrossRef]

Yamada, M.

Yariv, A.

A. Yariv, “Coupled mode theory for guide-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).
[CrossRef]

Zhao, Y.

Appl. Opt. (3)

Appl. Phys. Lett. (2)

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, “Photosensitivity in optical waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, J. Albert, “Bragg grating fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Filter response of nonuniform almost periodic structures,” Bell Syst. Tech. J. 55, 109–126 (1976).

Electron Lett. (1)

V. Mizrahi, T. Erdogan, D. J. DiGiovanni, P. J. Lemaire, W. M. MacDonald, S. G. Kosinski, S. Cabot, J. E. Sipe, “Four channel fibre grating demultiplexer,” Electron Lett. 30, 780–781 (1994).
[CrossRef]

Electron. Lett. (4)

J. L. Archambault, L. Reekie, P. St. J. Russel, “High reflectivity and narrow bandwidth fibre gratings written by single excimer pulse,” Electron. Lett. 21, 28–29 (1993).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Typical record of the spectral transmission of a tapered FP filter. Δσ is equal to σBσ, where σB is the Bragg wave number. a.u., arbitrary units.

Fig. 3
Fig. 3

Schematic diagram of the phase condition for a grating-based FP filter.

Fig. 4
Fig. 4

Calculated spectral transmission as a function of detuning Δσ = σBσ (where σB is the Bragg wave number) for two FP filters. Solid curve, results obtained assuming the resonance condition 2neff(e + L) = B + with k integer. Dotted curve, results obtained with the further assumption that neff is constant in the spectral response of the filter.

Fig. 5
Fig. 5

Schematic diagram of an elementary layer.

Fig. 6
Fig. 6

Influence of the numbers N of layers on the calculated spectral transmission of a tapered grating.

Fig. 7
Fig. 7

(a) Assumed refractive-index variations of the fiber core; (b) comparison of experimental and calculated transmissions of a tapered grating. Solid curve, experimental transmission. Dotted curve, calculated transmission, assuming the refractive-index profile shown in 7(a); dashed–dotted curve, calculated transmission, assuming that the refractive-index profile decreases linearly along the z axis of the fiber. Δσ is equal to σBσ, where σB is the Bragg wave number.

Fig. 8
Fig. 8

(a) Assumed refractive-index profile of a grating-based FP filter as a function of the z axis of the fiber; (b) calculated spectral transmission of a grating-based FP filter with use of the refractive-index profile of (a). Δσ is equal to σBσ, where σB is the Bragg wave number.

Fig. 9
Fig. 9

Calculated evolution of the FSR as a function of the grating reflectivities of the FP filter. The length e between the inside edges of the gratings is 25 mm. The grating lengths are 6 mm.

Tables (2)

Tables Icon

Table 1 Experimental and Calculated (from the Matrix Method) FSR of the Grating-Based FP Filter

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Table 2 Calculated (from the Matrix or the Analytic Method) FSR of a Grating-Based FP Filter, Assuming Perfect Gratingsa

Equations (22)

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d d z A ^ 1 ( z ) = - j Ω A ^ 2 ( z ) exp ( 2 j Δ β z ) , d d z A ^ 2 ( z ) = j Ω * A ^ 1 ( z ) exp ( - 2 j Δ β z ) .
A ^ 1 ( z ) = exp ( j Δ β z ) × { S cosh [ S ( L - z ) + j Δ β sinh [ S ( L - z ) ] D A ^ 1 ( 0 ) + - j Ω exp ( j Δ β L ) sinh ( S z ) D A ^ 2 ( L ) } , A ^ 2 ( z ) = exp ( - j Δ β z ) { - j Ω * sinh [ S ( L - z ) ] D A ^ 1 ( 0 ) + exp ( j Δ β L ) S cosh ( S z ) + j Δ β sinh ( S z ) D A ^ 2 ( L ) } ,
A ^ 1 ( L ) = exp ( j Δ β L ) { S D A ^ 1 ( 0 ) - j Ω exp ( j Δ β L ) sinh ( S L ) D A ^ 2 ( L ) } .
A ^ 2 ( L ) exp [ j β ( e + L ) ] = - j Ω * sinh ( S L ) D A ^ 1 ( L ) × exp [ - j β ( e + L ) ] , A ^ 1 ( 2 L + e ) = exp ( j Δ β L ) [ S D A ^ 1 ( L ) ] .
A ^ t A ^ 1 ( 0 ) = A ^ 1 ( 2 L + e ) exp [ - j β ( 2 L + e ) ] A ^ 1 ( 0 ) = S 2 exp ( 2 j Δ β L ) exp [ - j β ( 2 L + e ) ] D 2 + Ω 2 sinh 2 ( S L ) exp ( 2 j Δ β L ) exp [ - 2 j β ( L + e ) ] .
T = A ^ t * A ^ t A ^ 1 * ( 0 ) A ^ 1 ( 0 ) = 1 1 + 4 { Ω 2 sinh 2 ( S L ) [ Ω 2 cosh 2 ( S L ) - Δ β 2 ] ( Ω 2 - Δ β 2 ) 2 } cos 2 [ Δ β L - β ( e + L ) - ( ϕ / 2 ) ] ,
tan ϕ = 2 Δ β S sinh ( S L ) cosh ( S L ) S 2 cosh 2 ( S L ) - Δ β 2 sinh 2 ( S L ) .
R PF = 1 - T = 4 R G ( 1 + R G ) 2 ,
I ( z ) = I 0 f ( z ) { 1 + V ( z ) cos [ 2 π z / Λ ( z ) ] } ,
V ( z ) = sinc 2 ( z π z vis ) ,
n ( z ) = n 10 + Δ n ph ( z ) ,
Δ n i ph ( z ) = Δ n 0 i + Δ n 1 i cos ( 2 π z Λ i + β 1 i ) + Δ n 2 i cos ( 4 π z Λ i + β 2 i ) ,             0 z L i ,
[ E F ( i - 1 ) E B ( i - 1 ) ] = [ F i ] [ E F i E B i ] .
F 11 = [ cosh ( S L ) + i Δ β L sinh ( S L ) / S L ] exp ( i β L ) , F 12 = - Ω L sinh ( S L ) exp [ - i ( β L + Φ ) ] / S L , F 21 = F 12 * , F 22 = F 11 * .
F = i = 1 N F i ,
[ E F ( 0 ) E B ( 0 ) ] = F [ E F ( L ) E B ( L ) ] .
T ( λ ) = 1 F 11 2 ,             R ( λ ) = F 21 F 11 2 .
R + T = 1.
F e = [ exp - j 2 π n eff e λ 0 0 exp j 2 π n eff e λ ] .
F FP = i = 1 N F i F e i = 1 N F i .
Δ σ ( λ ) = 1 / [ 2 n eff ( λ ) t ] .
t ( λ ) = 1 2 n eff ( λ ) Δ σ ( λ ) .

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