Abstract

A summary of the prism technique for optical coupling to nonradiative surface waves, particularly surface plasmons, is given. Equations for dispersion relations, lifetimes, and leakages are presented in approximate form for small absorption, and in some cases, the exact equations are given. The details of design, fabrication, and use of a parallelopiped prism are discussed for commercial spectrometers. The information presented here should suffice for study of surface plasmons, surface phonons, etc., from the visible to the far infrared wavelengths.

© 1973 Optical Society of America

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References

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  1. A. Otto, Z. Phys. 216, 398 (1968).
    [Crossref]
  2. R. H. Ritchie, H. B. Eldridge, Phys. Rev. 126, 1935 (1962).
    [Crossref]
  3. N. Marschall, B. Fischer, H. J. Queisser, Phys. Rev. Lett. 27, 95 (1971).
    [Crossref]
  4. R. Fuchs, K. L. Kliewer, Phys. Rev. 3B, 2270 (1971).
  5. K. W. Chiu, J. J. Quinn, Phys. Lett. 35A, 469 (1971).
  6. N. Marschall, B. Fischer, Phys. Rev. Lett. 28, 811 (1972).
    [Crossref]
  7. R. Ruppin, Solid State Commun. 8, 1129 (1970).
    [Crossref]
  8. A. S. Barker, Phys. Rev. Lett. 28, 892 (1972).
    [Crossref]
  9. H. Ibach, Festkorperprobleme XI, Advances in Solid State Physics, O. Madelung, Ed. (Pergamon, Oxford, 1971), pp. 135–174.
    [Crossref]
  10. F. C. Levy, E. Ilisca, J. L. Motchane, Phys. Rev. B5, 187 (1972).
  11. W. E. Anderson, R. W. Alexander, R. J. Bell, Phys. Rev. Lett. 27, 1057 (1971).
    [Crossref]
  12. R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1968).
    [Crossref]
  13. D. Beaglehole, Phys. Rev. Lett. 22, 708 (1969).
    [Crossref]
  14. D. Beaglehole, IEEE ED-17(3), 240 (1970).
  15. D. W. Berreman, Phys. Rev. B1, 381 (1970).
  16. F. Sauter, Z. Phys. 203, 488 (1967).
    [Crossref]
  17. K. Sturm, Z. Phys. 209, 329 (1968).
    [Crossref]
  18. A. R. Melnyk, M. J. Harrison, Phys. Rev. 2B, 835 (1970).
  19. F. Forstmann, Z. Phys. 203, 495 (1967).
    [Crossref]
  20. F. Sauter, Physikertagung, Düsseldorf (1964).
  21. R. Fuchs, private communication.
  22. M. Cardona, Am. J. Phys. 39, 1277 (1971). It is best to express Snell’s law as sinα/sinβ = (∊1/η1)1/2 and k2 = η1ω2/c2 in his Eqs. (2) and (3), respectively, so as to avoid the error in Eq. (3) for η1 ≠ 1.
    [Crossref]
  23. V. V. Bryksin, Yu. M. Gerbstein, D. N. Mirlin, Phys. Stat. Sol. (b) 51, 901 (1972).
    [Crossref]
  24. N. J. Harrick, Internal Reflection Spectroscopy (Interscience Publishers, Wiley, New York, 1967.)
  25. H. Wolter, Handbuch der Physik, S. Fligge, Ed. (Springer-Verlag, Berlin, 1956), Vol. 24, p. 461.
    [Crossref]
  26. R. Ruppin, R. Englman, Rep. Prog. Phys. 33, 149 (1970).
    [Crossref]
  27. V. V. Bryksin, Yu.M. Gerbshtein, D. N. Mirlin, Fiz. Tver. Tela 14, 543 (1972).
  28. N. Marschall, B. Fischer, R. J. Bell, to be published.
  29. R. E. Hopkins, Applied Optics and Optical Engineering, R. Kingslake, Ed. (Academic Press, New York, 1965), Vol 3, p. 300.
  30. N. Marschall, unpublished dissertation, Frankfurt am Main University, June1971.
  31. C. M. Randell, R. D. Rawcliffe, Appl. Opt. 6, 1889 (1967).
    [Crossref]
  32. W. Brdgel, Physik und Technik der Ultrarotstrahlung (Curt R. Vincentz Verlag, Hannover, 1961).
  33. L. W. Tilton, E. K. Plyler, R. E. Stephens, J. Research Natl. Bur. Stand. U.S. 43, 81 (July, 1949).
  34. W. S. Rodney, I. H. Malitson, J. Opt. Soc. Am. 46, 956 (1956).
    [Crossref]

