Abstract

A leaky-wave theory is applied to the study of the lateral shift of a bounded optical beam reflected from a prism–air–metal (and prism–metal–air) layered configuration with surface-plasmon excitations. The locations of the pole and the zero of the reflection coefficient for the leaky surface-plasmon mode are calculated as one varies the thickness of the center layer. The excited surface-plasmon mode is leaky because of the presence of the prism. Both the real part and the imaginary part of the pole are affected by the energy leakage. The detailed structure of the reflected intensity and the forward and backward shifts of the reflected beam are illustrated.

© 1986 Optical Society of America

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References

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  1. A. Otto, in Optical Properties of Solids: New Development, B. O. Seraphin, ed. (North-Holland, Amsterdam, 1975).
  2. R. Tamir, Integrated Optics, 2nd ed. (Springer-Verlag, New York, 1979), Chap. 3, pp. 83–137.
  3. Von F. Goos, H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Physik 6, 333–346 (1947).
    [CrossRef]
  4. H. K. V. Lotsch, “Reflection and refraction of a beam of light at a plane interface,”J. Opt. Soc. Am. 58, 551–561 (1968).
    [CrossRef]
  5. T. Tamir, A. A. Oliner, “Role of the lateral wave in total reflection of light,”J. Opt. Soc. Am. 59, 942 (1969).
  6. B. R. Horowitz, T. Tamir, “Lateral displacement of a light beam at a dielectric interface,”J. Opt. Soc. Am. 61, 586–594 (1971).
    [CrossRef]
  7. H. L. Bertoni, T. Tamir, “Unified theory of Rayleigh-angle phenomena for acoustic beams at liquid–solid interfaces,” Appl. Phys. 2, 157–172 (1973).
    [CrossRef]
  8. T. Tamir, H. L. Bertoni, “Lateral displacement of optical beams at multilayered and periodic structures,”J. Opt. Soc. Am. 61, 1397–1413 (1971).
    [CrossRef]
  9. A. Amittay, P. D. Einziger, T. Tamir, “Experimental observation of anomalous electromagnetic absorption in thin-layered media,” Appl. Phys. Lett. 38, 754–756 (1981).
    [CrossRef]
  10. V. Shah, T. Tamir, “Absorption and lateral shift of beams incident upon lossy multilayered media,”J. Opt. Soc. Am. 73, 37–44 (1983).
    [CrossRef]
  11. P. Halevi, “Polariton modes at the interface between two conducting or dielectric media,” Surface Sci. 76, 64–89 (1978).
    [CrossRef]
  12. D. L. Mills, A. A. Maradudin, “Properties of surface polaritons in layered structures,” Phys. Rev. Lett. 31, 372–375 (1973).
    [CrossRef]
  13. A. D. Boardman, ed., Electromagnetic Surface Modes (Wiley, New York, 1982).
  14. W. P. Chen, J. M. Chen, “Use of surface plasma waves for determination of the thickness and optical constants of thin metallic films,”J. Opt. Soc. Am. 71, 189–191 (1981).
    [CrossRef]
  15. M. Tacke, “Far infrared laser spectroscopy of surface (Fano) waves for the determination of the optical constants of solid,” Sov. J. Quantum Electron. 12, 662–664 (1982).
    [CrossRef]
  16. M. Marschall, B. Fischer, H. J. Queisser, “Dispersion of surface plasmons in InSb,” Phys. Rev. Lett. 27, 95–97 (1971).
    [CrossRef]
  17. P. M. van den Berg, J. C. M. Borburgh, “Dispersion of surface plasmons in InSb-gratings,” Appl. Phys. 3, 55–60 (1974).
    [CrossRef]
  18. R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21, 1530–1533 (1968).
    [CrossRef]
  19. P. K. Tien, R. Ulrich, “Theory of prism–film coupler and thin-film light guides,”J. Opt. Soc. Am. 60, 1325–1337 (1970).
    [CrossRef]
  20. R. Ulrich, “Theory of the prism-film coupler by plane-wave analysis,”J. Opt. Soc. Am. 60, 1337–1350 (1970).
    [CrossRef]
  21. M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, “Grating coupler for efficient excitation of optical guided waves in thin films,” Appl. Phys. Lett. 16, 523–525 (1970).
    [CrossRef]
  22. D. L. Begley, D. A. Bryan, R. W. Alexander, R. J. Bell, “Optimization of prism coupling efficiency for surface electromagnetic wave excitation in the infrared,” Appl. Opt. 16, 1549–1552 (1977).
    [CrossRef] [PubMed]
  23. R. Miller, D. L. Begley, R. J. Bell, “Surface electromagnetic wave coupling efficiency dependence on prism gap height,” Appl. Opt. 16, 3077–3079 (1977).
    [CrossRef]
  24. R. T. Deck, D. Sarid, G. A. Olson, J. M. Elson, “Coupling between finite electromagnetic beam and long-range surface-plasmon mode,” Appl. Opt. 22, 3397–3405 (1983).
    [CrossRef] [PubMed]
  25. W. P. Chen, G. Ritchie, E. Burstein, “Excitation of surface electromagnetic waves in attenuated total-reflection prism configurations,” Phys. Rev. Lett. 37, 993–997 (1976).
    [CrossRef]
  26. P. Mazur, B. Djafari-Rouhani, “Effect of surface polaritons on the lateral displacement of a light beam at a dielectric interface,” Phys. Rev. B 30, 6759–6762 (1984).
    [CrossRef]
  27. J. A. Kong, Theory of Electromagnetic Waves (Wiley, New York, 1975), especially p. 119 for reflection coefficient and p. 218 for branch cuts.
  28. W. C. Chew, “The singularities of a Fourier-type integral in a multicylindrical layer problem,”IEEE Trans. Antennas Propag. AP-31, 653–655 (1983).
    [CrossRef]

