volume | PIER Journals

Abstract

In this paper we analyze the electromagnetic response of a metamaterial slab in the case of normal incidence using the point-dipole interaction model and an expansion of polarization by eigenmodes. The problem is simplified by assuming that the lattice dimensions are smaller than a half wavelength and invoking the nearest neighbor approximation. In this manner, we find the structure supports three modes: an ordinary mode and two extraordinary modes. In the long-wavelength limit, the ordinary mode propagates with the same wave number as that predicted using the classic Clausius-Mossotti relations, while, for most cases, the two extraordinary modes are confined to thin surface transition layers near the boundaries of the slab. A systematic method is presented to find the scattering from the slab, and the results are confirmed by full wave simulation using Ansoft HFSS.

1. Pendry, J. B., "Negative refraction makes a perfect lens," Physical Review Letters, Vol. 85, 3966-3969, Oct. 30 2000.
doi:10.1103/PhysRevLett.85.3966 Google Scholar

2. Maystre, D. and S. Enoch, "Perfect lenses made with left-handed materials: Alice's mirror?," Journal of the Optical Society of America A | Optics Image Science and Vision, Vol. 21, 122-131, Jan. 2004.
doi:10.1021/nl047957a Google Scholar

3. Larkin, I. A. and M. I. Stockman, "Imperfect perfect lens," Nano Letters, Vol. 5, 339-343, Feb. 2005.
doi:10.1063/1.1554779 Google Scholar

4. Smith, D. R., D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, "Limitations on subdiffraction imaging with a negative refractive index slab," Applied Physics Letters, Vol. 82, 1506-1508, Mar. 2003. Google Scholar

5. French, O. E., K. I. Hopcraft, and E. Jakeman, "Perturbation on the perfect lens: The near-perfect lens," New Journal of Physics, Vol. 8, No. 271, Nov. 13 2006.
doi:10.1063/1.1650548 Google Scholar

6. Merlin, R., "Analytical solution of the almost-perfect-lens problem," Applied Physics Letters, Vol. 84, 1290-1292, Feb. 23 2004. Google Scholar

7. Enoch, S., G. Tayeb, P. Sabouroux, N. Guerin, P. Vincent, and , "A metamaterial for directive emission," Physical Review Letters, Vol. 89, 213902-1-213902-4, Nov. 2002.
doi:10.1109/TAP.2006.875470 Google Scholar

8. Alu, A., F. Bilotti, N. Engheta, and L. Vegni, "Metamaterial covers over a small aperture," IEEE Transactions on Antennas and Propagation, Vol. 54, 1632-1643, Jun. 2006.
doi:10.2528/PIER05121101 Google Scholar

9. Li, B., B. Wu, and C. H. Liang, "Study on high gain circular waveguide array antenna with metamaterial structure," Progress In Electromagnetics Research, Vol. 60, 207-219, 2006. Google Scholar

10. Saenz, E., K. Guven, E. Ozbay, I. Ederra, and R. Gonzalo, "Enhanced directed emission from metamaterial based radiation source," Applied Physics Letters, Vol. 92, 204103-1-204103-3, May 2008.
doi:10.1109/LAWP.2002.802576 Google Scholar

11. Engheta, N., "An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability," IEEE Antennas and Wireless Propagation Letters, Vol. 1, 10-13, 2002.
doi:10.1109/LAWP.2004.836576 Google Scholar

12. Caiazzo, M., S. Maci, and N. Engheta, "A metamaterial surface for compact cavity resonators," IEEE Antennas and Wireless Propagation Letters, Vol. 3, 261-264, 2004.
doi:10.1049/iet-map:20060309 Google Scholar

13. Holloway, C. L., D. C. Love, E. F. Kuester, A. Salandrino, and N. Engheta, "Sub-wavelength resonators: On the use of metafilms to overcome the lambda/2 size limit," IET Microw. Antennas Propag., Vol. 2, 120-129, Mar. 2008.
doi:10.1002/mop.21891 Google Scholar

