Abstract

In this paper the Goos–Hänchen beam displacement at total internal reflection is reviewed. The basic theory of the beam shift is discussed from a classical approach, and measurement of the shift is discussed. Other experimental results are outlined. The theory of finite beam shift at total internal reflection is summarized. An application to nonlocal media is discussed. Finally, recent developments are outlined with implication for beam shifts in spatially dispersive media.

© 1986 Optical Society of America

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  1. I. Newton, Opticks (Dover, New York, 1952).
  2. F. Goos, H. Hänchen, “Ein neuer und fundamentales Versuch zur total reflexion,” Ann. Physik 6(1), 333–345 (1947), Ann. Physik 6(5), 251–252 (1949).
    [Crossref]
  3. J. Picht, Beitrag zur Theorie der total Reflexion,” Ann. Physik 5(3), 433–496 (1929).
    [Crossref]
  4. C. Schaefer, R. Pich, “Ein Beitrag zur Theorie der total Reflexion,” Ann. Physik 5(30), 245–266 (1937).
    [Crossref]
  5. K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Physik 6(2), 87–102 (1948).
    [Crossref]
  6. C. Von Fragstein, “Zuer Seitenversetzung des total reflektierten Lichtstrables,” Ann. Physik 6(4), 271–278 (1949).
  7. H. Wolter, “Zuer Frage des Lichtweges bei total Reflexion,”Z. Naturforsch. 5a, 276–283 (1950).
  8. R. H. Renard, “Total reflection: a new evaluation of the Goos–Hänchen Shift,”J. Opt. Soc. Am. 54, 1190–1197 (1964).
    [Crossref]
  9. H. K. V. Lotsch, “Beam displacement at total reflection: the Goos–Hänchen effect,” Optik 32, 116–137, 189–204, 299–319, 553–569 (1970/71).
  10. B. R. Horowitz, T. Tamir, “Lateral displacement of a light beam at a dielectric interface,”J. Opt. Soc. Am. 61, 586–592 (1971).
    [Crossref]
  11. B. B. Horowitz, T. Tamir, “Unified theory of total reflection phenomenon at a dielectric interface,” Appl. Phys. 1, 31 (1973).
    [Crossref]
  12. C. W. Hsue, T. Tamir, “Lateral displacement and distortion of beams incident upon a transmitting-layer configuration,”J. Opt. Soc. Am. 2, 978–987 (1985).
    [Crossref]
  13. See T. Tamir, “The lateral waves,” in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, New York, 1982), Chap. 13.
  14. H. Shih, N. Bloembergen, “Phase-matched critical total reflection and the Goos–Hänchen shift in second harmonic generation,” Phys. Rev. A 3, 412–420 (1971).
    [Crossref]
  15. N. Bloembergen, H. J. Simon, C. H. Lee, “Total-reflection phenomena in second-harmonic generation of light.” Phys. Rev. 181, 1261–1271 (1969).
    [Crossref]
  16. D. Marcuse, “Reflection of a Gaussian beam for a nonlinear interface,” Appl. Opt. 19, 3130–3139 (1980).
    [Crossref] [PubMed]
  17. W. J. Tomlinson, J. P. Gordon, P. W. Smith, “Reflection of a Gaussian beam at a nonlinear interface,” Appl. Opt. 21, 2041–2051 (1982).
    [Crossref] [PubMed]
  18. N. N. Akhmediev, V. I. Korneev, Yu. V. Kuz’menko, “Excitation of nonlinear surface waves by Gaussian light beams,” Sov. Phys. JETP 61, 62–67 (1985).
  19. J. L. Birman, D. N. Pattanayak, A. Puri, “Predicted resonance enhanced lateral beam displacement in semiconductors,” Phys. Rev. Lett. 50, 1664–1667 (1983).
    [Crossref]
  20. A. Puri, D. N. Pattanayak, J. L. Birman, “Resonance effects on total internal reflection and lateral (Goos–Hänchen) beam displacement at the interface between nonlocal and local dielectric,” Phys. Rev. B 28, 5877–5886 (1983).
    [Crossref]
