A one dimensional, parity-time \({\cal PT}\)-symmetric magnetic metamaterial comprising split-ring resonators having both gain and loss is investigated. In the linear regime, the transition from the exact to the broken \({\cal PT}\)-phase is determined through the calculation of the eigenfrequency spectrum for two different configurations; the one with equidistant split-rings and the other with the split-rings forming a binary pattern (\({\cal PT}\) dimer chain). The latter system features a two-band, gapped spectrum with its shape determined by the gain/loss coefficient as well as the inter-element coupling. In the presense of nonlinearity, the \({\cal PT}\) dimer chain with balanced gain and loss supports nonlinear localized modes in the form of novel discrete breathers below the lower branch of the linear spectrum. These breathers, that can be excited from a weak applied magnetic field by frequency chirping, can be subsequently driven solely by the gain for very long times. The effect of a small imbalance between gain and loss is also considered. Fundamendal gain-driven breathers occupy both sites of a dimer, while their energy is almost equally partitioned between the two split-rings, the one with gain and the other with loss. We also introduce a model equation for the investigation of classical \({\cal PT}\) symmetry in zero dimensions, realized by a simple harmonic oscillator with matched time-dependent gain and loss that exhibits a transition from oscillatory to diverging motion. This behaviour is similar to a transition from the exact to the broken \({\cal PT}\) phase in higher-dimensional \({\cal PT}-\)symmetric systems. A stability condition relating the parameters of the problem is obtained in the case of piecewise constant gain/loss function that allows for the construction of a phase diagram with alternating stable and unstable regions.

http://arxiv.org/abs/1304.0556
Pattern Formation and Solitons (nlin.PS); Materials Science (cond-mat.mtrl-sci); Optics (physics.optics)

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/dissipation matching a novel type of long-lived stable discrete breathers can form below the lower branch of the band with no attenuation. In these localized modes the energy is almost equally partitioned between two adjacent split rings on the one with gain and the other one with loss.

http://arxiv.org/abs/1210.2410
Materials Science (cond-mat.mtrl-sci); Pattern Formation and Solitons (nlin.PS); Optics (physics.optics)