Abstract

A new nondestructive, noncontact, and sensitive technique for fiber Bragg grating geometry and index-fault location measurements is presented. Two plane-wave probe laser beams are incident upon the grating from the side at angles that satisfy the Bragg-reflection condition. An interference pattern is formed behind the fiber between the first-order diffracted beam (from one probe beam) and the zero-order transmitted beam (from the second probe beam). The axial grating index modulation and the grating period are functions of the fringe visibility and the fringe period, respectively. The method is sensitive and is applicable even in the case of relatively weak gratings. Unchirped and chirped Bragg gratings have been studied with the proposed technique. We demonstrate accuracies of 1 × 10-4 for measurement of the index modulation and 0.01 nm for measurement of the period. As well as for the analysis of most already-fabricated gratings, this technique is useful for in situ analysis of a long fiber Bragg grating as such a grating is translated along its axis during the fabrication process.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Othonos, “Fiber Bragg gratings,” Rev. Sci. Instrum. 68, 4309–4341 (1997).
    [CrossRef]
  2. K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, “Photosensitivity in optical fibre waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
    [CrossRef]
  3. K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, “Photosensitivity in optical fibers,” Annu. Rev. Mater. Sci. 23, 125–157 (1993).
    [CrossRef]
  4. W. W. Morey, G. A. Ball, G. Meltz, “Photoinduced Bragg gratings in optical fibers,” Opt. Photon. News 5, 8–14 (1994).
    [CrossRef]
  5. 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]
  6. Y. Rao, “In-fibre Bragg grating sensors,” Meas. Sci. Technol. 8, 355–375 (1997).
    [CrossRef]
  7. D. Pastor, J. Capmany, D. Ortega, V. Tatay, J. Marti, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” J. Lightwave Technol. 14, 2581–2588 (1996).
    [CrossRef]
  8. B. J. Eggleton, P. A. Krug, L. Poladian, K. A. Ahmed, H. F. Liu, “Experimental demonstration of compression of dispersed optical pulses by reflection from self-chirped optical fiber Bragg gratings,” Opt. Lett. 19, 877–879 (1994).
    [CrossRef] [PubMed]
  9. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
    [CrossRef]
  10. J. E. Roman, K. A. Winick, “Waveguide grating filters for dispersion compensation and pulse compression,” IEEE J. Quantum Electron. 29, 975–982 (1993).
    [CrossRef]
  11. E. Brinkmeyer, “Simple algorithm for reconstructing fiber gratings from reflectometric data,” Opt. Lett. 20, 810–812 (1995).
    [CrossRef] [PubMed]
  12. K. Takada, I. Yokohama, K. Chida, J. Noda, “New measurement system for fault location in optical waveguide devices based on an interferometric technique,” Appl. Opt. 26, 1603–1606 (1987).
    [CrossRef] [PubMed]
  13. B. L. Danielson, C. D. Whittenberg, “Guided-wave reflectometry with micrometer resolution,” Appl. Opt. 26, 2836–2842 (1987).
    [CrossRef] [PubMed]
  14. P. Lambelet, P. Y. Fonjallaz, H. G. Limberger, R. P. Salathe, Ch. Zimmer, H. H. Gilgen, “Bragg grating characterization by optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 5, 565–567 (1993).
    [CrossRef]
  15. W. Margulis, I. G. Carvalho, P. M. Gouvea, “Heat scan: a simple technique to study gratings in fiber,” Opt. Lett. 18, 1016–1018 (1993).
    [CrossRef] [PubMed]
  16. J. Canning, M. Jason, M. G. Sceats, “Rayleigh z-scan profiling of grating structures and resonances in optical fibers using side scattered light,” in Twentieth Australian Conference on Optical Fibre Technology (Information, Telecommunications & Electronics Engineering Society, Kingston, Australia, 1995), pp. 303–306.
  17. E. Brinkmeyer, G. Soltze, D. Johlen, “Optical space domain reflectometry (OSDR) for determination of strength and chirp distribution along optical fiber gratings,” in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides: Applications and Fundamentals, Vol. 17 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 33–36.
  18. P. A. Krug, R. Stolte, R. Ulrich, “Measurement of index modulation along an optical fiber Bragg grating,” Opt. Lett. 20, 1767–1769 (1995).
    [CrossRef] [PubMed]
  19. N. Roussel, S. Magne, C. Martinez, P. Ferdinand, “Measurement of index modulation along fiber Bragg gratings by side scattering and local heating techniques,” Opt. Fiber Technol. 5, 119–132 (1999).
    [CrossRef]
  20. P.-Y. Fonjallaz, P. Borjel, “Interferometric side diffraction technique for the characterization of fibre gratings,” in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, E. J. Friebele, R. Kashyap, T. Erdogan, eds., Vol. 33 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000).
  21. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Sys. Tech. J. 48, 9209–2947 (1969).

