Abstract

We report experimental characterization of a very small rectangular phase shift (<0.3rad) obtained from the far-field diffraction patterns using a closed aperture Z-scan technique. The numerical simulations as well as the experimental results reveal a peak–valley configuration in the far-field normalized transmittance, allowing us to determine the sign of the dephasing. The conditions necessary to obtain useful Z-scan traces are discussed. We provide simple linear expressions relating the measured signal to the phase shift. A very good agreement between calculated and experimental Z-scan profiles validates our approach. We show that a very well known nonlinear characterization technique can be extended for linear optical parameter estimation (as refractive index or thickness).

© 2009 Optical Society of America

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References

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  1. W. H. Steel, Interferometry, 2nd ed. (Cambridge University, 1983).
  2. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. Hagan, and E. W. Stryland, “Sensitive measurements of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
    [CrossRef]
  3. B. M. Patterson, W. R. White, T. A. Robbins, and R. J. Knize, “Linear optical effects in Z-scan measurements of thin films,” Appl. Opt. 37, 1854-1857 (1998).
    [CrossRef]
  4. K. Fedus, G. Boudebs, C. B. de Araujo, M. Cathelinaud, F. Charpentier, and V. Nazabal, “Photo-induced effects in thin films of Te20As30Se50 glass with nonlinear characterization,” Appl. Phys. Lett. 94, 061122 (2009).
    [CrossRef]
  5. J. Cardin and D. Leduc, “Determination of refractive index, thickness, and the optical losses of thin films from prism-film coupling measurements,” Appl. Opt. 47, 894-900 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  8. G. Jin, R. Jansson, and H. Arwin, “Imaging ellipsometry revisited: developments for visualization of thin transparent layers on silicon substrates,” Rev. Sci. Instrum. 67,2930-2936 (1996).
    [CrossRef]
  9. A. Albersdorfer, G. Elender, G. Mathe, K. R. Neumaier, P. Paduschek, and E. Sackmann, “High resolution imaging microellipsometry of soft surfaces at 3 μm lateral and 5 A normal resolution,” Appl. Phys. Lett. 72, 2930-2932 (1998).
    [CrossRef]
  10. S. Otsuki, K. Tamada, and S. Wakida, “Two-dimensional thickness measurements based on internal reflection ellipsometry,” Appl. Opt. 44, 1410-1415 (2005).
    [CrossRef] [PubMed]
  11. C. Wang, J. Lin, H. Jian, and C. Lee, “Transparent thin-film characterization by using differential optical sectioning interference microscopy,” Appl. Opt. 46, 7460-7463 (2007).
    [CrossRef] [PubMed]
  12. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  13. G. Boudebs, K. Fedus, C. Cassagne, and H. Leblond, “Degenerate multiwave mixing using Z-scan technique,” Appl. Phys. Lett. 93, 021118 (2008).
    [CrossRef]
  14. G. Boudebs, M. Chis, and J. P. Bourdin, “Third-order susceptibility measurements by nonlinear image processing,” J. Opt. Soc. Am. B. 13, 1450-1456 (1996).
    [CrossRef]
  15. H. M. Zidan and M. Abu-Elnader, “Structural and optical properties of pure PMMA and metal chloride-doped PMMA films,” Physica B 355, 308-317 (2005).
    [CrossRef]

2009

K. Fedus, G. Boudebs, C. B. de Araujo, M. Cathelinaud, F. Charpentier, and V. Nazabal, “Photo-induced effects in thin films of Te20As30Se50 glass with nonlinear characterization,” Appl. Phys. Lett. 94, 061122 (2009).
[CrossRef]

2008

G. Boudebs, K. Fedus, C. Cassagne, and H. Leblond, “Degenerate multiwave mixing using Z-scan technique,” Appl. Phys. Lett. 93, 021118 (2008).
[CrossRef]

J. Cardin and D. Leduc, “Determination of refractive index, thickness, and the optical losses of thin films from prism-film coupling measurements,” Appl. Opt. 47, 894-900 (2008).
[CrossRef] [PubMed]

2007

2005

S. Otsuki, K. Tamada, and S. Wakida, “Two-dimensional thickness measurements based on internal reflection ellipsometry,” Appl. Opt. 44, 1410-1415 (2005).
[CrossRef] [PubMed]

