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).