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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 23 — Nov. 10, 2008
  • pp: 19152–19168

Correct definition of the Poynting vector in electrically and magnetically polarizable medium reveals that negative refraction is impossible

Vadim A. Markel  »View Author Affiliations

Optics Express, Vol. 16, Issue 23, pp. 19152-19168 (2008)

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I compute from first principles the local heating rate q (the amount of electromagnetic energy converted to heat per unit time per unit volume) for electromagnetic waves propagating in magnetically and electrically polarizable media. I find that, in magnetic media, this rate has two separate contributions, q(V) and q(S) , the first coming from the volume of the medium and the second from its surface. I argue that the second law of thermodynamics requires that the volume contribution be positive and that this requirement, in turn, prohibits negative refraction. This result holds for active or passive media and in the presence of anisotropy and spatial dispersion.

© 2008 Optical Society of America

OCIS Codes
(160.1245) Materials : Artificially engineered materials
(350.3618) Other areas of optics : Left-handed materials

ToC Category:

Original Manuscript: June 5, 2008
Revised Manuscript: October 31, 2008
Manuscript Accepted: November 3, 2008
Published: November 5, 2008

Vadim A. Markel, "Correct definition of the Poynting vector in electrically and magnetically polarizable medium reveals that negative refraction is impossible," Opt. Express 16, 19152-19168 (2008)

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  1. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ? and ?." Physics-Uspekhi 10, 509-514 (1968). [CrossRef]
  2. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000). [CrossRef] [PubMed]
  3. A. A. Ramakrishna, "Physics of negative refractive index materials," Rep. Prog. Phys. 68, 449-521 (2005). [CrossRef]
  4. C. M. Soukoulis, S. Linden, and M. Wegener, "Negative refraction index at optical wavelengths," Science 315, 47-49 (2007). [CrossRef] [PubMed]
  5. V. M. Shalaev, "Optical negative-index metamaterials," Nature Photonics 1, 41-48 (2007). [CrossRef]
  6. M. I. Stockman, "Criterion for negative refraction with low optical losses from a fundamental principle of causality," Phys. Rev. Lett. 98, 177404 (2007). [CrossRef]
  7. W. Gough, "Poynting in the wrong direction?" Eur. J. Phys. 3, 83-87 (1982). [CrossRef]
  8. R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics, vol. 2 (Addison-Wesley, 1964).
  9. D. F. Nelson, "Generalizing the Poynting vector," Phys. Rev. Lett. 76, 4713-4716 (1996). [CrossRef] [PubMed]
  10. I. Campos and J. L. Jimenez, "About Poynting’s theorem," Eur. J. Phys. 13, 117-121 (1992). [CrossRef]
  11. F. Richter, M. Florian, and K. Henneberger, "Poynting’s theorem and energy conservation in the propagation of light in bounded media," Europhys. Lett. 81, 67005 (2008). [CrossRef]
  12. R. A. Depine and A. Lakhtakia, "Comment I on ’Resonant and antiresonant frequency dependence of the effective parameters of metamaterial’," Phys. Rev. E 70, 048601 (2004). [CrossRef]
  13. A. L. Efros, "Comment II on ’Resonant and antiresonant frequency dependence of the effective parameters of metamaterial’," Phys. Rev. E 70, 048602 (2004). [CrossRef]
  14. J. Schwinger, L. L. DeRaad, K. A. Milton, and W. Tsai, Classical Electrodynamics (Perseus Books, Reading, MA, 1998).
  15. L. D. Landau and L. P. Lifshitz, Electrodynamics of Continuous Media (Pergamon Press, Oxford, 1984).
  16. In the zero-frequency limit, we must replace E? by 2E, where E is the real-valued electric field, and similarly for the magnetic field.
  17. J. B. Pendry, A. J. Holden, D. J. Robbins, andW. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory and Techniques 47, 2075-2084 (1999). [CrossRef]
  18. V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes and negative refraction in metal nanowire composites," Opt. Express 11, 735 (2003). [CrossRef] [PubMed]
  19. A. K. T. Assis, W. A. Rodrigues, and A. J. Mania, "The electric field outside a stationary resistive wire carrying a constant current," Foundations of Physics 29, 729-753 (1999). [CrossRef]
  20. P. S. Pershan, "Nonlinear optical properties of solids: energy considerations," Phys. Rev. 130, 919-929 (1963). [CrossRef]
  21. R. Marques, F. Martin, and M. Sorolla, Metamaterials with Negative Parameters (Wiley, 2008).
  22. I. Tsukerman, "Negative refraction and the minimum lattice cell size," J. Opt. Soc. Am. B 25, 927-936 (2008). [CrossRef]
  23. V. M. Agranovich, Y. N. Gartstein, and A. A. Zakhidov, "Negative refraction in gyrotropic media," Phys. Rev. B 73, 045114 (2006). [CrossRef]
  24. A. V. Kildishev, V. P. Drachev, U. K. Chettiar, V. M. Shalaev, D. H. Werner, and D. H. Kwon, "Comment on ’Negative refractive index in artificial metamaterials’," Opt. Lett. 32, 1510-1511 (2007). [CrossRef] [PubMed]
  25. A. N. Grigorenko, "Reply to comment on ’Negative refractive index in artificial metamaterials’," Opt. Lett. 32, 1512-1514 (2007). [CrossRef] [PubMed]
  26. C. R. Simovski and S. A. Tretyakov, "Local constitutive parameters of metamaterials from an effective-medium perspective," Phys. Rev. B 75, 195111 (2007). [CrossRef]
  27. R. J. Deissler, "Dipole in a magnetic field, work, and quantum spin," Phys. Rev. E 77, 036609 (2008). [CrossRef]

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