  We analyze the effect of microscopic disorder on the macroscopic properties
of composite metamaterials and study how weak statistically independent
fluctuations of the parameters of structure elements can modify their
collective magnetic response and left-handed properties. We demonstrate that
even a weak microscopic disorder may lead to a substantial modification of the
metamaterial magnetic properties, and 10% deviation in the parameters of the
microscopic resonant elements may lead to a substantial suppression of wave
propagation in a wide frequency range. A noticeable suppression occurs also if
more than 10% of resonant magnetic elements possess strongly different
properties, but in this latter case the defects can create an additional weak
resonant line. These results are of the key importance for characterizing and
optimizing the novel composite metamaterials with left-handed properties at
terahertz and optical frequencies.
