Advances in Radio Science www.adv-radio-sci.net 1684-9965 1684-9973 6 Kleinheubacher Berichte 2007 2008 10.5194/ars-6-77-2008 http://www.adv-radio-sci.net/6/77/2008/ http://www.adv-radio-sci.net/6/77/2008/ars-6-77-2008.html http://www.adv-radio-sci.net/6/77/2008/ars-6-77-2008.pdf 77 82 2008-05-26 Micro- and macroscopic simulation of periodic metamaterials R. Schuhmann schuhmann@tet.upb.de B. Bandlow G. Lubkowski T. Weiland Univ. Paderborn, EIM-E, FG Theoretische Elektrotechnik, Warburger Straße 100, 33098 Paderborn, Germany TU Darmstadt, Inst. für Theorie Elektromagnetischer Felder, Schloßgartenstraße 8, 64289 Darmstadt, Germany In order to characterize three-dimensional, left-handed metamaterials (LHM) we use electromagnetic field simulations of unit cells. For waves traveling in one of the main directions of the periodic LHM-arrays, the analysis is concentrated on the calculation of global quantities of the unit cells, such as scattering parameters or dispersion diagrams, and a careful interpretation of the results. We show that the concept of equivalent material values – which may be negative in a narrow frequency range – can be validated by large "global" simulations of a wedge structure. We also discuss the limitations of this concept, since in some cases the macroscopic behavior of an LHM cannot be accurately described by equivalent material values. Computer Simulation Technology GmbH: CST Studio Suite 2006, http://www.cst.com, 2007. Gutschling, S., Krüger, H., and Weiland, T.: Time Domain Simulation of Dispersive Media with the Finite Integration Technique, Int. J. Num. Modelling: Electronic Networks, Devices and Fields, 13, 329–348, 2000. Lubkowski, G., Schuhmann, R., and Weiland, T.: Extraction of effective metamaterial parameters by parameter fitting of dispersive models, Microwave Opt. Technol. Lett., 49, 285–288, 2006. Lubkowski, G., Hirtenfelder, F., Schuhmann, R., and Weiland, T.: 3D Full-wave Field Simulations of Double Negative Metamaterial Macrostructures, in: Proc. Metamaterials 2007, Rome, 22–24 October 2007, pp. 731–734, 2007. Pendry, J B., Holden, A J., Robbins, D J., and Stewart, W J.: Magnetism from conductors and enhanced nonlinear phenomena, IEEE T-MTT, 47, 2075, 1999. Shelby, R A., Smith, D R., and Schultz, S.: Experimental Verification of a Negative Index of Refraction, Science, 292, 77–79, 2001. Simovski, C R. and Tretyakov, S A.: Local constitutive parameters of metamaterials from an effective-medium perspective, Phys. Rev. B (Condensed Matter and Materials Physics), 75, 195111, \doi10.1103/PhysRevB.75.195111, prefixhttp://link.aps.org/abstract/PRB/v75/e195111, 2007. Smith, D R., Vier, D C., Kroll, N., and Schultz, S.: Direct calculation of permeability and permittivity for a left-handed metamaterial, Appl. Phys. Lett., 77, 2246–2248, 2000. Tsukerman, I.: The Anatomy of Negative Refraction, ICS Newsletter, 14, 3, 2007. Veselago, V.: The electrodynamics of substances with simultaneously negative values of $\epsilon$ and μ, Soviet Physics Uspekhi, 10, 509–514, 1968. Weiland, T.: Eine Methode zur Lösung der Maxwellschen Gleichungen für sechskomponentige Felder auf diskreter Basis, Archiv für Elektronik und Übertragungstechnik, 31, 116–120, 1977. Weiland, T.: Time domain electromagnetic field computation with finite difference methods, Int. J. Num. Modeling, 9, 295–319, 1996. Weiland, T., Schuhmann, R., Greegor, R., Parazzoli, C., Vetter, A., Smith, D., Vier, D., and Schultz, S.: Ab initio numerical simulation of left-handed metamaterials: Comparison of calculations and experiment, J. Appl. Phys., 90, 5419–5424, 2001. Yee, K S.: Numerical Solution of Initial Boundary Value Problems Involving Maxwell's Equations in Isotropic Media, IEEE Trans. Antennas and Propagation, 17, 585–589, 1966.