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$\mathcal{PT}$-symmetric nonlinear metamaterials and zero-dimensional systems.
- Source :
-
Applied Physics A: Materials Science & Processing . May2014, Vol. 115 Issue 2, p449-458. 10p. - Publication Year :
- 2014
-
Abstract
- A one dimensional, parity-time ( $\mathcal{PT}$)-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 $\mathcal{PT}$-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 ( $\mathcal{PT}$ dimer chain). The latter system features a two-band, gapped spectrum with its shape determined by the gain/loss coefficient as well as the interelement coupling. In the presence of nonlinearity, the $\mathcal{PT}$ dimer chain configuration with balanced gain and loss supports nonlinear localized modes in the form of a novel type of 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. Fundamental 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 $\mathcal{PT}$ 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 behavior is similar to a transition from the exact to the broken $\mathcal{PT}$ phase in higher-dimensional $\mathcal{PT}$-symmetric systems. A stability condition relating the parameters of the problem is obtained in the case of a piece-wise constant gain/loss function that allows the construction of a phase diagram with alternating stable and unstable regions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09478396
- Volume :
- 115
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Applied Physics A: Materials Science & Processing
- Publication Type :
- Academic Journal
- Accession number :
- 95711891
- Full Text :
- https://doi.org/10.1007/s00339-013-8035-2