  21. O. A. Godin, “Diffraction theory of beam displacement accompanying reflection: I,” Sov. Phys. Tech. Phys. 29, 1232–1237 (1985).
  22. L. M. Brekhovskikh, Waves in Layered Media, 2nd ed. (Academic, New York, 1980).
  23. O. A. Godin, “Lateral waves in absorbing media,” Sov. Phys. Accoust. 29, 173–180 (1983).
  24. N. J. Harrick, “Study of physics and chemistry of surfaces from frustrated total reflection,” Phys. Rev. Lett. 4, 224–226 (1960).
    [Crossref]
  25. A. Mazer, C. Imbert, C. R. Huard, Acad. Sci. Paris B 273, 592–594 (1971).
  26. O. Costa de Beauregard, C. Imbert, “Quantized longitudinal and transverse shifts associated with total internal reflection,” Phys. Rev. D 7, 3555–3563 (1973).
    [Crossref]
  27. L. de Broglie, J. P. Vigier, “Photon mass and new experiment results on longitudinal displacement of laser beams near total reflection,” Phys. Rev. Lett. 28, 1001–1004 (1972).
    [Crossref]
  28. K. W. Chiu, J. J. Quinn, “On the Goos–Hänchen effect: a simple example of a time delay scattering process,” Am. J. Phys. 40, 1847–1851 (1972).
    [Crossref]
  29. G. J. Troup, J. L. A. Francey, R. G. Turner, A. Tirkel “Photon mass and new experimental results on longitudinal displacements of laser beams near total reflection,” Phys. Rev. Lett. 28, 1540 (1972).
    [Crossref]
  30. M. Green, P. Kirkby, R. S. Timsit, “Experimental results on the longitudinal displacement of light beams near total reflection,” Phys. Lett. 45A, 259–260 (1973).
  31. O. Costa de Beauregard, C. Imbert, Y. Levy “Observation of shifts in total reflection of a light beam by a multilayer structure,” Phys. Rev. D 15, 3553–3562 (1977).
    [Crossref]
  32. J. J. Crown, B. Anicin, “Longitudinal and transverse displacements of a bounded microwave beam at total internal reflection,”J. Opt. Soc. Am. 67, 1307–1313 (1977).
    [Crossref]
  33. A. Von Schoch, “Seitliche Versetzung eines total Reflektierten Strahls bei Ultroschallwellen,” Acoustica 2, 1811 (1952).
  34. S. I. Pekar, “The theory of electromagnetic waves in a crystal in which excitons are produced,” Sov. Phys. JETP 6, 785–796 (1958); J. J. Hopfield, D. G. Thomas, “Theoretical and experimental effects of spatial dispersion on the optical properties of crystals,” Phys. Rev. 132, 563 (1963); V. M. Agranovich, V. L. Ginzburg, Spatial Dispersion in Crystal Optics and the Theory of Excitons (Interscience, New York, 1966).
    [Crossref]
  35. J. L. Birman “Electrodynamics and nonlocal optical effects mediated by exciton polaritons,” in Excitons, E. I. Rashba, M. D. Sturge, eds. (North-Holland, New York, 1982), Vol. 2.
  36. P. Mazur, B. Djafari-Rouhani, “Effect of surface polaritons on lateral displacement of light beam at a dielectric interface,” Phys. Rev. B 30, 6759–6762 (1984).
    [Crossref]
  37. J. S. Nikoma, “Surface Polariton reflection and transmission at rough surface,” Solid State Commun. 54, 729–731 (1985).
    [Crossref]
  38. V. M. Agranovich, V. E. Kravtsov, “Notes on crystal optics of superlattices,” Solid State Commun. 55, 85–90 (1985).
    [Crossref]
  39. H. Shi, C.-H. Tsai, “Polariton modes in superlattice media,” Solid State Commun. 52, 953–954 (1984).
    [Crossref]

1985 (5)

C. W. Hsue, T. Tamir, “Lateral displacement and distortion of beams incident upon a transmitting-layer configuration,”J. Opt. Soc. Am. 2, 978–987 (1985).
[Crossref]

N. N. Akhmediev, V. I. Korneev, Yu. V. Kuz’menko, “Excitation of nonlinear surface waves by Gaussian light beams,” Sov. Phys. JETP 61, 62–67 (1985).

