  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 mm to nm. We observe the expected saturation of the magnetic
resonance frequency when the structure length-scale goes to the sub-micron
regime, as well as weakening of the effective permeability resonance and
reduction of the spectral width of the negative permeability region. All these
results are explained by using an equivalent resistor-inductor-capacitor (RLC)
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 of 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
inferior performance regarding the width of the negative permeability region.