1984 (1)

P. Mazur, B. Djafari-Rouhani, “Effect of surface polaritons on the lateral displacement of a light beam at a dielectric interface,” Phys. Rev. B 30, 6759–6762 (1984).
[CrossRef]

1983 (3)

1982 (1)

M. Tacke, “Far infrared laser spectroscopy of surface (Fano) waves for the determination of the optical constants of solid,” Sov. J. Quantum Electron. 12, 662–664 (1982).
[CrossRef]

1981 (2)

A. Amittay, P. D. Einziger, T. Tamir, “Experimental observation of anomalous electromagnetic absorption in thin-layered media,” Appl. Phys. Lett. 38, 754–756 (1981).
[CrossRef]

W. P. Chen, J. M. Chen, “Use of surface plasma waves for determination of the thickness and optical constants of thin metallic films,”J. Opt. Soc. Am. 71, 189–191 (1981).
[CrossRef]

1978 (1)

P. Halevi, “Polariton modes at the interface between two conducting or dielectric media,” Surface Sci. 76, 64–89 (1978).
[CrossRef]

1977 (2)

1976 (1)

W. P. Chen, G. Ritchie, E. Burstein, “Excitation of surface electromagnetic waves in attenuated total-reflection prism configurations,” Phys. Rev. Lett. 37, 993–997 (1976).
[CrossRef]

1974 (1)

P. M. van den Berg, J. C. M. Borburgh, “Dispersion of surface plasmons in InSb-gratings,” Appl. Phys. 3, 55–60 (1974).
[CrossRef]

1973 (2)

D. L. Mills, A. A. Maradudin, “Properties of surface polaritons in layered structures,” Phys. Rev. Lett. 31, 372–375 (1973).
[CrossRef]

H. L. Bertoni, T. Tamir, “Unified theory of Rayleigh-angle phenomena for acoustic beams at liquid–solid interfaces,” Appl. Phys. 2, 157–172 (1973).
[CrossRef]

1971 (3)

1970 (3)

1969 (1)

1968 (2)

H. K. V. Lotsch, “Reflection and refraction of a beam of light at a plane interface,”J. Opt. Soc. Am. 58, 551–561 (1968).
[CrossRef]

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21, 1530–1533 (1968).
[CrossRef]

1947 (1)

Von F. Goos, H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Physik 6, 333–346 (1947).
[CrossRef]

Alexander, R. W.

Amittay, A.

A. Amittay, P. D. Einziger, T. Tamir, “Experimental observation of anomalous electromagnetic absorption in thin-layered media,” Appl. Phys. Lett. 38, 754–756 (1981).
[CrossRef]

Arakawa, E. T.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21, 1530–1533 (1968).
[CrossRef]

Begley, D. L.

Bell, R. J.

Bertoni, H. L.

H. L. Bertoni, T. Tamir, “Unified theory of Rayleigh-angle phenomena for acoustic beams at liquid–solid interfaces,” Appl. Phys. 2, 157–172 (1973).
[CrossRef]

T. Tamir, H. L. Bertoni, “Lateral displacement of optical beams at multilayered and periodic structures,”J. Opt. Soc. Am. 61, 1397–1413 (1971).
[CrossRef]

Borburgh, J. C. M.

