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Fundamental Field Equations in Temporally Dispersive Media

  • Kurt E. Oughstun
Chapter
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Part of the Springer Series in Optical Sciences book series (SSOS, volume 224)

Abstract

The fundamental macroscopic electromagnetic field equations and elementary plane wave solutions in linear, temporally dispersive absorptive media are developed in this chapter with particular emphasis on homogeneous, isotropic, locally linear (HILL), temporally absorptive dispersive media. The general frequency dependence of the dielectric permittivity, magnetic permeability, and electric conductivity is included in the analysis so that the resultant field equations rigorously apply to both perfect and imperfect dielectrics, conductors and semiconducting materials, as well as to metamaterials, over the entire frequency domain.

References

  1. 1.
    J. R. Wait, “Project Sanguine,” Science, vol. 178, pp. 272–275, 1972.ADSCrossRefGoogle Scholar
  2. 2.
    J. R. Wait, “Propagation of ELF electromagnetic waves and Project Sanguine/Seafarer,” IEEE Journal Oceanic Engineering, vol. 2, no. 2, pp. 161–172, 1977.ADSCrossRefGoogle Scholar
  3. 3.
    V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of 𝜖 and μ,” Sov. Phys. Uspekhi, vol. 10, no. 4, pp. 509–514, 1968.ADSCrossRefGoogle Scholar
  4. 4.
    R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E, vol. 64, no. 5, pp. 056625–1–056625–15, 2001.Google Scholar
  5. 5.
    M. S. Sodha and A. K. Ghatak, Inhomogeneous Optical Waveguides. New York: Plenum Press, 1977.CrossRefGoogle Scholar
  6. 6.
    M. Kline and I. W. Kay, Electromagnetic Theory and Geometrical Optics. New York: Wiley, 1965.zbMATHGoogle Scholar
  7. 7.
    J. B. Keller, “Geometrical theory of diffraction,” J. Opt. Soc. Am., vol. 52, no. 2, pp. 116–130, 1962.ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    V. M. Agranovich and V. L. Ginzburg, Crystal Optics with Spatial Dispersion, and Excitons. Berlin-Heidelberg: Springer-Verlag, second ed., 1984.Google Scholar
  9. 9.
    D. B. Melrose and R. C. McPhedran, Electromagnetic Processes in Dispersive Media: A Treatment Based on the Dielectric Tensor. Cambridge: Cambridge University Press, 1991.CrossRefGoogle Scholar
  10. 10.
    J. M. Stone, Radiation and Optics, An Introduction to the Classical Theory. New York: McGraw-Hill, 1963.Google Scholar
  11. 11.
    S. Bassiri, C. H. Papas, and N. Engheta, “Electromagnetic wave propagation through a dielectric-chiral interface and through a chiral slab,” J. OPt. Soc. Am. A, vol. 5, no. 9, pp. 1450–1459, 1988.ADSCrossRefGoogle Scholar
  12. 12.
    G. C. Sherman and K. E. Oughstun, “Description of pulse dynamics in Lorentz media in terms of the energy velocity and attenuation of time-harmonic waves,” Phys. Rev. Lett., vol. 47, pp. 1451–1454, 1981.ADSCrossRefGoogle Scholar
  13. 13.
    G. C. Sherman and K. E. Oughstun, “Energy velocity description of pulse propagation in absorbing, dispersive dielectrics,” J. Opt. Soc. Am. B, vol. 12, pp. 229–247, 1995.ADSCrossRefGoogle Scholar
  14. 14.
    N. A. Cartwright and K. E. Oughstun, “Pulse centroid velocity of the Poynting vector,” J. Opt. Soc. Am. A, vol. 21, no. 3, pp. 439–450, 2004.ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    W. S. Franklin, “Poynting’s theorem and the distribution of electric field inside and outside of a conductor carrying electric current,” Phys. Rev., vol. 13, no. 3, pp. 165–181, 1901.ADSGoogle Scholar
  16. 16.
    J. Neufeld, “Revised formulation of the macroscopic Maxwell theory. I. Fundamentals of the proposed formulation,” Il Nuovo Cimento, vol. LXV B, no. 1, pp. 33–68, 1970.CrossRefGoogle Scholar
  17. 17.
    J. Neufeld, “Revised formulation of the macroscopic Maxwell theory. II. Propagation of an electromagnetic disturbance in dispersive media,” Il Nuovo Cimento, vol. LXVI B, no. 1, pp. 51–76, 1970.CrossRefGoogle Scholar
  18. 18.