1999

N. Roussel, S. Magne, C. Martinez, P. Ferdinand, “Measurement of index modulation along fiber Bragg gratings by side scattering and local heating techniques,” Opt. Fiber Technol. 5, 119–132 (1999).
[CrossRef]

1997

A. Othonos, “Fiber Bragg gratings,” Rev. Sci. Instrum. 68, 4309–4341 (1997).
[CrossRef]

Y. Rao, “In-fibre Bragg grating sensors,” Meas. Sci. Technol. 8, 355–375 (1997).
[CrossRef]

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[CrossRef]

1996

D. Pastor, J. Capmany, D. Ortega, V. Tatay, J. Marti, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” J. Lightwave Technol. 14, 2581–2588 (1996).
[CrossRef]

1995

1994

1993

J. E. Roman, K. A. Winick, “Waveguide grating filters for dispersion compensation and pulse compression,” IEEE J. Quantum Electron. 29, 975–982 (1993).
[CrossRef]

P. Lambelet, P. Y. Fonjallaz, H. G. Limberger, R. P. Salathe, Ch. Zimmer, H. H. Gilgen, “Bragg grating characterization by optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 5, 565–567 (1993).
[CrossRef]

W. Margulis, I. G. Carvalho, P. M. Gouvea, “Heat scan: a simple technique to study gratings in fiber,” Opt. Lett. 18, 1016–1018 (1993).
[CrossRef] [PubMed]

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, “Photosensitivity in optical fibers,” Annu. Rev. Mater. Sci. 23, 125–157 (1993).
[CrossRef]

1989

1987

1978

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

1969

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Sys. Tech. J. 48, 9209–2947 (1969).

Ahmed, K. A.

Ball, G. A.

W. W. Morey, G. A. Ball, G. Meltz, “Photoinduced Bragg gratings in optical fibers,” Opt. Photon. News 5, 8–14 (1994).
[CrossRef]

Bilodeau, F.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, “Photosensitivity in optical fibers,” Annu. Rev. Mater. Sci. 23, 125–157 (1993).
[CrossRef]

Borjel, P.

P.-Y. Fonjallaz, P. Borjel, “Interferometric side diffraction technique for the characterization of fibre gratings,” in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, E. J. Friebele, R. Kashyap, T. Erdogan, eds., Vol. 33 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000).

Brinkmeyer, E.

E. Brinkmeyer, “Simple algorithm for reconstructing fiber gratings from reflectometric data,” Opt. Lett. 20, 810–812 (1995).
[CrossRef] [PubMed]

E. Brinkmeyer, G. Soltze, D. Johlen, “Optical space domain reflectometry (OSDR) for determination of strength and chirp distribution along optical fiber gratings,” in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides: Applications and Fundamentals, Vol. 17 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 33–36.

Canning, J.

J. Canning, M. Jason, M. G. Sceats, “Rayleigh z-scan profiling of grating structures and resonances in optical fibers using side scattered light,” in Twentieth Australian Conference on Optical Fibre Technology (Information, Telecommunications & Electronics Engineering Society, Kingston, Australia, 1995), pp. 303–306.

Capmany, J.

D. Pastor, J. Capmany, D. Ortega, V. Tatay, J. Marti, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” J. Lightwave Technol. 14, 2581–2588 (1996).
[CrossRef]

Carvalho, I. G.

Chida, K.

Danielson, B. L.

Eggleton, B. J.

Erdogan, T.

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[CrossRef]

Ferdinand, P.