P. M. van den Berg, J. C. M. Borburgh, “Dispersion of surface plasmons in InSb-gratings,” Appl. Phys. 3, 55–60 (1974).
[CrossRef]

Bryan, D. A.

Burstein, E.

W. P. Chen, G. Ritchie, E. Burstein, “Excitation of surface electromagnetic waves in attenuated total-reflection prism configurations,” Phys. Rev. Lett. 37, 993–997 (1976).
[CrossRef]

Chen, J. M.

Chen, W. P.

W. P. Chen, J. M. Chen, “Use of surface plasma waves for determination of the thickness and optical constants of thin metallic films,”J. Opt. Soc. Am. 71, 189–191 (1981).
[CrossRef]

W. P. Chen, G. Ritchie, E. Burstein, “Excitation of surface electromagnetic waves in attenuated total-reflection prism configurations,” Phys. Rev. Lett. 37, 993–997 (1976).
[CrossRef]

Chew, W. C.

W. C. Chew, “The singularities of a Fourier-type integral in a multicylindrical layer problem,”IEEE Trans. Antennas Propag. AP-31, 653–655 (1983).
[CrossRef]

Cowan, J. J.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21, 1530–1533 (1968).
[CrossRef]

Dakss, M. L.

M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, “Grating coupler for efficient excitation of optical guided waves in thin films,” Appl. Phys. Lett. 16, 523–525 (1970).
[CrossRef]

Deck, R. T.

Djafari-Rouhani, B.

P. Mazur, B. Djafari-Rouhani, “Effect of surface polaritons on the lateral displacement of a light beam at a dielectric interface,” Phys. Rev. B 30, 6759–6762 (1984).
[CrossRef]

Einziger, P. D.

A. Amittay, P. D. Einziger, T. Tamir, “Experimental observation of anomalous electromagnetic absorption in thin-layered media,” Appl. Phys. Lett. 38, 754–756 (1981).
[CrossRef]

Elson, J. M.

Fischer, B.

M. Marschall, B. Fischer, H. J. Queisser, “Dispersion of surface plasmons in InSb,” Phys. Rev. Lett. 27, 95–97 (1971).
[CrossRef]

Goos, Von F.

Von F. Goos, H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Physik 6, 333–346 (1947).
[CrossRef]

Halevi, P.

P. Halevi, “Polariton modes at the interface between two conducting or dielectric media,” Surface Sci. 76, 64–89 (1978).
[CrossRef]

Hamm, R. N.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21, 1530–1533 (1968).
[CrossRef]

Hänchen, H.

Von F. Goos, H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Physik 6, 333–346 (1947).
[CrossRef]

Heidrich, P. F.

M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, “Grating coupler for efficient excitation of optical guided waves in thin films,” Appl. Phys. Lett. 16, 523–525 (1970).
[CrossRef]

Horowitz, B. R.

Kong, J. A.

J. A. Kong, Theory of Electromagnetic Waves (Wiley, New York, 1975), especially p. 119 for reflection coefficient and p. 218 for branch cuts.

Kuhn, L.

M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, “Grating coupler for efficient excitation of optical guided waves in thin films,” Appl. Phys. Lett. 16, 523–525 (1970).
[CrossRef]

Lotsch, H. K. V.

Maradudin, A. A.

D. L. Mills, A. A. Maradudin, “Properties of surface polaritons in layered structures,” Phys. Rev. Lett. 31, 372–375 (1973).
[CrossRef]

Marschall, M.

M. Marschall, B. Fischer, H. J. Queisser, “Dispersion of surface plasmons in InSb,” Phys. Rev. Lett. 27, 95–97 (1971).
[CrossRef]

Mazur, P.

P. Mazur, B. Djafari-Rouhani, “Effect of surface polaritons on the lateral displacement of a light beam at a dielectric interface,” Phys. Rev. B 30, 6759–6762 (1984).
[CrossRef]

Miller, R.

Mills, D. L.

D. L. Mills, A. A. Maradudin, “Properties of surface polaritons in layered structures,” Phys. Rev. Lett. 31, 372–375 (1973).
[CrossRef]

Oliner, A. A.

Olson, G. A.

Otto, A.

A. Otto, in Optical Properties of Solids: New Development, B. O. Seraphin, ed. (North-Holland, Amsterdam, 1975).

Queisser, H. J.