1972 (5)

A. S. Barker, Phys. Rev. Lett. 28, 892 (1972).
[Crossref]

F. C. Levy, E. Ilisca, J. L. Motchane, Phys. Rev. B5, 187 (1972).

N. Marschall, B. Fischer, Phys. Rev. Lett. 28, 811 (1972).
[Crossref]

V. V. Bryksin, Yu. M. Gerbstein, D. N. Mirlin, Phys. Stat. Sol. (b) 51, 901 (1972).
[Crossref]

V. V. Bryksin, Yu.M. Gerbshtein, D. N. Mirlin, Fiz. Tver. Tela 14, 543 (1972).

1971 (5)

M. Cardona, Am. J. Phys. 39, 1277 (1971). It is best to express Snell’s law as sinα/sinβ = (∊1/η1)1/2 and k2 = η1ω2/c2 in his Eqs. (2) and (3), respectively, so as to avoid the error in Eq. (3) for η1 ≠ 1.
[Crossref]

W. E. Anderson, R. W. Alexander, R. J. Bell, Phys. Rev. Lett. 27, 1057 (1971).
[Crossref]

N. Marschall, B. Fischer, H. J. Queisser, Phys. Rev. Lett. 27, 95 (1971).
[Crossref]

R. Fuchs, K. L. Kliewer, Phys. Rev. 3B, 2270 (1971).

K. W. Chiu, J. J. Quinn, Phys. Lett. 35A, 469 (1971).

1970 (5)

R. Ruppin, Solid State Commun. 8, 1129 (1970).
[Crossref]

D. Beaglehole, IEEE ED-17(3), 240 (1970).

D. W. Berreman, Phys. Rev. B1, 381 (1970).

A. R. Melnyk, M. J. Harrison, Phys. Rev. 2B, 835 (1970).

R. Ruppin, R. Englman, Rep. Prog. Phys. 33, 149 (1970).
[Crossref]

1969 (1)

D. Beaglehole, Phys. Rev. Lett. 22, 708 (1969).
[Crossref]

1968 (3)

K. Sturm, Z. Phys. 209, 329 (1968).
[Crossref]

A. Otto, Z. Phys. 216, 398 (1968).
[Crossref]

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1968).
[Crossref]

1967 (3)

F. Forstmann, Z. Phys. 203, 495 (1967).
[Crossref]

F. Sauter, Z. Phys. 203, 488 (1967).
[Crossref]

C. M. Randell, R. D. Rawcliffe, Appl. Opt. 6, 1889 (1967).
[Crossref]

1964 (1)

F. Sauter, Physikertagung, Düsseldorf (1964).

1962 (1)

R. H. Ritchie, H. B. Eldridge, Phys. Rev. 126, 1935 (1962).
[Crossref]

1956 (1)

1949 (1)

L. W. Tilton, E. K. Plyler, R. E. Stephens, J. Research Natl. Bur. Stand. U.S. 43, 81 (July, 1949).

Alexander, R. W.

W. E. Anderson, R. W. Alexander, R. J. Bell, Phys. Rev. Lett. 27, 1057 (1971).
[Crossref]

Anderson, W. E.

W. E. Anderson, R. W. Alexander, R. J. Bell, Phys. Rev. Lett. 27, 1057 (1971).
[Crossref]

Arakawa, E. T.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1968).
[Crossref]

Barker, A. S.

A. S. Barker, Phys. Rev. Lett. 28, 892 (1972).
[Crossref]

Beaglehole, D.

D. Beaglehole, IEEE ED-17(3), 240 (1970).

D. Beaglehole, Phys. Rev. Lett. 22, 708 (1969).
[Crossref]

Bell, R. J.

W. E. Anderson, R. W. Alexander, R. J. Bell, Phys. Rev. Lett. 27, 1057 (1971).
[Crossref]

N. Marschall, B. Fischer, R. J. Bell, to be published.

Berreman, D. W.

D. W. Berreman, Phys. Rev. B1, 381 (1970).

Brdgel, W.

W. Brdgel, Physik und Technik der Ultrarotstrahlung (Curt R. Vincentz Verlag, Hannover, 1961).

Bryksin, V. V.

V. V. Bryksin, Yu. M. Gerbstein, D. N. Mirlin, Phys. Stat. Sol. (b) 51, 901 (1972).
[Crossref]

V. V. Bryksin, Yu.M. Gerbshtein, D. N. Mirlin, Fiz. Tver. Tela 14, 543 (1972).

Cardona, M.

