Abstract

The diffraction effects produced by light incident upon an interface at the critical angle of total reflection are examined for the purpose of explaining the weak illumination recently detected by Acloque and Guillemet, and by Osterberg and Smith. This illumination accompanies the rays reflected from the interface, but it occurs in a manner that cannot be interpreted in conventional geometric-optical terms. We show that a rigorous but simple approach that accounts for first-order-diffraction effects is capable of explaining the experimental results in terms of a lateral wave which in fact may provide the dominant field under certain circumstances. In particular, we examine the special case of a collimated light beam and show that the lateral wave is strongest, and accounts for the observed illumination, when the beam is incident at the critical angle of total reflection. The quasi-optical properties of this wave are emphasized and they are shown to provide straightforward physical interpretations for the various features of the weak-illumination field.

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  1. H. K. V. Lotsch, J. Opt. Soc. Am. 58, 551 (1968).
  2. F. Goos and H. Hänchen, Ann. Physik (6) 1, 333 (1947).
  3. H. Maecker, Ann. Physilk (6) 4, 409 (1949).
  4. H. Ott, Ann. Physik (6) 4, 432 (1949).
  5. P. Acloque and C. Guillemet, Compt. Rend. 250, 4328 (1960).
  6. H. Osterberg and L. W. Smith, J. Opt. Soc. Am. 54, 1073 (1964).
  7. See, for instance: C. B. Officer, Introduction to the Theory of Sound Transmission (McGraw-Hill Book Co., New York, 1958), 192–201; W. N. Ewing, W. S. Jardetzky, and F. Press, Elastic Waves in Layered Media (McGraw-Hill Book Co., New York, 1957), pp. 90–115.
  8. L. B. Felsen, in Electromagnetic Theory, J. Brown, Ed. (Pergamon Press, Oxford, 1967), p. 11.
  9. D. Staiman and T. Tamir, Proc. IEE (London) 113, 1299 (1966).
  10. L. M. Brekhovskikh, Waves in Layered Media (Academic Press Inc., New York, 1960), Ch. IV, p. 234.
  11. T. Tamir, IEEE Trans. Antennas Propagation AP-1S, 806 (1967).
  12. T. Tamir and L. B. Felsen, IEEE Trans. Antennas Propagation AP-13, 410 (1965).
  13. Because L appears as a factor in the denominator of Eq. (5), EIat becomes unbounded as L→0. However, Eq. (5) is not valid for small L and must be replaced10 by a different expression that yields a finite value of EInt as L→0. Such a case is excluded in the present discussion, since we assume that L is a large quantity.
  14. R. E. Collin, Field Theory of Guided Waves (McGraw—Hill Book Co., New York, 1960), Ch. 11, p. 453.
  15. T. Tamir and A. A. Oliner, Proc. 1EE (London) 110, 310 (1963).
  16. H. M. Barlow and A. L. Cullen, Proc. IEE (London) 100 (Part III), 329 (1953).
  17. B. J. Woodward and H. C. Bryant, J. Opt. Soc. Am. 57, 430 (1967).
  18. H. Osterberg and L. W. Smith, J. Opt. Soc. Am. 54, 1078 (1967).

1968

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

1967

T. Tamir, IEEE Trans. Antennas Propagation AP-1S, 806 (1967).

B. J. Woodward and H. C. Bryant, J. Opt. Soc. Am. 57, 430 (1967).

H. Osterberg and L. W. Smith, J. Opt. Soc. Am. 54, 1078 (1967).

1966

D. Staiman and T. Tamir, Proc. IEE (London) 113, 1299 (1966).

1965

T. Tamir and L. B. Felsen, IEEE Trans. Antennas Propagation AP-13, 410 (1965).

1964

H. Osterberg and L. W. Smith, J. Opt. Soc. Am. 54, 1073 (1964).

1963

T. Tamir and A. A. Oliner, Proc. 1EE (London) 110, 310 (1963).

1960

P. Acloque and C. Guillemet, Compt. Rend. 250, 4328 (1960).

1953

H. M. Barlow and A. L. Cullen, Proc. IEE (London) 100 (Part III), 329 (1953).

1949

H. Maecker, Ann. Physilk (6) 4, 409 (1949).

H. Ott, Ann. Physik (6) 4, 432 (1949).

1947

F. Goos and H. Hänchen, Ann. Physik (6) 1, 333 (1947).

Acloque, P.

P. Acloque and C. Guillemet, Compt. Rend. 250, 4328 (1960).

Barlow, H. M.

H. M. Barlow and A. L. Cullen, Proc. IEE (London) 100 (Part III), 329 (1953).

Brekhovskikh, L. M.

L. M. Brekhovskikh, Waves in Layered Media (Academic Press Inc., New York, 1960), Ch. IV, p. 234.

Bryant, H. C.

B. J. Woodward and H. C. Bryant, J. Opt. Soc. Am. 57, 430 (1967).

Collin, R. E.