M. Marschall, B. Fischer, H. J. Queisser, “Dispersion of surface plasmons in InSb,” Phys. Rev. Lett. 27, 95–97 (1971).
[CrossRef]

Ritchie, G.

W. P. Chen, G. Ritchie, E. Burstein, “Excitation of surface electromagnetic waves in attenuated total-reflection prism configurations,” Phys. Rev. Lett. 37, 993–997 (1976).
[CrossRef]

Ritchie, R. H.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21, 1530–1533 (1968).
[CrossRef]

Sarid, D.

Scott, B. A.

M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, “Grating coupler for efficient excitation of optical guided waves in thin films,” Appl. Phys. Lett. 16, 523–525 (1970).
[CrossRef]

Shah, V.

Tacke, M.

M. Tacke, “Far infrared laser spectroscopy of surface (Fano) waves for the determination of the optical constants of solid,” Sov. J. Quantum Electron. 12, 662–664 (1982).
[CrossRef]

Tamir, R.

R. Tamir, Integrated Optics, 2nd ed. (Springer-Verlag, New York, 1979), Chap. 3, pp. 83–137.

Tamir, T.

Tien, P. K.

Ulrich, R.

van den Berg, P. M.

P. M. van den Berg, J. C. M. Borburgh, “Dispersion of surface plasmons in InSb-gratings,” Appl. Phys. 3, 55–60 (1974).
[CrossRef]

Ann. Physik (1)

Von F. Goos, H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Physik 6, 333–346 (1947).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. (2)

H. L. Bertoni, T. Tamir, “Unified theory of Rayleigh-angle phenomena for acoustic beams at liquid–solid interfaces,” Appl. Phys. 2, 157–172 (1973).
[CrossRef]

P. M. van den Berg, J. C. M. Borburgh, “Dispersion of surface plasmons in InSb-gratings,” Appl. Phys. 3, 55–60 (1974).
[CrossRef]

Appl. Phys. Lett. (2)

A. Amittay, P. D. Einziger, T. Tamir, “Experimental observation of anomalous electromagnetic absorption in thin-layered media,” Appl. Phys. Lett. 38, 754–756 (1981).
[CrossRef]

M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, “Grating coupler for efficient excitation of optical guided waves in thin films,” Appl. Phys. Lett. 16, 523–525 (1970).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

W. C. Chew, “The singularities of a Fourier-type integral in a multicylindrical layer problem,”IEEE Trans. Antennas Propag. AP-31, 653–655 (1983).
[CrossRef]

J. Opt. Soc. Am. (8)

Phys. Rev. B (1)

P. Mazur, B. Djafari-Rouhani, “Effect of surface polaritons on the lateral displacement of a light beam at a dielectric interface,” Phys. Rev. B 30, 6759–6762 (1984).
[CrossRef]

Phys. Rev. Lett. (4)

M. Marschall, B. Fischer, H. J. Queisser, “Dispersion of surface plasmons in InSb,” Phys. Rev. Lett. 27, 95–97 (1971).
[CrossRef]

W. P. Chen, G. Ritchie, E. Burstein, “Excitation of surface electromagnetic waves in attenuated total-reflection prism configurations,” Phys. Rev. Lett. 37, 993–997 (1976).
[CrossRef]

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21, 1530–1533 (1968).
[CrossRef]

D. L. Mills, A. A. Maradudin, “Properties of surface polaritons in layered structures,” Phys. Rev. Lett. 31, 372–375 (1973).
[CrossRef]

Sov. J. Quantum Electron. (1)

M. Tacke, “Far infrared laser spectroscopy of surface (Fano) waves for the determination of the optical constants of solid,” Sov. J. Quantum Electron. 12, 662–664 (1982).
[CrossRef]

Surface Sci. (1)

P. Halevi, “Polariton modes at the interface between two conducting or dielectric media,” Surface Sci. 76, 64–89 (1978).
[CrossRef]

Other (4)

A. D. Boardman, ed., Electromagnetic Surface Modes (Wiley, New York, 1982).

A. Otto, in Optical Properties of Solids: New Development, B. O. Seraphin, ed. (North-Holland, Amsterdam, 1975).

R. Tamir, Integrated Optics, 2nd ed. (Springer-Verlag, New York, 1979), Chap. 3, pp. 83–137.

J. A. Kong, Theory of Electromagnetic Waves (Wiley, New York, 1975), especially p. 119 for reflection coefficient and p. 218 for branch cuts.

