We theoretically analyze the properties of metamaterials which have been designed by taking advantage of Babinet's principle. It is shown that the complementary structure exhibits both a complementary spectral response and field distribution of the respective eigenmodes. For comple-mentary split-ring resonators, we show that the spectral resonance features can be explained from two different perspectives. On one hand they can be explained as plasmon polariton resonances in dielectric nanostructures surrounded by metal, on the other hand they can be understood as guided mode resonances with vanishing propagation constant. The physical origin of these modes and differences to the conventional split-ring geometry are discussed. 15. R. Ullrich, " Far-infrared properties of metallic mesh and its complementary structure, " Infrared Phys. 7, 37-55 (1967). 16. L. C. Botton, R. C. McPhedran, and G. W. Milton, " Perfectly conducting lamellar gratings: Babinet's principle and circuit models, " J. Mod. Opt. 42, 2453-2473 (1995). 17. T. Zentgraf, C. Rockstuhl, T. P. Meyrath, A. Seidel, S. Kaiser, F. Lederer, and H. Giessen, " Babinet's principle for optical frequency metamaterials and nanoantennas, " Phys. Rev. B 76, 033407 (2007). 18. C. Rockstuhl and F. Lederer, " Negative-index metamaterials from nanoapertures, " Phys. Rev. B 76, 125426 (2007). 19. J. A. Porto, F. J. Garca-Vidal, and J. B. Pendry, " Transmission Resonances on Metallic Gratings with Very Narrow Slits, " Phys. Rev. Lett. 83, 2845-2848 (1999). 20. X. Shi, L. Hesselink, and R. L. Thornton, " Ultrahigh light transmission through a C-shaped nanoaperture, " Opt. Lett. 28, 1320-1322 (2003). 21. C. Rockstuhl, F. Lederer, T. Zentgraf, and H. Giessen, " Enhanced transmission of periodic, quasi-periodic, and random nanoaperture arrays, " Appl. Phys. Lett. 91, 151109 (2007). 22. F. J. García de Abajo, R. Gómez-Medina, and J. J. Sáenz, " Full transmission through perfect-conductor subwave-length hole arrays, " Phys. Rev. E 72, 016608 (2005). 23. F. J. García de Abajo, " Light scattering by particle and hole arrays, " Rev. Mod. Phys. 79, 1267-1290 (2007). 24. P. B. Johnson and R. W. Christy, " Optical constants of the noble metals, " Phys. Rev. B 6, 4370-4379 (1972). 25. D. H. Dawes, R. C. McPhedran, and L. B. Whitbourn, " Thin capacitive meshes on a dielectric boundary: theory and experiment, " Appl. Opt. 26, 3498-3510 (1989). 26. L. Li, " New formulation of the Fourier modal method for crossed surface-relief gratings, " J. Opt. Soc. Am. A 14, 2758-2767 (1997). 27. C. Rockstuhl, T. Zentgraf, C. Etrich, J. Kuhl, F. Lederer, and H. Giessen, " On the reinterpretation of resonances in split-ring-resonators at normal incidence, " Opt. Express 14, 8827-8836 (2006). 28. C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, " Resonances of split-ring resonator metamaterials in the near infrared, " Appl. Phys. B. 84, 219-227 (2006).
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