O. A. Godin, “Diffraction theory of beam displacement accompanying reflection: I,” Sov. Phys. Tech. Phys. 29, 1232–1237 (1985).

J. S. Nikoma, “Surface Polariton reflection and transmission at rough surface,” Solid State Commun. 54, 729–731 (1985).
[Crossref]

V. M. Agranovich, V. E. Kravtsov, “Notes on crystal optics of superlattices,” Solid State Commun. 55, 85–90 (1985).
[Crossref]

1984 (2)

H. Shi, C.-H. Tsai, “Polariton modes in superlattice media,” Solid State Commun. 52, 953–954 (1984).
[Crossref]

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

1983 (3)

O. A. Godin, “Lateral waves in absorbing media,” Sov. Phys. Accoust. 29, 173–180 (1983).

J. L. Birman, D. N. Pattanayak, A. Puri, “Predicted resonance enhanced lateral beam displacement in semiconductors,” Phys. Rev. Lett. 50, 1664–1667 (1983).
[Crossref]

A. Puri, D. N. Pattanayak, J. L. Birman, “Resonance effects on total internal reflection and lateral (Goos–Hänchen) beam displacement at the interface between nonlocal and local dielectric,” Phys. Rev. B 28, 5877–5886 (1983).
[Crossref]

1982 (1)

1980 (1)

1977 (2)

O. Costa de Beauregard, C. Imbert, Y. Levy “Observation of shifts in total reflection of a light beam by a multilayer structure,” Phys. Rev. D 15, 3553–3562 (1977).
[Crossref]

J. J. Crown, B. Anicin, “Longitudinal and transverse displacements of a bounded microwave beam at total internal reflection,”J. Opt. Soc. Am. 67, 1307–1313 (1977).
[Crossref]

1973 (3)

O. Costa de Beauregard, C. Imbert, “Quantized longitudinal and transverse shifts associated with total internal reflection,” Phys. Rev. D 7, 3555–3563 (1973).
[Crossref]

M. Green, P. Kirkby, R. S. Timsit, “Experimental results on the longitudinal displacement of light beams near total reflection,” Phys. Lett. 45A, 259–260 (1973).

B. B. Horowitz, T. Tamir, “Unified theory of total reflection phenomenon at a dielectric interface,” Appl. Phys. 1, 31 (1973).
[Crossref]

1972 (3)

L. de Broglie, J. P. Vigier, “Photon mass and new experiment results on longitudinal displacement of laser beams near total reflection,” Phys. Rev. Lett. 28, 1001–1004 (1972).
[Crossref]

K. W. Chiu, J. J. Quinn, “On the Goos–Hänchen effect: a simple example of a time delay scattering process,” Am. J. Phys. 40, 1847–1851 (1972).
[Crossref]

G. J. Troup, J. L. A. Francey, R. G. Turner, A. Tirkel “Photon mass and new experimental results on longitudinal displacements of laser beams near total reflection,” Phys. Rev. Lett. 28, 1540 (1972).
[Crossref]

1971 (3)

A. Mazer, C. Imbert, C. R. Huard, Acad. Sci. Paris B 273, 592–594 (1971).

H. Shih, N. Bloembergen, “Phase-matched critical total reflection and the Goos–Hänchen shift in second harmonic generation,” Phys. Rev. A 3, 412–420 (1971).
[Crossref]

B. R. Horowitz, T. Tamir, “Lateral displacement of a light beam at a dielectric interface,”J. Opt. Soc. Am. 61, 586–592 (1971).
[Crossref]

1969 (1)

