Abstract

Longitudinal and transverse shifts of an 8 cm parallel bounded beam of 34.2 GHz (8.77 mm) microwaves totally reflected from a paraffin prism have been investigated. The 45°- 45°- 90° prism is 18 cm high by 25 cm on the sides and the index of refraction is 1.491. Longitudinal shifts as large as 3 cm have been measured in a single reflection near the critical angle for a beam linearly polarized in the plane of incidence. The shift for perpendicular polarization is approximately half this value. The results are in general agreement with the classical theory for the Goos-Hänchen effect. An incident beam polarized at 45° to the incidence plane produces both parallel and perpendicular polarization shifts with values similar to the above. The shifts for both polarizations are reduced but are still distinctly separate if either a second prism or a metallic reflector is brought into the evanescent wave at millimeter distances from the interface. These results are in accordance with stationary phase calculations for two interfaces. It is found that a small (6 mm) transverse shift results if the prism is illuminated with circularly polarized microwaves.

© 1977 Optical Society of America

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  1. F. Goos and H. Hänchen, Ann. Physik (Leipz.) 1, 333 (1947).
  2. See, for example, the review by H. K. V. Lotsch, Optik 32, 116 (1970); 32, 189 (1970); 32, 299 (1971); 32, 553 (1970), and references therein.
  3. O. Bryngdahl, Prog. Opt. XI, 169 (1973).
  4. T. Tamir, Optik 36, 209 (1972); 37, 204 (1973); 38, 269 (1973). Both this reference and Refs. 2 and 3 above contain excellent descriptions of the physical phenomena involved. See also H. Kogelnik, in Integrated Optics, edited by T. Tamir, Topics in Applied Physics, Vol. 7 (Springer, New York, Heidelberg, Berlin, 1975), pp. 15–81.
  5. C. von Fragstein, Ann. Phys. (Leipz.) 4, 271 (1949); Remi H. Renard, J. Opt. Soc. Am. 54, 1190 (1964); J. Ricard, Nouv. Rev. Opt. Appl. 1, 5 (1970); the possibility of an energy flow into the evanescent wave was postulated several years before the experiment was performed. See J. Picht, Ann. Phys. (Leipz.) 3, 433 (1929).
  6. K. Artmann, Ann. Phys. (Leipz.) 2, 87 (1948).
  7. L. Agudin, Phys. Rev. 171, 1385 (1968).
  8. F. I. Fedorov, Dokil. Akad. Nauk. SSSR 105, 465 (1955).
  9. C. Imbert, Phys. Rev. D 5, 787 (1972), and references therein; O. Costa de Beauregard, Found. Phys. 2, 111 (1972).
  10. O. Costa de Beauregard and C. Imbert, Phys. Rev. D 7, 3555 (1973); A. Mozet, C. Imbert, and S. Huard, C. R. Acad. Sci. Paris B 273, 592 (1971). Goos and Hänchen also observed this effect with a beam linearly polarized at arbitrary incident azimuthal angles. See Ann. Phys. (Leipz.) 5, 251 (1949).
  11. Costa de Beauregard and Imbert (Ref. 10) claim that both the transverse and longitudinal shifts are quantized, each having characteristic eigenvalues. The longitudinal shift should then be characterized by the principal linear polarization states, and the transverse shift, by the circular polarization states: K. W. Chiu and J. J. Quinn, [Am. J. Phys. 40, 1847 (1972)] analyze the longitudinal shift by classical electrodynamics in terms of a time delay scattering process, and also arrive at the conclusion that an incident beam of arbitrary polarization splits exactly into p and s polarization states. A similar conclusion was also reached by G. J. Troup et al., Phys. Rev. Lett. 28, 1540 (1972).
  12. L. de Broglie and J. P. Vigier, Phys. Rev. Lett. 28, 1001 (1972).
  13. At the completion of our work we became aware of a concurrent study of the longitudinal shift due to microwaves that was ma–25 April 1974. See J. J. Cowan and B. Anibin, J. Opt. Soc. Am. 64, 525 (1974).
  14. H. Wolter, Handbuch der Physik (Springer-Verlag, Berlin, 1956), Vol. 24, p. 472.
  15. B. R. Horowitz and T. Tamir, J. Opt. Soc. Am. 61, 586 (1971).
  16. C. K. Carniglia (personal correspondence).
  17. M. McGuirk, C. K. Carniglia, J. J. Cowan (unpublished).
  18. In the acoustical case this distance is significant [M. A. Breazeale (personal correspondence)]. See also M. A. Breazeale, L. Adler, and G. W. Scott, J. Acoust. Soc. Am. Suppl. 57, 5–38 (1975).

