Abstract

A method of measuring the complex modulation of a Bragg grating is derived from a one-dimensional model of light propagating in an optical fiber. Interference fringes between the Bragg grating and a reference air-gap reflector are measured, and a Fourier transform of the interference fringes generated as a laser is swept through the wavelength is used to compute the complex modulation function of the Bragg grating over a restricted domain. Supporting data, taken by temperature tuning a distributed feedback diode laser, are shown.

© 1996 Optical Society of America

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References

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  1. D. K. W. Lam, B. K. Garside, “Characterization of single-mode optical fiber filters,” Appl. Opt. 20, 440–445 (1981).
    [CrossRef] [PubMed]
  2. D. Marcuse, “Coupled mode theory of round optical fibers,” Bell Sys. Tech. J. 52, 817–842 (1973).
  3. K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
    [CrossRef]
  4. K. O. Hill, “Aperiodic distributed-parameter waveguides for integrated optics,” Appl. Opt. 13, 1853–1856 (1974).
    [CrossRef] [PubMed]
  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. B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, J. Albert, “Point-by-point fabrication of micro-Bragg gratings in photosensitive fiber using single excimer pulse refractive index modification techniques,” Electron. Lett. 29, 1668–1669 (1993).
    [CrossRef]
  7. P. Lambelet, P. Y. Fonjallaz, 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]
  8. A. Yariv, Quantum Electronics (Wiley, New York, 1989), pp. 608–610.

1993

B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, J. Albert, “Point-by-point fabrication of micro-Bragg gratings in photosensitive fiber using single excimer pulse refractive index modification techniques,” Electron. Lett. 29, 1668–1669 (1993).
[CrossRef]

P. Lambelet, P. Y. Fonjallaz, 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]

1989

1981

1978

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

1974

1973

D. Marcuse, “Coupled mode theory of round optical fibers,” Bell Sys. Tech. J. 52, 817–842 (1973).

Albert, J.

B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, J. Albert, “Point-by-point fabrication of micro-Bragg gratings in photosensitive fiber using single excimer pulse refractive index modification techniques,” Electron. Lett. 29, 1668–1669 (1993).
[CrossRef]

Bilodeau, F.

B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, J. Albert, “Point-by-point fabrication of micro-Bragg gratings in photosensitive fiber using single excimer pulse refractive index modification techniques,” Electron. Lett. 29, 1668–1669 (1993).
[CrossRef]

Fonjallaz, P. Y.

P. Lambelet, P. Y. Fonjallaz, 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]

Fujii, Y.

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

Garside, B. K.

Gilgen, H. H.

P. Lambelet, P. Y. Fonjallaz, 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.

Hill, K. O.

B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, J. Albert, “Point-by-point fabrication of micro-Bragg gratings in photosensitive fiber using single excimer pulse refractive index modification techniques,” Electron. Lett. 29, 1668–1669 (1993).
[CrossRef]

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, “Photosensitivity in optical fiber 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.

B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, J. Albert, “Point-by-point fabrication of micro-Bragg gratings in photosensitive fiber using single excimer pulse refractive index modification techniques,” Electron. Lett. 29, 1668–1669 (1993).
[CrossRef]

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

Lam, D. K. W.

Lambelet, P.

P. Lambelet, P. Y. Fonjallaz, 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]

Malo, B.

B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, J. Albert, “Point-by-point fabrication of micro-Bragg gratings in photosensitive fiber using single excimer pulse refractive index modification techniques,” Electron. Lett. 29, 1668–1669 (1993).
[CrossRef]

Marcuse, D.

D. Marcuse, “Coupled mode theory of round optical fibers,” Bell Sys. Tech. J. 52, 817–842 (1973).

Meltz, G.

Morey, W. W.

Salathe, R. P.

P. Lambelet, P. Y. Fonjallaz, 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]

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, New York, 1989), pp. 608–610.

Zimmer, Ch.

P. Lambelet, P. Y. Fonjallaz, 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]

Appl. Opt.

Appl. Phys. Lett.

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

Bell Sys. Tech. J.

