Abstract

We report an accurate method to measure the group-velocity dispersion (GVD) of transparent materials by use of spectrally resolved phase-shifting interferometry. The GVD of silica glass slide measured using an eight-step phase-shifting algorithm agrees well with that calculated using the Sellmeier dispersion equation over the entire visible wavelength region, with a rms error of 0.0036μm2, better than that of other measurement methods reported so far.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. H. Knox, Appl. Phys. B 58, 225 (1994).
    [CrossRef]
  2. I. A. Walmsley, L. Waxer, and C. Dorrer, Rev. Sci. Instrum. 72, 1 (2001).
    [CrossRef]
  3. C. Doerrer and M. Joffre, C. R. Acad. Sci. Paris 4, 1415 (2001).
  4. M. Beck and I. A. Walmsley, Opt. Lett. 15, 492 (1990).
    [CrossRef] [PubMed]
  5. A. P. Kovacs, K. Osvay, Zs. Bor, and R. Szipocs, Opt. Lett. 20, 788 (1995).
    [CrossRef] [PubMed]
  6. C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, Opt. Commun. 110, 381 (1994).
    [CrossRef]
  7. V. N. Kumar and D. Narayana Rao, J. Opt. Soc. Am. B 12, 1559 (1995).
    [CrossRef]
  8. A. L. Guerrero, C. Sainz, and J. Calatroni, Opt. Commun. 109, 375 (1994).
    [CrossRef]
  9. J. Calatroni, C. Sainz, and R. Escalona, J. Opt. A 5, S207 (2003).
    [CrossRef]
  10. P. Hlubina, Opt. Commun. 193, 1 (2001).
    [CrossRef]
  11. P. Sandoz, G. Tribillon, and H. Perrin, J. Mod. Opt. 43, 701 (1996).
    [CrossRef]
  12. S. K. Debnath and M. P. Kothiyal, Opt. Eng. 44, 013606 (2005).
    [CrossRef]
  13. S. K. Debnath, M. P. Kothiyal, J. Schmit, and P. Hariharan, Opt. Express 14, 4662 (2006).
    [CrossRef] [PubMed]
  14. J. Schmit and K. Creath, Appl. Opt. 35, 5642 (1996).
    [CrossRef] [PubMed]
  15. D. Parrys, J-F. Allard, D. Morris, C. Pepin, D. Houde, and A. Cornet, J. Opt. A 7, 249 (2005).
    [CrossRef]
  16. A. Ghatak and K. Thyagarajan, Introduction to Fiber Optics, 1st ed. (Cambridge U. Press, 1998), pp. 78-83.

2006

2005

S. K. Debnath and M. P. Kothiyal, Opt. Eng. 44, 013606 (2005).
[CrossRef]

D. Parrys, J-F. Allard, D. Morris, C. Pepin, D. Houde, and A. Cornet, J. Opt. A 7, 249 (2005).
[CrossRef]

2003

J. Calatroni, C. Sainz, and R. Escalona, J. Opt. A 5, S207 (2003).
[CrossRef]

2001

P. Hlubina, Opt. Commun. 193, 1 (2001).
[CrossRef]

I. A. Walmsley, L. Waxer, and C. Dorrer, Rev. Sci. Instrum. 72, 1 (2001).
[CrossRef]

C. Doerrer and M. Joffre, C. R. Acad. Sci. Paris 4, 1415 (2001).

1996

P. Sandoz, G. Tribillon, and H. Perrin, J. Mod. Opt. 43, 701 (1996).
[CrossRef]

J. Schmit and K. Creath, Appl. Opt. 35, 5642 (1996).
[CrossRef] [PubMed]

1995

1994

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, Opt. Commun. 110, 381 (1994).
[CrossRef]

A. L. Guerrero, C. Sainz, and J. Calatroni, Opt. Commun. 109, 375 (1994).
[CrossRef]

W. H. Knox, Appl. Phys. B 58, 225 (1994).
[CrossRef]

1990

Allard, J-F.

D. Parrys, J-F. Allard, D. Morris, C. Pepin, D. Houde, and A. Cornet, J. Opt. A 7, 249 (2005).
[CrossRef]

Beck, M.

Bor, Zs.

Calatroni, J.

J. Calatroni, C. Sainz, and R. Escalona, J. Opt. A 5, S207 (2003).
[CrossRef]

A. L. Guerrero, C. Sainz, and J. Calatroni, Opt. Commun. 109, 375 (1994).
[CrossRef]

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, Opt. Commun. 110, 381 (1994).
[CrossRef]

Cornet, A.

D. Parrys, J-F. Allard, D. Morris, C. Pepin, D. Houde, and A. Cornet, J. Opt. A 7, 249 (2005).
[CrossRef]

Creath, K.

Debnath, S. K.

Doerrer, C.

C. Doerrer and M. Joffre, C. R. Acad. Sci. Paris 4, 1415 (2001).

Dorrer, C.

I. A. Walmsley, L. Waxer, and C. Dorrer, Rev. Sci. Instrum. 72, 1 (2001).
[CrossRef]

Escalona, R.

J. Calatroni, C. Sainz, and R. Escalona, J. Opt. A 5, S207 (2003).
[CrossRef]

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, Opt. Commun. 110, 381 (1994).
[CrossRef]

Ghatak, A.

A. Ghatak and K. Thyagarajan, Introduction to Fiber Optics, 1st ed. (Cambridge U. Press, 1998), pp. 78-83.

Guerrero, A. L.

A. L. Guerrero, C. Sainz, and J. Calatroni, Opt. Commun. 109, 375 (1994).
[CrossRef]

Hariharan, P.

Hlubina, P.

