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Analytical modelling of linear and nonlinear properties of metamaterials based on multipole expansion

: Petschulat, J.; Chipouline, A.; Pshenay-Severin, E.; Tünnermann, A.; Pertsch, T.; Menzel, C.; Rockstuhl, C.; Paul, T.; Lederer, F.


Kuzmiak, V. ; Society of Photo-Optical Instrumentation Engineers -SPIE-, Europe, Cardiff:
Metamaterials IV : 20 - 22 April 2009, Prague, Czech Republik; held at the SPIE Europe Congress on Optics and Optoelectronics
Bellingham, WA: SPIE, 2009 (Proceedings of SPIE 7353)
ISBN: 978-0-8194-7627-2
Paper 73530D
Conference "Metamaterials" <4, 2009, Prague>
Europe Optics + Optoelectronics Sympoium <2009, Prague>
Conference Paper
Fraunhofer IOF ()

A simple analytical model has been developed within the scopes of the macroscopic Maxwell's equations. In the framework of this model the dispersion relation for plane waves has been calculated for the case of Cut-Wire (CW) and Split Ring Resonator (SRR) geometries. The dispersion relation has been compared with rigorous numerical calculations. A possible way to introduce the electric and magnetic material parameters has been suggested. Validity criteria and applicability limitations of the developed model are discussed. A new type of nonlinearity specific for the metamaterials - Multipole Nonlinearity - is identified based on the developed model, wheras the second harmonic generation (SHG) process is considered in detail.