Abstract

In this paper we propose group refractive index measurement with a spectral interferometric set-up using a broadband supercontinuum generated in an air-silica Microstructured Optical Fibre (MOF) pumped with a picosecond pulsed microchip laser. This source authorizes high fringes visibility for dispersion measurements by Spectroscopic Analysis of White Light Interferograms (SAWLI). Phase calculation is assumed by a wavelet transform procedure combined with a curve fit of the recorded channelled spectrum intensity. This approach provides high resolution and absolute group refractive index measurements along one line of the sample by recording a single 2D spectral interferogram without mechanical scanning.

© 2006 Optical Society of America

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References

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  1. D. Reolon, M. Jacquot, I. Verrier, G. Brun, and C. Veillas, “Broadband supercontinuum interferometer for high-resolution profilometry,” Opt. Express 14, 128 (2006).
    [Crossref] [PubMed]
  2. P. Hlubina, “White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica,” Opt. Commun. 193, 1 (2001).
    [Crossref]
  3. Y. Wang, Y. Zhao, J. S. Nelson, and Z. Chen, “Ultrahigh-resolution optical coherence tomography by broadband continuum generation from a photonic crystal fiber,” Opt. Lett. 28, 182 (2003).
    [Crossref] [PubMed]
  4. Q. Ye, C. Xu, X. Liu, W. H. Knox, M. F. Yan, R. S. Windeler, and B. Eggleton, “Dispersion measurement of tapered air-silica microstructure fiber by white-light interferometry,” Appl. Opt. 41, 4467 (2002).
    [Crossref] [PubMed]
  5. P. Hlubina, T. Martynkien, and W. Urbańczyk, “Dispersion of group and phase modal birefringence in elliptical-core fiber measured by white-light spectral interferometry,” Opt. Express 11, 2793 (2003).
    [PubMed]
  6. J. Calatroni, C. Sáinz, and A. L. Guerrero, “Multi-channelled white-light interferometry for real-time dispersion measurements,” Opt. Commun. 157, 202 (1998).
    [Crossref]
  7. J. Calatroni, C. Sáinz, and R. Escalona, “The stationary phase in spectrally resolved white-light interferometry as a refractometry tool,” J. Opt. A: Pure Appl. Opt. 5, 207 (2003).
    [Crossref]
  8. A. Hirai and H. Matsumoto, “Measurement of group refractive index wavelength dependence using a low-coherence tandem interferometer,” Appl. Opt. 45, 5614 (2006).
    [Crossref] [PubMed]
  9. P. Champert, V. Couderc, P. Leproux, S. Février, V. Tombelaine, L. Labonté, P. Roy, C. Froehly, and P. Nérin, “White light supercontinuum generation in normally dispersive optical fiber using original multiwavelength pumping system,” Opt. Express 12, 4366 (2004).
    [Crossref] [PubMed]
  10. V. Tombelaine, C. Lesvigne, P. Leproux, L. Grossard, V. Couderc, J. L. Auguste, J. M. Blondy, G. Huss, and P. H. Pioger, “Ultra wide band supercontinuum generation in air-silica holey fibers by SHG-induced modulation instabilities,” Opt. Express 13, 7399 (2005).
    [Crossref] [PubMed]
  11. S. K. Debnath, N. K. Viswanathan, and M. P. Kothiyal, “Spectrally resolved phase-shifting interferometry for accurate group-velocity dispersion measurements,” Opt. Lett. 31, 3098 (2006).
    [Crossref] [PubMed]
  12. Y. Deng, Z. Wu, L. Chai, C. Wang, K. Yamane, R. Morita, M. Yamashita, and Z. Zhang, “Wavelet-transform analysis of spectral shearing interferometry for phase reconstruction of femtosecond optical pulses,” Opt. Express 13, 2120 (2005).
    [Crossref] [PubMed]
  13. Y. Fu, C. Jui, C. Quan, and H. Miao, “Wavelet analysis of speckle patterns with a temporal carrier,” Appl. Opt. 44, 959 (2005).
    [Crossref] [PubMed]

2006 (3)

2005 (3)

2004 (1)

2003 (3)

2002 (1)

2001 (1)

P. Hlubina, “White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica,” Opt. Commun. 193, 1 (2001).
[Crossref]

1998 (1)

J. Calatroni, C. Sáinz, and A. L. Guerrero, “Multi-channelled white-light interferometry for real-time dispersion measurements,” Opt. Commun. 157, 202 (1998).
[Crossref]

Auguste, J. L.

Blondy, J. M.

Brun, G.

Calatroni, J.

J. Calatroni, C. Sáinz, and R. Escalona, “The stationary phase in spectrally resolved white-light interferometry as a refractometry tool,” J. Opt. A: Pure Appl. Opt. 5, 207 (2003).
[Crossref]

J. Calatroni, C. Sáinz, and A. L. Guerrero, “Multi-channelled white-light interferometry for real-time dispersion measurements,” Opt. Commun. 157, 202 (1998).
[Crossref]

Chai, L.