N. Roussel, S. Magne, C. Martinez, P. Ferdinand, “Measurement of index modulation along fiber Bragg gratings by side scattering and local heating techniques,” Opt. Fiber Technol. 5, 119–132 (1999).
[CrossRef]

Fonjallaz, P. Y.

P. Lambelet, P. Y. Fonjallaz, H. G. Limberger, R. P. Salathe, Ch. Zimmer, H. H. Gilgen, “Bragg grating characterization by optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 5, 565–567 (1993).
[CrossRef]

Fonjallaz, P.-Y.

P.-Y. Fonjallaz, P. Borjel, “Interferometric side diffraction technique for the characterization of fibre gratings,” in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, E. J. Friebele, R. Kashyap, T. Erdogan, eds., Vol. 33 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000).

Fujii, Y.

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

Gilgen, H. H.

P. Lambelet, P. Y. Fonjallaz, H. G. Limberger, R. P. Salathe, Ch. Zimmer, H. H. Gilgen, “Bragg grating characterization by optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 5, 565–567 (1993).
[CrossRef]

Glenn, W. H.

Gouvea, P. M.

Hill, K. O.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, “Photosensitivity in optical fibers,” Annu. Rev. Mater. Sci. 23, 125–157 (1993).
[CrossRef]

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

Jason, M.

J. Canning, M. Jason, M. G. Sceats, “Rayleigh z-scan profiling of grating structures and resonances in optical fibers using side scattered light,” in Twentieth Australian Conference on Optical Fibre Technology (Information, Telecommunications & Electronics Engineering Society, Kingston, Australia, 1995), pp. 303–306.

Johlen, D.

E. Brinkmeyer, G. Soltze, D. Johlen, “Optical space domain reflectometry (OSDR) for determination of strength and chirp distribution along optical fiber gratings,” in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides: Applications and Fundamentals, Vol. 17 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 33–36.

Johnson, D. C.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, “Photosensitivity in optical fibers,” Annu. Rev. Mater. Sci. 23, 125–157 (1993).
[CrossRef]

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

Kawasaki, B. S.

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

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Sys. Tech. J. 48, 9209–2947 (1969).

Krug, P. A.

Lambelet, P.

P. Lambelet, P. Y. Fonjallaz, H. G. Limberger, R. P. Salathe, Ch. Zimmer, H. H. Gilgen, “Bragg grating characterization by optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 5, 565–567 (1993).
[CrossRef]

Limberger, H. G.

P. Lambelet, P. Y. Fonjallaz, H. G. Limberger, R. P. Salathe, Ch. Zimmer, H. H. Gilgen, “Bragg grating characterization by optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 5, 565–567 (1993).
[CrossRef]

Liu, H. F.

Magne, S.

N. Roussel, S. Magne, C. Martinez, P. Ferdinand, “Measurement of index modulation along fiber Bragg gratings by side scattering and local heating techniques,” Opt. Fiber Technol. 5, 119–132 (1999).
[CrossRef]

Malo, B.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, “Photosensitivity in optical fibers,” Annu. Rev. Mater. Sci. 23, 125–157 (1993).
[CrossRef]

Margulis, W.

Marti, J.

D. Pastor, J. Capmany, D. Ortega, V. Tatay, J. Marti, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” J. Lightwave Technol. 14, 2581–2588 (1996).
[CrossRef]

Martinez, C.

N. Roussel, S. Magne, C. Martinez, P. Ferdinand, “Measurement of index modulation along fiber Bragg gratings by side scattering and local heating techniques,” Opt. Fiber Technol. 5, 119–132 (1999).
[CrossRef]

Meltz, G.

W. W. Morey, G. A. Ball, G. Meltz, “Photoinduced Bragg gratings in optical fibers,” Opt. Photon. News 5, 8–14 (1994).
[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]

Morey, W. W.

W. W. Morey, G. A. Ball, G. Meltz, “Photoinduced Bragg gratings in optical fibers,” Opt. Photon. News 5, 8–14 (1994).
[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]

Noda, J.

Ortega, D.

D. Pastor, J. Capmany, D. Ortega, V. Tatay, J. Marti, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” J. Lightwave Technol. 14, 2581–2588 (1996).
[CrossRef]

Othonos, A.

