Toroidal dipoles generated in nonlinear plasmonic metamaterials

Toroidal multipoles are a class of electromagnetic moments which must be separately considered from the electric and magnetic multipoles in a multipole decomposition of the sources of the electromagnetic field. We present a plasmonic metamaterial exhibiting a resonant enhancement of the lowest order toroidal multipole at the second harmonic (SH). The total transmission, reflection and absorption spectra at the fundamental frequency (FF) show that the enhanced nonlinear optical response of the toroidal metamaterial is due to an excitation of an electromagnetic resonance at the FF. This connection is also illustrated by the spectral characteristics of the power radiated in the direction of transmission at the SH as well as the frequency dependence of the electric, magnetic, and toroidal dipole radiation at the SH.