  In this paper we consider the resonant frequency of split-ring resonators and
double-bar resonators used to create artificial magnetic response at terahertz
and optical frequencies. It is known that geometrical scaling of the resonant
frequency of split rings breaks down at high frequencies (in the visible) due
to electromagnetic properties of metals at those frequencies. Here we will
discuss this phenomenon in terms of equivalent inductance and capacitance of
the ring, derive an approximate formula for the resonant frequency of split
rings in the visible and show how the limiting value of the resonant frequency
of extremely small split rings and double bars depends on particle shape.
