Microscopic approach to reflection, transmission, and the Ewald-Oseen extinction theorem

American Journal of Physics

Volumn 64, Issue 8, 1996, Pages 986-995

  Fearn, Heidi ^a,b   James, Daniel F V ^a   Milonni, Peter W ^a  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b CALIFORNIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030523855     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.18315     Document Type: Article

References (32)

1. P. P. Ewald, On the Foundations of Crystal Optics (Air Force Cambridge Research Laboratories Report AFCRL-70-0580, Cambridge, MA, 1970). This is a translation by L. M. Hollingsworth of Ewald's 1912 Dissertation at the University of Munich.
2. C. W. Oseen, "Über die Wechselwirkung zwischen zwei elektischen Dipolen der Polarisationsebene in Kristallen und Flüssigkeiten," Ann. Phys. 48, 1-56 (1915).
3. L. Rosenfeld, Theory of Electrons (North-Holland, Amsterdam, 1951), p. 105.
4. M. Lax, "Multiple Scattering of Waves. II. The Effective Field in Dense Systems," Phys. Rev. 85, 621-629 (1952).
5. M. Born and E. Wolf, Principles of Optics, (Pergamon, Oxford, 1970), 4th ed., p. 102. Compare with the discussion in the fifth edition (1975), p. 102.
6. V. Weisskopf, "How light interacts with matter," in Lasers and Light, Readings from Scientific American (W. H. Freeman, San Francisco, 1969), p. 21.
7. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), 2nd ed. p. 513.
8. J. J. Sein, "An integral-equation formulation of the optics of spatially dispersive media," Ph.D. Thesis, Department of Physics, New York University, 1969; "A Note on the Ewald-Oseen Extinction Theorem," Opt. Commun. 2, 170-172 (1970).
9. J. J. Sein, "An integral-equation formulation of the optics of spatially dispersive media," Ph.D. Thesis, Department of Physics, New York University, 1969; "A Note on the Ewald-Oseen Extinction Theorem," Opt. Commun. 2, 170-172 (1970).
10. D. N. Pattanayak and E. Wolf, "General form and a new interpretation of the Ewald-Oseen extinction theorem," Opt. Commun. 6, 217-220 (1972).
11. See also E. Wolf, "Electromagnetic Scattering as a Non-Local Boundary Value Problem," in Symposia Mathematica (Academic, London and New York, 1976), Vol. XVIII, pp. 333-352.
12. J. Van Kranendonk and J. E. Sipe, "Foundations of the macroscopic electromagnetic theory of dielectric media," in Progress in Optics, edited by E. Wolf (North-Holland, Amsterdam, 1977), Vol. XV, p. 321.
13. J. M. Stone, Radiation and Optics (McGraw-Hill, New York, 1963), p. 340.
14. E. Wolf, "A generalized extinction theorem and its role in scattering theory," in Coherence and Quantum Optics, edited by L. Mandel and E. Wolf (Plenum, New York, 1973), pp. 339-357.
15. The analog of the extinction theorem in potential scattering problems in quantum mechanics has been discussed in detail in the following papers: D. N. Pattanayak and E. Wolf, "Scattering states and bound states as solutions of the Schrödinger equation with nonlocal boundary conditions," Phys. Rev. D 13, 913-923 (1976)
16. and D. N. Pattanayak and E. Wolf, "Resonance states as solutions of the Schrödinger equation with a nonlocal boundary condition," Phys. Rev. D 13, 2287-2290 (1976).
17. See, for instance, Ref. 7, pp. 147-148.
18. See, for instance, Ref. 7, pp. 153-155.
19. For a related discussion see L. L. Foldy, "The multiple scattering of waves," Phys. Rev. 67, 107-119 (1945).
20. E. Lalor and E. Wolf, "Exact solution of the equations of molecular optics for reflection and refraction of an electromagnetic wave on a semi-infinite dielectric," J. Opt. Soc. Am. 62, 1165-1174 (1972).
21. See, for instance, Ref. 7, p. 395.
22. See, for instance, R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading, MA, 1963), Vol. I, p. 30-11.
23. We have not included explicitly any local field correction. As in the example of Sec. II, a local field correction does not affect the final results.
24. We assume ∇·E≅0, which is consistent with the assumption made later that E can be approximated by a plane wave.
25. See, for instance, P. W. Milonni and J. H. Eberly, Lasers (Wiley, New York, 1988), Sec. 14.4.
26. See, for instance, L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon, Oxford, 1977), 3rd ed. Sec. 131.
27. A somewhat similar approach was used to explain the refractive index of a dielectric in the following paper: M. B. James and D. J. Griffiths, "Why the speed of light is reduced in a transparent medium," Am. J. Phys. 60, 309-313 (1992).
28. See Ref. 19, p. 31-2.
29. E. P. Wigner, "Lower limit for the energy derivative of the scattering phase shift," Phys. Rev. 98, 145-147 (1955).
30. F. Goos and H. Hänchen, "Ein neuer und fundamentales Versuch zur total reflexion," Ann. Phys. 6, 333-345 (1947); 251-252 (1949).
31. F. Goos and H. Hänchen, "Ein neuer und fundamentales Versuch zur total reflexion," Ann. Phys. 6, 333-345 (1947); 251-252 (1949).
32. M. Sargent, M. O. Scully, and W. E. Lamb, Jr., Laser Physics (Addison-Wesley, Reading, MA, 1977).