M. Cardona, Am. J. Phys. 39, 1277 (1971). It is best to express Snell’s law as sinα/sinβ = (∊1/η1)1/2 and k2 = η1ω2/c2 in his Eqs. (2) and (3), respectively, so as to avoid the error in Eq. (3) for η1 ≠ 1.
[Crossref]

Chiu, K. W.

K. W. Chiu, J. J. Quinn, Phys. Lett. 35A, 469 (1971).

Cowan, J. J.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1968).
[Crossref]

Eldridge, H. B.

R. H. Ritchie, H. B. Eldridge, Phys. Rev. 126, 1935 (1962).
[Crossref]

Englman, R.

R. Ruppin, R. Englman, Rep. Prog. Phys. 33, 149 (1970).
[Crossref]

Fischer, B.

N. Marschall, B. Fischer, Phys. Rev. Lett. 28, 811 (1972).
[Crossref]

N. Marschall, B. Fischer, H. J. Queisser, Phys. Rev. Lett. 27, 95 (1971).
[Crossref]

N. Marschall, B. Fischer, R. J. Bell, to be published.

Forstmann, F.

F. Forstmann, Z. Phys. 203, 495 (1967).
[Crossref]

Fuchs, R.

R. Fuchs, K. L. Kliewer, Phys. Rev. 3B, 2270 (1971).

R. Fuchs, private communication.

Gerbshtein, Yu.M.

V. V. Bryksin, Yu.M. Gerbshtein, D. N. Mirlin, Fiz. Tver. Tela 14, 543 (1972).

Gerbstein, Yu. M.

V. V. Bryksin, Yu. M. Gerbstein, D. N. Mirlin, Phys. Stat. Sol. (b) 51, 901 (1972).
[Crossref]

Hamm, R. N.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1968).
[Crossref]

Harrick, N. J.

N. J. Harrick, Internal Reflection Spectroscopy (Interscience Publishers, Wiley, New York, 1967.)

Harrison, M. J.

A. R. Melnyk, M. J. Harrison, Phys. Rev. 2B, 835 (1970).

Hopkins, R. E.

R. E. Hopkins, Applied Optics and Optical Engineering, R. Kingslake, Ed. (Academic Press, New York, 1965), Vol 3, p. 300.

Ibach, H.

H. Ibach, Festkorperprobleme XI, Advances in Solid State Physics, O. Madelung, Ed. (Pergamon, Oxford, 1971), pp. 135–174.
[Crossref]

Ilisca, E.

F. C. Levy, E. Ilisca, J. L. Motchane, Phys. Rev. B5, 187 (1972).

Kliewer, K. L.

R. Fuchs, K. L. Kliewer, Phys. Rev. 3B, 2270 (1971).

Levy, F. C.

F. C. Levy, E. Ilisca, J. L. Motchane, Phys. Rev. B5, 187 (1972).

Malitson, I. H.

Marschall, N.

N. Marschall, B. Fischer, Phys. Rev. Lett. 28, 811 (1972).
[Crossref]

N. Marschall, B. Fischer, H. J. Queisser, Phys. Rev. Lett. 27, 95 (1971).
[Crossref]

N. Marschall, unpublished dissertation, Frankfurt am Main University, June1971.

N. Marschall, B. Fischer, R. J. Bell, to be published.

Melnyk, A. R.

A. R. Melnyk, M. J. Harrison, Phys. Rev. 2B, 835 (1970).

Mirlin, D. N.

V. V. Bryksin, Yu. M. Gerbstein, D. N. Mirlin, Phys. Stat. Sol. (b) 51, 901 (1972).
[Crossref]

V. V. Bryksin, Yu.M. Gerbshtein, D. N. Mirlin, Fiz. Tver. Tela 14, 543 (1972).

Motchane, J. L.

F. C. Levy, E. Ilisca, J. L. Motchane, Phys. Rev. B5, 187 (1972).

Otto, A.

A. Otto, Z. Phys. 216, 398 (1968).
[Crossref]

Plyler, E. K.

L. W. Tilton, E. K. Plyler, R. E. Stephens, J. Research Natl. Bur. Stand. U.S. 43, 81 (July, 1949).

Queisser, H. J.

N. Marschall, B. Fischer, H. J. Queisser, Phys. Rev. Lett. 27, 95 (1971).
[Crossref]

Quinn, J. J.

K. W. Chiu, J. J. Quinn, Phys. Lett. 35A, 469 (1971).

Randell, C. M.

Rawcliffe, R. D.