1975

In the acoustical case this distance is significant [M. A. Breazeale (personal correspondence)]. See also M. A. Breazeale, L. Adler, and G. W. Scott, J. Acoust. Soc. Am. Suppl. 57, 5–38 (1975).

1974

At the completion of our work we became aware of a concurrent study of the longitudinal shift due to microwaves that was ma–25 April 1974. See J. J. Cowan and B. Anibin, J. Opt. Soc. Am. 64, 525 (1974).

1973

O. Costa de Beauregard and C. Imbert, Phys. Rev. D 7, 3555 (1973); A. Mozet, C. Imbert, and S. Huard, C. R. Acad. Sci. Paris B 273, 592 (1971). Goos and Hänchen also observed this effect with a beam linearly polarized at arbitrary incident azimuthal angles. See Ann. Phys. (Leipz.) 5, 251 (1949).

O. Bryngdahl, Prog. Opt. XI, 169 (1973).

1972

T. Tamir, Optik 36, 209 (1972); 37, 204 (1973); 38, 269 (1973). Both this reference and Refs. 2 and 3 above contain excellent descriptions of the physical phenomena involved. See also H. Kogelnik, in Integrated Optics, edited by T. Tamir, Topics in Applied Physics, Vol. 7 (Springer, New York, Heidelberg, Berlin, 1975), pp. 15–81.

C. Imbert, Phys. Rev. D 5, 787 (1972), and references therein; O. Costa de Beauregard, Found. Phys. 2, 111 (1972).

Costa de Beauregard and Imbert (Ref. 10) claim that both the transverse and longitudinal shifts are quantized, each having characteristic eigenvalues. The longitudinal shift should then be characterized by the principal linear polarization states, and the transverse shift, by the circular polarization states: K. W. Chiu and J. J. Quinn, [Am. J. Phys. 40, 1847 (1972)] analyze the longitudinal shift by classical electrodynamics in terms of a time delay scattering process, and also arrive at the conclusion that an incident beam of arbitrary polarization splits exactly into p and s polarization states. A similar conclusion was also reached by G. J. Troup et al., Phys. Rev. Lett. 28, 1540 (1972).

L. de Broglie and J. P. Vigier, Phys. Rev. Lett. 28, 1001 (1972).

1971

B. R. Horowitz and T. Tamir, J. Opt. Soc. Am. 61, 586 (1971).

1970

See, for example, the review by H. K. V. Lotsch, Optik 32, 116 (1970); 32, 189 (1970); 32, 299 (1971); 32, 553 (1970), and references therein.

1968

L. Agudin, Phys. Rev. 171, 1385 (1968).

1955

F. I. Fedorov, Dokil. Akad. Nauk. SSSR 105, 465 (1955).

1949

C. von Fragstein, Ann. Phys. (Leipz.) 4, 271 (1949); Remi H. Renard, J. Opt. Soc. Am. 54, 1190 (1964); J. Ricard, Nouv. Rev. Opt. Appl. 1, 5 (1970); the possibility of an energy flow into the evanescent wave was postulated several years before the experiment was performed. See J. Picht, Ann. Phys. (Leipz.) 3, 433 (1929).

1948

K. Artmann, Ann. Phys. (Leipz.) 2, 87 (1948).

Adler, L.

In the acoustical case this distance is significant [M. A. Breazeale (personal correspondence)]. See also M. A. Breazeale, L. Adler, and G. W. Scott, J. Acoust. Soc. Am. Suppl. 57, 5–38 (1975).

Agudin, L.

L. Agudin, Phys. Rev. 171, 1385 (1968).

Anibin, B.

At the completion of our work we became aware of a concurrent study of the longitudinal shift due to microwaves that was ma–25 April 1974. See J. J. Cowan and B. Anibin, J. Opt. Soc. Am. 64, 525 (1974).

Artmann, K.

K. Artmann, Ann. Phys. (Leipz.) 2, 87 (1948).

Breazeale, M. A.

In the acoustical case this distance is significant [M. A. Breazeale (personal correspondence)]. See also M. A. Breazeale, L. Adler, and G. W. Scott, J. Acoust. Soc. Am. Suppl. 57, 5–38 (1975).

