volume | PIER Journals

Abstract

An effective series RLC model for the electromagnetic response of weakly absorbing dielectric sphere near the first magnetic dipole resonance was developed, and the effective magnetic properties of Mie resonance-based dielectric metamaterials were obtained in terms of this model. In comparison with traditional effective medium theory such as extended Maxwell-Garnett (EMG) theory based on Mie model, this approach is more intuitive and can give an analytical dependence of the magnetic properties of the composite on the electromagnetic and geometric parameters of the constituting dielectric particles.

1. Ramakrishna, S. A., "Physics of negative refractive index materials," Rep. Prog. Phys., Vol. 68, 449-521, 2005.
doi:10.1088/0034-4885/68/2/R06 Google Scholar

2. Zhao, Q., J. Zhou, F. Zhang, and D. Lippens, "Mie resonance based dielectric metamaterial," Materials Today, Vol. 12, 60-69, 2009.
doi:10.1016/S1369-7021(09)70318-9 Google Scholar

3. Pendry, J. B., A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Techn., Vol. 47, 2075-2084, 1999.
doi:10.1109/22.798002 Google Scholar

4. Shelby, R., D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science, Vol. 292, 77-79, 2001.
doi:10.1126/science.1058847 Google Scholar

5. Smith, D. R., W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett., Vol. 84, 4184-4187, 2000.
doi:10.1103/PhysRevLett.84.4184 Google Scholar

6. Gorkunov, M., M. Lapine, E. Shamonina, and K. H. Ringhofer, "Effective magnetic properties of a composite material with circular conductive elements ," Eur. Phys. J. B, Vol. 28, 263-269, 2002.
doi:10.1140/epjb/e2002-00228-4 Google Scholar

7. Enkrich, C., M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett., Vol. 95, 203-901, 2005.
doi:10.1103/PhysRevLett.95.203901 Google Scholar

8. Linden, S., C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 Terahertz," Science, Vol. 306, 1351-1354, 2004.
doi:10.1126/science.1105371 Google Scholar

9. Chen, H., L. Ran, J. Huangfu, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Magnetic properties of S-shaped split-ring resonators," Progress In Electromagnetics Research, Vol. 51, 231, 2005.
doi:10.2528/PIER04051201 Google Scholar

10. Chen, H., L. X. Ran, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, "Crankled S-ring resonator with small electrical size," Progress In Electromagnetics Research, Vol. 66, 179-190, 2006.
doi:10.2528/PIER06112003 Google Scholar

11. Dolling, G., C. Enkrich, and M. Wegener, "Low-loss negative-index metamaterial at telecommunication wavelengths," Science, Vol. 312, 892-894, 2006.
doi:10.1126/science.1126021 Google Scholar

12. Kafesaki, M., I. Tsiapa, N. Katsarakis, T. Koschny, C. M. Soukoulis, and E. N. Economou, "Left-handed metamaterials: The fishnet structure and its variations," Phys. Rev. B, Vol. 75, 235114, 2007.
doi:10.1103/PhysRevB.75.235114 Google Scholar

13. Marqués, R., F. Medina, and R. Rafii-El-Idrissi, "Role of bian-isotropy in negative permeability and left-handed metamaterials," Phys. Rev. B, Vol. 65, 144440, 2002.
doi:10.1103/PhysRevB.65.144440 Google Scholar

14. Chen, H., L. Ran, and J. Huangfu, "Equivalent circuit model for left-handed metamaterials," J. Appl. Phys., Vol. 100, 024915, 2006.
doi:10.1063/1.2219986 Google Scholar

15. O'Brien, S. and J. B. Pendry, "Photonic band-gap effects and magnetic activity in dielectric composites," J. Phys.: Condens. Matter., Vol. 14, 4035-4044, 2002.
doi:10.1088/0953-8984/14/15/317 Google Scholar

16. Wang, R., J. Zhou, C.-Q. Sun, L. Kang, Q. Zhao, and J.-B. Sun, "Lefted-handed materials based on crystal lattice vibration," Progress In Electromagnetics Research Letters, Vol. 10, 145-155, 2009.
doi:10.2528/PIERL09070807 Google Scholar

17. Jylhä, L., I. Kolmakov, S. Maslovski, and S. Tretyakov, "Modeling of isotropic backward-wave materials composed of resonant spheres," J. Appl. Phys., Vol. 99, 043102, 200.
doi:10.1063/1.2173309 Google Scholar

18. Wheeler, M. S., J. S. Aitchison, and M. Mojahedi, "Coated nonmagnetic spheres with a negative index of refraction at infrared frequencie ," Phys. Rev. B, Vol. 73, 045105, 2006.
doi:10.1103/PhysRevB.73.045105 Google Scholar

19. Yannopapas, V. and N. V. Vitanov, "Photoexcitation-induced magnetism in arrays of semiconductor nanoparticles with a strong excitonic oscillator strength ," Phys. Rev. B, Vol. 74, 193304, 2006.
doi:10.1103/PhysRevB.74.193304 Google Scholar

20. Zhao, Q., L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, "Experimental demonstration of isotropic negative permeability in a three-dimensional dielectric composite," Phys. Rev. Lett., Vol. 101, 027402, 2008.
doi:10.1103/PhysRevLett.101.027402 Google Scholar

21. Doyle, W. T., "Optical properties of a suspension of metal spheres," Phys. Rev. B, Vol. 39, 9852-9858, 1989.
doi:10.1103/PhysRevB.39.9852 Google Scholar

22. Grimes, C. A. and D. M. Grimes, "Permeability and permittivity spectra of grannular materials," Phys. Rev. B, Vol. 43, 10780-10788, 1991.
doi:10.1103/PhysRevB.43.10780 Google Scholar

23. Ruppin, R., "Evaluation of extended Maxwell-Garnett theories," Opt. Commun., Vol. 182, 273-279, 2000.
doi:10.1016/S0030-4018(00)00825-7 Google Scholar

24. Videen, G. and W. S. Bickel, "Light-scattering resonances in small spheres," Phys. Rev. A, Vol. 45, 6008-6012, 1992.
doi:10.1103/PhysRevA.45.6008 Google Scholar

25. Chen, X., T. M. Grzegorczyk, B. Wu, J. Pacheco, Jr., and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E, Vol. 70, 016608, 2004.
doi:10.1103/PhysRevE.70.016608 Google Scholar

26. Smith, D. R., D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E, Vol. 71, 036617, 2005.
doi:10.1103/PhysRevE.71.036617 Google Scholar

27. Wheeler, M. S., J. S. Aitchison, and M. Mojahedi, "Coupled magnetic dipole resonances in sub-wavelength dielectric particle clusters," J. Opt. Soc. Am. B, Vol. 27, 1083-1091, 2010.
doi:10.1364/JOSAB.27.001083 Google Scholar

28. Peng, L., L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, "Experimental observation of left-handed behavior in an array of standard dielectric resonators," Phys. Rev. Lett., Vol. 98, 157403, 2010.
doi:10.1103/PhysRevLett.98.157403 Google Scholar

Dr. Lingyun Liu

Dr. Jingbo Sun

Dr. Xiaojian Fu

Dr. Ji Zhou

Prof. Qian Zhao

Dr. Bo Fu

Dr. Jiaping Liao

Prof. Didier Lippens