R. E. Collin, Field Theory of Guided Waves (McGraw—Hill Book Co., New York, 1960), Ch. 11, p. 453.

Cullen, A. L.

H. M. Barlow and A. L. Cullen, Proc. IEE (London) 100 (Part III), 329 (1953).

Felsen, L. B.

T. Tamir and L. B. Felsen, IEEE Trans. Antennas Propagation AP-13, 410 (1965).

L. B. Felsen, in Electromagnetic Theory, J. Brown, Ed. (Pergamon Press, Oxford, 1967), p. 11.

Goos, F.

F. Goos and H. Hänchen, Ann. Physik (6) 1, 333 (1947).

Guillemet, C.

P. Acloque and C. Guillemet, Compt. Rend. 250, 4328 (1960).

Hänchen, H.

F. Goos and H. Hänchen, Ann. Physik (6) 1, 333 (1947).

Lotsch, H. K. V.

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

Maecker, H.

H. Maecker, Ann. Physilk (6) 4, 409 (1949).

Officer, C. B.

See, for instance: C. B. Officer, Introduction to the Theory of Sound Transmission (McGraw-Hill Book Co., New York, 1958), 192–201; W. N. Ewing, W. S. Jardetzky, and F. Press, Elastic Waves in Layered Media (McGraw-Hill Book Co., New York, 1957), pp. 90–115.

Oliner, A. A.

T. Tamir and A. A. Oliner, Proc. 1EE (London) 110, 310 (1963).

Osterberg, H.

H. Osterberg and L. W. Smith, J. Opt. Soc. Am. 54, 1078 (1967).

H. Osterberg and L. W. Smith, J. Opt. Soc. Am. 54, 1073 (1964).

Ott, H.

H. Ott, Ann. Physik (6) 4, 432 (1949).

Smith, L. W.

H. Osterberg and L. W. Smith, J. Opt. Soc. Am. 54, 1078 (1967).

H. Osterberg and L. W. Smith, J. Opt. Soc. Am. 54, 1073 (1964).

Staiman, D.

D. Staiman and T. Tamir, Proc. IEE (London) 113, 1299 (1966).

Tamir, T.

T. Tamir, IEEE Trans. Antennas Propagation AP-1S, 806 (1967).

D. Staiman and T. Tamir, Proc. IEE (London) 113, 1299 (1966).

T. Tamir and L. B. Felsen, IEEE Trans. Antennas Propagation AP-13, 410 (1965).

T. Tamir and A. A. Oliner, Proc. 1EE (London) 110, 310 (1963).

Woodward, B. J.

B. J. Woodward and H. C. Bryant, J. Opt. Soc. Am. 57, 430 (1967).

Other

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

F. Goos and H. Hänchen, Ann. Physik (6) 1, 333 (1947).

H. Maecker, Ann. Physilk (6) 4, 409 (1949).

H. Ott, Ann. Physik (6) 4, 432 (1949).

P. Acloque and C. Guillemet, Compt. Rend. 250, 4328 (1960).

H. Osterberg and L. W. Smith, J. Opt. Soc. Am. 54, 1073 (1964).

See, for instance: C. B. Officer, Introduction to the Theory of Sound Transmission (McGraw-Hill Book Co., New York, 1958), 192–201; W. N. Ewing, W. S. Jardetzky, and F. Press, Elastic Waves in Layered Media (McGraw-Hill Book Co., New York, 1957), pp. 90–115.

L. B. Felsen, in Electromagnetic Theory, J. Brown, Ed. (Pergamon Press, Oxford, 1967), p. 11.

D. Staiman and T. Tamir, Proc. IEE (London) 113, 1299 (1966).

L. M. Brekhovskikh, Waves in Layered Media (Academic Press Inc., New York, 1960), Ch. IV, p. 234.

T. Tamir, IEEE Trans. Antennas Propagation AP-1S, 806 (1967).

T. Tamir and L. B. Felsen, IEEE Trans. Antennas Propagation AP-13, 410 (1965).

Because L appears as a factor in the denominator of Eq. (5), EIat becomes unbounded as L→0. However, Eq. (5) is not valid for small L and must be replaced10 by a different expression that yields a finite value of EInt as L→0. Such a case is excluded in the present discussion, since we assume that L is a large quantity.

R. E. Collin, Field Theory of Guided Waves (McGraw—Hill Book Co., New York, 1960), Ch. 11, p. 453.

T. Tamir and A. A. Oliner, Proc. 1EE (London) 110, 310 (1963).

H. M. Barlow and A. L. Cullen, Proc. IEE (London) 100 (Part III), 329 (1953).

B. J. Woodward and H. C. Bryant, J. Opt. Soc. Am. 57, 430 (1967).

H. Osterberg and L. W. Smith, J. Opt. Soc. Am. 54, 1078 (1967).

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