14. Bilotti, F., L. Nucci, and L. Vegni, "An SRR based microwave absorber," Microwave and Optical Technology Letters, Vol. 48, 2171-2175, Nov. 2006.
doi:10.1016/j.metmat.2009.02.001 Google Scholar

15. Scher, A. D. and E. F. Kuester, "Extracting the bulk effective parameters of a metamaterial via the scattering from a single planar array of particles," Metamaterials, Vol. 3, No. 1, 44-55, 2009. Google Scholar

16. Simovski, C. R. and S. A. Tretyakov, "Local constitutive parameters of metamaterials from an effective-medium perspective," Physical Review B, Vol. 75, No. 195111-1, 1-10, May 2007. Google Scholar

17. Smith, D. R., S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coe±cients," Physical Review B, Vol. 65, 195104-1-195104-5, May 15 2002. Google Scholar

18. Smith, D. R., D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Physical Review E, Vol. 71, No. 036617, 1-11, Mar. 2005.
doi:10.1016/0038-1098(80)90743-7 Google Scholar

19. Kar, N. and A. Bagchi, "Local-field effect near the surface of dipolar lattices," Solid State Communications, Vol. 33, 645-648, 1980.
doi:10.1016/0921-4526(90)90354-W Google Scholar

20. Poppe, G. P. M. and C. M. J. Wijers, "Exact solution of the optical-response of thick slabs in the discrete dipole approach," Physica B, Vol. 167, 221-237, Dec. 1990.
doi:10.1063/1.464534 Google Scholar

21. Clercx, H. J. H. and G. Bossis, "Electrostatic interactions in slabs of polarizable particles," Journal of Chemical Physics, Vol. 98, 8284-8293, May 1993.
doi:10.1119/1.1539100 Google Scholar

22. Berman, D. H., "An extinction theorem for electromagnetic waves in a point dipole model," American Journal of Physics, Vol. 71, 917-924, Sep. 2003. Google Scholar

23. Sivukhin, D. V., "Molecular theory of the reflection and refraction of light," Zh. Eksp. Teor. Fiz., Vol. 18, 976-994, 1948. Google Scholar

24. Scher, A. D., Boundary effects in the electromagnetic metamaterial using the point-dipole interaction model, Ph.D. Dissertation, University of Colorado, Boulder, 2008.

25. Belov, P. A. and C. R. Simovski, "Homogenization of electromagnetic crystals formed by uniaxial resonant scatterers," Physical Review E, Vol. 72, No. 026615, 1-15, Aug. 2005. Google Scholar

26 . Silveirinha, M. G., "Generalized Lorentz-Lorenz formulas for microstructured materials," Physical Review B, Vol. 76, 245117-1-245117-9, Dec. 2007. Google Scholar

27. Silveirinha, M. G., "Metamaterial homogenization approach with application to the characterization of microstructured composites with negative parameters," Physical Review B, Vol. 75, No. 115104, 1-15, Mar. 2007. Google Scholar

28. Ewald, P. P., On the Foundations of Crystal Optics, Air Force Cabridge Research Laboratories, 1970.
doi:10.1103/PhysRev.183.834

29. Mahan, G. D. and G. Obermair, "Polaritons at surfaces," Physical Review, Vol. 183, 834-841, 1969.
doi:10.1063/1.1681213 Google Scholar

30. Philpott , M. R., "Reflection of light by a semi-in¯nite dielectric," Journal of Chemical Physics, Vol. 60, 1410-1419, 1974.
doi:10.1103/PhysRevB.14.3471 Google Scholar

31. Philpott, M. R., "Polaritons in a spatially dispersive dielectric half space ," Physical Review B, Vol. 14, 3471-3487, 1976.
doi:10.1063/1.1681392 Google Scholar

32. Philpott, M. R., "Effect of spatial dispersion of S-polarized optical properties of a slab dielectric," Journal of Chemical Physics, Vol. 60, 2520-2529, 1974.
doi:10.1364/JOSAB.13.001679 Google Scholar

