Abstract

We report on an investigation of the trapezoidal design and fabrication defects in phase masks used to produce Bragg reflection gratings in optical fibers. We used a direct visualization technique to examine the nonuniformity of the interference patterns generated by several phase masks. Fringe patterns from the phase masks are compared with the analogous patterns resulting from two-beam interference. Atomic force microscope imaging of the actual phase gratings that give rise to anomalous fringe patterns is used to determine input parameters for a general theoretical model. Phase masks with pitches of 0.566 and 1.059 µm are modeled and investigated.

© 2000 Optical Society of America

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References

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  1. 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]
  2. D. R. Lyons, Internal reports (Lawrence Livermore National Laboratory, Livermore, Calif., 1986–1990).
  3. 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]
  4. 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]
  5. D. Z. Anderson, V. Mizrahi, T. Erdogan, A. W. White, “Production of infibre gratings using a diffractive optical element,” Electron. Lett. 29, 566–568 (1993).
    [CrossRef]
  6. H. R. Lee, D. R. Lyons, “Image reproduction of Bragg gratings,” Seventeenth Congress of the International Commission for Optics: Optics for Science and New Technology, J. Chang, J. Lee, S. Lee, C. H. Nam, eds., Proc. SPIE2778, 157–158 (1996).
  7. P. J. Lemaire, R. M. Atkins, V. Mizrahi, W. A. Reed, “High pressure H2 loading as a technique for achieving ultrahigh UV photosensitivity and thermal sensitivity in GeO2 doped optical fibres,” Electron. Lett. 29, 1191–1193 (1993).
    [CrossRef]
  8. T. Erdogan, V. Mizrahi, “Fiber phase gratings reflect advances in lightwave technology,” Laser Focus World 30(2), 73–74, 76, 78, 80 (1994).
  9. E. J. Thompson, E. D. Brass, K. Samuel, S. R. Bullock, J. Lindesay, D. R. Lyons, “Formation of phase gratings on the end of gradient-index lenses with ultraviolet ablation at 193 nm,” Appl. Opt. 38, 6494–6497 (1999).
    [CrossRef]

1999 (1)

1994 (1)

T. Erdogan, V. Mizrahi, “Fiber phase gratings reflect advances in lightwave technology,” Laser Focus World 30(2), 73–74, 76, 78, 80 (1994).

1993 (3)

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]

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

P. J. Lemaire, R. M. Atkins, V. Mizrahi, W. A. Reed, “High pressure H2 loading as a technique for achieving ultrahigh UV photosensitivity and thermal sensitivity in GeO2 doped optical fibres,” Electron. Lett. 29, 1191–1193 (1993).
[CrossRef]

1989 (1)

1978 (1)

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]

Albert, J.

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]

Anderson, D. Z.

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

Atkins, R. M.

P. J. Lemaire, R. M. Atkins, V. Mizrahi, W. A. Reed, “High pressure H2 loading as a technique for achieving ultrahigh UV photosensitivity and thermal sensitivity in GeO2 doped optical fibres,” Electron. Lett. 29, 1191–1193 (1993).
[CrossRef]

Bilodeau, F.

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]

Brass, E. D.

Bullock, S. R.

Erdogan, T.

T. Erdogan, V. Mizrahi, “Fiber phase gratings reflect advances in lightwave technology,” Laser Focus World 30(2), 73–74, 76, 78, 80 (1994).

D. Z. Anderson, V. Mizrahi, T. Erdogan, A. W. White, “Production of infibre gratings using a diffractive optical element,” Electron. Lett. 29, 566–568 (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]

Glenn, W. H.

Hill, K. O.

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 fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Johnson, D. C.

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 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]

Lee, H. R.

H. R. Lee, D. R. Lyons, “Image reproduction of Bragg gratings,” Seventeenth Congress of the International Commission for Optics: Optics for Science and New Technology, J. Chang, J. Lee, S. Lee, C. H. Nam, eds., Proc. SPIE2778, 157–158 (1996).

Lemaire, P. J.

