Vol. 44

Latest Volume
All Volumes
All Issues
2012-09-12

Perturbation Theory in the Design of Degenerate Rectangular Dielectric Resonators

By Larry Kevin Warne, Lorena I. Basilio, William L. Langston, William A. Johnson, and Michael B. Sinclair
Progress In Electromagnetics Research B, Vol. 44, 1-29, 2012
doi:10.2528/PIERB12071610

Abstract

The design of resonators with degenerate magnetic and electric modes usually requires the ability to perturb one or both types of modes in order to induce alignment of magnetic and electric properties. In this paper perturbation theory is used to identify different types of inclusions that can be used to realize fundamental-mode degeneracy in a rectangular dielectric resonator and thus, can ultimately be used in the design of negative-index metamaterials. For reasons associated with fabrication in the infrared-frequency regime, rectangular resonator designs are of particular interest.

Citation


Larry Kevin Warne, Lorena I. Basilio, William L. Langston, William A. Johnson, and Michael B. Sinclair, "Perturbation Theory in the Design of Degenerate Rectangular Dielectric Resonators," Progress In Electromagnetics Research B, Vol. 44, 1-29, 2012.
doi:10.2528/PIERB12071610
http://www.jpier.org/PIERB/pier.php?paper=12071610

References


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

    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

    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

    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

    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

    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

    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.

    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.

    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

    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

    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

    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

    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

    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.

    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

    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 .

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

    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.

    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.

    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

    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.

    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

    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

    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

    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

    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.

    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

    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.

    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.