P. Hlubina, Opt. Commun. 193, 1 (2001).
[CrossRef]

Houde, D.

D. Parrys, J-F. Allard, D. Morris, C. Pepin, D. Houde, and A. Cornet, J. Opt. A 7, 249 (2005).
[CrossRef]

Joffre, M.

C. Doerrer and M. Joffre, C. R. Acad. Sci. Paris 4, 1415 (2001).

Jourdain, P.

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, Opt. Commun. 110, 381 (1994).
[CrossRef]

Knox, W. H.

W. H. Knox, Appl. Phys. B 58, 225 (1994).
[CrossRef]

Kothiyal, M. P.

Kovacs, A. P.

Kumar, V. N.

Morris, D.

D. Parrys, J-F. Allard, D. Morris, C. Pepin, D. Houde, and A. Cornet, J. Opt. A 7, 249 (2005).
[CrossRef]

Narayana Rao, D.

Osvay, K.

Parrys, D.

D. Parrys, J-F. Allard, D. Morris, C. Pepin, D. Houde, and A. Cornet, J. Opt. A 7, 249 (2005).
[CrossRef]

Pepin, C.

D. Parrys, J-F. Allard, D. Morris, C. Pepin, D. Houde, and A. Cornet, J. Opt. A 7, 249 (2005).
[CrossRef]

Perrin, H.

P. Sandoz, G. Tribillon, and H. Perrin, J. Mod. Opt. 43, 701 (1996).
[CrossRef]

Sainz, C.

J. Calatroni, C. Sainz, and R. Escalona, J. Opt. A 5, S207 (2003).
[CrossRef]

A. L. Guerrero, C. Sainz, and J. Calatroni, Opt. Commun. 109, 375 (1994).
[CrossRef]

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, Opt. Commun. 110, 381 (1994).
[CrossRef]

Sandoz, P.

P. Sandoz, G. Tribillon, and H. Perrin, J. Mod. Opt. 43, 701 (1996).
[CrossRef]

Schmit, J.

Szipocs, R.

Thyagarajan, K.

A. Ghatak and K. Thyagarajan, Introduction to Fiber Optics, 1st ed. (Cambridge U. Press, 1998), pp. 78-83.

Tribillon, G.

P. Sandoz, G. Tribillon, and H. Perrin, J. Mod. Opt. 43, 701 (1996).
[CrossRef]

Walmsley, I. A.

I. A. Walmsley, L. Waxer, and C. Dorrer, Rev. Sci. Instrum. 72, 1 (2001).
[CrossRef]

M. Beck and I. A. Walmsley, Opt. Lett. 15, 492 (1990).
[CrossRef] [PubMed]

Waxer, L.

I. A. Walmsley, L. Waxer, and C. Dorrer, Rev. Sci. Instrum. 72, 1 (2001).
[CrossRef]

Appl. Opt.

Appl. Phys. B

W. H. Knox, Appl. Phys. B 58, 225 (1994).
[CrossRef]

C. R. Acad. Sci. Paris

C. Doerrer and M. Joffre, C. R. Acad. Sci. Paris 4, 1415 (2001).

J. Mod. Opt.

P. Sandoz, G. Tribillon, and H. Perrin, J. Mod. Opt. 43, 701 (1996).
[CrossRef]

J. Opt. A

D. Parrys, J-F. Allard, D. Morris, C. Pepin, D. Houde, and A. Cornet, J. Opt. A 7, 249 (2005).
[CrossRef]

J. Calatroni, C. Sainz, and R. Escalona, J. Opt. A 5, S207 (2003).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

A. L. Guerrero, C. Sainz, and J. Calatroni, Opt. Commun. 109, 375 (1994).
[CrossRef]

P. Hlubina, Opt. Commun. 193, 1 (2001).
[CrossRef]

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, Opt. Commun. 110, 381 (1994).
[CrossRef]

Opt. Eng.

S. K. Debnath and M. P. Kothiyal, Opt. Eng. 44, 013606 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Rev. Sci. Instrum.

I. A. Walmsley, L. Waxer, and C. Dorrer, Rev. Sci. Instrum. 72, 1 (2001).
[CrossRef]

Other

A. Ghatak and K. Thyagarajan, Introduction to Fiber Optics, 1st ed. (Cambridge U. Press, 1998), pp. 78-83.

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 (4)

Fig. 1
Fig. 1

Schematic of the experimental setup. WLS, white-light source; BS, beam splitter; M1, M2, mirrors; SS, silica sample; PZT, piezoelectric transducer; Sp, spectrometer.

Fig. 2
Fig. 2

(a) Spectral interferogram with silica sample in one of the interferometer arms. (b) Phase map corresponding to the interferogram shown in (a), calculated using the eight-step algorithm.

Fig. 3
Fig. 3

Phase versus wavenumber for different σ = σ 0 .

Fig. 4
Fig. 4

Plot of d 2 n d λ 0 2 versus λ 0 for silica glass slide. Open circle 엯, eight-step, phase-shifting algorithm; asterisks, five-step algorithm; curve, results calculated using the Sellmeier dispersion relation.

Equations (4)

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

I ( σ ) = I 0 ( σ ) [ 1 + V cos ϕ ( σ ) ] ,
ϕ ( σ ) = 4 π 2 L k c 2 ( σ σ 0 ) 2 = A σ 2 + B σ + C ,
k = λ 0 3 2 π c 2 d 2 n d λ 0 2 ,
tan ϕ = I 1 5 I 2 + 11 I 3 + 15 I 4 15 I 5 11 I 6 + 5 I 7 + I 8 I 1 5 I 2 11 I 3 + 15 I 4 + 15 I 5 11 I 6 5 I 7 + I 8 .

Metrics