volume | PIER Journals

Abstract

We study the propagation of waves on infinite and finite size arrays made of subwavelength magnetoelectric resonators. We propose an analytical study where each magnetoelectric resonator is modelled simultaneously by an electric and a magnetic dipole. We show how near field coupling and wavenumber quantification due to the finite size of the structure induce a frequency splitting of the resonator fundamental mode. We theoretically demonstrate that despite a spatial period of the waves smaller than half wavelength (in vacuum), the structure can efficiently emits radiations. An analytic expression of the Q factor associated to the radiation losses is proposed. To correctly estimate this factor, we show that not only near but also far field interaction terms between the dipoles must to be considered.

1. Montgomery, J., "Scattering by an infinite periodic array of thin conductors on a dielectric sheet," IEEE Transactions on Antennas and Propagation, Vol. 23, 70-75, Jan. 1975.
doi:10.1109/TAP.1975.1141006

2. Tsao, C.-H. and R. Mittra, "Spectral-domain analysis of frequency selective surfaces comprised of periodic arrays of cross dipoles and Jerusalem crosses," IEEE Transactions on Antennas and Propagation, Vol. 32, 478-486, May 1984.
doi:10.1109/TAP.1984.1143348

3. Zarrillo, G. and K. Aguiar, "Closed-form low frequency solutions for electromagnetic waves through a frequency selective surface," IEEE Transactions on Antennas and Propagation, Vol. 35, 1406-1417, Dec. 1987.
doi:10.1109/TAP.1987.1144035

4. Smith, D. R., S. Schultz, N. Kroll, M. Sigalas, K. M. Ho, and C. M. Soukoulis, "Experimental and theoretical results for a two-dimensional metal photonic band-gap cavity," Applied Physics Letters, Vol. 65, No. 5, 645-647, 1994.
doi:10.1063/1.112258

5. Sigalas, M. M., C. T. Chan, K. M. Ho, and C. M. Soukoulis, "Metallic photonic band-gap materials," Phys. Rev. B, Vol. 52, 11744-11751, Oct. 1995.

6. Suzuki, T. and P. K. L. Yu, "Dispersion relation at point l in the photonic band structure of the face-centered-cubic lattice with active or conductive dielectric media," J. Opt. Soc. Am. B, Vol. 12, 583-591, Apr. 1995.
doi:10.1364/JOSAB.12.000583

7. Sievenpiper, D. F., M. E. Sickmiller, and E. Yablonovitch, "3d wire mesh photonic crystals," Phys. Rev. Lett., Vol. 76, 2480-2483, Apr. 1996.
doi:10.1103/PhysRevLett.76.2480

8. Maier, S. A., P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater., Vol. 2, 229-232, Apr. 2003.
doi:10.1038/nmat852

9. Pendry, J. B., A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett., Vol. 76, 4773-4776, Jun. 1996.
doi:10.1103/PhysRevLett.76.4773

10. Smith, D. R., D. C. Vier, W. Padilla, S. C. Nemat-Nasser, and S. Schultz, "Loop-wire medium for investigating plasmons at microwave frequencies," Applied Physics Letters, Vol. 75, No. 10, 1425-1427, 1999.
doi:10.1063/1.124714

11. Maier, S. A., M. L. Brongersma, and H. A. Atwater, "Electromagnetic energy transport along arrays of closely spaced metal rods as an analogue to plasmonic devices," Applied Physics Letters, Vol. 78, No. 1, 16-18, 2001.
doi:10.1063/1.1337637

12. Maier, S. A., P. G. Kik, and H. A. Atwater, "Observation of coupled plasmon-polariton modes in au nanoparticle chain waveguides of di®erent lengths: Estimation of waveguide loss," Applied Physics Letters, Vol. 81, No. 9, 1714-1716, 2002.
doi:10.1063/1.1503870

13. Smith, D. R., W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity ," Phys. Rev. Lett., Vol. 84, 4184-4187, May 2000.
doi:10.1103/PhysRevLett.84.4184

14. Guida, G., D. Maystre, G. Tayeb, and P. Vincent, "Mean-field theory of two-dimensional metallic photonic crystals," J. Opt. Soc. Am. B, Vol. 15, 2308-2315, Aug. 1998.
doi:10.1364/JOSAB.15.002308

15. Abdeddaim, R., A. Ourir, and J. de Rosny, "Realizing a negative index metamaterial by controlling hybridization of trapped modes," Phys. Rev. B, Vol. 83, 033101, Jan. 2011.
doi:10.1103/PhysRevB.83.033101

16. Ourir, A., R. Abdeddaim, and J. de Rosny, "Double-t metamaterial for parallel and normal transverse electric incident waves ," Optics Letters, Vol. 36, 1527-1529, May 2011.
doi:10.1364/OL.36.001527

17. Podolskiy, V. A., A. K. Sarychev, and V. M. Shalaev, "Plasmon modes in metal nanowires and left-handed materials," Journal of Nonlinear Optical Physics & Materials, Vol. 11, No. 1, 65-74, 2002.
doi:10.1142/S0218863502000833