Ritchie, R. H.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1968).
[Crossref]

R. H. Ritchie, H. B. Eldridge, Phys. Rev. 126, 1935 (1962).
[Crossref]

Rodney, W. S.

Ruppin, R.

R. Ruppin, R. Englman, Rep. Prog. Phys. 33, 149 (1970).
[Crossref]

R. Ruppin, Solid State Commun. 8, 1129 (1970).
[Crossref]

Sauter, F.

F. Sauter, Z. Phys. 203, 488 (1967).
[Crossref]

F. Sauter, Physikertagung, Düsseldorf (1964).

Stephens, R. E.

L. W. Tilton, E. K. Plyler, R. E. Stephens, J. Research Natl. Bur. Stand. U.S. 43, 81 (July, 1949).

Sturm, K.

K. Sturm, Z. Phys. 209, 329 (1968).
[Crossref]

Tilton, L. W.

L. W. Tilton, E. K. Plyler, R. E. Stephens, J. Research Natl. Bur. Stand. U.S. 43, 81 (July, 1949).

Wolter, H.

H. Wolter, Handbuch der Physik, S. Fligge, Ed. (Springer-Verlag, Berlin, 1956), Vol. 24, p. 461.
[Crossref]

Am. J. Phys. (1)

M. Cardona, Am. J. Phys. 39, 1277 (1971). It is best to express Snell’s law as sinα/sinβ = (∊1/η1)1/2 and k2 = η1ω2/c2 in his Eqs. (2) and (3), respectively, so as to avoid the error in Eq. (3) for η1 ≠ 1.
[Crossref]

Appl. Opt. (1)

Fiz. Tver. Tela (1)

V. V. Bryksin, Yu.M. Gerbshtein, D. N. Mirlin, Fiz. Tver. Tela 14, 543 (1972).

IEEE (1)

D. Beaglehole, IEEE ED-17(3), 240 (1970).

J. Opt. Soc. Am. (1)

J. Research Natl. Bur. Stand. U.S. (1)

L. W. Tilton, E. K. Plyler, R. E. Stephens, J. Research Natl. Bur. Stand. U.S. 43, 81 (July, 1949).

Phys. Lett. (1)

K. W. Chiu, J. J. Quinn, Phys. Lett. 35A, 469 (1971).

Phys. Rev. (5)

R. H. Ritchie, H. B. Eldridge, Phys. Rev. 126, 1935 (1962).
[Crossref]

R. Fuchs, K. L. Kliewer, Phys. Rev. 3B, 2270 (1971).

D. W. Berreman, Phys. Rev. B1, 381 (1970).

F. C. Levy, E. Ilisca, J. L. Motchane, Phys. Rev. B5, 187 (1972).

A. R. Melnyk, M. J. Harrison, Phys. Rev. 2B, 835 (1970).

Phys. Rev. Lett. (6)

W. E. Anderson, R. W. Alexander, R. J. Bell, Phys. Rev. Lett. 27, 1057 (1971).
[Crossref]

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1968).
[Crossref]

D. Beaglehole, Phys. Rev. Lett. 22, 708 (1969).
[Crossref]

N. Marschall, B. Fischer, H. J. Queisser, Phys. Rev. Lett. 27, 95 (1971).
[Crossref]

N. Marschall, B. Fischer, Phys. Rev. Lett. 28, 811 (1972).
[Crossref]

A. S. Barker, Phys. Rev. Lett. 28, 892 (1972).
[Crossref]

Phys. Stat. Sol. (b) (1)

V. V. Bryksin, Yu. M. Gerbstein, D. N. Mirlin, Phys. Stat. Sol. (b) 51, 901 (1972).
[Crossref]

Physikertagung, Düsseldorf (1)

F. Sauter, Physikertagung, Düsseldorf (1964).

Rep. Prog. Phys. (1)

R. Ruppin, R. Englman, Rep. Prog. Phys. 33, 149 (1970).
[Crossref]

Solid State Commun. (1)

R. Ruppin, Solid State Commun. 8, 1129 (1970).
[Crossref]

Z. Phys. (4)

A. Otto, Z. Phys. 216, 398 (1968).
[Crossref]

F. Sauter, Z. Phys. 203, 488 (1967).
[Crossref]

K. Sturm, Z. Phys. 209, 329 (1968).
[Crossref]

F. Forstmann, Z. Phys. 203, 495 (1967).
[Crossref]

Other (8)

R. Fuchs, private communication.

N. J. Harrick, Internal Reflection Spectroscopy (Interscience Publishers, Wiley, New York, 1967.)

H. Wolter, Handbuch der Physik, S. Fligge, Ed. (Springer-Verlag, Berlin, 1956), Vol. 24, p. 461.
[Crossref]

W. Brdgel, Physik und Technik der Ultrarotstrahlung (Curt R. Vincentz Verlag, Hannover, 1961).

N. Marschall, B. Fischer, R. J. Bell, to be published.

R. E. Hopkins, Applied Optics and Optical Engineering, R. Kingslake, Ed. (Academic Press, New York, 1965), Vol 3, p. 300.

