1. Tretyakov, S., "Analytical Modeling in Applied Electromagnetics," Artech House, 2003.        Google Scholar

2. Smith, D. R. and J. B. Pendry, "Homogenization of metamaterials by field averaging," J. Opt. Soc. Am. B, Vol. 23, No. 3, Mar. 2006.
doi:10.1364/JOSAB.23.000391        Google Scholar

3. Lerat, J. M., N. Mallejac, and O. Acher, "Determination of the e®ective parameters of a metamaterial by field summation," Journal of Appl. Phys., Vol. 100, 084908, 2006.
doi:10.1063/1.2355427        Google Scholar

4. Liu, R., R. J. Cui, D. Huang, B. Zhao, and D. R. Smith, "Description and explanation of electromagnetic behaviors in arti¯cial metamaterials based on e®ective medium theory," Physical Review E, Vol. 76, 026606, 2007.
doi:10.1103/PhysRevE.76.026606        Google Scholar

5. Koschny, T., P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Physical Review B, Vol. 71, 245105, 2005.
doi:10.1103/PhysRevB.71.245105        Google Scholar

6. Belov, P. A. and C. R. Simovski, "On homogenization of electromagnetic crystals formed by uniaxial resonant scatterers," Physical Review E, Vol. 72, 026615, 2005.
doi:10.1103/PhysRevE.72.026615        Google Scholar

7. Pendry, J. B., A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory and Tech., Vol. 47, No. 11, Nov. 1999.        Google Scholar

8. Tretyakov, S., S. Maslovski, and P. Belov, "An analytical model of metamaterials based on loaded wire dipoles," IEEE Trans. on Antennas and Propag., Vol. 51, 2562, 2003.        Google Scholar

9. Tretyakov, S., "Meta-materials with wideband negative permittivity and permeability," Microwave and Optical Technology Letters, Vol. 31, No. 3, 163, 2001.
doi:10.1002/mop.1387        Google Scholar

10. Basilio, L. I., L. K. Warne, W. L. Langston, W. A. Johnson, and M. B. Sinclair, "A quick and easy simulation procedure to aid in metamaterial unit-cell design," IEEE Antennas Wireless Propag. Lett., Vol. 10, 1567-1570, 2011.
doi:10.1109/LAWP.2011.2171470        Google Scholar

11. Simovski, C. R. and S. A. Tretyakov, "Model of isotropic resonant magnetism in the visible range based on core-shell clusters," Phys. Rev. B, Vol. 79, 045111, 2009.
doi:10.1103/PhysRevB.79.045111        Google Scholar

12. Kim, J. and A. Gopinath, "Simulation of metamaterial containing cubic high dielectric resonators," Phys. Rev. B, Vol. 76, 115126, 2007.
doi:10.1103/PhysRevB.76.115126        Google Scholar

13. Popa, B. and S. Cummer, "Compact dielectric particles as a building block for low-loss magnetic materials," Phys. Rev. Lett., Vol. 100, 207401, 2008.
doi:10.1103/PhysRevLett.100.207401        Google Scholar

14. Sinclair, , M., J. Ginn, J. Wendt, J. Stevens, D. Peters, L. Basilio, L. Warne, P. Clem, and J. Ihlefeld, "All dielectric infrared metamaterial," SPIE Optics + Photonics, Paper 8093-44, 2011.        Google Scholar

15. Kuester, E., N. Memic, S. Shen, A. D. Scher, S. Kim, K. Kumley, and H. Loui, "A negative refractive index metamaterial based on a cubic array of layered nonmagnetic spherical particles," Progress In Electromagnetics Research B, Vol. 33, 175-202, 2011.
doi:10.2528/PIERB11042206        Google Scholar

16. Basilio, L., L. Warne, W. Langston, W. Johnson, and M. Sinclair, "A negative-index metamaterial design based on metal-core, dielectric shell resonators," IEEE Antennas and Propagation Society International Symposium, Spokane, Washington, USA,2011 .        Google Scholar

