Abstract

Many planar structures, including multilayered media and periodic configurations of the optical-grating type, are capable of supporting an electromagnetic field of the leaky-wave form. By exciting this field, an incident light beam transfers a portion of its energy into the leaky-wave structure; after being guided longitudinally for a certain distance along the structure, this energy is leaked back to form part of the reflected beam. Owing to the longitudinal energy flow, the complete reflected beam exhibits a lateral displacement that appears either as a forward beam shift, similar to the Goos-Hänchen effect along a single dielectric interface, or as a backward beam shift, which has not been identified before. By deriving a general expression for the field excited by a gaussian light beam incident upon a leaky-wave structure, we find that the reflected beam may undergo a lateral displacement of the order of the beam width; the magnitude of this beam shift may therefore be much larger than the maximum shift produced at a single dielectric boundary. In the case of periodic structures, all of the higher-order diffracted beams are shifted laterally whenever the specularly reflected beam is displaced. The dependence of the lateral displacement on the beam width, the angle of incidence, and the leakage distance is examined in detail and the relevance of the beam shift to optical-beam couplers is discussed.

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  1. H. K. V. Lotsch, Optik 32, 116, 189, 299, 553 (1970/1971).
  2. B. R. Horowitz and T. Tamir, J. Opt. Soc. Am. 61, 586 (1971).
  3. A. Schoch, Nuovo Cimento (Suppl.) 7, (9), 302 (1950).
  4. A. Schoch, Acustica 2, 1 (1952).
  5. Reference 1, Sec. 6, p. 554.
  6. J. E. Midwinter and F. Zernike, Appl. Phys. Letters 16, 198 (1970).
  7. H. K. V. Lotsch, J. Opt. Soc. Am. 58, 551 (1968).
  8. L. M. Brekhovskikh, Waves in Layered Media (Academic, New York, 1960), Ch. 22, pp. 281–292.
  9. T. Tamir and A. A. Oliner, J. Opt. Soc. Am. 59, 942 (1969).
  10. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), Sec. 9–13, pp. 516–520.
  11. R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, New York, 1960), Ch. 11, pp. 453–506.
  12. T. Tamir and A. A. Oliner, Proc. IEE 110, 310 (1963).
  13. Antenna Theory, edited by R. E. Collin and F. J. Zucker (McGraw-Hill, New York, 1969), Chs. 19, 20, pp. 151–297.
  14. J. H. Harris, R. Shubert, and J. N. Polky, J. Opt. Soc. Am. 60, 1007 (1970).
  15. R. Ulrich, J. Opt. Soc. Am. 60, 1337 (1970).
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  17. J. J. Burke, Appl. Opt. 9, 2444 (1970).
  18. T. Tamir and A. A. Oliner, Proc. IEEE 51, 317 (1963).
  19. M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, Appl. Phys. Letters 16, 523 (1970).
  20. H. Kogelnik and T. P. Sosnowski, Bell System Tech. J. 49, 1602 (1970).
  21. A. Hessel and A. A. Oliner, Appl. Opt. 4, 1275 (1965).
  22. Reference 8, Sec. 8, pp. 100–117.
  23. Reference 8, Sec. 5, p. 44.
  24. Reference 8, Sec. 20, p. 261.
  25. Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover, New York, 1965), Ch. 7, p. 297.
  26. T. Tamir and A. A. Oliner, Proc. IEE 110, 325 (1963).
  27. L. V. Iogansen, Sov. Phys.-Tech. Phys. 7, 295 (1962); 8, 985 (1964); 11, 1529 (1967).

Brekhovskikh, L. M.

L. M. Brekhovskikh, Waves in Layered Media (Academic, New York, 1960), Ch. 22, pp. 281–292.

Burke, J. J.

J. J. Burke, Appl. Opt. 9, 2444 (1970).

Collin, R. E.

R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, New York, 1960), Ch. 11, pp. 453–506.

Dakss, M. L.

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, Appl. Phys. Letters 16, 523 (1970).

Harris, J. H.

J. H. Harris, R. Shubert, and J. N. Polky, J. Opt. Soc. Am. 60, 1007 (1970).

Heidrich, P. F.

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, Appl. Phys. Letters 16, 523 (1970).

Hessel, A.

A. Hessel and A. A. Oliner, Appl. Opt. 4, 1275 (1965).

Horowitz, B. R.

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

Iogansen, L. V.

L. V. Iogansen, Sov. Phys.-Tech. Phys. 7, 295 (1962); 8, 985 (1964); 11, 1529 (1967).

Kogelnik, H.

