  Superconducting metamaterials comprising rf SQUIDs (Superconducting QUantum
Interference Devices) have been recently realized and investigated with respect
to their tuneability, permeability and dynamic multistability properties. These
properties are a consequence of intrinsic nonlinearities due to the sensitivity
of the superconducting state to external stimuli. SQUIDs, made of a
superconducting ring interrupted by a Josephson junction, possess yet another
source of nonlinearity, which makes them widely tuneable with an applied dc
dlux. A model SQUID metamaterial, based on electric equivalent circuits, is
used in the weak coupling approximation to demonstrate the dc flux tuneability,
dynamic multistability, and nonlinear transmission in SQUID metamaterials
comprising non-hysteretic SQUIDs. The model equations reproduce the
experimentally observed tuneability patterns, and predict tuneability with the
power of an applied ac magnetic magnetic field. Moreover, the results indicate
the opening of nonlinear frequency bands for energy transmission through SQUID
metamaterials, for sufficiently strong ac fields.