D. Marcuse, “Coupled mode theory of round optical fibers,” Bell Sys. Tech. J. 52, 817–842 (1973).

Electron. Lett.

B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, J. Albert, “Point-by-point fabrication of micro-Bragg gratings in photosensitive fiber using single excimer pulse refractive index modification techniques,” Electron. Lett. 29, 1668–1669 (1993).
[CrossRef]

IEEE Photon. Technol. Lett.

P. Lambelet, P. Y. Fonjallaz, 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]

Opt. Lett.

Other

A. Yariv, Quantum Electronics (Wiley, New York, 1989), pp. 608–610.

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Figures (4)

Fig. 1
Fig. 1

Schematic of the optical system used for Bragg grating complex modulation measurement.

Fig. 2
Fig. 2

Detected reflected power as a function of wave number from a fiber-optic system comprised of five 3-mm Bragg gratings located 17 cm behind an air-gap reflector.

Fig. 3
Fig. 3

Amplitude plot of the Fourier-transformed interference spectrum from a fiber-optic Bragg grating–reflector comprising five 3-mm Bragg gratings located 17 cm behind an air-gap reflector.

Fig. 4
Fig. 4

Expanded view of the grating region showing the five grating peaks separated by ~0.6 cm.

Equations (14)

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δ 2 E δ z 2 + β 2 [ 1 + Δ ɛ r ( z ) ɛ r ] E = 0.
E = ψ + ( z , ξ ) exp [ i ( β + ξ ) z ] + ψ - ( z , ξ ) exp [ - i ( β + ξ ) z ] .
Δ ɛ r ( z ) ɛ r = κ ( z ) exp ( i 2 β z ) + κ * ( z ) exp ( - i 2 β z ) .
δ ψ + ( z , ξ ) δ z = ( β + ξ ) 2 i κ ( z ) ψ - ( z , ξ ) exp ( - 2 i ξ z ) ,
δ ψ - ( z , ξ ) δ z = - ( β + ξ ) 2 i κ * ( z ) ψ + ( z , ξ ) exp ( 2 i ξ z ) .
ψ + ( z 0 - , ξ ) = 1 ,
ψ - ( , ξ ) = 0 ,
ψ + ( x , ξ ) = 1 + ( β + ξ ) 2 i z 0 - x κ ( z ) ψ - ( z , ξ ) exp ( - 2 i ξ z ) d z ,
ψ - ( x , ξ ) = ( β + ξ ) 2 i x κ * ( z ) ψ + ( z , ξ ) exp ( 2 i ξ z ) d z .
ψ - ( z 0 - , ξ ) = ( β + ξ ) 2 i - κ * ( z ) exp ( 2 i ξ z ) d z .
ψ - ( z 0 - , ξ ) = ( 1 - a 2 ) 1 / 2 ( β + ξ ) 2 i z 0 - κ * ( z ) exp ( 2 i ξ z ) d z + a exp ( 2 i ξ z 0 ) ,
ψ - ( z 0 - , ξ ) ψ - * ( z 0 - , ξ ) = a 2 + ( 1 - a 2 ) ( β + ξ ) 2 4 × z 0 - κ * ( z ) exp ( 2 i ξ z ) d z z 0 - κ ( z ) exp ( - 2 i ξ z ) d z - a ( 1 - a 2 ) 1 / 2 ( β + ξ ) 2 i z 0 - κ ( z ) exp [ - 2 i ξ ( z - z 0 ) ] d z + a ( 1 - a 2 ) 1 / 2 ( β + ξ ) 2 i z 0 - κ * ( z ) exp [ 2 i ξ ( z - z 0 ) ] d z .
F { ψ ψ * } = κ ˜ ( x 2 ) = a 2 δ ( x ) + ( 1 - a 2 ) β 2 8 × - κ * ( z + x 2 ) κ ( z ) d z + a ( 1 - a 2 ) 1 / 2 β 2 i × [ κ * ( z 0 + x 2 ) - κ ( z 0 - x 2 ) ] ,
κ ˜ ( x 2 ) = a ( 1 - a 2 ) 1 / 2 β 2 i κ * ( z 0 + x 2 ) .

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