Abstract

The exact solution of the basic equations of molecular optics is obtained for the problem of refraction and reflection of any given monochromatic electromagnetic wave (not necessarily a plane one) that is incident on a linear, homogeneous, isotropic, nonmagnetic dielectric filling a half-space. Our analysis provides a new derivation of the laws of refraction and reflection and of Fresnel formulas and throws some light on the role played by the Ewald-Oseen extinction theorem in solving the molecular-optics equations. The methods developed in this paper may be employed in determining solutions of the molecular-optics equations for other problems that involve the interaction of electromagnetic radiation and bulk matter.

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  1. M. Born, Optik, 2nd ed. (Springer, Berlin, 1965), Ch. 7.
  2. L. Rosenfeld, Theory of Electrons (North-Holland, Amsterdam, 1951), Ch. VI.
  3. M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford and New York, 1970), Sec. 2.4.
  4. For example, N. Bloembergen and P. S. Pershan [Phys. Rev. 127, 1918 (1962), Sec. VII] applied this approach to some problems encountered in nonlinear optics. R. Bullough [J. Phys. A 1, 409 (1968); 2, 477 (1969); 3, 708 (1970); 3, 726 (1970); 3, 751 (1970)] showed that the extinction theorem plays an important role in a variety of problems of many-body optics. J. J. Sein [Ref. 9 below and Phys. Letters 3, 141 (1970)] showed that a certain generalization of the classical extinction theorem is of considerable importance in the theory of spatial dispersion and the theory of excitons. In this connection, see also a recent paper by G. S. Agarwal, D. N. Pattanayak, and E. Wolf, Opt. Commun. 4, 260 (1972).
  5. P. P. Ewald, Ann. Phys. 49, 1 (1916).
  6. R. Lundblad, Untersuchungen über die Optik der dispergierenden Medien (Univ. Arsskrift, Uppsala, 1920).
  7. W. Boethe, Ann. Phys. 64, 693 (1921).
  8. C. G. Darwin, Trans. Cambridge Phil. Soc. 23, 137 (1924).
  9. J. J. Sein, An Integral-Equation Formulation of the Optics of Spatially Dispersive Media (Ph.D. dissertation, New York University, 1969).
  10. É. Lalor and E. Wolf, Phys. Rev. Letters 26, 1274 (1971).
  11. From the basic equation of molecular optics, it may actually be shown that the transversality condition (1.6) must hold for fields of all frequencies ω that are not too close to a resonance frequency of the medium.
  12. The significance of the Ewald-Oseen extinction theorem, expressed by Eq. (1.8), appears to have been largely misunderstood. It is frequently asserted that the theorem implies that the incident field is extinguished everywhere inside the medium by the dipoles situated on its boundary. It is also sometimes asserted that Eq. (1.8) is an integral equation for the field on the boundary S. Neither of these two statements is correct. An excellent discussion of the Ewald-Oseen theorem is given by Sein (Ref. 9, Appendix III).
  13. For a brief discussion of the angular-spectrum representation of wave fields, see, for example, C. J. Bouwkamp, Rept. Progr. Phys. 17, 41 (1954); J. R. Shewell and E. Wolf, J. Opt. Soc. Am. 58, 1596 (1968); or J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Sec. 3.7.
  14. H. Weyl, Ann. Phys. 60, 481 (1919).
  15. A. Banos, Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, Oxford, 1966), Eq. (2.19).

Banos, A.

A. Banos, Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, Oxford, 1966), Eq. (2.19).

Bloembergen, N.

For example, N. Bloembergen and P. S. Pershan [Phys. Rev. 127, 1918 (1962), Sec. VII] applied this approach to some problems encountered in nonlinear optics. R. Bullough [J. Phys. A 1, 409 (1968); 2, 477 (1969); 3, 708 (1970); 3, 726 (1970); 3, 751 (1970)] showed that the extinction theorem plays an important role in a variety of problems of many-body optics. J. J. Sein [Ref. 9 below and Phys. Letters 3, 141 (1970)] showed that a certain generalization of the classical extinction theorem is of considerable importance in the theory of spatial dispersion and the theory of excitons. In this connection, see also a recent paper by G. S. Agarwal, D. N. Pattanayak, and E. Wolf, Opt. Commun. 4, 260 (1972).

Boethe, W.

W. Boethe, Ann. Phys. 64, 693 (1921).

Born, M.

M. Born, Optik, 2nd ed. (Springer, Berlin, 1965), Ch. 7.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford and New York, 1970), Sec. 2.4.

Bouwkamp, C. J.