A. Othonos, “Fiber Bragg gratings,” Rev. Sci. Instrum. 68, 4309–4341 (1997).
[CrossRef]

Pastor, D.

D. Pastor, J. Capmany, D. Ortega, V. Tatay, J. Marti, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” J. Lightwave Technol. 14, 2581–2588 (1996).
[CrossRef]

Poladian, L.

Rao, Y.

Y. Rao, “In-fibre Bragg grating sensors,” Meas. Sci. Technol. 8, 355–375 (1997).
[CrossRef]

Roman, J. E.

J. E. Roman, K. A. Winick, “Waveguide grating filters for dispersion compensation and pulse compression,” IEEE J. Quantum Electron. 29, 975–982 (1993).
[CrossRef]

Roussel, N.

N. Roussel, S. Magne, C. Martinez, P. Ferdinand, “Measurement of index modulation along fiber Bragg gratings by side scattering and local heating techniques,” Opt. Fiber Technol. 5, 119–132 (1999).
[CrossRef]

Salathe, R. P.

P. Lambelet, P. Y. Fonjallaz, H. G. Limberger, R. P. Salathe, Ch. Zimmer, H. H. Gilgen, “Bragg grating characterization by optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 5, 565–567 (1993).
[CrossRef]

Sceats, M. G.

J. Canning, M. Jason, M. G. Sceats, “Rayleigh z-scan profiling of grating structures and resonances in optical fibers using side scattered light,” in Twentieth Australian Conference on Optical Fibre Technology (Information, Telecommunications & Electronics Engineering Society, Kingston, Australia, 1995), pp. 303–306.

Soltze, G.

E. Brinkmeyer, G. Soltze, D. Johlen, “Optical space domain reflectometry (OSDR) for determination of strength and chirp distribution along optical fiber gratings,” in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides: Applications and Fundamentals, Vol. 17 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 33–36.

Stolte, R.

Takada, K.

Tatay, V.

D. Pastor, J. Capmany, D. Ortega, V. Tatay, J. Marti, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” J. Lightwave Technol. 14, 2581–2588 (1996).
[CrossRef]

Ulrich, R.

Whittenberg, C. D.

Winick, K. A.

J. E. Roman, K. A. Winick, “Waveguide grating filters for dispersion compensation and pulse compression,” IEEE J. Quantum Electron. 29, 975–982 (1993).
[CrossRef]

Yokohama, I.

Zimmer, Ch.

P. Lambelet, P. Y. Fonjallaz, H. G. Limberger, R. P. Salathe, Ch. Zimmer, H. H. Gilgen, “Bragg grating characterization by optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 5, 565–567 (1993).
[CrossRef]

Annu. Rev. Mater. Sci.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, “Photosensitivity in optical fibers,” Annu. Rev. Mater. Sci. 23, 125–157 (1993).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

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

Bell Sys. Tech. J.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Sys. Tech. J. 48, 9209–2947 (1969).

IEEE J. Quantum Electron.

J. E. Roman, K. A. Winick, “Waveguide grating filters for dispersion compensation and pulse compression,” IEEE J. Quantum Electron. 29, 975–982 (1993).
[CrossRef]

IEEE Photon. Technol. Lett.

P. Lambelet, P. Y. Fonjallaz, H. G. Limberger, R. P. Salathe, Ch. Zimmer, H. H. Gilgen, “Bragg grating characterization by optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 5, 565–567 (1993).
[CrossRef]

J. Lightwave Technol.

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[CrossRef]

D. Pastor, J. Capmany, D. Ortega, V. Tatay, J. Marti, “Design of apodized linearly chirped fiber gratings for dispersion compensation,” J. Lightwave Technol. 14, 2581–2588 (1996).
[CrossRef]

Meas. Sci. Technol.

Y. Rao, “In-fibre Bragg grating sensors,” Meas. Sci. Technol. 8, 355–375 (1997).
[CrossRef]

Opt. Fiber Technol.