N. Marschall, unpublished dissertation, Frankfurt am Main University, June1971.

H. Ibach, Festkorperprobleme XI, Advances in Solid State Physics, O. Madelung, Ed. (Pergamon, Oxford, 1971), pp. 135–174.
[Crossref]

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Figures (3)

Fig. 1
Fig. 1

Representative drawing of the prism P situated in the interferometer with gap G determined by spacers S in front of the absorbing sample A. The axis of rotation is indicated on the central ray, and the internal angle of incidence is ϕ. The plane mirror M1 can be translated while the plane mirror M2 is fixed.

Fig. 2
Fig. 2

The Fresnel rhomb—a parallelopiped prism. The lines AB, CD, EF, and GH are normals to the prism faces.

Fig. 3
Fig. 3

A virtual image diagram for a ray incident normally on the prism face AB. Arrows on ΔI, ΔR1, ΔT, ΔR2, and ΔE indicate direction of positive walk. These directions are fixed with respect to the prism on rotation. The arbitrary rotation origin is located at x = 0, y = 0 inside the first image. The x axis is parallel to the incident beam. Note the direction of positive θ. As θ is varied, the beam-image beam IE′ will walk along the surfaces AB and CD′ exactly as though the prism and its two images were replaced by an equivalently rotating slab of glass of thickness and refractive index np whose two faces are the extensions of AB and CD′. At normal incidence, the beam intersects the prism at (x0,y0). The detector plane PP′ is normal to the fixed incident beam.

Tables (1)

Tables Icon

Table I Typical Results for KRS-5 prism, β = 45°, np = 2.57 at λ = 6328 Å

Equations (19)

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E = E 0 { [ 1 , 0 , i k x ( k x 2 - η eff ω 2 / c 2 ) 1 / 2 ] exp [ - ( k x 2 - η eff ω 2 / c 2 ) 1 / 2 · z ] exp [ i ( k x · x - ω t ) ]             z > 0 [ 1 , 0 , - i k x ( k x 2 - eff ω 2 / c 2 ) 1 / 2 ] exp [ - ( k x 2 - eff ω 2 / c 2 ) 1 / 2 · z ] exp [ i ( k x · x - ω t ) ]             z > 0 }
k x = ω / c [ η eff eff / ( eff + η eff ) ] 1 / 2 .
k x = ω / c · [ η 1 1 / ( 1 + η 1 ) ] 1 / 2
v ph = ω 1 / k x = c / ( n p sin α ) .
ω / c k x n p ( ω / c ) .
α max min = β ± sin - 1 ( n p ) - 1 .
β > 2 sin - 1 ( n p ) - 1 .
Δ T = { [ y 0 ( 1 - cos θ ) - x 0 sin θ ] / cos θ } - [ t sin θ / ( n p 2 - sin 2 θ ) 1 / 2 ]
Δ T = ( - t / n p ) tan θ - t ( n p 2 - sin 2 θ ) - 1 / 2 sin θ .
Δ I = - x 0 tan θ .
B C b = 2 a tan β sin β .
θ T ( T ) = cos - 1 [ ( n p 2 - 1 ) 1 / 2 ( 1 - n p 2 t / x 0 ) - 1 / 3 ] .
R 1 ( x 0 , θ T ) = - Δ R 1 ( x 0 , θ m ) ,
l = 2 a tan β
x 0 = - ( a tan β ) / ( 2 n p ) .
Δ x = - { R [ cos ( θ - θ 0 ) - cos θ ] + x 0 [ ( cos θ ) - 1 - 1 ] + n p 2 l [ ( n p 2 - sin 2 θ ) - 1 - 1 ] } ,
Δ y = R sin ( θ - θ 0 ) - Δ E ( θ ) cos θ
R = a [ 1 + sin ( 2 β - 90 ° ) ] ( sin θ 0 ) - 1
θ 0 = tan - 1 { a [ 1 + sin ( 2 β - 90 0 ) ] / ( x 0 + a sin 2 β ) } .

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