Abstract

The possibility of building angular and displacement sensors based on the phenomenon of attenuated total reflection (ATR) is explored both numerically and experimentally. ATR occurs when a surface wave is excited by an incoming TM electromagnetic wave through a resonant phase-matching process, as in the Kretschmann coupling scheme. The reflected intensity strongly depends on the angle of incidence of the beam. We first show some computations of the sensitivity and the linearity of an ATR-based sensor, then proceed to the experiment, illustrating how an angular resolution of the order of 0.1 arc sec can be obtained with moderate effort. Finally we show how the sensor, combined with a simple optical arrangement, can be used to detect and measure nanometric displacements, as those provided by piezoelectric actuators.

© 1997 Optical Society of America

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References

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  1. E. Kretschmann, “Die bestimmung optischer Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen,” Z. Phys. 241, 313–324 (1971).
    [CrossRef]
  2. J. Rohlin, “An interferometer for precision angle measurement,” Appl. Opt. 2, 762–763 (1963).
    [CrossRef]
  3. D. Malacara, O. Harris, “Interferometric measurement of angles,” Appl. Opt. 9, 1630–1633 (1970).
    [CrossRef] [PubMed]
  4. G. D. Chapman, “Interferometric angular measurement,” Appl. Opt. 13, 1646–1651 (1974).
    [CrossRef] [PubMed]
  5. P. Shi, E. Stijns, “New optical method for measuring small-angle rotations,” Appl. Opt. 27, 4342–4344 (1988).
    [CrossRef] [PubMed]
  6. K. V. Sriram, P. Senthilkumaran, M. P. Kothiyal, R. S. Sironi, “Double-wedge-plate interferometer for collimation testing: new configurations,” Appl. Opt. 32, 4199–4203 (1993).
    [CrossRef] [PubMed]
  7. P. Shi, E. Stijns, “Improving the linearity of the Michelson interferometric angular measurement by a parameter compensation method,” Appl. Opt. 32, 4342–4347 (1993).
    [CrossRef]
  8. P. R. Yoder, E. E. Schlesinger, J. Chickvary, “Active annular-beam laser autocollimator system,” Appl. Opt. 14, 1890–1895 (1975).
    [CrossRef] [PubMed]
  9. L. D. Hutcheson, “Practical electro-optic deflection measurement systems,” Opt. Eng. 15, 61–63 (1976).
    [CrossRef]
  10. G. G. Luther, R. D. Deslattes, “Single-axis photoelectronic autocollimator,” Rev. Sci. Instrum. 55, 747–750 (1984).
    [CrossRef]
  11. P. S. Huang, S. Kiyono, O. Kamada, “Angle measurement based on the internal-reflection effect: a new method,” Appl. Opt. 31, 6047–6055 (1992).
    [CrossRef] [PubMed]
  12. P. S. Huang, J. Ni, “Angle measurement based on the internal total reflection and the use of right angle prisms,” Appl. Opt. 34, 4976–4981 (1995).
    [CrossRef] [PubMed]
  13. T. Tamir, “Inhomogeneous wave types at planar interfaces: II—Surface waves,” Optik 37, 204–228 (1972).
  14. T. Tamir, “Inhomogeneous wave types at planar interfaces: III—Leaky waves,” Optik 38, 269–297 (1972).
  15. P. Ferguson, R. F. Wallis, M. Belakhovsky, J. P. Jadot, J. Tomkinson, “Surface plasma waves in silver and gold,” Surf. Sci. 76, 483–498 (1978).
    [CrossRef]
  16. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1989), Chap. 1, pp. 61–66.
  17. H. E. de Bruijn, R. P. H. Kooyman, J. Greve, “Determination of dielectric permittivity and thickness of a metal layer from a surface plasmon resonance experiment,” Appl. Opt. 29, 1974–1978 (1990).
    [CrossRef]
  18. J. G. Gordon, J. D. Swalen, “The effect of thin organic films on the surface plasma resonance on gold,” Opt. Commun. 22, 374–376 (1977).
    [CrossRef]
  19. H. E. de Bruijn, B. S. F. Altenburg, R. P. H. Kooyman, J. Greve, “Determination of thickness of thin transparent dielectric layers using surface plasmon resonance,” Opt. Commun. 82, 425–432 (1991).
    [CrossRef]

1995 (1)

1993 (2)

K. V. Sriram, P. Senthilkumaran, M. P. Kothiyal, R. S. Sironi, “Double-wedge-plate interferometer for collimation testing: new configurations,” Appl. Opt. 32, 4199–4203 (1993).
[CrossRef] [PubMed]

