Abstract

The fabrication of Bragg gratings inside the core of single-mode optical fibers has been greatly simplified by the application of contact printing[ Appl. Phys. Lett. 62, 1035 ( 1993)]. According to this technique, the fiber is placed in proximity to an appropriate phase grating, which is illuminated with nominally monochromatic UV light. The transmitted light is redistributed into an ideally sinusoidal variation of optical intensity (more properly, irradiance), which is imprinted into the core as a result of photoinduced refractive index changes. In accordance with normal practice in this field, intensity is used instead of optical intensity throughout the text. The main advantage of such a writing method, apart from its simplicity, is that the illumination source need not be highly coherent. Rigorous analysis of this method is given with a new phase grating design.

© 1997 Optical Society of America

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References

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  1. 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]
  2. 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]
  3. M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1392 (1982).
    [CrossRef]
  4. Lord Rayleigh, “On copying diffraction-gratings, and on some phenomena connected therewith,” in Scientific Papers (Cambridge U. Press, Cambridge, England, 1899), Vol. 1, pp. 504–512; Philos. Mag. XI, 196–205 (1881).
  5. J. D. Prohaska, E. Snitzer, J. Wintrop, “Theoretical description of fiber Bragg reflectors prepared by Fresnel diffraction images,” Appl. Opt. 33, 3896–3900 (1994).
    [CrossRef] [PubMed]

1994

1993

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

1982

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]

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]

Gaylord, T. K.

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]

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]

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.

Moharam, M. G.

Morey, W. W.

Prohaska, J. D.

Rayleigh, Lord

Lord Rayleigh, “On copying diffraction-gratings, and on some phenomena connected therewith,” in Scientific Papers (Cambridge U. Press, Cambridge, England, 1899), Vol. 1, pp. 504–512; Philos. Mag. XI, 196–205 (1881).

Snitzer, E.

Wintrop, J.

Appl. Opt.

Appl. Phys. Lett.

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]

J. Opt. Soc. Am.

Opt. Lett.

Other

Lord Rayleigh, “On copying diffraction-gratings, and on some phenomena connected therewith,” in Scientific Papers (Cambridge U. Press, Cambridge, England, 1899), Vol. 1, pp. 504–512; Philos. Mag. XI, 196–205 (1881).

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Figures (8)

Fig. 1
Fig. 1

Zero-order intensity distribution of TE and TMpolarizations as a function of groove depth for a lamellar grating with a50% duty cycle as calculated by RCWA. The illuminating wavelength and the refractive index of the phase mask are shown.

Fig. 2
Fig. 2

Diffraction efficiencies of all propagating diffracted orders (except ±1) of a lamellar phase grating with a duty cycle of q = 0.5.

Fig. 3
Fig. 3

Schematic arrangement of contact printing (top) and coordinate system and grating geometry (bottom).

Fig. 4
Fig. 4

Distribution of diffracted intensity in the(x, z) > 0 plane for a phase grating with four nonzero diffracted orders, I±1= 0.3 and I±2= 0.003, (left), six nonzero diffracted orders,I±1 = 0.03I±2 = 0.003, andI±3 = 0.003(middle), and with all orders above 1set to 0.003(right).

Fig. 5
Fig. 5

Distribution of diffracted intensity in the(x, z) > 0 plane for a phase grating with zero-order contributions of I0 =I±1/100 (left),I0 =I±1/10 (middle), andI0 =I±1 (right). All higher orders are set to zero.

Fig. 6
Fig. 6

Diffraction efficiency of all diffracted orders(except ±1) as a function of duty cycle: TE polarization,q = 0.45, q = 0.50, and q = 0.55.

Fig. 7
Fig. 7

Distribution of diffracted intensity in the(x, z) plane for lamellar phase gratings with duty cycles of q = 0.45, 0.50, and 0.55.

Fig. 8
Fig. 8

Distribution of the average intensity within a3-µm layer of the diffracted fields shown in Fig.7. The solid and dashed curves refer to intensities averaged in the vicinity of successive Talbot planes. The three diagrams refer to the same three master gratings as in Fig.7.

Equations (4)

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A N = a N   exp i 2 π n λ x   sin   ϑ N + z   cos   ϑ N .
ϑ N = sin - 1 N λ np .
A 0 = a 0   exp i 2 π n λ z .
I ± 1 = 4 a 1 2   cos 2 2 π n λ ϑ 1 x .

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