H. M. Zidan and M. Abu-Elnader, “Structural and optical properties of pure PMMA and metal chloride-doped PMMA films,” Physica B 355, 308-317 (2005).
[CrossRef]

1998

A. Albersdorfer, G. Elender, G. Mathe, K. R. Neumaier, P. Paduschek, and E. Sackmann, “High resolution imaging microellipsometry of soft surfaces at 3 μm lateral and 5 A normal resolution,” Appl. Phys. Lett. 72, 2930-2932 (1998).
[CrossRef]

B. M. Patterson, W. R. White, T. A. Robbins, and R. J. Knize, “Linear optical effects in Z-scan measurements of thin films,” Appl. Opt. 37, 1854-1857 (1998).
[CrossRef]

1996

G. Jin, R. Jansson, and H. Arwin, “Imaging ellipsometry revisited: developments for visualization of thin transparent layers on silicon substrates,” Rev. Sci. Instrum. 67,2930-2936 (1996).
[CrossRef]

G. Boudebs, M. Chis, and J. P. Bourdin, “Third-order susceptibility measurements by nonlinear image processing,” J. Opt. Soc. Am. B. 13, 1450-1456 (1996).
[CrossRef]

1994

1990

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. Hagan, and E. W. Stryland, “Sensitive measurements of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

Abu-Elnader, M.

H. M. Zidan and M. Abu-Elnader, “Structural and optical properties of pure PMMA and metal chloride-doped PMMA films,” Physica B 355, 308-317 (2005).
[CrossRef]

Albersdorfer, A.

A. Albersdorfer, G. Elender, G. Mathe, K. R. Neumaier, P. Paduschek, and E. Sackmann, “High resolution imaging microellipsometry of soft surfaces at 3 μm lateral and 5 A normal resolution,” Appl. Phys. Lett. 72, 2930-2932 (1998).
[CrossRef]

Arwin, H.

G. Jin, R. Jansson, and H. Arwin, “Imaging ellipsometry revisited: developments for visualization of thin transparent layers on silicon substrates,” Rev. Sci. Instrum. 67,2930-2936 (1996).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, 1987).

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, 1987).

Boudebs, G.

K. Fedus, G. Boudebs, C. B. de Araujo, M. Cathelinaud, F. Charpentier, and V. Nazabal, “Photo-induced effects in thin films of Te20As30Se50 glass with nonlinear characterization,” Appl. Phys. Lett. 94, 061122 (2009).
[CrossRef]

G. Boudebs, K. Fedus, C. Cassagne, and H. Leblond, “Degenerate multiwave mixing using Z-scan technique,” Appl. Phys. Lett. 93, 021118 (2008).
[CrossRef]

G. Boudebs, M. Chis, and J. P. Bourdin, “Third-order susceptibility measurements by nonlinear image processing,” J. Opt. Soc. Am. B. 13, 1450-1456 (1996).
[CrossRef]

Bourdin, J. P.

G. Boudebs, M. Chis, and J. P. Bourdin, “Third-order susceptibility measurements by nonlinear image processing,” J. Opt. Soc. Am. B. 13, 1450-1456 (1996).
[CrossRef]

Cardin, J.

Cassagne, C.

G. Boudebs, K. Fedus, C. Cassagne, and H. Leblond, “Degenerate multiwave mixing using Z-scan technique,” Appl. Phys. Lett. 93, 021118 (2008).
[CrossRef]

Cathelinaud, M.

K. Fedus, G. Boudebs, C. B. de Araujo, M. Cathelinaud, F. Charpentier, and V. Nazabal, “Photo-induced effects in thin films of Te20As30Se50 glass with nonlinear characterization,” Appl. Phys. Lett. 94, 061122 (2009).
[CrossRef]

Charpentier, F.

K. Fedus, G. Boudebs, C. B. de Araujo, M. Cathelinaud, F. Charpentier, and V. Nazabal, “Photo-induced effects in thin films of Te20As30Se50 glass with nonlinear characterization,” Appl. Phys. Lett. 94, 061122 (2009).
[CrossRef]

Chis, M.

G. Boudebs, M. Chis, and J. P. Bourdin, “Third-order susceptibility measurements by nonlinear image processing,” J. Opt. Soc. Am. B. 13, 1450-1456 (1996).
[CrossRef]

de Araujo, C. B.

