Magnetic response of nanoscale left-handed metamaterials

Using detailed simulations we investigate the magnetic response of metamaterials consisting of pairs of parallel slabs or combinations of slabs with wires (including the fishnet design) as the length scale of the structures is reduced from millimeter to nanometer. We observe the expected saturation of the magnetic-resonance frequency when the structure length scale goes to the submicron regime, as well as weakening of the effective permeability resonance and reduction in the spectral width of the negative permeability region. All these results are explained by using an equivalent resistor-inductor-capacitor circuit model, taking into account the current-connected kinetic energy of the electrons inside the metallic parts through an equivalent inductance, added to the magnetic field inductance in the unit cell. Using this model we derive simple optimization rules for achieving optical negative permeability metamaterials with improved performance. Finally, we analyze the magnetic response of the fishnet design and we explain its superior performance regarding the high attainable magnetic-resonance frequency, as well as its poor performance regarding the width of the negative permeability region.