Bryngdahl, O.

O. Bryngdahl, Prog. Opt. XI, 169 (1973).

Carniglia, C. K.

C. K. Carniglia (personal correspondence).

Cowan, J. J.

At the completion of our work we became aware of a concurrent study of the longitudinal shift due to microwaves that was ma–25 April 1974. See J. J. Cowan and B. Anibin, J. Opt. Soc. Am. 64, 525 (1974).

de Beauregard, Costa

Costa de Beauregard and Imbert (Ref. 10) claim that both the transverse and longitudinal shifts are quantized, each having characteristic eigenvalues. The longitudinal shift should then be characterized by the principal linear polarization states, and the transverse shift, by the circular polarization states: K. W. Chiu and J. J. Quinn, [Am. J. Phys. 40, 1847 (1972)] analyze the longitudinal shift by classical electrodynamics in terms of a time delay scattering process, and also arrive at the conclusion that an incident beam of arbitrary polarization splits exactly into p and s polarization states. A similar conclusion was also reached by G. J. Troup et al., Phys. Rev. Lett. 28, 1540 (1972).

de Beauregard, O. Costa

O. Costa de Beauregard and C. Imbert, Phys. Rev. D 7, 3555 (1973); A. Mozet, C. Imbert, and S. Huard, C. R. Acad. Sci. Paris B 273, 592 (1971). Goos and Hänchen also observed this effect with a beam linearly polarized at arbitrary incident azimuthal angles. See Ann. Phys. (Leipz.) 5, 251 (1949).

de Broglie, L.

L. de Broglie and J. P. Vigier, Phys. Rev. Lett. 28, 1001 (1972).

Fedorov, F. I.

F. I. Fedorov, Dokil. Akad. Nauk. SSSR 105, 465 (1955).

Goos, F.

F. Goos and H. Hänchen, Ann. Physik (Leipz.) 1, 333 (1947).

Hänchen, H.

F. Goos and H. Hänchen, Ann. Physik (Leipz.) 1, 333 (1947).

Horowitz, B. R.

B. R. Horowitz and T. Tamir, J. Opt. Soc. Am. 61, 586 (1971).

Imbert,

Costa de Beauregard and Imbert (Ref. 10) claim that both the transverse and longitudinal shifts are quantized, each having characteristic eigenvalues. The longitudinal shift should then be characterized by the principal linear polarization states, and the transverse shift, by the circular polarization states: K. W. Chiu and J. J. Quinn, [Am. J. Phys. 40, 1847 (1972)] analyze the longitudinal shift by classical electrodynamics in terms of a time delay scattering process, and also arrive at the conclusion that an incident beam of arbitrary polarization splits exactly into p and s polarization states. A similar conclusion was also reached by G. J. Troup et al., Phys. Rev. Lett. 28, 1540 (1972).

Imbert, C.

O. Costa de Beauregard and C. Imbert, Phys. Rev. D 7, 3555 (1973); A. Mozet, C. Imbert, and S. Huard, C. R. Acad. Sci. Paris B 273, 592 (1971). Goos and Hänchen also observed this effect with a beam linearly polarized at arbitrary incident azimuthal angles. See Ann. Phys. (Leipz.) 5, 251 (1949).

C. Imbert, Phys. Rev. D 5, 787 (1972), and references therein; O. Costa de Beauregard, Found. Phys. 2, 111 (1972).

Lotsch, H. K. V.

See, for example, the review by H. K. V. Lotsch, Optik 32, 116 (1970); 32, 189 (1970); 32, 299 (1971); 32, 553 (1970), and references therein.

McGuirk, M.

M. McGuirk, C. K. Carniglia, J. J. Cowan (unpublished).

Scott, G. W.

In the acoustical case this distance is significant [M. A. Breazeale (personal correspondence)]. See also M. A. Breazeale, L. Adler, and G. W. Scott, J. Acoust. Soc. Am. Suppl. 57, 5–38 (1975).

Tamir, T.

T. Tamir, Optik 36, 209 (1972); 37, 204 (1973); 38, 269 (1973). Both this reference and Refs. 2 and 3 above contain excellent descriptions of the physical phenomena involved. See also H. Kogelnik, in Integrated Optics, edited by T. Tamir, Topics in Applied Physics, Vol. 7 (Springer, New York, Heidelberg, Berlin, 1975), pp. 15–81.