K. Fedus, G. Boudebs, C. B. de Araujo, M. Cathelinaud, F. Charpentier, and V. Nazabal, “Photo-induced effects in thin films of Te20As30Se50 glass with nonlinear characterization,” Appl. Phys. Lett. 94, 061122 (2009).
[CrossRef]

Elender, G.

A. Albersdorfer, G. Elender, G. Mathe, K. R. Neumaier, P. Paduschek, and E. Sackmann, “High resolution imaging microellipsometry of soft surfaces at 3 μm lateral and 5 A normal resolution,” Appl. Phys. Lett. 72, 2930-2932 (1998).
[CrossRef]

Fedus, K.

K. Fedus, G. Boudebs, C. B. de Araujo, M. Cathelinaud, F. Charpentier, and V. Nazabal, “Photo-induced effects in thin films of Te20As30Se50 glass with nonlinear characterization,” Appl. Phys. Lett. 94, 061122 (2009).
[CrossRef]

G. Boudebs, K. Fedus, C. Cassagne, and H. Leblond, “Degenerate multiwave mixing using Z-scan technique,” Appl. Phys. Lett. 93, 021118 (2008).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Hagan, D.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. Hagan, and E. W. Stryland, “Sensitive measurements of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

Jansson, R.

G. Jin, R. Jansson, and H. Arwin, “Imaging ellipsometry revisited: developments for visualization of thin transparent layers on silicon substrates,” Rev. Sci. Instrum. 67,2930-2936 (1996).
[CrossRef]

Jian, H.

Jin, G.

G. Jin, R. Jansson, and H. Arwin, “Imaging ellipsometry revisited: developments for visualization of thin transparent layers on silicon substrates,” Rev. Sci. Instrum. 67,2930-2936 (1996).
[CrossRef]

Knize, R. J.

Leblond, H.

G. Boudebs, K. Fedus, C. Cassagne, and H. Leblond, “Degenerate multiwave mixing using Z-scan technique,” Appl. Phys. Lett. 93, 021118 (2008).
[CrossRef]

Leduc, D.

Lee, C.

Lin, J.

Liu, A.-H.

Mathe, G.

A. Albersdorfer, G. Elender, G. Mathe, K. R. Neumaier, P. Paduschek, and E. Sackmann, “High resolution imaging microellipsometry of soft surfaces at 3 μm lateral and 5 A normal resolution,” Appl. Phys. Lett. 72, 2930-2932 (1998).
[CrossRef]

Nazabal, V.

K. Fedus, G. Boudebs, C. B. de Araujo, M. Cathelinaud, F. Charpentier, and V. Nazabal, “Photo-induced effects in thin films of Te20As30Se50 glass with nonlinear characterization,” Appl. Phys. Lett. 94, 061122 (2009).
[CrossRef]

Neumaier, K. R.

A. Albersdorfer, G. Elender, G. Mathe, K. R. Neumaier, P. Paduschek, and E. Sackmann, “High resolution imaging microellipsometry of soft surfaces at 3 μm lateral and 5 A normal resolution,” Appl. Phys. Lett. 72, 2930-2932 (1998).
[CrossRef]

Otsuki, S.

Paduschek, P.

A. Albersdorfer, G. Elender, G. Mathe, K. R. Neumaier, P. Paduschek, and E. Sackmann, “High resolution imaging microellipsometry of soft surfaces at 3 μm lateral and 5 A normal resolution,” Appl. Phys. Lett. 72, 2930-2932 (1998).
[CrossRef]

Patterson, B. M.

Plawsky, J. L.

Robbins, T. A.

Sackmann, E.

A. Albersdorfer, G. Elender, G. Mathe, K. R. Neumaier, P. Paduschek, and E. Sackmann, “High resolution imaging microellipsometry of soft surfaces at 3 μm lateral and 5 A normal resolution,” Appl. Phys. Lett. 72, 2930-2932 (1998).
[CrossRef]

Said, A. A.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. Hagan, and E. W. Stryland, “Sensitive measurements of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. Hagan, and E. W. Stryland, “Sensitive measurements of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

Steel, W. H.