33. Gadomsky, O. N. and K. V. Krutitsky, "Near-field effect in surface optics," Journal of the Optical Society of America B --- Optical Physics, Vol. 13, 1679-1690, Aug. 1996.
doi:10.1088/0953-4075/30/22/027 Google Scholar

34. Krutitsky, K. V. and S. V. Suhov, "Near-field effect in classical optics of ultra-thin films," Journal of Physics B --- Atomic Molecular and Optical Physics, Vol. 30, 5341-5358, Nov. 1997.
doi:10.1163/156939399X00826 Google Scholar

35. Simovski, C. R., P. A. Belov, M. S. Kondratjev, and , "Electromagnetic interaction of chiral particles in three-dimensional arrays," Journal of Electromagnetic Waves and Applications,, Vol. 13, No. 2, 189-204, 1999.
doi:10.1117/12.396407 Google Scholar

36. Belov, P. A. and C. R. Simovski, "Oblique propagation of electromagnetic waves in regular 3D lattices of scatterers (dipole approximation)," Proc. SPIE, Vol. 4073, 266-276, 2000.
doi:10.1134/1.1307445 Google Scholar

37. Gadomskii, O. N. and S. V. Sukhov, "Microscopic theory of a transition layer on the ideal surface of semiinfinite dielectric media and the near-field effect," Optics and Spectroscopy, Vol. 89, 261-267, Aug. 2000.
doi:10.1103/PhysRevB.62.13718 Google Scholar

38. Simovski, C. R., M. Popov, and S. L. He, "Dielectric properties of a thin film consisting of a few layers of molecules or particles," Physical Review B, Vol. 62, 13718-13730, Nov. 15 2000.
doi:10.1364/JOSAA.17.001791 Google Scholar

39. Tretyakov, S. A. and A. J. Viitanen, "Plane waves in regular arrays of dipole scatterers and effective-medium modeling," Journal of the Optical Society of America A --- Optics Image Science and Vision, Vol. 17, 1791-1797, Oct. 2000.
doi:10.1016/S0375-9601(03)00494-8 Google Scholar

40. Simovski, C. R. and S. L. He, "Frequency range and explicit expressions for negative permittivity and permeability for an isotropic medium formed by a lattice of perfectly conducting omega particles," Physics Letters A, Vol. 311, 254-263, May 12 2003.
doi:10.1016/j.metmat.2007.09.002 Google Scholar

41. Simovski, C. R., "Bloch material parameters of magneto-dielectric metamaterials and the concept of Bloch lattices," Metamaterials, Vol. 1, 62-80, 2007.
doi:10.1016/j.metmat.2008.09.003 Google Scholar

42. Simovski, C. R., "Analytical modelling of double-negative composites," Metamaterials, Vol. 2, 169-185, 2008. Google Scholar

43. Belov, P. A. and C. R. Simovski, "Boundary conditions for interfaces of electromagnetic crystals and the generalized Ewald Oseen extinction principle," Physical Review B, Vol. 73, No. 045102, 1-14, Jan. 2006.
doi:10.2528/PIERB09021107 Google Scholar

44. Scher, A. D. and E. F. Kuester, "Boundary effects in the electromagnetic response of a metamaterial in the case of normal incidence," Progress In Electromagnetics Research B, Vol. 14, 341-381, 2009.
doi:10.1093/ietcom/e91-b.6.1819 Google Scholar

45. Shore, Shore and A. D. Yaghjian, "Electromagnetic waves on partially ¯nite periodic arrays of lossless or lossy penetrable spheres," IEICE Transactions on Communications, Vol. E91b, 1819-1824, Jun. 2008. Google Scholar

46. Sipe, J. E. and J. V. Kranendonk, "Macroscopic electromagnetic theory of resonant dielectrics," Physical Review A, Vol. 9, 1806-1822, 1976. Google Scholar

Dr. Aaron D. Scher

Dr. Edward F. Kuester