Abstract

A comparison is made between the modeled and experimentally determined microscopic images of a type I Bragg grating produced in the core of an optical fiber using the ultraviolet irradiation of a phase mask. The simulated image of the refractive-index distribution, which assumes a linear relationship between the irradiation intensity and the refractive-index change, is in good agreement with the measured image.

© 2006 Optical Society of America

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References

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  1. A. Othonos and K. Kalli, "Fiber Bragg gratings: fundamentals and applications in telecommunications and sensing," (Artech House, Boston, Mass, 1999).
  2. R. Kashyap, Fiber Bragg Gratings, (Academic Press, San Diego, 1999), Chap. 8.
  3. D. Dyer, R. J. Farely, and R. Giedl, "Analysis of Grating Formation with Excimer Laser Irradiated Phase Masks,"Opt. Commum. 115, 327-334 (1995).
    [CrossRef]
  4. J. D. Mills, C. W. J. Hillman, B. H. Blott, and W. S. Brocklesby, "Imaging of free-space interference patterns used to manufacture Fiber Bragg Gratings," Appl. Opt. 39, 6128-6135 (2000).
    [CrossRef]
  5. C. W. Smelser, S. J. Mihailov, D. Grobnic, P. Lu, R. B. Walker, H. Ding and X. Dai, "Multiple-beam interference patterns in Optical Fiber generated with ultrafast pulses and a phase mask,"Optics Lett. 29, 1458-1460, (2004).
    [CrossRef]
  6. N. M. Dragomir, C. Rollinson, S. A. Wade, A. J. Stevenson, S. F. Collins, G. W. Baxter, P. M. Farrell and A. Roberts, "Nondestructive Imaging of a Type I Optical Fiber Bragg Grating," Opt. Lett. 28, 789-791 (2003).
    [CrossRef] [PubMed]
  7. M. Born and E. Wolf, Principles of Optics Electromagnetic Theory of Propagation Interference and Diffraction of Light, 6th ed. (Pergamon Press Ltd, Oxford, 1980), Chap. 8.
    [PubMed]
  8. Charles Kittel, Introduction to Solid State Physics, 6th ed. (John Wiley & Sons, New York, 1986), Chap. 2.
  9. M. Pluta, Advanced Light Microscopy: Specialized Methods, In Advanced Light Microscopy: Specialized Methods, M. Pluta (Ed.), 2, (Elsevier, Amsterdam, 1980).
  10. K. J. Dana, "Three Dimensional Reconstruction of Tectorial Membrane: An Image Processing Method using Nomarski Differential Interference Contrast Microscop," Master Thesis, Massachusetts Institute of Technology, Massachusetts, (1992).
  11. C. Preza, "Phase Estimation Using Rotational Diversity For Differential Interference Contrast Microscopy," Doctor of Science Dissertation, Sever Institute of Washington University, Saint Louis, Missouri, USA, (2000).
  12. N. Dragomir, G. Baxter, P. Farrell, E. Ampem-Lassen and A. Roberts, "Near-Field Measurement of a Wolloston Shear Displacement," Biennn. Congress AIP, 331-333, (2002).

2004

C. W. Smelser, S. J. Mihailov, D. Grobnic, P. Lu, R. B. Walker, H. Ding and X. Dai, "Multiple-beam interference patterns in Optical Fiber generated with ultrafast pulses and a phase mask,"Optics Lett. 29, 1458-1460, (2004).
[CrossRef]

2003

2000

1995

D. Dyer, R. J. Farely, and R. Giedl, "Analysis of Grating Formation with Excimer Laser Irradiated Phase Masks,"Opt. Commum. 115, 327-334 (1995).
[CrossRef]

Baxter, G. W.

Blott, B. H.

Brocklesby, W. S.

Collins, S. F.

Dai, X.

C. W. Smelser, S. J. Mihailov, D. Grobnic, P. Lu, R. B. Walker, H. Ding and X. Dai, "Multiple-beam interference patterns in Optical Fiber generated with ultrafast pulses and a phase mask,"Optics Lett. 29, 1458-1460, (2004).
[CrossRef]

Ding, H.

C. W. Smelser, S. J. Mihailov, D. Grobnic, P. Lu, R. B. Walker, H. Ding and X. Dai, "Multiple-beam interference patterns in Optical Fiber generated with ultrafast pulses and a phase mask,"Optics Lett. 29, 1458-1460, (2004).
[CrossRef]

Dragomir, N. M.

Dyer, D.

D. Dyer, R. J. Farely, and R. Giedl, "Analysis of Grating Formation with Excimer Laser Irradiated Phase Masks,"Opt. Commum. 115, 327-334 (1995).
[CrossRef]

Farely, R. J.

D. Dyer, R. J. Farely, and R. Giedl, "Analysis of Grating Formation with Excimer Laser Irradiated Phase Masks,"Opt. Commum. 115, 327-334 (1995).
[CrossRef]

Farrell, P. M.

Giedl, R.

D. Dyer, R. J. Farely, and R. Giedl, "Analysis of Grating Formation with Excimer Laser Irradiated Phase Masks,"Opt. Commum. 115, 327-334 (1995).
[CrossRef]

Grobnic, D.

