Abstract

A method for obtaining phase-shifted Bragg gratings by use of phase plates is presented. A comparison of experimental and theoretical results allows us to describe the utility of such a component.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. O. Hill, D. C. Johnson, B. S. Kawasaki, “Photosensivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
    [CrossRef]
  2. S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, “Formation of moiré grating in core of germanosilicate fibre by transverse holographic double exposure method,” Electron. Lett. 27, 1945–1946 (1991).
    [CrossRef]
  3. J. Canning, M. G. Sceats, “π-phase-shifted periodic distributed structures in optical fibers by UV post-processing,” Electron. Lett. 30, 1344–1345 (1994).
    [CrossRef]
  4. R. Kashyap, P. F. Mckee, D. Armes, “UV written reflection grating structures in photosensitive optical fibres using phase-shifted phase masks,” Electron. Lett. 30, 1977–1978 (1994).
    [CrossRef]
  5. M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, S. Barcelos, “Moving fibre/phase mask-scanning beam technique for enhanced flexibility in producing fibre gratings with uniform phase mask,” Electron. Lett. 31, 1488–1490 (1995).
    [CrossRef]
  6. C. Martinez, P. Ferdinand, “Phase-shifted fibre Bragg grating photowriting using a UV phase plate in a modified Lloyd mirror configuration,” Electron. Lett. 34, 1687–1688 (1998).
    [CrossRef]
  7. 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]
  8. G. P. Agrawal, S. Radic, “Phase-shifted fiber Bragg gratings and their application for wavelength demultiplexing,” IEEE Photon. Technol. Lett. 6, 995–997 (1994).
    [CrossRef]
  9. A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).
    [CrossRef]
  10. D. K. W. Lam, B. K. Garside, “Characterization of single-mode optical fiber filters,” Appl. Opt. 20, 440–445 (1981).
    [CrossRef] [PubMed]

1998 (1)

C. Martinez, P. Ferdinand, “Phase-shifted fibre Bragg grating photowriting using a UV phase plate in a modified Lloyd mirror configuration,” Electron. Lett. 34, 1687–1688 (1998).
[CrossRef]

1995 (1)

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, S. Barcelos, “Moving fibre/phase mask-scanning beam technique for enhanced flexibility in producing fibre gratings with uniform phase mask,” Electron. Lett. 31, 1488–1490 (1995).
[CrossRef]

1994 (3)

G. P. Agrawal, S. Radic, “Phase-shifted fiber Bragg gratings and their application for wavelength demultiplexing,” IEEE Photon. Technol. Lett. 6, 995–997 (1994).
[CrossRef]

J. Canning, M. G. Sceats, “π-phase-shifted periodic distributed structures in optical fibers by UV post-processing,” Electron. Lett. 30, 1344–1345 (1994).
[CrossRef]

R. Kashyap, P. F. Mckee, D. Armes, “UV written reflection grating structures in photosensitive optical fibres using phase-shifted phase masks,” Electron. Lett. 30, 1977–1978 (1994).
[CrossRef]

1991 (1)

S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, “Formation of moiré grating in core of germanosilicate fibre by transverse holographic double exposure method,” Electron. Lett. 27, 1945–1946 (1991).
[CrossRef]

1987 (1)

1981 (1)

1978 (1)

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

1973 (1)

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

Agrawal, G. P.

G. P. Agrawal, S. Radic, “Phase-shifted fiber Bragg gratings and their application for wavelength demultiplexing,” IEEE Photon. Technol. Lett. 6, 995–997 (1994).
[CrossRef]

Armes, D.

R. Kashyap, P. F. Mckee, D. Armes, “UV written reflection grating structures in photosensitive optical fibres using phase-shifted phase masks,” Electron. Lett. 30, 1977–1978 (1994).
[CrossRef]

Barcelos, S.

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, S. Barcelos, “Moving fibre/phase mask-scanning beam technique for enhanced flexibility in producing fibre gratings with uniform phase mask,” Electron. Lett. 31, 1488–1490 (1995).
[CrossRef]

Bernage, P.

S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, “Formation of moiré grating in core of germanosilicate fibre by transverse holographic double exposure method,” Electron. Lett. 27, 1945–1946 (1991).
[CrossRef]

Canning, J.

J. Canning, M. G. Sceats, “π-phase-shifted periodic distributed structures in optical fibers by UV post-processing,” Electron. Lett. 30, 1344–1345 (1994).
[CrossRef]

Cole, M. J.

