Abstract

Asymptotic approximations are obtained for the reflected and refracted fields that result when an arbitrary monochromatic electromagnetic wave is incident on a plane interface separating two linear, homogeneous, isotropic dielectrics. The results are the first one or two terms in the asymptotic expansion of the fields valid as the point of observation moves away from the interface a distance large compared to the wavelength in any fixed direction apart from certain specified critical angles. The approximations are obtained from the exact solutions by applying the method of stationary phase extended to allow for the nonstandard form of the integrands in the integral representations of the fields. Although the method is applicable only when the medium containing the point of observation is nonabsorbing, the results probably have more general applicability.

© 1976 Optical Society of America

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References

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  1. See the extensive list of references in Ref. 2.
  2. A. Baños, Jr., Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, New York, 1966).
  3. A. Sommerfeld, Ann. Phys. (Leipzig) 28, 665 (1909).
  4. For examples, see the problems treated in Sec. 5.5 of L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N.J., 1973).
  5. G. C. Sherman, J. J. Stamnes, and É. Lalor, J. Math. Phys. 17, 760 (1976).
  6. É. Lalor and E. Wolf, J. Opt. Soc. Am. 62, 1165 (1972).
  7. E. T. Whittaker, Proc. Lond. Math. Soc. 1, 367 (1903).
  8. A. J. Devaney and G. C. Sherman, SIAM Rev. 15, 765 (1973).
  9. Reference 8 obtains the angular-spectrum representation of scalar fields radiated by sources. The modifications needed to obtain the vector representations presented here are straightforward. See Ref. 10 and É. Lalor, Ph. D. thesis (University of Rochester, 1970) (unpublished).
  10. A. J. Devaney, Ph. D. thesis (University of Rochester, 1971) (unpublished).
  11. Section 1.1 of Ref. 4.
  12. This result may be obtained by a straightforward modification of the work in Ref. 10.
  13. M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 40.

Baños, Jr., A.

A. Baños, Jr., Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, New York, 1966).

Born, M.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 40.

Devaney, A. J.

A. J. Devaney, Ph. D. thesis (University of Rochester, 1971) (unpublished).

A. J. Devaney and G. C. Sherman, SIAM Rev. 15, 765 (1973).

Felsen, L. B.

For examples, see the problems treated in Sec. 5.5 of L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N.J., 1973).

Lalor, É.

G. C. Sherman, J. J. Stamnes, and É. Lalor, J. Math. Phys. 17, 760 (1976).

Reference 8 obtains the angular-spectrum representation of scalar fields radiated by sources. The modifications needed to obtain the vector representations presented here are straightforward. See Ref. 10 and É. Lalor, Ph. D. thesis (University of Rochester, 1970) (unpublished).

É. Lalor and E. Wolf, J. Opt. Soc. Am. 62, 1165 (1972).

Marcuvitz, N.

For examples, see the problems treated in Sec. 5.5 of L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N.J., 1973).

Sherman, G. C.

A. J. Devaney and G. C. Sherman, SIAM Rev. 15, 765 (1973).

G. C. Sherman, J. J. Stamnes, and É. Lalor, J. Math. Phys. 17, 760 (1976).

Sommerfeld, A.

A. Sommerfeld, Ann. Phys. (Leipzig) 28, 665 (1909).

Stamnes, J. J.

G. C. Sherman, J. J. Stamnes, and É. Lalor, J. Math. Phys. 17, 760 (1976).

Whittaker, E. T.

E. T. Whittaker, Proc. Lond. Math. Soc. 1, 367 (1903).

Wolf, E.

É. Lalor and E. Wolf, J. Opt. Soc. Am. 62, 1165 (1972).

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 40.

Other

See the extensive list of references in Ref. 2.

A. Baños, Jr., Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, New York, 1966).

A. Sommerfeld, Ann. Phys. (Leipzig) 28, 665 (1909).

For examples, see the problems treated in Sec. 5.5 of L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N.J., 1973).

G. C. Sherman, J. J. Stamnes, and É. Lalor, J. Math. Phys. 17, 760 (1976).

É. Lalor and E. Wolf, J. Opt. Soc. Am. 62, 1165 (1972).

E. T. Whittaker, Proc. Lond. Math. Soc. 1, 367 (1903).

A. J. Devaney and G. C. Sherman, SIAM Rev. 15, 765 (1973).

Reference 8 obtains the angular-spectrum representation of scalar fields radiated by sources. The modifications needed to obtain the vector representations presented here are straightforward. See Ref. 10 and É. Lalor, Ph. D. thesis (University of Rochester, 1970) (unpublished).

A. J. Devaney, Ph. D. thesis (University of Rochester, 1971) (unpublished).

Section 1.1 of Ref. 4.

This result may be obtained by a straightforward modification of the work in Ref. 10.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 40.

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