N. Roussel, S. Magne, C. Martinez, P. Ferdinand, “Measurement of index modulation along fiber Bragg gratings by side scattering and local heating techniques,” Opt. Fiber Technol. 5, 119–132 (1999).
[CrossRef]

Opt. Lett.

Opt. Photon. News

W. W. Morey, G. A. Ball, G. Meltz, “Photoinduced Bragg gratings in optical fibers,” Opt. Photon. News 5, 8–14 (1994).
[CrossRef]

Rev. Sci. Instrum.

A. Othonos, “Fiber Bragg gratings,” Rev. Sci. Instrum. 68, 4309–4341 (1997).
[CrossRef]

Other

J. Canning, M. Jason, M. G. Sceats, “Rayleigh z-scan profiling of grating structures and resonances in optical fibers using side scattered light,” in Twentieth Australian Conference on Optical Fibre Technology (Information, Telecommunications & Electronics Engineering Society, Kingston, Australia, 1995), pp. 303–306.

E. Brinkmeyer, G. Soltze, D. Johlen, “Optical space domain reflectometry (OSDR) for determination of strength and chirp distribution along optical fiber gratings,” in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides: Applications and Fundamentals, Vol. 17 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 33–36.

P.-Y. Fonjallaz, P. Borjel, “Interferometric side diffraction technique for the characterization of fibre gratings,” in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, E. J. Friebele, R. Kashyap, T. Erdogan, eds., Vol. 33 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Schematic representation of the experimental setup: SF, spatial filter; M’s, mirrors; WP’s, half-wave plates; BS, beam splitter; A, attenuator; CL’s, cylindrical lenses.

Fig. 2
Fig. 2

Measured transmission spectrum through the unchirped fiber Bragg grating analyzed in the experiments. The resolution of the optical spectrum analyzer is 0.1 nm.

Fig. 3
Fig. 3

Experimentally measured ultraviolet-induced refractive-index modulation for the unchirped fiber Bragg grating. Data are normalized to the peak value.

Fig. 4
Fig. 4

Experimentally measured variation of the grating period about a nominal value of 530.72 nm for the unchirped fiber Bragg grating. The error bars show a constant error estimate of ±0.01 nm associated with the error in determining the position of the peak of the Fourier transform of the interference fringes for the particular choice of angles in the experiment.

Fig. 5
Fig. 5

Plot of the measured, normalized index modulation of the unchirped grating with additional Gaussian-shaped tails added to the extreme wings of the grating profile.

Fig. 6
Fig. 6

Plots of, top, the measured and, bottom, the simulated transmission spectrum through the unchirped fiber Bragg grating.

Fig. 7
Fig. 7

Measured transmission spectrum through the chirped fiber Bragg grating analyzed in the experiments. The resolution of the optical spectrum analyzer is 0.1 nm.

Fig. 8
Fig. 8

Experimentally measured ultraviolet-induced refractive-index modulation for the chirped fiber Bragg grating. Data are normalized to the peak value.

Fig. 9
Fig. 9

Experimentally measured variation of the grating period about a nominal value of 536.05 nm for the chirped fiber Bragg grating. The symbols used in the plot are approximately equal in size to the (vertical) error bars that reflect an error estimate of ±0.01 nm.

Equations (17)

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

nz=n0+Δn cosKz,
K=2π/Λ,
θi=θr=sin-1λ/2Λ,
η=|S2a|2|R0|2,
η=sin2ν2+ξ21/21+ξ2/ν2.
ηmax=sin2νπ22a2λ cos θ Δn2=c2Δn2,
V=2IdIt1/2Id+It=2IrIi1/2tη1/2tIr+ηIi=2Ir/Ii1/2tη1/2η+tIr/Ii.
η-2VtIrIi1/2η+tIrIi=0,
η=cΔn=1VtIrIi1/2±tIrV2Ii-tIrIi1/2
=1VtIrIi1/21±1-V21/2.
Δn=tIrIi1/21-1-V21/2cV.
I=tIr+ηIi+2ηtIiIr1/2 cos2πfx,
α=2 sin-1λf/2.
Λ=λ2 sinθ+α,
Λλ2 sin θ1-αtan θ.
ΛΛ0-Λ0λ2 tan θf.
ΔΛ=Λλ2 tan θ f.

Metrics