H. Kogelnik and T. P. Sosnowski, Bell System Tech. J. 49, 1602 (1970).

Kuhn, L.

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, Appl. Phys. Letters 16, 523 (1970).

Lotsch, H. K. V.

H. K. V. Lotsch, Optik 32, 116, 189, 299, 553 (1970/1971).

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

Midwinter, J. E.

J. E. Midwinter and F. Zernike, Appl. Phys. Letters 16, 198 (1970).

J. E. Midwinter, IEEE J. QE-6, 583 (1970).

Oliner, A. A.

T. Tamir and A. A. Oliner, Proc. IEE 110, 310 (1963).

A. Hessel and A. A. Oliner, Appl. Opt. 4, 1275 (1965).

T. Tamir and A. A. Oliner, Proc. IEEE 51, 317 (1963).

T. Tamir and A. A. Oliner, Proc. IEE 110, 325 (1963).

T. Tamir and A. A. Oliner, J. Opt. Soc. Am. 59, 942 (1969).

Polky, J. N.

J. H. Harris, R. Shubert, and J. N. Polky, J. Opt. Soc. Am. 60, 1007 (1970).

Schoch, A.

A. Schoch, Nuovo Cimento (Suppl.) 7, (9), 302 (1950).

A. Schoch, Acustica 2, 1 (1952).

Scott, B. A.

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, Appl. Phys. Letters 16, 523 (1970).

Shubert, R.

J. H. Harris, R. Shubert, and J. N. Polky, J. Opt. Soc. Am. 60, 1007 (1970).

Sosnowski, T. P.

H. Kogelnik and T. P. Sosnowski, Bell System Tech. J. 49, 1602 (1970).

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), Sec. 9–13, pp. 516–520.

Tamir, T.

T. Tamir and A. A. Oliner, J. Opt. Soc. Am. 59, 942 (1969).

T. Tamir and A. A. Oliner, Proc. IEE 110, 310 (1963).

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

T. Tamir and A. A. Oliner, Proc. IEE 110, 325 (1963).

T. Tamir and A. A. Oliner, Proc. IEEE 51, 317 (1963).

Ulrich, R.

R. Ulrich, J. Opt. Soc. Am. 60, 1337 (1970).

Zernike, F.

J. E. Midwinter and F. Zernike, Appl. Phys. Letters 16, 198 (1970).

Other (27)

H. K. V. Lotsch, Optik 32, 116, 189, 299, 553 (1970/1971).

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

A. Schoch, Nuovo Cimento (Suppl.) 7, (9), 302 (1950).

A. Schoch, Acustica 2, 1 (1952).

Reference 1, Sec. 6, p. 554.

J. E. Midwinter and F. Zernike, Appl. Phys. Letters 16, 198 (1970).

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

L. M. Brekhovskikh, Waves in Layered Media (Academic, New York, 1960), Ch. 22, pp. 281–292.

T. Tamir and A. A. Oliner, J. Opt. Soc. Am. 59, 942 (1969).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), Sec. 9–13, pp. 516–520.

R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, New York, 1960), Ch. 11, pp. 453–506.

T. Tamir and A. A. Oliner, Proc. IEE 110, 310 (1963).

Antenna Theory, edited by R. E. Collin and F. J. Zucker (McGraw-Hill, New York, 1969), Chs. 19, 20, pp. 151–297.

J. H. Harris, R. Shubert, and J. N. Polky, J. Opt. Soc. Am. 60, 1007 (1970).

R. Ulrich, J. Opt. Soc. Am. 60, 1337 (1970).

J. E. Midwinter, IEEE J. QE-6, 583 (1970).

J. J. Burke, Appl. Opt. 9, 2444 (1970).

T. Tamir and A. A. Oliner, Proc. IEEE 51, 317 (1963).

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, Appl. Phys. Letters 16, 523 (1970).

H. Kogelnik and T. P. Sosnowski, Bell System Tech. J. 49, 1602 (1970).

A. Hessel and A. A. Oliner, Appl. Opt. 4, 1275 (1965).

Reference 8, Sec. 8, pp. 100–117.

Reference 8, Sec. 5, p. 44.

Reference 8, Sec. 20, p. 261.

Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover, New York, 1965), Ch. 7, p. 297.

T. Tamir and A. A. Oliner, Proc. IEE 110, 325 (1963).

L. V. Iogansen, Sov. Phys.-Tech. Phys. 7, 295 (1962); 8, 985 (1964); 11, 1529 (1967).

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