Abstract

The reflection of a beam of light at a plane interface is treated using the angular spectrum representation. The Goos-Hänchen shift is found to be proportional to the first derivative of the phase of the reflectance. The second derivative of the phase gives rise to a shift of the reflected beam along its direction of propagation. This new shift, called a focal shift, is different from the extra propagation distance of the beam predicted on the basis of a ray model for total internal reflection. Expressions are presented for the Goos-Hänchen and focal shifts for both <i>s</i> and <i>p</i> polarization.

© 1977 Optical Society of America

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  1. F. Goos and H. Hänchen, Ann. Phys. (Leipz.) 1, 333 (1947).
  2. K. Artmann, Ann. Physik (6) 2, 87 (1948).
  3. B. R. Horowitz and T. Tamir, J. Opt. Soc. Am. 61, 586 (1971).
  4. M. McGuirk and C. K. Carniglia, J. Opt. Soc. Am. 65, 1168 (1975).
  5. N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, New York, 1972), p. 74.
  6. H. Kogelnik and H. P.. Weber, J. Opt. Soc. Am. 64, 174 (1974).
  7. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 48 ff.
  8. E. Lalor, J. Opt. Soc. Am. 58, 1235 (1968).
  9. W. H. Carter, Opt. Acta 21, 871 (1974).
  10. M. Green, P. Kirkby, and R. S. Timsit, Phys. Lett. A 45, 259 (1973).
  11. H. K. V. Lotsch, J. Opt. Soc. Am. 58, 551 (1968).
  12. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 49.
  13. R. H. Renard, J. Opt. Soc. Am. 54, 1190 (1964).
  14. I. Newton, Optiks (Dover, New York, 1952).

Artmann, K.

K. Artmann, Ann. Physik (6) 2, 87 (1948).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 49.

Burke, J. J.

N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, New York, 1972), p. 74.

Carniglia, C. K.

M. McGuirk and C. K. Carniglia, J. Opt. Soc. Am. 65, 1168 (1975).

Carter, W. H.

W. H. Carter, Opt. Acta 21, 871 (1974).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 48 ff.

Goos, F.

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

Green, M.

M. Green, P. Kirkby, and R. S. Timsit, Phys. Lett. A 45, 259 (1973).

Hänchen, H.

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

Horowitz, B. R.

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

Kapany, N. S.

N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, New York, 1972), p. 74.

Kirkby, P.

M. Green, P. Kirkby, and R. S. Timsit, Phys. Lett. A 45, 259 (1973).

Kogelnik, H.

H. Kogelnik and H. P.. Weber, J. Opt. Soc. Am. 64, 174 (1974).

Lalor, E.

E. Lalor, J. Opt. Soc. Am. 58, 1235 (1968).

Lotsch, H. K. V.

H. K. V. Lotsch, J. Opt. Soc. Am. 58, 551 (1968).

McGuirk, M.

M. McGuirk and C. K. Carniglia, J. Opt. Soc. Am. 65, 1168 (1975).

Newton, I.

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

Renard, R. H.

R. H. Renard, J. Opt. Soc. Am. 54, 1190 (1964).

Tamir, T.

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

Timsit, R. S.

M. Green, P. Kirkby, and R. S. Timsit, Phys. Lett. A 45, 259 (1973).

Weber, H. P..

H. Kogelnik and H. P.. Weber, J. Opt. Soc. Am. 64, 174 (1974).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 49.

Other

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

K. Artmann, Ann. Physik (6) 2, 87 (1948).

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

M. McGuirk and C. K. Carniglia, J. Opt. Soc. Am. 65, 1168 (1975).

N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, New York, 1972), p. 74.

H. Kogelnik and H. P.. Weber, J. Opt. Soc. Am. 64, 174 (1974).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 48 ff.

E. Lalor, J. Opt. Soc. Am. 58, 1235 (1968).

W. H. Carter, Opt. Acta 21, 871 (1974).

M. Green, P. Kirkby, and R. S. Timsit, Phys. Lett. A 45, 259 (1973).

H. K. V. Lotsch, J. Opt. Soc. Am. 58, 551 (1968).

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 49.

R. H. Renard, J. Opt. Soc. Am. 54, 1190 (1964).

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

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