P. J. Lemaire, R. M. Atkins, V. Mizrahi, W. A. Reed, “High pressure H2 loading as a technique for achieving ultrahigh UV photosensitivity and thermal sensitivity in GeO2 doped optical fibres,” Electron. Lett. 29, 1191–1193 (1993).
[CrossRef]

Lindesay, J.

Lyons, D. R.

E. J. Thompson, E. D. Brass, K. Samuel, S. R. Bullock, J. Lindesay, D. R. Lyons, “Formation of phase gratings on the end of gradient-index lenses with ultraviolet ablation at 193 nm,” Appl. Opt. 38, 6494–6497 (1999).
[CrossRef]

H. R. Lee, D. R. Lyons, “Image reproduction of Bragg gratings,” Seventeenth Congress of the International Commission for Optics: Optics for Science and New Technology, J. Chang, J. Lee, S. Lee, C. H. Nam, eds., Proc. SPIE2778, 157–158 (1996).

D. R. Lyons, Internal reports (Lawrence Livermore National Laboratory, Livermore, Calif., 1986–1990).

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.

Mizrahi, V.

T. Erdogan, V. Mizrahi, “Fiber phase gratings reflect advances in lightwave technology,” Laser Focus World 30(2), 73–74, 76, 78, 80 (1994).

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

P. J. Lemaire, R. M. Atkins, V. Mizrahi, W. A. Reed, “High pressure H2 loading as a technique for achieving ultrahigh UV photosensitivity and thermal sensitivity in GeO2 doped optical fibres,” Electron. Lett. 29, 1191–1193 (1993).
[CrossRef]

Morey, W. W.

Reed, W. A.

P. J. Lemaire, R. M. Atkins, V. Mizrahi, W. A. Reed, “High pressure H2 loading as a technique for achieving ultrahigh UV photosensitivity and thermal sensitivity in GeO2 doped optical fibres,” Electron. Lett. 29, 1191–1193 (1993).
[CrossRef]

Samuel, K.

Thompson, E. J.

White, A. W.

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

Appl. Opt. (1)

Appl. Phys. Lett. (2)

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, 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. (2)

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

P. J. Lemaire, R. M. Atkins, V. Mizrahi, W. A. Reed, “High pressure H2 loading as a technique for achieving ultrahigh UV photosensitivity and thermal sensitivity in GeO2 doped optical fibres,” Electron. Lett. 29, 1191–1193 (1993).
[CrossRef]

Laser Focus World (1)

T. Erdogan, V. Mizrahi, “Fiber phase gratings reflect advances in lightwave technology,” Laser Focus World 30(2), 73–74, 76, 78, 80 (1994).

Opt. Lett. (1)

Other (2)

D. R. Lyons, Internal reports (Lawrence Livermore National Laboratory, Livermore, Calif., 1986–1990).

H. R. Lee, D. R. Lyons, “Image reproduction of Bragg gratings,” Seventeenth Congress of the International Commission for Optics: Optics for Science and New Technology, J. Chang, J. Lee, S. Lee, C. H. Nam, eds., Proc. SPIE2778, 157–158 (1996).

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Figures (13)

Fig. 1
Fig. 1

(a) Schematic of ideal phase mask of spatial period w and amplitude h (b) trapezoidal structure used to model general defects and reproduce observed UV fringe pattern.

Fig. 2
Fig. 2

Diffracted first- and second-order beams in the fiber region.

Fig. 3
Fig. 3

Trapezoidal grating structure showing the paths examined to describe the diffraction pattern.

Fig. 4
Fig. 4

Diffraction/interference patterns with 1.04-µm pitch generated by theoretical model.

Fig. 5
Fig. 5

Pattern for phase mask with 1.059-µm pitch.

Fig. 6
Fig. 6

Experimental arrangement for detection of Bragg grating in a D-shaped optical fiber.

Fig. 7
Fig. 7

Experimental setup used for examining phase-mask interference patterns.

Fig. 8
Fig. 8

Bragg signal at 825.5 nm in a D fiber with an exposure time of 10 min. SM, single-mode.

