Abstract

A new technique for writing extremely short-length Bragg gratings in optical fibers is demonstrated. A physical model describes the diffraction effects on the spatial and wavelength spectra of the Bragg gratings. Selection of appropriate diffraction patterns and related parameters permits self-apodized Bragg gratings with a typical spatial length of several hundred micrometers and a bandwidth of several nanometers to be obtained. These gratings with well-defined spectra are suitable for use as miniature distributed strain sensors and other applications requiring small physical dimensions and broadband spectra.

© 2003 Optical Society of America

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References

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  1. C. R. Giles, “Lightwave applications of fiber Bragg gratings,” J. Lightwave Technol. 15, 1391–1404 (1997).
    [CrossRef]
  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]
  3. A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
    [CrossRef]
  4. M. A. Davis, A. D. Kersey, “All-fiber Bragg grating strain-sensor demodulation technique using a wavelength division coupler,” Electron. Lett. 30, 75–77 (1994).
    [CrossRef]
  5. K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62, 1035–1037 (1993).
    [CrossRef]
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    [CrossRef]
  8. A. Ghatak, K. Thyagarajan, Introduction to Fiber Optics (Cambridge U. Press, Cambridge, UK, 1998).
    [CrossRef]
  9. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
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    [CrossRef]

2000 (1)

1998 (1)

1997 (2)

C. R. Giles, “Lightwave applications of fiber Bragg gratings,” J. Lightwave Technol. 15, 1391–1404 (1997).
[CrossRef]

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

1996 (1)

P. E. Dyer, R. J. Farley, R. Giedl, “Analysis and application of a 0/1 order Talbot interferometer for 193 nm laser grating formation,” Opt. Commun. 129, 98–108 (1996).
[CrossRef]

1994 (1)

M. A. Davis, A. D. Kersey, “All-fiber Bragg grating strain-sensor demodulation technique using a wavelength division coupler,” Electron. Lett. 30, 75–77 (1994).
[CrossRef]

1993 (1)

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

1989 (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]

Albert, J.

S. J. Mihailov, F. Bilodeau, K. O. Hill, D. C. Johnson, J. Albert, A. S. Holmes, “Apodization technique for fiber grating fabrication with a halftone transmission amplitude mask,” Appl. Opt. 39, 3670–3677 (2000).
[CrossRef]

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

Askins, C. G.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Bilodeau, F.

S. J. Mihailov, F. Bilodeau, K. O. Hill, D. C. Johnson, J. Albert, A. S. Holmes, “Apodization technique for fiber grating fabrication with a halftone transmission amplitude mask,” Appl. Opt. 39, 3670–3677 (2000).
[CrossRef]

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

Davis, M. A.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

M. A. Davis, A. D. Kersey, “All-fiber Bragg grating strain-sensor demodulation technique using a wavelength division coupler,” Electron. Lett. 30, 75–77 (1994).
[CrossRef]

Dyer, P. E.

P. E. Dyer, R. J. Farley, R. Giedl, “Analysis and application of a 0/1 order Talbot interferometer for 193 nm laser grating formation,” Opt. Commun. 129, 98–108 (1996).
[CrossRef]

Farley, R. J.

P. E. Dyer, R. J. Farley, R. Giedl, “Analysis and application of a 0/1 order Talbot interferometer for 193 nm laser grating formation,” Opt. Commun. 129, 98–108 (1996).
[CrossRef]

Fowlers, G. R.

G. R. Fowlers, Introduction to Modern Optics, 2nd ed. (Dover, New York, 1975).

Friebele, E. J.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Froggatt, M.

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]

Ghatak, A.

A. Ghatak, K. Thyagarajan, Introduction to Fiber Optics (Cambridge U. Press, Cambridge, UK, 1998).
[CrossRef]

Giedl, R.

P. E. Dyer, R. J. Farley, R. Giedl, “Analysis and application of a 0/1 order Talbot interferometer for 193 nm laser grating formation,” Opt. Commun. 129, 98–108 (1996).
[CrossRef]

Giles, C. R.

C. R. Giles, “Lightwave applications of fiber Bragg gratings,” J. Lightwave Technol. 15, 1391–1404 (1997).
[CrossRef]

Glenn, W. H.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Hill, K. O.

S. J. Mihailov, F. Bilodeau, K. O. Hill, D. C. Johnson, J. Albert, A. S. Holmes, “Apodization technique for fiber grating fabrication with a halftone transmission amplitude mask,” Appl. Opt. 39, 3670–3677 (2000).
[CrossRef]

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, J. Albert, “Bragg gratings 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]

Holmes, A. S.

