Abstract

We demonstrate a novel interferometric technique for highly accurate characterization of phase masks used in optical fiber grating fabrication. The principle of the measurement scheme is based on the analysis of the interference pattern formed between the first- and zero-order beams transmitted through or reflected from the grating under test. For spatial resolution of a few millimeters, our methods allow the determination of local variations of the order of 1-µm grating period with an accuracy of a few picometers. These methods are applicable to a broad class of diffractive grating structures.

© 2003 Optical Society of America

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References

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  1. C. Palmer, Diffraction Grating Handbook, E. Loewen, ed. (Richardson Grating Laboratory, Rochester, New York, 2002), and references therein; available at http://www.gratinglab.com .
  2. E. G. Loewen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997).
  3. R. Kashyap, Fiber Bragg Gratings (Academic, New York, 1999).
  4. B. J. Eggleton, A. Ahuja, P. S. Westbrook, J. A. Rogers, P. Kuo, T. N. Nielsen, B. Mikkelsen, “Integrated tunable fiber gratings for dispersion management in high-bit rate system,” J. Lightwave Technol. 18, 1418–1432 (2000).
    [CrossRef]
  5. M. Sumetsky, B. J. Eggleton, C. M. de Sterke, “Theory of group delay ripple generated by chirped fiber gratings,” Opt. Express 10, 332–340 (2002); http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  6. F. Barnier, P. E. Dyer, H. V. Snelling, R. M. De la Rue, “Sub-nanometer metrology of chirped phase masks by optical Moiré,” Opt. Commun. 170, 175–179 (1999).
    [CrossRef]
  7. K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, Amsterdam, 1988), Vol. 26, pp. 349–393.
    [CrossRef]
  8. F. El-Diasty, A. Heaney, T. Erdogan, “Analysis of fiber Bragg gratings by a side-diffraction interference technique,” Appl. Opt. 40, 890–896 (2001).
    [CrossRef]
  9. M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, New York, 1999).
    [CrossRef]

2002 (1)

2001 (1)

2000 (1)

1999 (1)

F. Barnier, P. E. Dyer, H. V. Snelling, R. M. De la Rue, “Sub-nanometer metrology of chirped phase masks by optical Moiré,” Opt. Commun. 170, 175–179 (1999).
[CrossRef]

Ahuja, A.

Barnier, F.

F. Barnier, P. E. Dyer, H. V. Snelling, R. M. De la Rue, “Sub-nanometer metrology of chirped phase masks by optical Moiré,” Opt. Commun. 170, 175–179 (1999).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, New York, 1999).
[CrossRef]

Creath, K.

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, Amsterdam, 1988), Vol. 26, pp. 349–393.
[CrossRef]

De la Rue, R. M.

F. Barnier, P. E. Dyer, H. V. Snelling, R. M. De la Rue, “Sub-nanometer metrology of chirped phase masks by optical Moiré,” Opt. Commun. 170, 175–179 (1999).
[CrossRef]

de Sterke, C. M.

Dyer, P. E.

F. Barnier, P. E. Dyer, H. V. Snelling, R. M. De la Rue, “Sub-nanometer metrology of chirped phase masks by optical Moiré,” Opt. Commun. 170, 175–179 (1999).
[CrossRef]

Eggleton, B. J.

El-Diasty, F.

Erdogan, T.

Heaney, A.

Kashyap, R.

R. Kashyap, Fiber Bragg Gratings (Academic, New York, 1999).

Kuo, P.

Loewen, E. G.

E. G. Loewen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997).

Mikkelsen, B.

Nielsen, T. N.

Palmer, C.

C. Palmer, Diffraction Grating Handbook, E. Loewen, ed. (Richardson Grating Laboratory, Rochester, New York, 2002), and references therein; available at http://www.gratinglab.com .

Popov, E.

E. G. Loewen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997).

Rogers, J. A.

Snelling, H. V.

F. Barnier, P. E. Dyer, H. V. Snelling, R. M. De la Rue, “Sub-nanometer metrology of chirped phase masks by optical Moiré,” Opt. Commun. 170, 175–179 (1999).
[CrossRef]

Sumetsky, M.

Westbrook, P. S.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, New York, 1999).
[CrossRef]

Appl. Opt. (1)

J. Lightwave Technol. (1)

Opt. Commun. (1)

F. Barnier, P. E. Dyer, H. V. Snelling, R. M. De la Rue, “Sub-nanometer metrology of chirped phase masks by optical Moiré,” Opt. Commun. 170, 175–179 (1999).
[CrossRef]

Opt. Express (1)

Other (5)

C. Palmer, Diffraction Grating Handbook, E. Loewen, ed. (Richardson Grating Laboratory, Rochester, New York, 2002), and references therein; available at http://www.gratinglab.com .

E. G. Loewen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997).

R. Kashyap, Fiber Bragg Gratings (Academic, New York, 1999).

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, Amsterdam, 1988), Vol. 26, pp. 349–393.
[CrossRef]

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, New York, 1999).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Setup for phase mask characterization in transmission.

Fig. 2
Fig. 2

Interference pattern recorded by the CCD camera for grating characterization in transmission.

Fig. 3
Fig. 3

Results of grating period variation measurement by the transmission technique averaged over 5 mm of mask length and over 1 mm of mask width. 1a and 1b, period variation and ripple for mask 1; 2a and 2b, period variation and ripple for mask 2. The their curves show repeatability of measurements.

Fig. 4
Fig. 4

Setup for phase mask characterization in reflection: (a) normal and (b) Littrow position of the phase mask with respect to the PMI reference flat.

Fig. 5
Fig. 5

Interference pattern recorded by the PMI system for grating characterization at (a) a normal angle and (b) the Littrow angle.

Fig. 6
Fig. 6

Results of the grating period variation measurement by the reflection technique averaged over 4 mm of mask length and over 1 mm of mask width for mask 2. (a) Grating period variation (F) that is calculated with Eq. (2) where we subtract the contributions of measurement at the Littrow angle (L) and at a normal angle (N); the dashed curve is the period variation of the same mask measured by the transmission method. (b) Corresponding grating period ripples. The thin solid curves show repeatability of measurements.

Equations (6)

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

sinθ21x=sinθ10-λdx+const,
2πPx=2πλ|sinθ21x-sinθ10|=2πdx-2πλconst,
Δdx=±d02Px+const1,
hLittmeasx=1cos θLitt hnormxcos θLitt+12xΔθxcos ϕLittdx,
Δθx=2Δdxd0tan θLitt.
Δdx=2d0sin2θLittdhLittxdxcosθLitt-dhnormxdx+const,

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