B. R. Horowitz and T. Tamir, J. Opt. Soc. Am. 61, 586 (1971).

Vigier, J. P.

L. de Broglie and J. P. Vigier, Phys. Rev. Lett. 28, 1001 (1972).

von Fragstein, C.

C. von Fragstein, Ann. Phys. (Leipz.) 4, 271 (1949); Remi H. Renard, J. Opt. Soc. Am. 54, 1190 (1964); J. Ricard, Nouv. Rev. Opt. Appl. 1, 5 (1970); the possibility of an energy flow into the evanescent wave was postulated several years before the experiment was performed. See J. Picht, Ann. Phys. (Leipz.) 3, 433 (1929).

Wolter, H.

H. Wolter, Handbuch der Physik (Springer-Verlag, Berlin, 1956), Vol. 24, p. 472.

Other

F. Goos and H. Hänchen, Ann. Physik (Leipz.) 1, 333 (1947).

See, for example, the review by H. K. V. Lotsch, Optik 32, 116 (1970); 32, 189 (1970); 32, 299 (1971); 32, 553 (1970), and references therein.

O. Bryngdahl, Prog. Opt. XI, 169 (1973).

T. Tamir, Optik 36, 209 (1972); 37, 204 (1973); 38, 269 (1973). Both this reference and Refs. 2 and 3 above contain excellent descriptions of the physical phenomena involved. See also H. Kogelnik, in Integrated Optics, edited by T. Tamir, Topics in Applied Physics, Vol. 7 (Springer, New York, Heidelberg, Berlin, 1975), pp. 15–81.

C. von Fragstein, Ann. Phys. (Leipz.) 4, 271 (1949); Remi H. Renard, J. Opt. Soc. Am. 54, 1190 (1964); J. Ricard, Nouv. Rev. Opt. Appl. 1, 5 (1970); the possibility of an energy flow into the evanescent wave was postulated several years before the experiment was performed. See J. Picht, Ann. Phys. (Leipz.) 3, 433 (1929).

K. Artmann, Ann. Phys. (Leipz.) 2, 87 (1948).

L. Agudin, Phys. Rev. 171, 1385 (1968).

F. I. Fedorov, Dokil. Akad. Nauk. SSSR 105, 465 (1955).

C. Imbert, Phys. Rev. D 5, 787 (1972), and references therein; O. Costa de Beauregard, Found. Phys. 2, 111 (1972).

O. Costa de Beauregard and C. Imbert, Phys. Rev. D 7, 3555 (1973); A. Mozet, C. Imbert, and S. Huard, C. R. Acad. Sci. Paris B 273, 592 (1971). Goos and Hänchen also observed this effect with a beam linearly polarized at arbitrary incident azimuthal angles. See Ann. Phys. (Leipz.) 5, 251 (1949).

Costa de Beauregard and Imbert (Ref. 10) claim that both the transverse and longitudinal shifts are quantized, each having characteristic eigenvalues. The longitudinal shift should then be characterized by the principal linear polarization states, and the transverse shift, by the circular polarization states: K. W. Chiu and J. J. Quinn, [Am. J. Phys. 40, 1847 (1972)] analyze the longitudinal shift by classical electrodynamics in terms of a time delay scattering process, and also arrive at the conclusion that an incident beam of arbitrary polarization splits exactly into p and s polarization states. A similar conclusion was also reached by G. J. Troup et al., Phys. Rev. Lett. 28, 1540 (1972).

L. de Broglie and J. P. Vigier, Phys. Rev. Lett. 28, 1001 (1972).

At the completion of our work we became aware of a concurrent study of the longitudinal shift due to microwaves that was ma–25 April 1974. See J. J. Cowan and B. Anibin, J. Opt. Soc. Am. 64, 525 (1974).

H. Wolter, Handbuch der Physik (Springer-Verlag, Berlin, 1956), Vol. 24, p. 472.

B. R. Horowitz and T. Tamir, J. Opt. Soc. Am. 61, 586 (1971).

C. K. Carniglia (personal correspondence).

M. McGuirk, C. K. Carniglia, J. J. Cowan (unpublished).

In the acoustical case this distance is significant [M. A. Breazeale (personal correspondence)]. See also M. A. Breazeale, L. Adler, and G. W. Scott, J. Acoust. Soc. Am. Suppl. 57, 5–38 (1975).

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