volume | PIER Journals

Abstract

Mathematical modeling of composites made of a dielectric base and randomly oriented metal inclusions is considered. Different sources of frequency-dependent metal conductivity at optical frequencies are taken into account. These include the skin-effect, dimensional (length-size) resonance of metal particles, and the Drude model. Also, the mean free path of electrons in metals can be smaller than the characteristic sizes of nanoparticles, and this leads to the decrease in conductivity of the metal inclusions. These effects are incorporated in the Maxwell Garnett mixing formulation, and give degrees of freedom for forming desirable optical frequency characteristics of composite media containing conducting particles.

1. Maxwell, G. and J. C., "Colours in metal glasses and metal films," Philos. Trans. R. Soc. London, Vol. 3, 385-420, 1904.

2. Koledintseva, M. Y.P. C. Ravva, R. E. DuBroff, J. L. Drewniak, K. N. Rozanov, and B. Archambeault, "Engineering of composite media for shields at microwave frequencies," Proc. IEEE EMC Symposium, Vol. 1, No. 8, 169-174, 2005.

3. Koledintseva, M. Y.J. Wu, J. Zhang, J. L. Drewniak, and K. N. Rozanov, "Representation of permittivity for multi-phase dielectric mixtures in FDTD modeling," Proc. IEEE Symp. Electromag. Compat., Vol. 1, 9-13, 2004.

4. Matitsine, S. M., K. M. Hock, L. Liu, and et. al., "Shift of resonance frequency of long conducting fibers embedded in a composite," J. Appl. Phys., Vol. 94, No. 2, 1146-1154, 2003.
doi:10.1063/1.1577395

5. Huang, J.M. Y. Koledintseva, P. C. Ravva, J. L. Drewniak, R. E. DuBroff, B. Archambeault, and K. N. Rozanov, "Design of a metafilm-composite dielectric shielding structure using a genetic algorithm," Proc. Progress in Electromagnetic Research Symposium (PIERS), 26-29, 2006.

6. Lagarkov, A. N. and A. K. Sarychev, "Electromagnetic properties of composites containing elongated conducting inclusions," Phys. Review B, Vol. 53, No. 9, 6318-6336, 1996.
doi:10.1103/PhysRevB.53.6318

7. Landau, L. D., E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2 Ed., 1984.

8. Gottlieb, D. and V. Halpern, "The electrical conductivity of very thin metal films," J. Phys. F: Metal. Phys., Vol. 6, No. 12, 2333-2339, 1976.
doi:10.1088/0305-4608/6/12/019

9. Chen and D. Gardner, "Influence of line dimensions on the resistance of Cu interconnections," IEEE Electr. Dev. Lett., Vol. 19, No. 12, 508, 1998.
doi:10.1109/55.735762

10. Kapur, P., J. P. McVittie, and K. C. Saraswat, "Technology and reliability constrained future copper interconnects â€” Part I: Resistance modeling," IEEE Trans. Electr. Dev., Vol. 49, No. 4, 590-597, 2002.
doi:10.1109/16.992867

11. Im, S.N. Srivastava, K. Banerjee, and K. Goodson, "Thermal scaling analysis of multilevel C/low-k interconnect structures in deep nanometer scale technologies," Proc. 22th Int. VLSI Multilevel Interconnect Conf. (VMIC), 3-6, 2005.

12. Zhang, R., S. Dods, and P. Catrysse, "FDTD approach for optical metallic material," Laser Focus World, 68, July 2004.

13. Veronis, G., R. W. Dutton, and S. Fan, "Metallic photonic crystals with strong broadband absorption at optical frequencies over wide angular range," J. Appl. Phys., Vol. 97, No. 9, 2005.
doi:10.1063/1.1889248

14. Ordal, M. A., L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, Jr., and C. A. Ward, "Optical properties of the metals Al, Co, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared," Appl. Optics, Vol. 22, No. 7, 4493-4499, 1983.

15. Ordal, M. A., R. J. Bell, R. W. Alexander, Jr., L. L. Long, and M. R. Querry, "Optical properties of the metals Al, Co, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared," Appl. Optics, Vol. 24, No. 24, 1099-1120, 1985.

16. Tretyakov, S. A., F. Mariotte, C. R. Simovski, T. G. Kharina, and J.-P. Heliot, "Analytical antenna model for chiral scatterers: comparison with numerical and experimental data," IEEE Trans. Antennas and Propagat., Vol. 44, No. 7, 1006-1014, 1996.
doi:10.1109/8.504309

17. Tretyakov, S. A., "Metamaterials with wideband negative permittivity and permeability," Microw. Opt. Techn. Lett., Vol. 31, No. 3, 163-165, 2001.
doi:10.1002/mop.1387

18. King, R. W. P. and C. W. Harrison, Antennas and Waves: A Modern Approach, MIT Press, 1969.

19. Orfanidis, S. J., Electromagnetic Waves and Antennas, http://www.ece.rutgers.edu/ orfanidi/ewa.

20. Sazonov, D.M., Anntennas and Microwave Devices, Vysschaya Shkola, 1988.

21. Risko, J. J., L. J. Brillson, R. W. Bigelow, and T. J. Fabish, "Electron energy loss spectroscopy and the optical properties of polymethylmethacrylate from 1 to 300 eV," J. Chem Phys., Vol. 69, No. 9, 3931-3939, 1978.
doi:10.1063/1.437131

22. Koledintseva, M. Y., J. L. Drewniak, D. J. Pommerenke, K. N. Rozanov, G. Antonini, and A. Orlandi, "Wideband lorentzian media in the FDTD algorithm," IEEE Trans. Electromag. Compat., Vol. 47, No. 2, 392-398, 2005.
doi:10.1109/TEMC.2005.847406

23. Colored Optical Glass, http://www.lzos.ru/en/glass color.htm.

Professor Marina Koledintseva

Professor Richard DuBroff

Professor Robert Schwartz