17. Ahmadi, A. and H. Mosallaei, "Physical configuration and performance modeling of all-dielectric metamaterials," Phys. Rev. B, Vol. 77, Art. 045104, 2008.        Google Scholar

18. Jylha, L., I. Kolmakov, S. Maslovski, and S. Tretyakov, "Modeling of isotropic backward-wave materials composed of resonant spheres," J. Appl. Phys., Vol. 99, Art. 043102, 2006.        Google Scholar

19. Palik, E., Handbook of Optical Constants and Solids, Academic,Orlando, Fla., 1986.

20. Warne, L. K., L. I. Basilio, W. L. Langston, W. A. Johnson, and M. B. Sinclair, "Perturbation theory in the design of degenerate spherical dielectric metamaterial resonators," Sandia National Laboratories Internal Report, 2011.        Google Scholar

21. Basilio, L. I., L. K. Warne, W. L. Langston, W. A. Johnson, and M. B. Sinclair, "Microwave-frequency, negative-index metamaterial designs based on degenerate dielectric resonators," IEEE Antennas Wireless Propag. Lett., Vol. 11, 113-116, 2012.
doi:10.1109/LAWP.2012.2184252        Google Scholar

22. Johnson, W., L. Basilio, J. Kotulski, R. Jorgenson, L. Warne, R. Coats, D. Wilton, N. Champagne, F. Capolino, J. Grant, and M. Khayat, "Eiger: An open-source frequency domain electromagnetics code," IEEE Antennas and Propagation Society International Symposium, Honolulu, Hawaii, USA, 2007.        Google Scholar

23. Van Bladel, J., "On the resonances of a dielectric resonator of very high permittivity," IEEE Trans. on Microwave Theory and Tech., Vol. 23, No. 2, 199-208, Feb. 1975.
doi:10.1109/TMTT.1975.1128528        Google Scholar

24. Van Bladel, J., "The excitation of dielectric resonators of very high permittivity," IEEE Trans. on Microwave Theory and Tech., Vol. 23, No. 2, 208-217, Feb. 1975.
doi:10.1109/TMTT.1975.1128529        Google Scholar

25. Mongia, R. and A. Ittipiboon, "Theoretical and experimental investigations on rectangular dielectric resonator antennas," IEEE Trans. on Antennas and Propag., Vol. 45, No. 9, 1348, 1997.
doi:10.1109/8.623123        Google Scholar

26. Harrington, R. F., Time-harmonic Electromagnetic Fields, 317-326, McGraw-Hill Book Company, New York, 1961.

27. Lin, X. Q., T. J. Cui, J. Y. Chin, X. M. Yang, Q. Cheng, and R. Liu, "Controlling electromagnetic waves using tunable gradient dielectric metamaterial lens," Applied Phys. Lett., Vol. 92, 131904, 2008.
doi:10.1063/1.2896308        Google Scholar

28. Antar, Y. M. M. and D. Guha, "Composite and hybrid dielectric resonator antennas: Recent advances and challenges," 23rd National Radio Science Conference, Menoufiya University, Egypt, Mar. 14-16, 2006.        Google Scholar

29. Poplavko, Y. M., Y. P. Prokopenko, V. I. Molchanov, and A. Dogan, "Frequency-tunable microwave dielectric resonator ," IEEE Trans. on Microwave Theory and Tech., Vol. 49, No. 6, 2001.
doi:10.1109/22.925485        Google Scholar

30. Derneryd, A., U. M. Khan, A. A. Kishk, M. Milutinovic, and P. Persson, "Dual-polarized dielectric resonator antennas for base station applications," 5th European Conference on Antennas and Propagation, Rome, Italy, 2011.        Google Scholar

31. Borginis, F. E. and and C. H. Papas, Electromagnetic Waveguides and Resonators, Hanbuch Der Physik, S. Flugge, Editor, Vol. XVI,411{414, Springer-Verlag, Berlin, 1958.