N. Bloembergen, H. J. Simon, C. H. Lee, “Total-reflection phenomena in second-harmonic generation of light.” Phys. Rev. 181, 1261–1271 (1969).
[Crossref]

1964 (1)

1960 (1)

N. J. Harrick, “Study of physics and chemistry of surfaces from frustrated total reflection,” Phys. Rev. Lett. 4, 224–226 (1960).
[Crossref]

1958 (1)

S. I. Pekar, “The theory of electromagnetic waves in a crystal in which excitons are produced,” Sov. Phys. JETP 6, 785–796 (1958); J. J. Hopfield, D. G. Thomas, “Theoretical and experimental effects of spatial dispersion on the optical properties of crystals,” Phys. Rev. 132, 563 (1963); V. M. Agranovich, V. L. Ginzburg, Spatial Dispersion in Crystal Optics and the Theory of Excitons (Interscience, New York, 1966).
[Crossref]

1952 (1)

A. Von Schoch, “Seitliche Versetzung eines total Reflektierten Strahls bei Ultroschallwellen,” Acoustica 2, 1811 (1952).

1950 (1)

H. Wolter, “Zuer Frage des Lichtweges bei total Reflexion,”Z. Naturforsch. 5a, 276–283 (1950).

1949 (1)

C. Von Fragstein, “Zuer Seitenversetzung des total reflektierten Lichtstrables,” Ann. Physik 6(4), 271–278 (1949).

1948 (1)

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Physik 6(2), 87–102 (1948).
[Crossref]

1947 (1)

F. Goos, H. Hänchen, “Ein neuer und fundamentales Versuch zur total reflexion,” Ann. Physik 6(1), 333–345 (1947), Ann. Physik 6(5), 251–252 (1949).
[Crossref]

1937 (1)

C. Schaefer, R. Pich, “Ein Beitrag zur Theorie der total Reflexion,” Ann. Physik 5(30), 245–266 (1937).
[Crossref]

1929 (1)

J. Picht, Beitrag zur Theorie der total Reflexion,” Ann. Physik 5(3), 433–496 (1929).
[Crossref]

Agranovich, V. M.

V. M. Agranovich, V. E. Kravtsov, “Notes on crystal optics of superlattices,” Solid State Commun. 55, 85–90 (1985).
[Crossref]

Akhmediev, N. N.

N. N. Akhmediev, V. I. Korneev, Yu. V. Kuz’menko, “Excitation of nonlinear surface waves by Gaussian light beams,” Sov. Phys. JETP 61, 62–67 (1985).

Anicin, B.

Artmann, K.

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Physik 6(2), 87–102 (1948).
[Crossref]

Birman, J. L.

A. Puri, D. N. Pattanayak, J. L. Birman, “Resonance effects on total internal reflection and lateral (Goos–Hänchen) beam displacement at the interface between nonlocal and local dielectric,” Phys. Rev. B 28, 5877–5886 (1983).
[Crossref]

J. L. Birman, D. N. Pattanayak, A. Puri, “Predicted resonance enhanced lateral beam displacement in semiconductors,” Phys. Rev. Lett. 50, 1664–1667 (1983).
[Crossref]

J. L. Birman “Electrodynamics and nonlocal optical effects mediated by exciton polaritons,” in Excitons, E. I. Rashba, M. D. Sturge, eds. (North-Holland, New York, 1982), Vol. 2.

Bloembergen, N.

H. Shih, N. Bloembergen, “Phase-matched critical total reflection and the Goos–Hänchen shift in second harmonic generation,” Phys. Rev. A 3, 412–420 (1971).
[Crossref]

N. Bloembergen, H. J. Simon, C. H. Lee, “Total-reflection phenomena in second-harmonic generation of light.” Phys. Rev. 181, 1261–1271 (1969).
[Crossref]

Brekhovskikh, L. M.

L. M. Brekhovskikh, Waves in Layered Media, 2nd ed. (Academic, New York, 1980).

Chiu, K. W.