W. H. Steel, Interferometry, 2nd ed. (Cambridge University, 1983).

Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. Hagan, and E. W. Stryland, “Sensitive measurements of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

Tamada, K.

Wakida, S.

Wang, C.

Wayner, P. C.

Wei, T. H.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. Hagan, and E. W. Stryland, “Sensitive measurements of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

White, W. R.

Zidan, H. M.

H. M. Zidan and M. Abu-Elnader, “Structural and optical properties of pure PMMA and metal chloride-doped PMMA films,” Physica B 355, 308-317 (2005).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

A. Albersdorfer, G. Elender, G. Mathe, K. R. Neumaier, P. Paduschek, and E. Sackmann, “High resolution imaging microellipsometry of soft surfaces at 3 μm lateral and 5 A normal resolution,” Appl. Phys. Lett. 72, 2930-2932 (1998).
[CrossRef]

K. Fedus, G. Boudebs, C. B. de Araujo, M. Cathelinaud, F. Charpentier, and V. Nazabal, “Photo-induced effects in thin films of Te20As30Se50 glass with nonlinear characterization,” Appl. Phys. Lett. 94, 061122 (2009).
[CrossRef]

G. Boudebs, K. Fedus, C. Cassagne, and H. Leblond, “Degenerate multiwave mixing using Z-scan technique,” Appl. Phys. Lett. 93, 021118 (2008).
[CrossRef]

IEEE J. Quantum Electron.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. Hagan, and E. W. Stryland, “Sensitive measurements of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

J. Opt. Soc. Am. B.

G. Boudebs, M. Chis, and J. P. Bourdin, “Third-order susceptibility measurements by nonlinear image processing,” J. Opt. Soc. Am. B. 13, 1450-1456 (1996).
[CrossRef]

Physica B

H. M. Zidan and M. Abu-Elnader, “Structural and optical properties of pure PMMA and metal chloride-doped PMMA films,” Physica B 355, 308-317 (2005).
[CrossRef]

Rev. Sci. Instrum.

G. Jin, R. Jansson, and H. Arwin, “Imaging ellipsometry revisited: developments for visualization of thin transparent layers on silicon substrates,” Rev. Sci. Instrum. 67,2930-2936 (1996).
[CrossRef]

Other

W. H. Steel, Interferometry, 2nd ed. (Cambridge University, 1983).

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, 1987).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

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Figures (7)

Fig. 1
Fig. 1

Schematic of the 4 f coherent system imager. The sample is moved around the focal region. The labels refer to the amplitude field E ( x , y ) , lenses ( L 1 L 3 ), mirrors ( M 1 , M 2 ), and beam splitters ( B S 1 , B S 2 ).

Fig. 2
Fig. 2

Scan made by mechanical profilemeter showing the geometrical parameters of the rectangular groove (width and deepness).

Fig. 3
Fig. 3

Images at the output of the 4 f system for z = 45 mm : (a) experimental acquisition, (b) numerical simulation. The coordinates (x, y) are in pixels.

Fig. 4
Fig. 4

Experimental (dots) closed aperture Z-scan normalized transmittance T ( z ) and the corresponding theoretical simulation (solid line).

Fig. 5
Fig. 5

The similarity between the cross section of (a) rectangular groove embedded in thin film and the diverging lens (dashed line), and (b) rectangular strip layer on thin film and the converging lens (dashed line)

Fig. 6
Fig. 6

Comparison of the Z-scan normalized transmittances. The solid line is the simulation reported in Fig. 4 for φ 0 = 0.34 ( L x = 1.2 mm , L y = 60 μm ). The dashed line is the simulation given for the same parameters with a larger width of the rectangular phase object, L y = 250 μm .

Fig. 7
Fig. 7

(a) Calculated Δ T p v as a function of the on-axis phase shift ( φ 0 ) for S = 0.4 , L y 2 ω f , and L x L y . (b) Calculated influence of L x on the proportionality factor (α) for a fixed value of L y : solid line L y 2 ω f ( = 60 μm ), dashed line L y 2 ω f .

Equations (3)

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< 0.3 rad
S ( u , v ) = F ˜ [ E ( x , y ) ] = + + E ( x , y ) exp [ j 2 π ( u x + v y ) ] d x d y ,
Δ T p v = α | φ 0 | ,

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