Scaling theory for homogenization of the Maxwell equations

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 60, Issue 1, 1999, Pages 987-993

  Vinogradov, A P ^a   Aivazyan, A V ^a  

^a RUSSIAN ACADEMY OF SCIENCES   (Russian Federation)

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ARTICLE;

EID: 0345833884     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.60.987     Document Type: Article

References (41)

1. A. N. Lagarkov and A. K. Sarychev, Phys. Rev. B 53, 6318 (1996).
2. A. P. Vinogradov, Proceedings of the International Seminar on Electrodynamics of Chiral and Bianisotropic Media “Bianisotropics ’93” (Helsinki University of Technology, Espoo, 1993), Rep. 159, p. 22.
3. C. R. Simovski, S. A. Tretyakov, A. A. Sochava, B. Sauviac, F. Mariotte, and T. G. Kharina, J. Electromagn. Waves Appl. 11, 1509 (1997).
4. M. V. Kostin and V. V. Shevchenko, J. Commun. Technol. Electron. 38, 72 (1993).
5. A. K. Sarychev and Yu. R. Smychkovich, Actual Problems of Technology of Composite Materials for Microelectronics Information Systems, Proceedings of the first National Conference, Yalta, 1990 (Simferopol State University, Simferopol, 1990) (in Russian)
6. I. V. Kukolev, A. N. Lagarkov, S. M. Matitsin, K. N. Rozanov, and A. P. Vinogradov, Proceedings of the Spring Meeting (MRS, San Francisco, 1992), p. L6.14.
7. A. P. Vinogradov, A. N. Lagarkov, and V. E. Romanenko, Electromagnetics 17, 213 (1997).
8. R. Landauer, in Electrical Transport and Optical Properties of Inhomogeneous Media, Ohio State University, 1977, edited by J. C. Garland and D. B. Tanner, AIP Conf. Proc. No. 40 (AIP, New York, 1978).
9. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Butterworth Heinemann, Oxford, 1995).
10. I. E. Tamm, Basic Electricity Theory (GITTL, Moscow, 1956) (in Russian).
11. J. D. Jackson, Classical Electrodynamics, 2d ed. (John Wiley, Singapore, 1990).
12. E. B. Graham, J. Pierrus, and R. E. Raab, J. Phys. B 25, 4673 (1992).
13. G. Russakoff, Am. J. Phys. 38, 1188 (1970).
14. D. E. Logan, Mol. Phys. 46, 271 (1982).
15. A. P. Vinogradov, Physica A 241, 216 (1997).
16. M. M. Bredov, V. V. Rumyantzev, and I. N. Toptyghin, Classical Electrodynamics (Nauka, Moscow, 1985) (in Russian).
17. A. N. Lagarkov and A. P. Vinogradov, Advances in Complex Electromagnetic Materials, edited by A. Priou et al., Vol. 28 of NATO Advanced Study Institute Partnership Sub Series 3. High Technology (Kluwer, Dordrecht, 1997), p. 117.
18. S. R. deGroot and L. G. Suttorp, Foundations of Electrodynamics (North-Holland Publishing Company, Amsterdam, 1972).
19. V. P. Silin and A. A. Rukhadze, Electromagnetic Properties of Plasma and Plasma Like Media (GosAtomIzdat, Moscow, 1961) (in Russian).
20. A. A. Golubkov and V. A. Makarov, Usp Fiz. Nauk 165, 339 (1995) [Phys. Usp. 38, 325 (1995)].
21. Certainly, there are other representations. One example was presented by R. Raab (private communication), (Formula presented)where (Formula presented) (Formula presented) (Formula presented)Unfortunately, contrary to Eqs. (6789), some of the terms have no clear physical sense.
22. K. D. Wilson and J. Kogut, Phys. Rep. 12c, 75 (1974).
23. We imply that the scale of this level is still much less than the wavelength.
24. A. P. Vinogradov, L. V. Panina, and A. K. Sarychev, Dokl. Akad. Nauk (SSSR) 306, 847 (1989) [Sov. Phys. Dokl. 34, 530 (1989)].
25. V. M. Dubovik and S. V. Shabanov, Essay on The Formal Aspects of Electromagnetic Theory, edited by A. Lakhtakia (World Scientific, New York, 1993), p. 339
26. V. M. Dubovik, A. A. Cheshkov, Fiz. Elem. Chastits. At. Yadra. 5, 791 (1974) [Sov. J. Part. Nucl. 5, 318 (1975)]
27. Sov. J. Part. Nucl.V. M. Dubovik and L. A. Tousunyan, ibid. 14, 1193 (1983) [ 14, 323 (1983)].
28. Ya. B. Zeld´ovich, Zh. Éksp. Teor. Fiz. 33, 1531 (1957) Zh. Éksp. Teor. Fiz. 33, 1531 (1957) [ Sov. Phys. JETP 6, 1184 (1958)].
29. L. A. Weinstein, Theory of Diffraction and Microwave Electronics (Radio i Sviaz, Moscow, 1995), p. 179 (in Russian).
30. A. P. Vinogradov, I. G. Busarov, O. P. Posudnevsky, and V. E. Romanenco, J. Phys.: Condens. Matter 6, 4351 (1994).
31. A. P. Vinogradov, A. A. Kalachev, A. N. Lagarkov, V. E. Romanenko, and G. V. Kazantseva, Dokl. Acad. Nauk 349, 182 (1996) [Sov. Phys. Dokl. 41, 291 (1996)].
32. V. M. Agranovich and V. I. Yudson, Opt. Commun. 7, 121 (1973).
33. R. P. Feynman, R. B. Leghton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley Publishing Company, Reading, MA, 1996), Vol. I, Chap. 33–35.
34. Owing to symmetry of the cell, the mean value of the current (Formula presented) is equal to (Formula presented).
35. The patterns in Figs. 11(b) and 11(c) are of the same order. One can comprise the (Formula presented) pattern employing (Formula presented) and (Formula presented) patterns (see Fig. 22), which is a graphical analog of Eq. (6): Fig. 11(a) =Fig. 11(b) + Fig. 11(c). So, in some sense, Eq. (6) is the presentation of the field as the sum of a part symmetric in (Formula presented) and a part that is antisymmetric.
36. The restriction to Eq. (17) or even to Eq. (1) does not mean that the fields generated by the current from the PISVE have dipole-quadrupole character. As is shown in 10, multipole expansion of these radiated fields in a source-free region contains, in the general case, all multipole contributions (see Chap. 16.2 in 10).
37. L. Tsang, J. A. Kong, and R. W. Newton, IEEE Trans. Antennas Propag. 30, 292 (1982)
38. B. Michel and A. Lakhtakia, Optik (Stuttgart) 96, 25 (1995)
39. V. I. Tatarskii and M. E. Gertsenshtein, Zh. Éksp. Teor. Fiz. 44, 676 (1963) [Sov. Phys. JETP 17, 458 (1963)].
40. J. E. Sipe and J. Van Kranendonk, Phys. Rev. A 9, 1806 (1974)
41. J. E. SipeJ. Van KranendonkCan. J. Phys. 53, 2095 (1975).