K. W. Chiu, J. J. Quinn, “On the Goos–Hänchen effect: a simple example of a time delay scattering process,” Am. J. Phys. 40, 1847–1851 (1972).
[Crossref]

Costa de Beauregard, O.

O. Costa de Beauregard, C. Imbert, Y. Levy “Observation of shifts in total reflection of a light beam by a multilayer structure,” Phys. Rev. D 15, 3553–3562 (1977).
[Crossref]

O. Costa de Beauregard, C. Imbert, “Quantized longitudinal and transverse shifts associated with total internal reflection,” Phys. Rev. D 7, 3555–3563 (1973).
[Crossref]

Crown, J. J.

de Broglie, L.

L. de Broglie, J. P. Vigier, “Photon mass and new experiment results on longitudinal displacement of laser beams near total reflection,” Phys. Rev. Lett. 28, 1001–1004 (1972).
[Crossref]

Djafari-Rouhani, B.

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

Francey, J. L. A.

G. J. Troup, J. L. A. Francey, R. G. Turner, A. Tirkel “Photon mass and new experimental results on longitudinal displacements of laser beams near total reflection,” Phys. Rev. Lett. 28, 1540 (1972).
[Crossref]

Godin, O. A.

O. A. Godin, “Diffraction theory of beam displacement accompanying reflection: I,” Sov. Phys. Tech. Phys. 29, 1232–1237 (1985).

O. A. Godin, “Lateral waves in absorbing media,” Sov. Phys. Accoust. 29, 173–180 (1983).

Goos, F.

F. Goos, H. Hänchen, “Ein neuer und fundamentales Versuch zur total reflexion,” Ann. Physik 6(1), 333–345 (1947), Ann. Physik 6(5), 251–252 (1949).
[Crossref]

Gordon, J. P.

Green, M.

M. Green, P. Kirkby, R. S. Timsit, “Experimental results on the longitudinal displacement of light beams near total reflection,” Phys. Lett. 45A, 259–260 (1973).

Hänchen, H.

F. Goos, H. Hänchen, “Ein neuer und fundamentales Versuch zur total reflexion,” Ann. Physik 6(1), 333–345 (1947), Ann. Physik 6(5), 251–252 (1949).
[Crossref]

Harrick, N. J.

N. J. Harrick, “Study of physics and chemistry of surfaces from frustrated total reflection,” Phys. Rev. Lett. 4, 224–226 (1960).
[Crossref]

Horowitz, B. B.

B. B. Horowitz, T. Tamir, “Unified theory of total reflection phenomenon at a dielectric interface,” Appl. Phys. 1, 31 (1973).
[Crossref]

Horowitz, B. R.

Hsue, C. W.

C. W. Hsue, T. Tamir, “Lateral displacement and distortion of beams incident upon a transmitting-layer configuration,”J. Opt. Soc. Am. 2, 978–987 (1985).
[Crossref]

Huard, C. R.

A. Mazer, C. Imbert, C. R. Huard, Acad. Sci. Paris B 273, 592–594 (1971).

Imbert, C.

O. Costa de Beauregard, C. Imbert, Y. Levy “Observation of shifts in total reflection of a light beam by a multilayer structure,” Phys. Rev. D 15, 3553–3562 (1977).
[Crossref]

O. Costa de Beauregard, C. Imbert, “Quantized longitudinal and transverse shifts associated with total internal reflection,” Phys. Rev. D 7, 3555–3563 (1973).
[Crossref]

A. Mazer, C. Imbert, C. R. Huard, Acad. Sci. Paris B 273, 592–594 (1971).

Kirkby, P.

M. Green, P. Kirkby, R. S. Timsit, “Experimental results on the longitudinal displacement of light beams near total reflection,” Phys. Lett. 45A, 259–260 (1973).

Korneev, V. I.

N. N. Akhmediev, V. I. Korneev, Yu. V. Kuz’menko, “Excitation of nonlinear surface waves by Gaussian light beams,” Sov. Phys. JETP 61, 62–67 (1985).

Kravtsov, V. E.

