Abstract

In this work we use the multipole expansion approach developed in [1] in order to describe analytically linear and nonlinear optical properties of metamaterials. We show that especially the consideration of electric quadrupole multipoles (not only the magnetic dipole one) is required by basic principles and provides the possibility to adequately analyse an effective magnetic material response. To motivate the appearance of such multipole terms we applied numerical methods to calculate the near field radiation patterns as well as far field properties. The dispersion relation of a single metamaterial layer and 3D infinitely expanded bulk metamaterials are derived as well. In order to validate our model for particular cases, we applied the formalism for the split-ring resonator and the cut-wire structure. In principle, the formalism is not restricted by any special metaatom geometry. Only the intrinsic electron dynamics in the respective metaatom must be known.

© 2009 IEEE