Magnetism and homogenization of microresonators

Multiscale Modeling and Simulation

Volumn 7, Issue 1, 2008, Pages 62-92

  Kohn, Robert V ^a   Shipman, Stephen P ^b  

^a NEW YORK UNIVERSITY   (United States)

^b LOUISIANA STATE UNIVERSITY   (United States)

Author keywords

Homogenization; Magnetism; Metamaterial; Microresonator; Quasi static

Indexed keywords

CELL AVERAGES; DIELECTRIC COEFFICIENTS; DIELECTRIC MATRIXES; HOMOGENIZATION; HOMOGENIZATION ANALYSIS; LEADING ORDERS; MAGNETIC BEHAVIORS; METAMATERIAL; METHOD OF AVERAGING; MICRO RESONATORS; MICRORESONATOR; MICROSCOPIC STRUCTURES; MICROSTRUCTURED COMPOSITES; POLARIZED FIELDS; QUASI-STATIC; SCATTERING DATUMS;

REAL TIME SYSTEMS;

HOMOGENIZATION METHOD;

EID: 55149117091     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/070699226     Document Type: Article

References (23)

1. G. ALLAIRE, Homogenization and two-scale convergence, SIAM J. Math. Anal., 23 (1992), pp. 1482-1518.
2. G. ALLAIRE, A. DAMLAMIAN, and U. HORNUNG, Two-scale convergence on periodic surfaces and applications, in Mathematical Modelling of Flow through Porous Media, World Scientific, Singapore, 1995, pp. 15-25.
3. A.-S. BONNET-BENDHIA and F. STARLING, Guided waves by electromagnetic gratings and nonuniqueness examples for the diffraction problem, Math. Methods Appl. Sci., 17 (1994), pp. 305-338.
4. G. BOUCHITT́E and D. FELBACQ, Homogenization near resonances and artificial magnetism from dielectrics, C. R. Math. Acad. Sci. Paris, 339 (2004), pp. 377-382.
5. G. BOUCHITT́E and D. FELBACQ, Theory of mesoscopic magnetism in photonic crystals, Phys. Rev. Lett., 94 (2005), 183902.
6. G. BOUCHITT́E and D. FELBACQ, Homogenization of a wire photonic crystal: The case of small volume fraction, SIAM J. Appl. Math., 66 (2006), pp. 2061-2084.
7. K. D. CHEREDNICHENKO, V. P. SMYSHLYAEV, and V. V. ZHIKOV, Non-local homogenized limits for composite media with highly anisotropic fibres, Proc. Roy. Soc. Edinburgh Sect. A, 136 (2006), pp. 87-114.
8. D. CIORANESCU and J. SAINT JEAN PAULIN, Homogenization in open sets with holes, J. Math. Anal. Appl., 71 (1979), pp. 590-607.
9. D. FELBACQ and G. BOUCHITT́E, Left-handed media and homogenization of photonic crystals, Optics Letters, 30 (2005), pp. 1189-1191.
10. D. FELBACQ and G. BOUCHITT́E, Negative refraction in periodic and random photonic crystals, New J. Phys., 7 (2005), 159.
11. S. GUENNEAU and F. ZOLLA, Homogenization of 3D finite chiral photonic crystals, Phys. B: Condens. Matter, 394 (2007), pp. 145-147.
12. M. NEUSS-RADU, Some extensions of two-scale convergence, C. R. Acad. Sci. Paris Śer. I Math., 322 (1996), pp. 899-904.
13. S. O'BRIEN and J. B. PENDRY, Magnetic activity at infrared frequencies in structured metallic photonic crystal, J. Phys.: Condens. Matter, 14 (2002), pp. 6383-6394.
14. S. O'BRIEN and J. B. PENDRY, Photonic band-gap effects and magnetic activity in dielectric composites, J. Phys.: Condens. Matter, 14 (2002), pp. 4035-4044.
15. J. B. PENDRY, A chiral route to negative refraction, Science, 306 (2004), pp. 1353-1355.
16. J. B. PENDRY, A. J. HOLDEN, D. J. ROBBINS, and W. J. STEWART, Low frequency plasmons in thin-wire structures, J. Phys.: Condens. Matter, 10 (1998), pp. 4785-4809.
17. J. B. PENDRY, A. J. HOLDEN, D. J. ROBBINS, and W. J. STEWART, Magnetism from conductors and enhanced nonlinear phenomena, IEEE Trans. Microw. Theory Tech., 47 (1999), pp. 2075-2084.
18. J. B. PENDRY, Negative refraction, Contemp. Phys., 45 (2004), pp. 191-202.
19. S. A. RAMAKRISHNA, Physics of negative refractive index materials, Rep. Progr. Phys., 68 (2005), pp. 449-521.
20. D. F. SIEVENPIPER, E. YABLONOVITCH, J. N. WINN, S. FAN, P. R. VILLENEUVE, and J. D. JOANNOPOULOS, 3D metallo-dielectric photonic crystals with strong capacitive coupling between metallic islands, Phys. Rev. Lett., 80 (1998), pp. 2829-2832.
21. D. R. SMITH, W. J. PADILLA, D. C. VIER, S. C. NEMAT-NASSER, and S. SCHULTZ, Composite medium with simultaneously negative permeability and permittivity, Phys. Rev. Lett., 84 (2000), pp. 4184-4187.
22. D. R. SMITH, S. SCHULTZ, P. MARKO, and C. M. SOUKOULIS, Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients, Phys. Rev. B, 65 (2002), 195104.
23. C. M. SOUKOULIS, M. KAFESAKI, and E. N. ECONOMOU, Negative-index materials: New frontiers in optics, Advanced Materials, 18 (2006), pp. 1941-1952.