V. M. Agranovich, V. E. Kravtsov, “Notes on crystal optics of superlattices,” Solid State Commun. 55, 85–90 (1985).
[Crossref]

Kuz’menko, Yu. V.

N. N. Akhmediev, V. I. Korneev, Yu. V. Kuz’menko, “Excitation of nonlinear surface waves by Gaussian light beams,” Sov. Phys. JETP 61, 62–67 (1985).

Lee, C. H.

N. Bloembergen, H. J. Simon, C. H. Lee, “Total-reflection phenomena in second-harmonic generation of light.” Phys. Rev. 181, 1261–1271 (1969).
[Crossref]

Levy, Y.

O. Costa de Beauregard, C. Imbert, Y. Levy “Observation of shifts in total reflection of a light beam by a multilayer structure,” Phys. Rev. D 15, 3553–3562 (1977).
[Crossref]

Lotsch, H. K. V.

H. K. V. Lotsch, “Beam displacement at total reflection: the Goos–Hänchen effect,” Optik 32, 116–137, 189–204, 299–319, 553–569 (1970/71).

Marcuse, D.

Mazer, A.

A. Mazer, C. Imbert, C. R. Huard, Acad. Sci. Paris B 273, 592–594 (1971).

Mazur, P.

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

Newton, I.

I. Newton, Opticks (Dover, New York, 1952).

Nikoma, J. S.

J. S. Nikoma, “Surface Polariton reflection and transmission at rough surface,” Solid State Commun. 54, 729–731 (1985).
[Crossref]

Pattanayak, D. N.

A. Puri, D. N. Pattanayak, J. L. Birman, “Resonance effects on total internal reflection and lateral (Goos–Hänchen) beam displacement at the interface between nonlocal and local dielectric,” Phys. Rev. B 28, 5877–5886 (1983).
[Crossref]

J. L. Birman, D. N. Pattanayak, A. Puri, “Predicted resonance enhanced lateral beam displacement in semiconductors,” Phys. Rev. Lett. 50, 1664–1667 (1983).
[Crossref]

Pekar, S. I.

S. I. Pekar, “The theory of electromagnetic waves in a crystal in which excitons are produced,” Sov. Phys. JETP 6, 785–796 (1958); J. J. Hopfield, D. G. Thomas, “Theoretical and experimental effects of spatial dispersion on the optical properties of crystals,” Phys. Rev. 132, 563 (1963); V. M. Agranovich, V. L. Ginzburg, Spatial Dispersion in Crystal Optics and the Theory of Excitons (Interscience, New York, 1966).
[Crossref]

Pich, R.

C. Schaefer, R. Pich, “Ein Beitrag zur Theorie der total Reflexion,” Ann. Physik 5(30), 245–266 (1937).
[Crossref]

Picht, J.

J. Picht, Beitrag zur Theorie der total Reflexion,” Ann. Physik 5(3), 433–496 (1929).
[Crossref]

Puri, A.

J. L. Birman, D. N. Pattanayak, A. Puri, “Predicted resonance enhanced lateral beam displacement in semiconductors,” Phys. Rev. Lett. 50, 1664–1667 (1983).
[Crossref]

A. Puri, D. N. Pattanayak, J. L. Birman, “Resonance effects on total internal reflection and lateral (Goos–Hänchen) beam displacement at the interface between nonlocal and local dielectric,” Phys. Rev. B 28, 5877–5886 (1983).
[Crossref]

Quinn, J. J.

K. W. Chiu, J. J. Quinn, “On the Goos–Hänchen effect: a simple example of a time delay scattering process,” Am. J. Phys. 40, 1847–1851 (1972).
[Crossref]

Renard, R. H.

Schaefer, C.

C. Schaefer, R. Pich, “Ein Beitrag zur Theorie der total Reflexion,” Ann. Physik 5(30), 245–266 (1937).
[Crossref]

Shi, H.

H. Shi, C.-H. Tsai, “Polariton modes in superlattice media,” Solid State Commun. 52, 953–954 (1984).
[Crossref]

Shih, H.