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, S. Barcelos, “Moving fibre/phase mask-scanning beam technique for enhanced flexibility in producing fibre gratings with uniform phase mask,” Electron. Lett. 31, 1488–1490 (1995).
[CrossRef]

Douay, M.

S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, “Formation of moiré grating in core of germanosilicate fibre by transverse holographic double exposure method,” Electron. Lett. 27, 1945–1946 (1991).
[CrossRef]

Ferdinand, P.

C. Martinez, P. Ferdinand, “Phase-shifted fibre Bragg grating photowriting using a UV phase plate in a modified Lloyd mirror configuration,” Electron. Lett. 34, 1687–1688 (1998).
[CrossRef]

Fertein, E.

S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, “Formation of moiré grating in core of germanosilicate fibre by transverse holographic double exposure method,” Electron. Lett. 27, 1945–1946 (1991).
[CrossRef]

Garside, B. K.

Hill, K. O.

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

Johnson, D. C.

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

Kashyap, R.

R. Kashyap, P. F. Mckee, D. Armes, “UV written reflection grating structures in photosensitive optical fibres using phase-shifted phase masks,” Electron. Lett. 30, 1977–1978 (1994).
[CrossRef]

Kawasaki, B. S.

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

Lam, D. K. W.

Laming, R. I.

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, S. Barcelos, “Moving fibre/phase mask-scanning beam technique for enhanced flexibility in producing fibre gratings with uniform phase mask,” Electron. Lett. 31, 1488–1490 (1995).
[CrossRef]

Legoubin, S.

S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, “Formation of moiré grating in core of germanosilicate fibre by transverse holographic double exposure method,” Electron. Lett. 27, 1945–1946 (1991).
[CrossRef]

Loh, W. H.

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, S. Barcelos, “Moving fibre/phase mask-scanning beam technique for enhanced flexibility in producing fibre gratings with uniform phase mask,” Electron. Lett. 31, 1488–1490 (1995).
[CrossRef]

Martinez, C.

C. Martinez, P. Ferdinand, “Phase-shifted fibre Bragg grating photowriting using a UV phase plate in a modified Lloyd mirror configuration,” Electron. Lett. 34, 1687–1688 (1998).
[CrossRef]

Mckee, P. F.

R. Kashyap, P. F. Mckee, D. Armes, “UV written reflection grating structures in photosensitive optical fibres using phase-shifted phase masks,” Electron. Lett. 30, 1977–1978 (1994).
[CrossRef]

Niay, P.

S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, “Formation of moiré grating in core of germanosilicate fibre by transverse holographic double exposure method,” Electron. Lett. 27, 1945–1946 (1991).
[CrossRef]

Radic, S.

G. P. Agrawal, S. Radic, “Phase-shifted fiber Bragg gratings and their application for wavelength demultiplexing,” IEEE Photon. Technol. Lett. 6, 995–997 (1994).
[CrossRef]

Sakuda, K.

Sceats, M. G.

J. Canning, M. G. Sceats, “π-phase-shifted periodic distributed structures in optical fibers by UV post-processing,” Electron. Lett. 30, 1344–1345 (1994).
[CrossRef]

Yamada, M.

Yariv, A.

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

Zervas, M. N.

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, S. Barcelos, “Moving fibre/phase mask-scanning beam technique for enhanced flexibility in producing fibre gratings with uniform phase mask,” Electron. Lett. 31, 1488–1490 (1995).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

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

Electron. Lett. (5)

S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, “Formation of moiré grating in core of germanosilicate fibre by transverse holographic double exposure method,” Electron. Lett. 27, 1945–1946 (1991).
[CrossRef]

J. Canning, M. G. Sceats, “π-phase-shifted periodic distributed structures in optical fibers by UV post-processing,” Electron. Lett. 30, 1344–1345 (1994).
[CrossRef]

R. Kashyap, P. F. Mckee, D. Armes, “UV written reflection grating structures in photosensitive optical fibres using phase-shifted phase masks,” Electron. Lett. 30, 1977–1978 (1994).
[CrossRef]

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, S. Barcelos, “Moving fibre/phase mask-scanning beam technique for enhanced flexibility in producing fibre gratings with uniform phase mask,” Electron. Lett. 31, 1488–1490 (1995).
[CrossRef]

C. Martinez, P. Ferdinand, “Phase-shifted fibre Bragg grating photowriting using a UV phase plate in a modified Lloyd mirror configuration,” Electron. Lett. 34, 1687–1688 (1998).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

IEEE Photon. Technol. Lett. (1)

G. P. Agrawal, S. Radic, “Phase-shifted fiber Bragg gratings and their application for wavelength demultiplexing,” IEEE Photon. Technol. Lett. 6, 995–997 (1994).
[CrossRef]

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 (7)

Fig. 1
Fig. 1

Phase-shifted interference through the phase plate in the Lloyd mirror configuration.