For a brief discussion of the angular-spectrum representation of wave fields, see, for example, C. J. Bouwkamp, Rept. Progr. Phys. 17, 41 (1954); J. R. Shewell and E. Wolf, J. Opt. Soc. Am. 58, 1596 (1968); or J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Sec. 3.7.

Darwin, C. G.

C. G. Darwin, Trans. Cambridge Phil. Soc. 23, 137 (1924).

Ewald, P. P.

P. P. Ewald, Ann. Phys. 49, 1 (1916).

Lalor, É.

É. Lalor and E. Wolf, Phys. Rev. Letters 26, 1274 (1971).

Lundblad, R.

R. Lundblad, Untersuchungen über die Optik der dispergierenden Medien (Univ. Arsskrift, Uppsala, 1920).

Pershan, P. S.

For example, N. Bloembergen and P. S. Pershan [Phys. Rev. 127, 1918 (1962), Sec. VII] applied this approach to some problems encountered in nonlinear optics. R. Bullough [J. Phys. A 1, 409 (1968); 2, 477 (1969); 3, 708 (1970); 3, 726 (1970); 3, 751 (1970)] showed that the extinction theorem plays an important role in a variety of problems of many-body optics. J. J. Sein [Ref. 9 below and Phys. Letters 3, 141 (1970)] showed that a certain generalization of the classical extinction theorem is of considerable importance in the theory of spatial dispersion and the theory of excitons. In this connection, see also a recent paper by G. S. Agarwal, D. N. Pattanayak, and E. Wolf, Opt. Commun. 4, 260 (1972).

Rosenfeld, L.

L. Rosenfeld, Theory of Electrons (North-Holland, Amsterdam, 1951), Ch. VI.

Sein, J. J.

J. J. Sein, An Integral-Equation Formulation of the Optics of Spatially Dispersive Media (Ph.D. dissertation, New York University, 1969).

Weyl, H.

H. Weyl, Ann. Phys. 60, 481 (1919).

Wolf, E.

É. Lalor and E. Wolf, Phys. Rev. Letters 26, 1274 (1971).

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford and New York, 1970), Sec. 2.4.

Other (15)

M. Born, Optik, 2nd ed. (Springer, Berlin, 1965), Ch. 7.

L. Rosenfeld, Theory of Electrons (North-Holland, Amsterdam, 1951), Ch. VI.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford and New York, 1970), Sec. 2.4.

For example, N. Bloembergen and P. S. Pershan [Phys. Rev. 127, 1918 (1962), Sec. VII] applied this approach to some problems encountered in nonlinear optics. R. Bullough [J. Phys. A 1, 409 (1968); 2, 477 (1969); 3, 708 (1970); 3, 726 (1970); 3, 751 (1970)] showed that the extinction theorem plays an important role in a variety of problems of many-body optics. J. J. Sein [Ref. 9 below and Phys. Letters 3, 141 (1970)] showed that a certain generalization of the classical extinction theorem is of considerable importance in the theory of spatial dispersion and the theory of excitons. In this connection, see also a recent paper by G. S. Agarwal, D. N. Pattanayak, and E. Wolf, Opt. Commun. 4, 260 (1972).

P. P. Ewald, Ann. Phys. 49, 1 (1916).

R. Lundblad, Untersuchungen über die Optik der dispergierenden Medien (Univ. Arsskrift, Uppsala, 1920).

W. Boethe, Ann. Phys. 64, 693 (1921).

C. G. Darwin, Trans. Cambridge Phil. Soc. 23, 137 (1924).

J. J. Sein, An Integral-Equation Formulation of the Optics of Spatially Dispersive Media (Ph.D. dissertation, New York University, 1969).

É. Lalor and E. Wolf, Phys. Rev. Letters 26, 1274 (1971).

From the basic equation of molecular optics, it may actually be shown that the transversality condition (1.6) must hold for fields of all frequencies ω that are not too close to a resonance frequency of the medium.

The significance of the Ewald-Oseen extinction theorem, expressed by Eq. (1.8), appears to have been largely misunderstood. It is frequently asserted that the theorem implies that the incident field is extinguished everywhere inside the medium by the dipoles situated on its boundary. It is also sometimes asserted that Eq. (1.8) is an integral equation for the field on the boundary S. Neither of these two statements is correct. An excellent discussion of the Ewald-Oseen theorem is given by Sein (Ref. 9, Appendix III).

For a brief discussion of the angular-spectrum representation of wave fields, see, for example, C. J. Bouwkamp, Rept. Progr. Phys. 17, 41 (1954); J. R. Shewell and E. Wolf, J. Opt. Soc. Am. 58, 1596 (1968); or J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Sec. 3.7.

H. Weyl, Ann. Phys. 60, 481 (1919).

A. Banos, Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, Oxford, 1966), Eq. (2.19).

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