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Figures (8)

Fig. 1
Fig. 1

The reflection of a bounded beam from a prism–air–metal or prism–metal–air configuration.

Fig. 2
Fig. 2

(a) The branch cuts and the locations of the branch points, the pole kp/k, and the zero kn/k in the complex κ plane for a prism–air–silver configuration. (b) The trajectories of the poles and zeros on the κ plane when the air–gap thickness is varied.

Fig. 3
Fig. 3

(a) The branch cuts and the locations of the branch points, the pole kp/k, and the zero kn/k in the complex κ plane for a prism–silver–air configuration. (b) The trajectories of the poles and the zeros on the complex κ plane when the silver thickness is varied.

Fig. 4
Fig. 4

Optical beam shift for the prism–air–silver configuration with d/λ = 0.4 for four beamwidths. The dashed curves represent the incident-beam intensities |Hi(x, 0)|2, and the solid curves are for the reflected-beam intensities |Hr(x, 0)|2.

Fig. 5
Fig. 5

Optical beam shift for the prism–air–silver configuration with d/λ = 0.7 for four beamwidths. Backward beam shifts occur here. Dashed curves, incident-beam intensities; solid curves, reflected-beam intensities.

Fig. 6
Fig. 6

Optical beam shift for the prism–air–silver configuration with Wx/λ = 20 and four different air-gap thicknesses, d/λ = 0.2, 0.6, 0.7, and 1.0. Dashed curves, incident-beam intensities; solid curves, reflected-beam intensities.

Fig. 7
Fig. 7

Optical beam shift for the prism–silver–air configuration with Wx/λ = 20 and four different silver-film thicknesses, d/λ = 0.01, 0.08, 0.15, and 0.2.

Fig. 8
Fig. 8

Optical beam shift for the prism–silver–air configuration with d/λ = 0.025. As can be seen from Fig. 3(b), the location of the pole is right above the branch point at κ = 1.0. Thus a direct numerical integration of Eq. (4) is required to obtain the reflected field. Dashed curves, incident-beam intensities; dotted curves, reflected-beam intensities using Eq. (9); solid curves, reflected-beam intensities using the direct numerical integration.

Equations (27)

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H i = y ^ H i ( x , 0 ) = y ^ exp [ - ( x W x ) 2 + i k x i x ]
H i ( x , 0 ) = - d k x 2 π h ( k x ) exp ( i k x x ) ,
h ( k x ) = π W x exp [ - ( k x - k x i ) 2 ( W x 2 ) 2 ] ,
H R = y ^ H r ( x , z ) = y ^ - d k x 2 π R ( k x ) h ( k x ) exp [ i k x x + i k 1 z z ] ,
k x - k x i < 2 W x .
R ( k x ) R 0 k x - k n k x - k p ,
k p = β p + i α p ,
k n = β n + i α n .
H r ( x , 0 ) = R 0 [ 1 + i π 2 ( k p - k n ) W x exp ( γ 2 ) erfc ( γ ) ] × exp [ - ( x w x ) 2 + i k x i x ] ,
γ = α p W x 2 - ( x W x ) + i ( k x i - β p ) W x 2
R ( k x ) = R 12 - R 23 + + R 12 + R 23 - exp ( i 2 k 2 z d ) R 12 + R 23 + + R 12 - R 23 - exp ( i 2 k 2 z d ) ,
R i j ± k i z i ± k j z j ,
k i z = ( ω 2 μ 0 i - k x 2 ) 1 / 2 .
κ = k x / k ,
n 1 = 1 / 0
n 3 = 3 / 0
Re [ k 1 z ] = 0
Im [ k 3 z ] = 0 ,
k x = k [ 2 3 0 ( 2 + 3 ) ] 1 / 2 .
R ( k x ) R 12 - R 23 + R 12 + R 23 + = R 12 .
R ( k x ) 1 1 k 1 z - 1 3 k 3 z 1 1 k 1 z + 1 3 k 3 z = R 13 - R 13 + = R 13 ,
( k x ) prism - Ag = k [ 1 3 0 ( 1 + 3 ) ] 1 / 2 ,
k p k ( 1 3 0 ( 1 + 3 ) ) 1 / 2 + i δ = 0.8370 + i δ
k n k 0.8370 - i δ ,
D i [ d d k x ln R ( k x ) ] k x = k x i i ( k n - k p ) ( k x i - k n ) ( k x i - k p ) ,
β n β p = k x i ,
D = α n - α p α n α p .

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