H. Shih, N. Bloembergen, “Phase-matched critical total reflection and the Goos–Hänchen shift in second harmonic generation,” Phys. Rev. A 3, 412–420 (1971).
[Crossref]

Simon, H. J.

N. Bloembergen, H. J. Simon, C. H. Lee, “Total-reflection phenomena in second-harmonic generation of light.” Phys. Rev. 181, 1261–1271 (1969).
[Crossref]

Smith, P. W.

Tamir, T.

C. W. Hsue, T. Tamir, “Lateral displacement and distortion of beams incident upon a transmitting-layer configuration,”J. Opt. Soc. Am. 2, 978–987 (1985).
[Crossref]

B. B. Horowitz, T. Tamir, “Unified theory of total reflection phenomenon at a dielectric interface,” Appl. Phys. 1, 31 (1973).
[Crossref]

B. R. Horowitz, T. Tamir, “Lateral displacement of a light beam at a dielectric interface,”J. Opt. Soc. Am. 61, 586–592 (1971).
[Crossref]

See T. Tamir, “The lateral waves,” in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, New York, 1982), Chap. 13.

Timsit, R. S.

M. Green, P. Kirkby, R. S. Timsit, “Experimental results on the longitudinal displacement of light beams near total reflection,” Phys. Lett. 45A, 259–260 (1973).

Tirkel, A.

G. J. Troup, J. L. A. Francey, R. G. Turner, A. Tirkel “Photon mass and new experimental results on longitudinal displacements of laser beams near total reflection,” Phys. Rev. Lett. 28, 1540 (1972).
[Crossref]

Tomlinson, W. J.

Troup, G. J.

G. J. Troup, J. L. A. Francey, R. G. Turner, A. Tirkel “Photon mass and new experimental results on longitudinal displacements of laser beams near total reflection,” Phys. Rev. Lett. 28, 1540 (1972).
[Crossref]

Tsai, C.-H.

H. Shi, C.-H. Tsai, “Polariton modes in superlattice media,” Solid State Commun. 52, 953–954 (1984).
[Crossref]

Turner, R. G.

G. J. Troup, J. L. A. Francey, R. G. Turner, A. Tirkel “Photon mass and new experimental results on longitudinal displacements of laser beams near total reflection,” Phys. Rev. Lett. 28, 1540 (1972).
[Crossref]

Vigier, J. P.

L. de Broglie, J. P. Vigier, “Photon mass and new experiment results on longitudinal displacement of laser beams near total reflection,” Phys. Rev. Lett. 28, 1001–1004 (1972).
[Crossref]

Von Fragstein, C.

C. Von Fragstein, “Zuer Seitenversetzung des total reflektierten Lichtstrables,” Ann. Physik 6(4), 271–278 (1949).

Von Schoch, A.

A. Von Schoch, “Seitliche Versetzung eines total Reflektierten Strahls bei Ultroschallwellen,” Acoustica 2, 1811 (1952).

Wolter, H.

H. Wolter, “Zuer Frage des Lichtweges bei total Reflexion,”Z. Naturforsch. 5a, 276–283 (1950).

Acad. Sci. Paris B (1)

A. Mazer, C. Imbert, C. R. Huard, Acad. Sci. Paris B 273, 592–594 (1971).

Acoustica (1)

A. Von Schoch, “Seitliche Versetzung eines total Reflektierten Strahls bei Ultroschallwellen,” Acoustica 2, 1811 (1952).

Am. J. Phys. (1)

K. W. Chiu, J. J. Quinn, “On the Goos–Hänchen effect: a simple example of a time delay scattering process,” Am. J. Phys. 40, 1847–1851 (1972).
[Crossref]

Ann. Physik (5)

F. Goos, H. Hänchen, “Ein neuer und fundamentales Versuch zur total reflexion,” Ann. Physik 6(1), 333–345 (1947), Ann. Physik 6(5), 251–252 (1949).
[Crossref]

