Why is the propagation velocity of a photon in a transparent medium reduced?

American Journal of Physics

Volumn 65, Issue 12, 1997, Pages 1156-1164

  De Grooth, Bart G ^a  

^a UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031477583     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.18754     Document Type: Article

References (23)

1. Steve Blau and Brad Halfpap, "Question #21. Snell's law in quantum mechanics," Am. J. Phys. 63(7), 583 (1995).
2. Richard P. Feynman, QED, the Strange Theory of Light and Matter (Princeton U.P., Princeton, 1985).
3. Richard P. Feynman, The Feynman Lectures on Physics (Addison-Wesley, Reading, MA, 1963), Part I, Sec. 26-6.
4. John A. Wheeler, "The young Feynman," Phys. Today 42(2), 24-28 (1989).
5. Mary B. James and David J. Griffiths, "Why the speed of light is reduced in a transparent medium," Am. J. Phys. 60(4), 309-313 (1992).
6. Richard P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965). For further interpretation of amplitudes see also the first chapters in the Feynman lectures Part III (Ref. 3).
7. Eugene Hecht, Optics (Addison-Wesley, Reading, MA, 1987), 2nd ed.
8. John David Jackson, Classical Electrodynamics (Wiley, New York, 1975), 2nd ed.
9. Technically, some of the integration regions in Eq. (14)-(19) violate the condition x-x′ ≫ λ needed for the evaluation of Eq. (A2) and therefore (A3) given in the Appendix to be valid. In view of the alternative approach indicated in the Appendix, however, use of Eq. (A3) seems to be justified for all values of x-x′.
10. See Ref. 3, Sec. 30-7. Physically this term is due to scattering contributions at x approaching infinity. The term disappears if we take into account that the light was turned on in the distant past or we account for a small loss in the material. The problem can be mathematically handled by introducing an attenuation term exp(-εx) in the integral where ε can be taken arbitrarily small but finite. See also the notes in Ref. 5.
11. in the evaluation of this integral we obtain a value that is formally equal to ∞ exp(/∞). Again this term disappears for realistic physical situations using the reasoning in Ref. 10.
12. Reference 7, p. 366.
13. Richard P. Feynman, "Space-Time Approach to Non Relativistic Quantum Mechanics," Rev. Mod. Phys. 20, 367-387 (1948). A reprint of this paper can be found in: Julian Schwinger, Selected Papers on Quantum Electrodynamics (Dover, New York, 1958).
14. Richard P. Feynman, "Space-Time Approach to Non Relativistic Quantum Mechanics," Rev. Mod. Phys. 20, 367-387 (1948). A reprint of this paper can be found in: Julian Schwinger, Selected Papers on Quantum Electrodynamics (Dover, New York, 1958).
15. Reference 7, p. 252.
16. Leon Brillouin, Wave Propagation and Group Velocity (Academic, New York, 1960).
17. S. C. Bloch, "Eighth Velocity of Light," Am. J. Phys. 45(6) 538-549 (1977).
18. Reference 3, Chap. 26; Ref. 2.
19. Max Born and Emil Wolf, Principles of Optics (Pergamon, New York, 1980), 6th ed., See. 2.4.2.
20. R. J. Cook and P. W. Milonni, "Quantum theory of an atom near partially reflecting walls," Phys. Rev. A 35(12) 5081-5087 (1987). In this article the interaction between a single atom and a layer of atoms is obtained by starting from the Schrödinger equation. The treatment is limited to one dimension and single backscattering events. As the material of the present article is basically concerned with the contributions of multiscattering in three dimension, the combination will yield a fully quantum mechanical description, including source-related effects.
21. Rodney Loudon, The Theory of Light (Clarendon, Oxford, 1983), 2nd ed., Sec. 5.3.
22. Reference 20, p. 316.
23. Reference 3, Sec. 30-7. In the case of "scalar" dipole scattering, f(θ) = cos θ. In reality, polarization effects will result in a somewhat steeper decay to 0 as θ approaches 90 deg. In any case the effect of f(θ) is to taper off the contributions to the integral for large values of r, as discussed in Ref. 3.