Abstract

Several different expressions for the Goos-Hänchen shift have been given in the literature. By looking at the problem from the point of view of the conservation of energy, new and more accurate expressions can be derived. For light waves, classical optics is used; for waves associated with particles, a quantum-mechanical approach is used. A comparison is made of the results of the present work with the earlier theories.

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  1. R. W. Wood, Physical Optics (The Macmillan Company, New York, 1934), 3rd ed., p. 418.
  2. F. Goos and H. Hanchen, Ann. Physik 1, 333 (1947).
  3. F. Goos and H. Lindberg-Hänchen, Ann. Physik 5, 251 (1949).
  4. K. Artmann, Ann. Physik 2, 87 (1948).
  5. C. V. Fragstein, Ann. Physik 4, 271 (1949).
  6. J. Picht, Ann. Physik 3, 433 (1929).
  7. J. Picht, Z. Phys. 30, 905 (1929).
  8. J. Picht, Optik 12, 41 (1955).
  9. C. Schaefer and R. Pich, Ann. Physik 30, 245 (1937).
  10. K. Artmann, Ann. Physik 7, 209 (1950).
  11. K. Artmann, Ann. Physik 8, 270, 285 (1950).
  12. K. Artmann, Ann. Physik 15, 1 (1954).
  13. C. V. Fragstein and C. Schaefer, Ann. Physik 12, 84 (1953).
  14. H. Hora, Optik 17, 409 (1960).
  15. P. Dehye, Ann. Physik 30, 755 (1909).
  16. H. Arzelies, Ann. Phys. (Paris) 12/1, 5 (1946).
  17. H. Arzelies, Rev. Opt. 27, 205 (1948).
  18. Born and Wolf, Principles of Oplics (Perganmon Press, Inc., New York, 1959), pp. 46–50.
  19. The critical angle of total reflection is denoted in this paper by ic. It should he noted that German authors usually use iG and French authors use il. Sometimes the angle of incidence is designated by α instead of i.
  20. A referee has pointe(l out that the experimental optical systems used in studying the Goos-Hänchen shift may not match the ideal optics assumed in the theoretical treatment because of the difficulty of removing contaminant films and of getting a good optical homogeneity, a perfect surface polish and flatness, and parallelism of the plates used.
  21. We have used j for √-1 in order to avoid the confusion with the symbol i used for the angle of incidence.
  22. J. C. Slater, Quantum Theory of Atomnic Structure (McGraw-Hill Book Company, Inc., New York, 1960), p. 107.

Artmann, K.

K. Artmann, Ann. Physik 8, 270, 285 (1950).

K. Artmann, Ann. Physik 15, 1 (1954).

K. Artmann, Ann. Physik 7, 209 (1950).

K. Artmann, Ann. Physik 2, 87 (1948).

Arzelies, H.

H. Arzelies, Rev. Opt. 27, 205 (1948).

H. Arzelies, Ann. Phys. (Paris) 12/1, 5 (1946).

Dehye, P.

P. Dehye, Ann. Physik 30, 755 (1909).

Fragstein, C. V.

C. V. Fragstein, Ann. Physik 4, 271 (1949).

C. V. Fragstein and C. Schaefer, Ann. Physik 12, 84 (1953).

Goos, F.

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

F. Goos and H. Lindberg-Hänchen, Ann. Physik 5, 251 (1949).

Hänchen, H.

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

Hora, H.

H. Hora, Optik 17, 409 (1960).

Lindberg-Hänchen, H.

F. Goos and H. Lindberg-Hänchen, Ann. Physik 5, 251 (1949).

Pich, R.

C. Schaefer and R. Pich, Ann. Physik 30, 245 (1937).

Picht, J.

J. Picht, Z. Phys. 30, 905 (1929).

J. Picht, Optik 12, 41 (1955).

J. Picht, Ann. Physik 3, 433 (1929).

Schaefer, C.

C. V. Fragstein and C. Schaefer, Ann. Physik 12, 84 (1953).

C. Schaefer and R. Pich, Ann. Physik 30, 245 (1937).

Slater, J. C.

J. C. Slater, Quantum Theory of Atomnic Structure (McGraw-Hill Book Company, Inc., New York, 1960), p. 107.

Wood, R. W.

R. W. Wood, Physical Optics (The Macmillan Company, New York, 1934), 3rd ed., p. 418.

Other (22)

R. W. Wood, Physical Optics (The Macmillan Company, New York, 1934), 3rd ed., p. 418.

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

F. Goos and H. Lindberg-Hänchen, Ann. Physik 5, 251 (1949).

K. Artmann, Ann. Physik 2, 87 (1948).

C. V. Fragstein, Ann. Physik 4, 271 (1949).

J. Picht, Ann. Physik 3, 433 (1929).

J. Picht, Z. Phys. 30, 905 (1929).

J. Picht, Optik 12, 41 (1955).

C. Schaefer and R. Pich, Ann. Physik 30, 245 (1937).

K. Artmann, Ann. Physik 7, 209 (1950).

K. Artmann, Ann. Physik 8, 270, 285 (1950).

K. Artmann, Ann. Physik 15, 1 (1954).

C. V. Fragstein and C. Schaefer, Ann. Physik 12, 84 (1953).

H. Hora, Optik 17, 409 (1960).

P. Dehye, Ann. Physik 30, 755 (1909).

H. Arzelies, Ann. Phys. (Paris) 12/1, 5 (1946).

H. Arzelies, Rev. Opt. 27, 205 (1948).

Born and Wolf, Principles of Oplics (Perganmon Press, Inc., New York, 1959), pp. 46–50.

The critical angle of total reflection is denoted in this paper by ic. It should he noted that German authors usually use iG and French authors use il. Sometimes the angle of incidence is designated by α instead of i.

A referee has pointe(l out that the experimental optical systems used in studying the Goos-Hänchen shift may not match the ideal optics assumed in the theoretical treatment because of the difficulty of removing contaminant films and of getting a good optical homogeneity, a perfect surface polish and flatness, and parallelism of the plates used.

We have used j for √-1 in order to avoid the confusion with the symbol i used for the angle of incidence.

J. C. Slater, Quantum Theory of Atomnic Structure (McGraw-Hill Book Company, Inc., New York, 1960), p. 107.

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