Fig. 9
Fig. 9

Near-field projected image of UV fringes and D fiber with a 40× quartz microscope objective.

Fig. 10
Fig. 10

(a) Interference fringes from 0.566-µm-pitch phase mask, (b) corresponding fringes from transverse holographic setup with half-angle of 25°.

Fig. 11
Fig. 11

Atomic force micrographs of 0.566-µm phase mask.

Fig. 12
Fig. 12

Calculated Bragg patterns for 0.566-µm-pitch phase mask of height 0.25 µm and slope 1.47, its calculated relative intensities, and true scale cross-sectional depiction.

Fig. 13
Fig. 13

Atomic force micrographs of 1.059-µm phase mask.

Equations (5)

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ψϕ=paths jpath limits AjϕexpikΔljx, ϕdx,
Tp=2 cosϕinsinϕoutsinϕin+ϕout,Rp=-sinϕin-ϕoutsinϕin+ϕout,Tt=2 cosϕinsinϕoutsinϕin+ϕoutcosϕin-ϕout,Rt=tanϕin-ϕouttanϕin+ϕout.
ξleftx, ϕ=x tanθs+b tan ϕ/tanθs-tan ϕ,ξrightx, ϕ=x tanθs+b tan ϕ/tanθs+tan ϕ,yleftx, ϕ=Θθsb+ξleftx, ϕcotθs+1-Θθsξleftx, ϕ-xcot ϕ,yrightx, ϕ=Θθsb-ξleftx, ϕcotθs+1-Θθsξleftx, ϕ-xcot ϕ,
A1=Tϕin, ϕout,Δl1=nh secϕin+a-h tanϕin-xsinϕout,n sin ϕin=sin ϕout,max-b, -a+h tanϕin]xa-tan(ϕin. A2=Rπ/2-θs+ϕ2inTϕin, ϕout,Δl2=y2 secϕ2in+nh-y2secϕ2in+a-x2-h-y2tanϕinsinϕout,ϕ2in=2θs-ϕinx2=ξleftx, ϕ2iny2=yleftx, ϕ2in-bxmin-a+h tanϕ2in, b. A3=Tπ/2-θs-ϕ3in, π/2-θs-ϕout,Δl3=ny3 secϕ3in+x3-acosϕout+θs/sinθs,ϕ3in=arccoscosϕout+θs/n-θs,x3=ξrightx, ϕ3in,y3=yrightx, ϕ3in,max-b, a-h tan ϕ3inxb. A4=Rπ/2-θs+ϕoutTϕ4, ϕ4in,Δl4=y4 secϕ4in+h-y4cosϕout-x4-asinϕout,ϕ4in=2θs-ϕout,n sin ϕ4=sin ϕ4in,x4=ξleftx, ϕ4in,max(b-2w, -a-h tan ϕ4inx-b. A5=Tϕin, ϕout,Δl5=a-xsinϕout+h cosϕout,-wx-bΘθs-ϕout-a+h tan ϕoutΘϕout-θs,bxminw, 2w-a-h tan ϕout. A6=Rπ/2-θs-ϕoutTϕ6, ϕ6in,Δl6=y6 secϕ6in+x6-acosϕout+θs/sinθs,ϕ6in=-2θs+ϕout,x6=ξrightx, ϕ6in,y6=yrightx, ϕ6in,bxmina-h tan ϕ6in, 2w-b. A7=Tπ/2-θs+ϕ7in, π/2-θs+ϕout,Δl7=ny7 secϕ7in+h-y7cosϕout-x7-asinϕout,ϕ7in=θs-arccoscosθs-ϕout/n,x7=ξleftx, ϕ7in,y7=yleftx, ϕ7in,-bxmin-a+h tan ϕ7in, b.
|ΨpBraggx, z|2=all ψϕexpikz cos ϕ×cosk2a-xsin ϕdϕ2, |ΨtBraggx, z|2=allψϕexpikz cos ϕcos ϕ×cosk2a-xsin ϕdϕ2+alliψϕexpikz cos ϕsin×ϕ sink2a-xsin ϕdψ2.

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