J. Picht, Beitrag zur Theorie der total Reflexion,” Ann. Physik 5(3), 433–496 (1929).
[Crossref]

C. Schaefer, R. Pich, “Ein Beitrag zur Theorie der total Reflexion,” Ann. Physik 5(30), 245–266 (1937).
[Crossref]

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Physik 6(2), 87–102 (1948).
[Crossref]

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Appl. Opt. (2)

Appl. Phys. (1)

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[Crossref]

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Optik (1)

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Phys. Lett. (1)

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Phys. Rev. (1)

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[Crossref]

Phys. Rev. A (1)

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[Crossref]

Phys. Rev. B (2)

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic of the experiment of Goos and Hänchen, (b) multiple reflecting plate with total reflecting prisms P1, P2 (magnification of beam shift).

Fig. 2
Fig. 2

Pictorial representation of flow of energy from the denser medium to the rarer medium at total internal reflection.

Fig. 3
Fig. 3

Beam shift D in case of total reflection. The beams shown by dashed lines correspond to geometrical reflection (silvered). Solid reflected lines correspond to total reflection.

Fig. 4
Fig. 4

Geometry used in study of Goos–Hänchen effect at the nonlocal–local interface.

Fig. 5
Fig. 5

Lateral beam shift X11 plotted against log10 (|θθc|), θ below and above θc for various beam widths. Material parameters used for CdS are = 0 = 2.55 eV, m* = 0.9 me, 4πα0 = 0.0125, me = 0.51 MeV, and Γ/2ω0 = 10−3. Curves labeled ABC1, ABC2, and ABC3 follow from Ref. 20. This case corresponds to upper polariton branch.

Fig. 6
Fig. 6

X22c plotted against (ωω0)/ω0 in the resonance region for CdS parameters given in Fig. 5. Here X22 is taken at the critical angle, and plots are shown for three beam widths.

Equations (18)

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sin θ > sin θ c = n 2 n 1 .
k x = 2 π λ 1 sin θ .
ψ = ( exp [ i ( k x x + ϕ ) ] + exp { i [ k x + Δ k x ) x + Δ ϕ ] } ) = exp [ i ( k x x + ϕ ) ] { 1 + exp [ i ( Δ k x x + Δ ϕ ) ] } .
Δ k x x + Δ ϕ = 2 π ν ,
Δ k x x silvered = 2 π ν .
X = x - x silvered = - Δ ϕ Δ k x .
X = - d ϕ d k x .
D = X cos θ .
D = - cos θ d ϕ d k x = - λ 1 2 π d ϕ d θ .
ϕ E = - 2 tan - 1 { [ sin 2 θ - ( n 2 / n 1 ) 2 ] 1 / 2 cos θ } ,
ϕ H = - 2 tan - 1 { [ sin 2 θ - ( n 2 / n 1 ) 2 ] 1 / 2 ( n 2 / n 1 ) 2 cos θ } .
D E = 1 π n 1 n 2 λ 1 ( sin 2 θ - sin 2 θ c ) 1 / 2 ,
D H = ( n 1 n 2 ) 2 1 π n 1 n 2 λ 1 ( sin 2 θ - sin 2 θ c ) 1 / 2 .
k α 2 = ( ω / c ) 2 ( ω , k α ) ,             α = 1 , 2 ,
( ω , k ) = + 4 π α 0 ω 0 2 ( ω 0 2 - ω 2 - i ω Γ + D k 2 ) ,
X j j = - 1 2 cos θ Re { A j j ( θ ) z j 1 + A j j ( θ ) [ y j - δ j 1 / 2 ] } ,
z j = f 1 / 2 w r exp ( - i π / 4 + γ j 2 / 4 ) D - 1 / 2 ( γ j ) , y i = f 1 / 2 exp ( - i π / 4 + γ j 2 / 4 ) D 1 / 2 ( γ j ) ,
A j j ( θ ) i 2 1 / 2 n T 1 / 2 cos 1 / 2 θ { 1 k 0 - α R - [ i , j , ( 3 - j ) ] - 1 k 1 } ,             j = 1 , 2.

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