18. Zhang, S., W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of nearinfrared negative-index metamaterials," Phys. Rev. Lett., Vol. 95, 137404, Sep. 2005.
doi:10.1103/PhysRevLett.95.137404

19. Dolling, G., C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Optics Letters, Vol. 30, 3198-3200, Dec. 2005.
doi:10.1364/OL.30.003198

20. Linden, S., M. Decker, and M. Wegener, "Model system for a one-dimensional magnetic photonic crystal," Phys. Rev. Lett., Vol. 97, 083902, Aug. 2006.
doi:10.1103/PhysRevLett.97.083902

21. Pendry, J. B., "Negative refraction makes a perfect lens," Phys. Rev. Lett., Vol. 85, 3966-3969, Oct. 2000.
doi:10.1103/PhysRevLett.85.3966

22. Alù, A. and N. Engheta, "Theory of linear chains of metamaterial/plasmonic particles as subdiffraction optical nanotransmission lines," Phys. Rev. B, Vol. 74, 205436, Nov. 2006.

22. Shvets, G., S. Trenda¯lov, J. B. Pendry, and A. Sarychev, "Guiding, focusing, and sensing on the subwavelength scale using metallic wire arrays," Phys. Rev. Lett., Vol. 99, 053903, Aug. 2007.
doi:10.1103/PhysRevLett.99.053903

24. Lemoult, F., G. Lerosey, J. de Rosny, and M. Fink, "Resonant metalenses for breaking the diffraction barrier," Phys. Rev. Lett., Vol. 104, 203901, May 2010.
doi:10.1103/PhysRevLett.104.203901

25. Li, X. and M. I. Stockman, "Highly efficient spatiotemporal coherent control in nanoplasmonics on a nanometer-femtosecond scale by time reversal," Phys. Rev. B, Vol. 77, 195109, May 2008.
doi:10.1103/PhysRevB.77.195109

26. Harrington, R., "Matrix methods for field problems," Proceedings of the IEEE, Vol. 55, 136-149, Feb. 1967.
doi:10.1109/PROC.1967.5433

27. Chen, C.-C., "Scattering by a two-dimensional periodic array of conducting plates," IEEE Transactions on Antennas and Propagation, Vol. 18, 660-665, Sep. 1970.
doi:10.1109/TAP.1970.1139760

28. Shamonina, E., V. A. Kalinin, K. H. Ringhofer, and L. Solymar, "Magnetoinductive waves in one, two, and three dimensions," Journal of Applied Physics, Vol. 92, 6252-6261, Nov. 2002.
doi:10.1063/1.1510945

29. Shamonina, E. and L. Solymar, "Magneto-inductive waves supported by metamaterial elements: Components for a onedimensional waveguide," Journal of Physics D-applied Physics, Vol. 37, Int. Phys. Dielectr. Grp., Feb. 2004.

30. Liu, N., H. Liu, S. Zhu, and H. Giessen, "Stereometamaterials," Nature Photonics, Vol. 3, 157-162, Mar. 2009.
doi:10.1038/nphoton.2009.4

31. Zhou, J., T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett., Vol. 95, 223902, Nov. 2005.

32. Aydin, K., I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonances for different split-ring resonator parameters and designs," New Journal of Physics, Vol. 7, No. 1, 168, 2005.
doi:10.1088/1367-2630/7/1/168

33. Penciu, R. S., K. Aydin, M. Kafesaki, T. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, "Multi-gap individual and coupled split-ring resonator structures," Optics Express, Vol. 16, 18131-18144, Oct. 2008.

34. Orfanidis, S. J., Electromagnetic Waves and Antennas, Electronic book, Chap. 16, 655, Aug. 2010, http://www.ece.rutgers.edu/ orfanidi/ewa/.

35. Sydoruk, O., O. Zhuromskyy, A. Radkovskaya, E. Shamonina, and L. Solymar, Theory and Phenomena of Metamaterials, Meta-materials Handbook, Chap. 7, 36-1{36-13, CRC Press/Taylor & Francis, 2009.

36. Liu, H., D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, "Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures," Phys. Rev. B, Vol. 76, 073101, Aug. 2007.
doi:10.1103/PhysRevB.76.073101

37. Balanis, C., Antenna Theory: Analysis and Design/Constantine A. Balanis, J. Wiley, New York, 1982.

38. Purcell, E. M., "Spontaneous emission probabilities at radio frequencies," Proceedings of the American Physical Society, Vol. 69, 674 American Physical Society, Apr. 1946.

39. Lemoult, F., M. Fink, and G. Lerosey, "Revisiting the wire medium: An ideal resonant metalens," Waves in Random and Complex Media, Vol. 21, No. 4, 591-613, 2011.
doi:10.1080/17455030.2011.611836

Dr. Camille Jouvaud

Dr. Abdelwaheb Ourir

Dr. Julien de Rosny