P. Shi, E. Stijns, “Improving the linearity of the Michelson interferometric angular measurement by a parameter compensation method,” Appl. Opt. 32, 4342–4347 (1993).
[CrossRef]

1992 (1)

1991 (1)

H. E. de Bruijn, B. S. F. Altenburg, R. P. H. Kooyman, J. Greve, “Determination of thickness of thin transparent dielectric layers using surface plasmon resonance,” Opt. Commun. 82, 425–432 (1991).
[CrossRef]

1990 (1)

1988 (1)

1984 (1)

G. G. Luther, R. D. Deslattes, “Single-axis photoelectronic autocollimator,” Rev. Sci. Instrum. 55, 747–750 (1984).
[CrossRef]

1978 (1)

P. Ferguson, R. F. Wallis, M. Belakhovsky, J. P. Jadot, J. Tomkinson, “Surface plasma waves in silver and gold,” Surf. Sci. 76, 483–498 (1978).
[CrossRef]

1977 (1)

J. G. Gordon, J. D. Swalen, “The effect of thin organic films on the surface plasma resonance on gold,” Opt. Commun. 22, 374–376 (1977).
[CrossRef]

1976 (1)

L. D. Hutcheson, “Practical electro-optic deflection measurement systems,” Opt. Eng. 15, 61–63 (1976).
[CrossRef]

1975 (1)

1974 (1)

1972 (2)

T. Tamir, “Inhomogeneous wave types at planar interfaces: II—Surface waves,” Optik 37, 204–228 (1972).

T. Tamir, “Inhomogeneous wave types at planar interfaces: III—Leaky waves,” Optik 38, 269–297 (1972).

1971 (1)

E. Kretschmann, “Die bestimmung optischer Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen,” Z. Phys. 241, 313–324 (1971).
[CrossRef]

1970 (1)

1963 (1)

Altenburg, B. S. F.

H. E. de Bruijn, B. S. F. Altenburg, R. P. H. Kooyman, J. Greve, “Determination of thickness of thin transparent dielectric layers using surface plasmon resonance,” Opt. Commun. 82, 425–432 (1991).
[CrossRef]

Belakhovsky, M.

P. Ferguson, R. F. Wallis, M. Belakhovsky, J. P. Jadot, J. Tomkinson, “Surface plasma waves in silver and gold,” Surf. Sci. 76, 483–498 (1978).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1989), Chap. 1, pp. 61–66.

Chapman, G. D.

Chickvary, J.

de Bruijn, H. E.

H. E. de Bruijn, B. S. F. Altenburg, R. P. H. Kooyman, J. Greve, “Determination of thickness of thin transparent dielectric layers using surface plasmon resonance,” Opt. Commun. 82, 425–432 (1991).
[CrossRef]

H. E. de Bruijn, R. P. H. Kooyman, J. Greve, “Determination of dielectric permittivity and thickness of a metal layer from a surface plasmon resonance experiment,” Appl. Opt. 29, 1974–1978 (1990).
[CrossRef]

Deslattes, R. D.

G. G. Luther, R. D. Deslattes, “Single-axis photoelectronic autocollimator,” Rev. Sci. Instrum. 55, 747–750 (1984).
[CrossRef]

Ferguson, P.

P. Ferguson, R. F. Wallis, M. Belakhovsky, J. P. Jadot, J. Tomkinson, “Surface plasma waves in silver and gold,” Surf. Sci. 76, 483–498 (1978).
[CrossRef]

Gordon, J. G.

J. G. Gordon, J. D. Swalen, “The effect of thin organic films on the surface plasma resonance on gold,” Opt. Commun. 22, 374–376 (1977).
[CrossRef]

Greve, J.

H. E. de Bruijn, B. S. F. Altenburg, R. P. H. Kooyman, J. Greve, “Determination of thickness of thin transparent dielectric layers using surface plasmon resonance,” Opt. Commun. 82, 425–432 (1991).
[CrossRef]

H. E. de Bruijn, R. P. H. Kooyman, J. Greve, “Determination of dielectric permittivity and thickness of a metal layer from a surface plasmon resonance experiment,” Appl. Opt. 29, 1974–1978 (1990).
[CrossRef]

Harris, O.

Huang, P. S.

Hutcheson, L. D.

L. D. Hutcheson, “Practical electro-optic deflection measurement systems,” Opt. Eng. 15, 61–63 (1976).
[CrossRef]

Jadot, J. P.

P. Ferguson, R. F. Wallis, M. Belakhovsky, J. P. Jadot, J. Tomkinson, “Surface plasma waves in silver and gold,” Surf. Sci. 76, 483–498 (1978).
[CrossRef]

Kamada, O.

Kiyono, S.

Kooyman, R. P. H.