Fig. 2
Fig. 2

Atomic-force microscopy photograph of the depth step transition on plate 2.

Fig. 3
Fig. 3

Coupling between the two counterpropagative waves in the phase-shifted FBG.

Fig. 4
Fig. 4

Spectral transmission of a phase-shifted Bragg grating for three values of Δn 0 for Δϕ = π and l = l′ = 2 mm: Δn 0 = 10-4, Δn 0 = 2 × 10-4, and Δn 0 = 5 × 10-4.

Fig. 5
Fig. 5

Experimental spectral transmission of 4-mm-long phase-shifted FBG’s (solid curves) for three values of phase plate 1 tilt angles ψ compared with the theoretical transmission (open circles) for three values of the phase shift, plotted versus the wavelength detuning Δλ = λ - λ B : (a) ψ = 0° (Δϕ = π - 0.25), (b) ψ = 30° (Δϕ = π), (c) ψ = 60° (Δϕ = π + 1).

Fig. 6
Fig. 6

Comparison of experimental and theoretical phase-shift values at various plate tilting angles for plates 1 and 2.

Fig. 7
Fig. 7

Comparison of experimental (solid curves) and theoretical (open circles) spectral transmissions of 4.5-mm-long π-phase-shifted FBG’s for three values of the phase-shift position δl on the grating, plotted versus wavelength detuning Δλ = λ - λ B .

Tables (1)

Tables Icon

Table 1 Phase-Shifted Bragg Grating Parameters Allowed by the Phase-Plate Setup

Equations (32)

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

E1r=E0 exp-jk·r,
E2r=E0 exp-jk·r+Δϕr,
Δϕr=Δϕ0=2πλn-1δe.
Iz=2E021+cos4πλsin θ×z,
Iz=2E021+cos4πλsin θ×z+Δϕ0.
Λ=λ2 sinθ.
Δϕψ=2πλ δencosψ-1cosψ+sinψtanψ-tanψ,
Δϕ0=2K+1π.
δe=2K+1λ2n-1.
Δnz=Δn01+cos2πΛ z+ϕz,
λB=2neffΛ.
dAi-dz=iΩAi+ expi2Δβz+ϕz,
dAi+dz=-iΩAi- exp-i2Δβz+ϕz,
Ω=πΔn0η/λ,
Δβ=πΛ-2πneffλ.
2Ai-2z-i2Δβ+ϕzAi-z-Ω2Ai-=0.
2A1-2z-i2Δβ A1-z-Ω2A1-=0,
A1+=-iΩA1-zexp-i2Δβz;
2A2-2z-i2Δβ A2-z-Ω2A2-=0,
A2+=-iΩA2-zexp-i2Δβz+Δϕ.
A1+0=1,  A1+zt=A2+zt, A2-ze=0,  A1-zt=A2-zt.
T=A2+zeA1+02=|A2+ze|2
γ2=Ω2-Δβ2, Γ1=iΔβ-γ, Γ2=iΔβ+γ.
A2-z=B2 expΓ1z+C2 expΓ2z,
A2+z=-B2Ω Γ1 expΓ1z-C2Ω Γ2 expΓ2z×exp-i2Δβz+Δϕ.
T=1/Ω2|Γ1B2 expΓ1ze+Γ2C2 expΓ2ze|2.
Tλ=γ4/(Γ2+D1-ΓD1-Γ1-2 cosΔϕ+D2D2-2Γ sinΔϕ),
Γ=Ω2 sinhγlsinhγl,  γ2=Ω2-Δβ2, D1=γ2 coshγL,  D2=Δβγ sinhγL.
Tλ=Ω2-Δβ2-Δβ2+Ω2 cosh2γL.
Tλ=γ4/Δβ2Δβ2 cosh2γL+γ2 sinh2γL-2Ω2 coshγL+Ω4.
TλB=1cosh2Ωl-l.
δl=l-L2=l-l2.

Metrics