Johnson, D. C.

S. J. Mihailov, F. Bilodeau, K. O. Hill, D. C. Johnson, J. Albert, A. S. Holmes, “Apodization technique for fiber grating fabrication with a halftone transmission amplitude mask,” Appl. Opt. 39, 3670–3677 (2000).
[CrossRef]

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, J. Albert, “Bragg gratings 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]

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]

Kersey, A. D.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

M. A. Davis, A. D. Kersey, “All-fiber Bragg grating strain-sensor demodulation technique using a wavelength division coupler,” Electron. Lett. 30, 75–77 (1994).
[CrossRef]

Koo, K. P.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

LeBlanc, M.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Malo, B.

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

Meltz, G. W.

Mihailov, S. J.

Moore, J.

Morey, W.

Patrick, H. J.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Putnam, M. A.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Southwell, W. H.

Thyagarajan, K.

A. Ghatak, K. Thyagarajan, Introduction to Fiber Optics (Cambridge U. Press, Cambridge, UK, 1998).
[CrossRef]

Appl. Opt. (2)

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 gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

Electron. Lett. (1)

M. A. Davis, A. D. Kersey, “All-fiber Bragg grating strain-sensor demodulation technique using a wavelength division coupler,” Electron. Lett. 30, 75–77 (1994).
[CrossRef]

J. Lightwave Technol. (2)

C. R. Giles, “Lightwave applications of fiber Bragg gratings,” J. Lightwave Technol. 15, 1391–1404 (1997).
[CrossRef]

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

P. E. Dyer, R. J. Farley, R. Giedl, “Analysis and application of a 0/1 order Talbot interferometer for 193 nm laser grating formation,” Opt. Commun. 129, 98–108 (1996).
[CrossRef]

Opt. Lett. (1)

Other (3)

A. Ghatak, K. Thyagarajan, Introduction to Fiber Optics (Cambridge U. Press, Cambridge, UK, 1998).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

G. R. Fowlers, Introduction to Modern Optics, 2nd ed. (Dover, New York, 1975).

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Figures (7)

Fig. 1
Fig. 1

Schematic representing the interferometric technique used to generate FBGs. The Bragg wavelength λ B is determined by the adjustable θ B .

Fig. 2
Fig. 2

Diffraction geometry of an aperture.

Fig. 3
Fig. 3

Fresnel diffraction patterns from a single slit of various widths at a fixed distance (resulting in various N F ’s). The two vertical lines in each graph indicate the actual slit widths and u is the normalized distance.

Fig. 4
Fig. 4

(a) Spatial spectrum and (b) the wavelength spectrum of a written Bragg grating with a slit width of 2 mm. With the same parameters, (c) is a Fresnel diffraction pattern and (d) is its fast-Fourier-transform wavelength spectrum.

Fig. 5
Fig. 5

(a) Spatial and (b) wavelength spectra of a Bragg grating written at a distance z of 0.24 m and a slit width b of 530 μm (with N F = 1.2). (c) The calculated Fresnel pattern that was calculated with the same parameters as (a) and (b).

Fig. 6
Fig. 6

Series of FBGs written at a fixed distance z and with various slit widths b. Shown in the left-hand graphs are the spatial spectra, and their respective wavelength spectra are shown in the right-hand graphs.

Fig. 7
Fig. 7

Series of FBGs written at various distances z and with a fixed slit width b. (a) Spatial spectra, (b) their respective wavelength spectra.

Tables (1)

Tables Icon

Table 1 Calculated Fresnel Number NF and the Magnification Number MF for a Series of Written Bragg Gratings as Shown in Fig. 6 a

Equations (17)

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

Δλ=λB2πLneffκ2L2+π21/2,
Δλ=λB2neffL.
Ux, y=zjλAUξ, ηexpjkr01r012dξdη,
r01=z2+x-ξ2+y-η21/2.
z  ξ2+η2max/λ
Ix=|Ux|2=I0sin β/β2,
MF=ΔW/b=2zλ/b2,
z3  π4λx-ξ2+y-η2max2.
Ux, y=expjkzjzλ-b/2b/2expj πzλx-ξ2+y-η2dξdη.
Cs=0scosπt2/2dt,
Ss=0ssinπt2/2dt.
Ix=12Cα2-Cα12+Sα2-Sα12,
α1=-2zλb2+x, α2=2zλb2-x.
NF=b/22zλ,
NF < 0.25.
MF > 2,
ΔW > 2b.

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