H. E. de Bruijn, B. S. F. Altenburg, R. P. H. Kooyman, J. Greve, “Determination of thickness of thin transparent dielectric layers using surface plasmon resonance,” Opt. Commun. 82, 425–432 (1991).
[CrossRef]

H. E. de Bruijn, R. P. H. Kooyman, J. Greve, “Determination of dielectric permittivity and thickness of a metal layer from a surface plasmon resonance experiment,” Appl. Opt. 29, 1974–1978 (1990).
[CrossRef]

Kothiyal, M. P.

Kretschmann, E.

E. Kretschmann, “Die bestimmung optischer Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen,” Z. Phys. 241, 313–324 (1971).
[CrossRef]

Luther, G. G.

G. G. Luther, R. D. Deslattes, “Single-axis photoelectronic autocollimator,” Rev. Sci. Instrum. 55, 747–750 (1984).
[CrossRef]

Malacara, D.

Ni, J.

Rohlin, J.

Schlesinger, E. E.

Senthilkumaran, P.

Shi, P.

P. Shi, E. Stijns, “Improving the linearity of the Michelson interferometric angular measurement by a parameter compensation method,” Appl. Opt. 32, 4342–4347 (1993).
[CrossRef]

P. Shi, E. Stijns, “New optical method for measuring small-angle rotations,” Appl. Opt. 27, 4342–4344 (1988).
[CrossRef] [PubMed]

Sironi, R. S.

Sriram, K. V.

Stijns, E.

P. Shi, E. Stijns, “Improving the linearity of the Michelson interferometric angular measurement by a parameter compensation method,” Appl. Opt. 32, 4342–4347 (1993).
[CrossRef]

P. Shi, E. Stijns, “New optical method for measuring small-angle rotations,” Appl. Opt. 27, 4342–4344 (1988).
[CrossRef] [PubMed]

Swalen, J. D.

J. G. Gordon, J. D. Swalen, “The effect of thin organic films on the surface plasma resonance on gold,” Opt. Commun. 22, 374–376 (1977).
[CrossRef]

Tamir, T.

T. Tamir, “Inhomogeneous wave types at planar interfaces: III—Leaky waves,” Optik 38, 269–297 (1972).

T. Tamir, “Inhomogeneous wave types at planar interfaces: II—Surface waves,” Optik 37, 204–228 (1972).

Tomkinson, J.

P. Ferguson, R. F. Wallis, M. Belakhovsky, J. P. Jadot, J. Tomkinson, “Surface plasma waves in silver and gold,” Surf. Sci. 76, 483–498 (1978).
[CrossRef]

Wallis, R. F.

P. Ferguson, R. F. Wallis, M. Belakhovsky, J. P. Jadot, J. Tomkinson, “Surface plasma waves in silver and gold,” Surf. Sci. 76, 483–498 (1978).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1989), Chap. 1, pp. 61–66.

Yoder, P. R.

Appl. Opt. (10)

P. Shi, E. Stijns, “Improving the linearity of the Michelson interferometric angular measurement by a parameter compensation method,” Appl. Opt. 32, 4342–4347 (1993).
[CrossRef]

D. Malacara, O. Harris, “Interferometric measurement of angles,” Appl. Opt. 9, 1630–1633 (1970).
[CrossRef] [PubMed]

G. D. Chapman, “Interferometric angular measurement,” Appl. Opt. 13, 1646–1651 (1974).
[CrossRef] [PubMed]

P. R. Yoder, E. E. Schlesinger, J. Chickvary, “Active annular-beam laser autocollimator system,” Appl. Opt. 14, 1890–1895 (1975).
[CrossRef] [PubMed]

P. Shi, E. Stijns, “New optical method for measuring small-angle rotations,” Appl. Opt. 27, 4342–4344 (1988).
[CrossRef] [PubMed]

H. E. de Bruijn, R. P. H. Kooyman, J. Greve, “Determination of dielectric permittivity and thickness of a metal layer from a surface plasmon resonance experiment,” Appl. Opt. 29, 1974–1978 (1990).
[CrossRef]

P. S. Huang, J. Ni, “Angle measurement based on the internal total reflection and the use of right angle prisms,” Appl. Opt. 34, 4976–4981 (1995).
[CrossRef] [PubMed]

P. S. Huang, S. Kiyono, O. Kamada, “Angle measurement based on the internal-reflection effect: a new method,” Appl. Opt. 31, 6047–6055 (1992).
[CrossRef] [PubMed]

K. V. Sriram, P. Senthilkumaran, M. P. Kothiyal, R. S. Sironi, “Double-wedge-plate interferometer for collimation testing: new configurations,” Appl. Opt. 32, 4199–4203 (1993).
[CrossRef] [PubMed]

