Abstract

Fiber Bragg gratings were fabricated in all-silica core fiber by focusing 125-fs 800-nm pulses with an 80-mm lens through a phase mask with 4.28µm pitch onto a fiber sample. When the phase-mask–fiber separation was 5 mm the observed structure was clearly the result of two-beam interference between the ±1 orders. The elimination of the remaining 9 orders is a consequence of the walk-off experienced by the mask orders and the short duration of the femtosecond pulse. This effect is unique to the fabrication of Bragg gratings with femtosecond sources and would not be observed with a longer pulse duration or incoherent UV sources.

© 2004 Optical Society of America

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References

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  1. K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, Appl. Phys. Lett. 62, 1035 (1993).
    [CrossRef]
  2. P. E. Dyer, R. J. Farley, and R. Giedl, Opt. Commun. 115, 327 (1995).
    [CrossRef]
  3. J. D. Mills, C. W. J. Hillman, B. H. Blott, and W. S. Brocklesby, Appl. Opt. 39, 6128 (2000).
    [CrossRef]
  4. S. J. Mihailov, C. W. Smelser, P. Lu, R. B. Walker, D. Grobnic, H. Ding, G. Henderson, and J. Unruh, Opt. Lett. 28, 995 (2003).
    [CrossRef] [PubMed]
  5. S. J. Mihailov, C. W. Smelser, and D. Grobnic, in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, Vol. 93 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), paper TuB2.
  6. C. W. Smelser, S. J. Mihailov, D. Grobnic, P. Lu, R. B. Walker, H. Ding, and X. Dai, Opt. Lett. 29, 1458 (2004).
    [CrossRef] [PubMed]

2004 (1)

2003 (1)

2000 (1)

1995 (1)

P. E. Dyer, R. J. Farley, and R. Giedl, Opt. Commun. 115, 327 (1995).
[CrossRef]

1993 (1)

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, Appl. Phys. Lett. 62, 1035 (1993).
[CrossRef]

Albert, J.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, Appl. Phys. Lett. 62, 1035 (1993).
[CrossRef]

Bilodeau, F.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, Appl. Phys. Lett. 62, 1035 (1993).
[CrossRef]

Blott, B. H.

Brocklesby, W. S.

Dai, X.

Ding, H.

Dyer, P. E.

P. E. Dyer, R. J. Farley, and R. Giedl, Opt. Commun. 115, 327 (1995).
[CrossRef]

Farley, R. J.

P. E. Dyer, R. J. Farley, and R. Giedl, Opt. Commun. 115, 327 (1995).
[CrossRef]

Giedl, R.

P. E. Dyer, R. J. Farley, and R. Giedl, Opt. Commun. 115, 327 (1995).
[CrossRef]

Grobnic, D.

C. W. Smelser, S. J. Mihailov, D. Grobnic, P. Lu, R. B. Walker, H. Ding, and X. Dai, Opt. Lett. 29, 1458 (2004).
[CrossRef] [PubMed]

S. J. Mihailov, C. W. Smelser, P. Lu, R. B. Walker, D. Grobnic, H. Ding, G. Henderson, and J. Unruh, Opt. Lett. 28, 995 (2003).
[CrossRef] [PubMed]

S. J. Mihailov, C. W. Smelser, and D. Grobnic, in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, Vol. 93 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), paper TuB2.

Henderson, G.

Hill, K. O.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, Appl. Phys. Lett. 62, 1035 (1993).
[CrossRef]

Hillman, C. W. J.

Johnson, D. C.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, Appl. Phys. Lett. 62, 1035 (1993).
[CrossRef]

Lu, P.

Malo, B.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, Appl. Phys. Lett. 62, 1035 (1993).
[CrossRef]

Mihailov, S. J.

C. W. Smelser, S. J. Mihailov, D. Grobnic, P. Lu, R. B. Walker, H. Ding, and X. Dai, Opt. Lett. 29, 1458 (2004).
[CrossRef] [PubMed]

S. J. Mihailov, C. W. Smelser, P. Lu, R. B. Walker, D. Grobnic, H. Ding, G. Henderson, and J. Unruh, Opt. Lett. 28, 995 (2003).
[CrossRef] [PubMed]

S. J. Mihailov, C. W. Smelser, and D. Grobnic, in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, Vol. 93 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), paper TuB2.

Mills, J. D.

Smelser, C. W.

C. W. Smelser, S. J. Mihailov, D. Grobnic, P. Lu, R. B. Walker, H. Ding, and X. Dai, Opt. Lett. 29, 1458 (2004).
[CrossRef] [PubMed]

S. J. Mihailov, C. W. Smelser, P. Lu, R. B. Walker, D. Grobnic, H. Ding, G. Henderson, and J. Unruh, Opt. Lett. 28, 995 (2003).
[CrossRef] [PubMed]

S. J. Mihailov, C. W. Smelser, and D. Grobnic, in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, Vol. 93 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), paper TuB2.

Unruh, J.

Walker, R. B.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, Appl. Phys. Lett. 62, 1035 (1993).
[CrossRef]

Opt. Commun. (1)

P. E. Dyer, R. J. Farley, and R. Giedl, Opt. Commun. 115, 327 (1995).
[CrossRef]

Opt. Lett. (2)

Other (1)

S. J. Mihailov, C. W. Smelser, and D. Grobnic, in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, Vol. 93 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), paper TuB2.

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Figures (3)

Fig. 1
Fig. 1

Order propagation through space: (a) propagation of the phase-mask orders after the 0 order has traveled 3000 µm. Here the ±2 orders lag behind the 0 and the ±1 orders. The 0 and ±1 orders will still interfere at this distance, but the interference pattern will vary along the x direction. (b) Case where the 0 order has propagated 5000 µm. The 0 order no longer overlaps the ±1 order, resulting in two-beam interference. In these images a 1/e beam width of 5 mm and a temporal pulse length of approximately 60 fs were chosen, as those values are similar to the experimental parameters. The phase-mask position is y=0.

Fig. 2
Fig. 2

(a) and (c) Microscope images of the structure at the ±1-mm edge of a 2-mm-long grating, (b) structure in the middle of the grating x=0 mm. The grating was written with a 4.28µm mask at a distance of 2.5 mm. The pattern has a pitch of 2.14 µm, or half that of the mask at the edges of the grating, while in the middle region the pitch is 4.28 µm, or the same as the mask. This suggests that there is strong three-beam interference in the center of the grating, whereas the interference between the more energetic ±1 orders dominates toward the edge.

Fig. 3
Fig. 3

Comparison of the modeled five-, three-, and two-beam interference patterns with the observed structure in the fiber at progressively larger distance from the phase mask. (a)–(c) Modeled five-, three-, and two-beam interference patterns. For comparison, (d)–(f) depict the observed grating structures at 200, 500, and 5000 µm. At 5000 µm only two-beam interference is present.

Equations (1)

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Ex,y2=mam expikx sinθm+iky cosθm2.

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