C. W. Smelser, S. J. Mihailov, D. Grobnic, P. Lu, R. B. Walker, H. Ding and X. Dai, "Multiple-beam interference patterns in Optical Fiber generated with ultrafast pulses and a phase mask,"Optics Lett. 29, 1458-1460, (2004).
[CrossRef]

Hillman, C. W. J.

Lu, P.

C. W. Smelser, S. J. Mihailov, D. Grobnic, P. Lu, R. B. Walker, H. Ding and X. Dai, "Multiple-beam interference patterns in Optical Fiber generated with ultrafast pulses and a phase mask,"Optics Lett. 29, 1458-1460, (2004).
[CrossRef]

Mihailov, S. J.

C. W. Smelser, S. J. Mihailov, D. Grobnic, P. Lu, R. B. Walker, H. Ding and X. Dai, "Multiple-beam interference patterns in Optical Fiber generated with ultrafast pulses and a phase mask,"Optics Lett. 29, 1458-1460, (2004).
[CrossRef]

Mills, J. D.

Roberts, A.

Rollinson, C.

Smelser, C. W.

C. W. Smelser, S. J. Mihailov, D. Grobnic, P. Lu, R. B. Walker, H. Ding and X. Dai, "Multiple-beam interference patterns in Optical Fiber generated with ultrafast pulses and a phase mask,"Optics Lett. 29, 1458-1460, (2004).
[CrossRef]

Stevenson, A. J.

Wade, S. A.

Walker, R. B.

C. W. Smelser, S. J. Mihailov, D. Grobnic, P. Lu, R. B. Walker, H. Ding and X. Dai, "Multiple-beam interference patterns in Optical Fiber generated with ultrafast pulses and a phase mask,"Optics Lett. 29, 1458-1460, (2004).
[CrossRef]

Appl. Opt.

Opt. Commum.

D. Dyer, R. J. Farely, and R. Giedl, "Analysis of Grating Formation with Excimer Laser Irradiated Phase Masks,"Opt. Commum. 115, 327-334 (1995).
[CrossRef]

Opt. Lett.

Optics Lett.

C. W. Smelser, S. J. Mihailov, D. Grobnic, P. Lu, R. B. Walker, H. Ding and X. Dai, "Multiple-beam interference patterns in Optical Fiber generated with ultrafast pulses and a phase mask,"Optics Lett. 29, 1458-1460, (2004).
[CrossRef]

Other

A. Othonos and K. Kalli, "Fiber Bragg gratings: fundamentals and applications in telecommunications and sensing," (Artech House, Boston, Mass, 1999).

R. Kashyap, Fiber Bragg Gratings, (Academic Press, San Diego, 1999), Chap. 8.

M. Born and E. Wolf, Principles of Optics Electromagnetic Theory of Propagation Interference and Diffraction of Light, 6th ed. (Pergamon Press Ltd, Oxford, 1980), Chap. 8.
[PubMed]

Charles Kittel, Introduction to Solid State Physics, 6th ed. (John Wiley & Sons, New York, 1986), Chap. 2.

M. Pluta, Advanced Light Microscopy: Specialized Methods, In Advanced Light Microscopy: Specialized Methods, M. Pluta (Ed.), 2, (Elsevier, Amsterdam, 1980).

K. J. Dana, "Three Dimensional Reconstruction of Tectorial Membrane: An Image Processing Method using Nomarski Differential Interference Contrast Microscop," Master Thesis, Massachusetts Institute of Technology, Massachusetts, (1992).

C. Preza, "Phase Estimation Using Rotational Diversity For Differential Interference Contrast Microscopy," Doctor of Science Dissertation, Sever Institute of Washington University, Saint Louis, Missouri, USA, (2000).

N. Dragomir, G. Baxter, P. Farrell, E. Ampem-Lassen and A. Roberts, "Near-Field Measurement of a Wolloston Shear Displacement," Biennn. Congress AIP, 331-333, (2002).

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Figures (2)

Fig. 1.
Fig. 1.

Refractive-index profile of a single mode optical fiber. The measured data (dotted line) is fitted with a top hat profile (solid line) generated from the measured RI for the purpose of this work.

Fig. 2.
Fig. 2.

Left panel: (a) FBG structure written in a single mode fiber with a 1.059 μm phase mask. (a) DIC image, 47 μm × 47 μm, of the FBG viewed in a direction orthogonal to the UV writing beam. (b) Inset representing DIC numerical simulation of the core region including the FBG structure. Right panel: Comparison of profiles through the observed and modeled image: (c) Profiles across the fiber core, observed data (dotted line) and numerical simulation (solid line). (d) Profiles along the fiber core observed data (dotted line) and numerical simulation (solid line)

Tables (2)

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Table 1. Diffracted orders measured in the far field

Tables Icon

Table 2. Calculated range across grating in which diffracted orders overlap coherently

Equations (3)

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E y x = m C m exp ( imGy ) exp ( i k m x ) ,
I ( x , y ) = a λ f con + + f ( x 0 , y 0 ) h ( x x 0 , y y 0 ) d x 0 d y 0 2 ,
I ( r ) = I 0 e 2 ( r w ) n , with n > 2

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