Nonlinear Localization in Metamaterials

The existence and stability of dissipative breathers in rf SQUID (Superconducting Quantum Interference Device) arrays is investigated numerically. In such arrays, the nonlinearity which is intrinsic to each SQUID, along with the weak magnetic coupling of each SQUID to its nearest neighbors, result in the formation of discrete breathers. We analyze several discrete breather excitations in rf SQUID arrays driven by alternating flux sources in the presence of losses. The delicat...

The existence and stability of dissipative discrete breathers (DDBs) in rf superconducting quantum interference device (SQUID) arrays in both one and two dimensions is investigated numerically. In an rf SQUID array, the nonlinearity which is intrinsic to each SQUID due to the presence of the Josephson junction (on-site nonlinearity), along with the weak coupling of each SQUID to its nearest neighbors through magnetic forces, result in the appearance of discrete breathers. We ...

On a two-dimensional planar parity-time-($\mathcal{PT}$-)symmetric nonlinear magnetic metamaterial, consisting of split-ring dimers with balanced gain and loss, discrete breather solutions can be found. We extend these studies and by numerical calculations reveal the existence of further stable, long-lived oscillations, with certain frequencies, in the breather spectrum. We describe these oscillations in terms of an analytical breather theory, and show that they can be interp...

The dynamic equations for the fluxes through the SQUIDs that form a two-dimensional metamamaterial on a Lieb lattice are derived, and then linearized around zero flux to obtain the linear frequency spectrum according to the standard procedure. That spectrum, due to the Lieb lattice geometry, possesses a frequency band structure exhibiting two characteristic features; two dispersive bands, which form a Dirac cone at the corners of the first Brillouin zone, and a flat band cros...

Metamaterials (MMs), i.e. artificial media designed to achieve properties not available in natural materials, have been the focus of intense research during the last two decades. Many properties have been discovered and multiple designs have been devised that lead to multiple conceptual and practical applications. Superconducting MMs have the advantage of ultra low losses, a highly desirable feature. The additional use of the Josephson effect and SQUID configurations produce ...

Magnetic metamaterials composed of split-ring resonators or $U-$type elements may exhibit discreteness effects in THz and optical frequencies due to weak coupling. We consider a model one-dimensional metamaterial formed by a discrete array of nonlinear split-ring resonators with each ring interacting with its nearest neighbours. On-site nonlinearity and weak coupling among the individual array elements result in the appearence of discrete breather excitations or intrinsic loc...

We introduce a one dimensional parity-time (PT)-symmetric nonlinear magnetic metamaterial consisted of split ring dimers having both gain and loss. When nonlinearity is absent we find a transition between an exact to a broken PT-phase; in the former the system features a two band gapped spectrum with shape determined by the gain and loss coefficients as well as the inter-unit coupling. In the presence of nonlinearity we show numerically that as a result of the gain/dissipatio...

A SQUID (Superconducting QUantum Interference Device) metamaterial on a Lieb lattice with nearest-neighbor coupling supports simultaneously stable dissipative breather families which are generated through a delicate balance of input power and intrinsic losses. Breather multistability is possible due to the peculiar snaking flux ampitude - frequency curve of single dissipative-driven SQUIDs, which for relatively high sinusoidal flux field amplitudes exhibits several stable and...

Breathing solitons consist of a fast beating wave within a compact envelope of stable shape and velocity. They manifest themselves in a variety of contexts such as plasmas, optical fibers and cold atoms, but have remained elusive when energy conservation is broken. Here, we report on the observation of breathing, unidirectional, arbitrarily long-lived solitons in non-reciprocal, non-conservative active metamaterials. Combining precision desktop experiments, numerical simulati...

Discrete breathers, or intrinsic localized modes, are spatially localized, time--periodic, nonlinear excitations that can exist and propagate in systems of coupled dynamical units. Recently, some experiments show the sighting of a form of discrete breather that exist at the atomic scale in a magnetic solid. Other observations of breathers refer to systems such as Josephson--junction arrays, photonic crystals and optical-switching waveguide arrays. All these observations under...