Microscopic Disorder in Metamaterials

We analyze the effect of microscopic disorder on macroscopic properties of composite metamaterials; we study how weak, statistically independent fluctuations of the parameters of the structure elements 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. We argue that these results are important for characterizing and optimizing novel composite metamaterials with the left-handed properties at terahertz and optical frequencies.