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

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageEnglish
Title of host publicationMetamaterials IV
Publication statusPublished - 2009
Externally publishedYes
EventMetamaterials IV - Prague, Czech Republic
Duration: 20 Apr 200922 Apr 2009

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X


ConferenceMetamaterials IV
Country/TerritoryCzech Republic


  • Analytical modeling
  • Metamaterials
  • Nonlinear optics
  • Plasmonics


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