J. Rohlin, “An interferometer for precision angle measurement,” Appl. Opt. 2, 762–763 (1963).
[CrossRef]

Opt. Commun. (2)

J. G. Gordon, J. D. Swalen, “The effect of thin organic films on the surface plasma resonance on gold,” Opt. Commun. 22, 374–376 (1977).
[CrossRef]

H. E. de Bruijn, B. S. F. Altenburg, R. P. H. Kooyman, J. Greve, “Determination of thickness of thin transparent dielectric layers using surface plasmon resonance,” Opt. Commun. 82, 425–432 (1991).
[CrossRef]

Opt. Eng. (1)

L. D. Hutcheson, “Practical electro-optic deflection measurement systems,” Opt. Eng. 15, 61–63 (1976).
[CrossRef]

Optik (2)

T. Tamir, “Inhomogeneous wave types at planar interfaces: II—Surface waves,” Optik 37, 204–228 (1972).

T. Tamir, “Inhomogeneous wave types at planar interfaces: III—Leaky waves,” Optik 38, 269–297 (1972).

Rev. Sci. Instrum. (1)

G. G. Luther, R. D. Deslattes, “Single-axis photoelectronic autocollimator,” Rev. Sci. Instrum. 55, 747–750 (1984).
[CrossRef]

Surf. Sci. (1)

P. Ferguson, R. F. Wallis, M. Belakhovsky, J. P. Jadot, J. Tomkinson, “Surface plasma waves in silver and gold,” Surf. Sci. 76, 483–498 (1978).
[CrossRef]

Z. Phys. (1)

E. Kretschmann, “Die bestimmung optischer Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen,” Z. Phys. 241, 313–324 (1971).
[CrossRef]

Other (1)

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1989), Chap. 1, pp. 61–66.

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Figures (6)

Fig. 1
Fig. 1

Kretschmann coupling to a surface plasmon resonance. The phase-matching condition is achieved by choosing the proper angle of incidence of the input beam θsp.

Fig. 2
Fig. 2

Surface plasmon resonance for an Ag layer ∼500 Å thick deposited on BK7 glass. The wavelength of the incident radiation is 632.8 nm. Experimental points as well as a best-fit curve are shown. The size of the diamonds is not related to the uncertainty of the measurements, which is too small to be displayed effectively on the chart.

Fig. 3
Fig. 3

Linearity of the ATR sensor near the point of maximum slope of the curve of reflectance for the prism–metal–air system considered in Fig. 2.

Fig. 4
Fig. 4

Experimental setup for the evaluation of the sensitivity of the ATR sensor. The setup comprises for angular measurements, 1, an He–Ne laser; 2, a half-wave plate; 3, a calcite polarizer; 4, a micrometric screw; 5, a negative lens (focal length, 1 m); 6, a LVDT displacement sensor; 7, processing electronic of the LVDT sensor; 8, a 50/50 beam splitter; 9, a BK7 prism with Ag deposition; 10, a reference detector; 11, an ATR signal detector; 12, a multimeter with a GPIB (general purpose interface bus) interface; 13, a PC. For the detection of linear displacement, as indicated in the inset, the negative lens is replaced by an optical assembly made up of a microscope objective and a GRIN-rod lens. At the same time the LVDT (linear variable differential transformer) position-sensing unit is removed, and the micrometric screw is substituted with a PZT actuator.

Fig. 5
Fig. 5

Changes in reflectance induced by a 2-arc sec tilt of the incoming beam in the Kretschmann configuration of Fig. 1 when the sensor is used close to the point of maximum slope of the reflectance curve. The thickness of the noise band gives an estimate of the angular resolution. Data were acquired for 20 s, covering a time interval longer than that required for the laser beam to be tilted at the desired angle.

Fig. 6
Fig. 6

Response of a piezoelectric actuator to an applied voltage measured with the setup described in Fig. 3. Each voltage step of the digital-to-analog converter that drives the high-voltage amplifier corresponds to ∼4 nm of nominal displacement. The different sensitivity of the ceramics in expansion and in contraction is apparent.

Tables (1)

Tables Icon

Table 1 Maximum Sensivity of the ATR Sensora

Equations (4)

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

θsp=sin-11n0 Rekspkvac.
α1ε2α2ε1+ε0α1+ε1α0+ε0α1+ε1α0exp-2α1dε0α1+ε1α0-ε0α1+ε1α0exp-2α1d=0,  ai2=k2-k02ε0,  i=0, 1, 2,
ksp=ωc Reε1ε2ε1+ε21/2,
Rϑ=r01+r12 exp2ik12d1+r01r12 exp2ik12d2.

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