    C. Jeffries, “A new conservation law for classical electrodynamics,” SIAM Review, vol. 34, no. 4, pp. 386–405, 1992.MathSciNetCrossRefGoogle Scholar
  19. 19.
    H. G. Schantz, “On the localization of electromagnetic energy,” in Ultra-Wideband, Short-Pulse Electromagnetics 5 (P. D. Smith and S. R. Cloude, eds.), pp. 89–96, New York: Kluwer Academic, 2002.Google Scholar
  20. 20.
    F. N. H. Robinson, “Poynting’s vector: Comments on a recent paper by Clark Jeffries,” SIAM Review, vol. 36, no. 4, pp. 633–637, 1994.MathSciNetCrossRefGoogle Scholar
  21. 21.
    C. Jeffries, “Response to a commentary by F. N. H. Robinson,” SIAM Review, vol. 36, no. 4, pp. 638–641, 1994.MathSciNetCrossRefGoogle Scholar
  22. 22.
    L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media. Oxford: Pergamon, 1960. Ch. IX.Google Scholar
  23. 23.
    Y. S. Barash and V. L. Ginzburg, “Expressions for the energy density and evolved heat in the electrodynamics of a dispersive and absorptive medium,” Usp. Fiz. Nauk., vol. 118, pp. 523–530, 1976. [English translation: Sov. Phys.-Usp. vol. 19, 163–270 (1976)].Google Scholar
  24. 24.
    J. M. Carcione, “On energy definition in electromagnetism: An analogy with viscoelasticity,” J. Acoust. Soc. Am., vol. 105, no. 2, pp. 626–632, 1999.ADSCrossRefGoogle Scholar
  25. 25.
    M. Born and E. Wolf, Principles of Optics. Cambridge: Cambridge University Press, seventh (expanded) ed., 1999.Google Scholar
  26. 26.
    R. Loudon, “The propagation of electromagnetic energy through an absorbing dielectric,” Phys. A, vol. 3, pp. 233–245, 1970.ADSCrossRefGoogle Scholar
  27. 27.
    R. Loudon, The Quantum Theory of Light. London: Oxford University Press, 1973.zbMATHGoogle Scholar
  28. 28.
    K. E. Oughstun and S. Shen, “Velocity of energy transport for a time-harmonic field in a multiple-resonance Lorentz medium,” J. Opt. Soc. Am. B, vol. 5, no. 11, pp. 2395–2398, 1988.ADSCrossRefGoogle Scholar
  29. 29.
    K. E. Oughstun and G. C. Sherman, “Propagation of electromagnetic pulses in a linear dispersive medium with absorption (the Lorentz medium),” J. Opt. Soc. Am. B, vol. 5, no. 4, pp. 817–849, 1988.ADSCrossRefGoogle Scholar
  30. 30.
    S. Shen and K. E. Oughstun, “Dispersive pulse propagation in a double-resonance Lorentz medium,” J. Opt. Soc. Am. B, vol. 6, pp. 948–963, 1989.ADSCrossRefGoogle Scholar
  31. 31.
    K. E. Oughstun and G. C. Sherman, “Optical pulse propagation in temporally dispersive Lorentz media,” J. Opt. Soc. Am., vol. 65, no. 10, p. 1224A, 1975.Google Scholar
  32. 32.
    L. Brillouin, Wave Propagation and Group Velocity. New York: Academic, 1960.zbMATHGoogle Scholar
  33. 33.
    J. D. Jackson, Classical Electrodynamics. New York: John Wiley & Sons, third ed., 1999.zbMATHGoogle Scholar
  34. 34.
    R. A. Chipman, Theory and Problems of Transmission Lines. New York: McGraw-Hill, 1968.Google Scholar
  35. 35.
    R. E. Collin, Field Theory of Guided Waves. Piscataway, NJ: IEEE, second ed., 1991.Google Scholar
  36. 36.
    D. Marcuse, Theory of Dielectric Optical Waveguides. New York: Academic, 1974.Google Scholar
  37. 37.
    H. Minkowski, “Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpen,” Nachr. Königl. Ges. Wiss. Göttingen, pp. 53–111, 1908. Reprinted in Math. Ann, 68, pages 472–525 (1910).Google Scholar
  38. 38.
    S. M. Barnett and R. Loudon, “On the electromagnetic force on a dielectric medium,” Journal of Physics B: Atomic, Molecular and Optical Physics, vol. 39, no. 15, p. S671, 2006.ADSCrossRefGoogle Scholar
  39. 39.
    A. Shevchenko and M. Kaivola, “Electromagnetic force density and energy-momentum tensor in an arbitrary continuous medium,” Journal of Physics B: Atomic, Molecular and Optical Physics, vol. 44, no. 17, p. 175401, 2011.ADSCrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Kurt E. Oughstun
    • 1
  1. 1.College of Engineering and Mathematical Sciences, University of VermontBurlingtonUSA

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