Lefthanded materials and negative refraction: Transfer matrix and FDTD calculations
Abstract
We will present transfer matrix calculations of metallic wires, split ring resonators (SRR) and lefthanded materials (LHM). Our results [1] show that the transfer matrix method can capture all the details characteristics of the metamaterials. In particular the dependence of the resonance frequency and its width on the structural parameters of the SRR and the size of the unit cell is studied. Also the dependence of the imaginary part of effective permittivity of arrays of metallic wires is studied in detail. It is found [2,3] that the imaginary part of effective permittivity has small values even for wires as small as 20 micron in diameter. The transfer matrix is very useful in calculating both the amplitude and the phase of the transmission and reflection coefficient. These numerical data was used [4] in the determination of the effective parameters of the metamaterials. It was indeed found that the refractive index was unambiguously negative in the frequency region where both ɛ and μ were negative. Finally, we will show that SRR have a strong electric response, equivalent to that of cut wires [5], which dominates the response of LHM. A new criterion is introduced to clearly identify if an experimental expression peak is left or right handed. Finite difference time domain (FDTD) simulations will be presented for the transmission of the EM wave through the interface of the positive and negative refraction index. It is found [6] that the wave is trapped temporarily at the interface and after a long time the wave front moves eventually in the direction of negative refraction. The differences between negative refraction in photonic crystals and lefthanded materials will be also discussed. Work supported by USDOE, DARPA, NSF and EU (DALHM project). References: [1] P. Markos and C. M. Soukoulis, Phys. Rev. B 65, 033401 (2002); Phys. Rev. E 65, 036622 (2002). [2] P. Markos, I. Rousochatzakis and C. M. Soukoulis, Phys. Rev. B 66, 045601 (2002). [3] P. Markos and C. M. Soukoulis, Optics Letters 28, 846 (2003); Optics Express 11, 649 (2003). [4] D. R. Smith, S. Schultz, P. Markos and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002). [5] Th. Koschny, P. Markos, D. R. Smith and C. M. Soukoulis, Phys. Rev. E 67, xxxx (2003) [6] S. Foteinopoulou, E. N. Economou and C. M. Soukoulis, Phys. Rev. Lett. 90, 107402 (2003); S. Foteinopoulou and C. M. Soukoulis, Phys. Rev. B 67, 235107 (2003)
 Publication:

APS March Meeting Abstracts
 Pub Date:
 March 2004
 Bibcode:
 2004APS..MAR.U3003S