Champert, P.

Chen, Z.

Couderc, V.

Debnath, S. K.

Deng, Y.

Eggleton, B.

Escalona, R.

J. Calatroni, C. Sáinz, and R. Escalona, “The stationary phase in spectrally resolved white-light interferometry as a refractometry tool,” J. Opt. A: Pure Appl. Opt. 5, 207 (2003).
[Crossref]

Février, S.

Froehly, C.

Fu, Y.

Grossard, L.

Guerrero, A. L.

J. Calatroni, C. Sáinz, and A. L. Guerrero, “Multi-channelled white-light interferometry for real-time dispersion measurements,” Opt. Commun. 157, 202 (1998).
[Crossref]

Hirai, A.

Hlubina, P.

P. Hlubina, T. Martynkien, and W. Urbańczyk, “Dispersion of group and phase modal birefringence in elliptical-core fiber measured by white-light spectral interferometry,” Opt. Express 11, 2793 (2003).
[PubMed]

P. Hlubina, “White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica,” Opt. Commun. 193, 1 (2001).
[Crossref]

Huss, G.

Jacquot, M.

Jui, C.

Knox, W. H.

Kothiyal, M. P.

Labonté, L.

Leproux, P.

Lesvigne, C.

Liu, X.

Martynkien, T.

Matsumoto, H.

Miao, H.

Morita, R.

Nelson, J. S.

Nérin, P.

Pioger, P. H.

Quan, C.

Reolon, D.

Roy, P.

Sáinz, C.

J. Calatroni, C. Sáinz, and R. Escalona, “The stationary phase in spectrally resolved white-light interferometry as a refractometry tool,” J. Opt. A: Pure Appl. Opt. 5, 207 (2003).
[Crossref]

J. Calatroni, C. Sáinz, and A. L. Guerrero, “Multi-channelled white-light interferometry for real-time dispersion measurements,” Opt. Commun. 157, 202 (1998).
[Crossref]

Tombelaine, V.

Urbanczyk, W.

Veillas, C.

Verrier, I.

Viswanathan, N. K.

Wang, C.

Wang, Y.

Windeler, R. S.

Wu, Z.

Xu, C.

Yamane, K.

Yamashita, M.

Yan, M. F.

Ye, Q.

Zhang, Z.

Zhao, Y.

Appl. Opt. (3)

J. Opt. A: Pure Appl. Opt. (1)

J. Calatroni, C. Sáinz, and R. Escalona, “The stationary phase in spectrally resolved white-light interferometry as a refractometry tool,” J. Opt. A: Pure Appl. Opt. 5, 207 (2003).
[Crossref]

Opt. Commun. (2)

J. Calatroni, C. Sáinz, and A. L. Guerrero, “Multi-channelled white-light interferometry for real-time dispersion measurements,” Opt. Commun. 157, 202 (1998).
[Crossref]

P. Hlubina, “White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica,” Opt. Commun. 193, 1 (2001).
[Crossref]

Opt. Express (5)

Opt. Lett. (2)

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Figures (5)

Fig. 1.
Fig. 1.

Experimental set-up: white light spectral supercontinuum interferometer: with L1 (f1=60mm), L2 (f2=200mm), L3 (f3=400mm), L4 (f4=65mm), and L5 (f5=50mm).

Fig. 2.
Fig. 2.

Recorded channelled spectrum with a BK7 plate sample of 2.39 mm thickness.

Fig. 3.
Fig. 3.

Ridge extraction applied on one line of the analysed interferogram from the intensity wavelet transform (a) and from the phase wavelet transform (b).

Fig. 4.
Fig. 4.

Experimental BK7 group refractive index profile along the 18mm line (a) and its variation for y=9mm position in dashed line compared with the theoretical law deduced from Sellmeier equation in solid line (b); (δ=-1220µm, e=2390µm, A=2.2308×103, B=-1.3689×104, C=3.1672×104, D=-3.1736×104, and E=1.1961×104).

Fig. 5.
Fig. 5.

Group refractive index laws of the BK7 glass plate measured for three mirror positions δ 1=-1210µm (+), δ 2=-1220µm (•), and δ 3=-1230µm (-).

Equations (4)

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I ( y , σ ) = I 0 ( y , σ ) · ( 1 + V ( y , σ ) · cos ( Δ Φ 12 ( y , σ ) ) ) ,
Δ Φ 12 ( y , σ ) = 4 π σ ( δ + ( n ( y , σ ) 1 ) · e ( y ) ) ,
{ W ( a , b ) = + f ( v ) · ψ a , b * ( v ) · d v with : ψ a , b ( v ) = 1 a exp { ( v b ) 2 2 a 2 } · exp { 2 i π v 0 ( v b ) a }
n g ( σ ) = n ( σ ) + σ · n ( σ ) σ = 1 4 π e · Δ Φ exp ( σ ) σ ( δ e e )

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