Nonlinear Magnetoinductive Transmission Lines

Lazarides, N.; Paltoglou, Vassilis; Tsironis, G. P.

doi:10.1142/s0218127411029689

Cited by 23 publications

(21 citation statements)

References 54 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1. For our considerations below, we will now derive an equation for the charge Q n of the capacitor of the nth SRR, similarly to what was done in [Lazarides et al, 2011]. Taking into regard that the charge Q n is given by:…”

Section: The Nonlinear Magnetic Metamaterials Modelmentioning

confidence: 99%

“…relevant experimental works on three-dimensional ("metacrystal") MMs [Huang et al, 2010] and on the modulation instability in MM waveguides [Tamayama et al, 2013]. In such settings, various studies have been performed, including the localization of EM energy and the formation of discrete breathers [Lazarides et al, 2006], magneto-inductive envelope solitons [Kourakis et al, 2007] and gap solitons [Cui et al, 2007], transfer of EM power in MM transmission lines [Lazarides et al, 2011] and others.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Bifurcation Results for Traveling Waves in Nonlinear Magnetic Metamaterials

Agaoglou

Rothos

Frantzeskakis

et al. 2014

Int. J. Bifurcation Chaos

View full text Add to dashboard Cite

In this work, we study a model of a one-dimensional magnetic metamaterial formed by a discrete array of nonlinear resonators. We focus on periodic and localized traveling waves of the model, in the presence of loss and an external drive. Employing a Melnikov analysis we study the existence and persistence of such traveling waves, and study their linear stability. We show that, under certain conditions, the presence of dissipation and/or driving may stabilize or destabilize the solutions. Our analytical results are found to be in good agreement with direct numerical computations.

show abstract

Section: The Nonlinear Magnetic Metamaterials Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bifurcation Results for Traveling Waves in Nonlinear Magnetic Metamaterials

Agaoglou

Rothos

Frantzeskakis

et al. 2014

Int. J. Bifurcation Chaos

View full text Add to dashboard Cite

show abstract

“…1). The SRRs are coupled magnetically and/or electrically through dipole-dipole forces [13][14][15][16] and are regarded as RLC circuits, featuring a resistance R, an inductance L, and a capacitance C. In the equivalent circuit model picture [16,[26][27][28], ex- …”

mentioning

confidence: 99%

“…In the equivalent circuit model picture [16,[26][27][28], ex-tended for the PT dimer chain, the dynamics of the charge q n in the capacitor of the nth SRR is governed by…”

mentioning

confidence: 99%

Gain-Driven Discrete Breathers inPT-Symmetric Nonlinear Metamaterials

2013

Self Cite

View full text Add to dashboard Cite

We introduce a one dimensional parity-time (PT )-symmetric nonlinear magnetic metamaterial consisting 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.PACS numbers: 63.20. Pw, 11.30.Er, 78.67.Pt Considerable research effort has recently focused in the investigation and developement of artificial materials that exhibit properties not found in nature. In the electromagnetic domain, these advances resulted in the construction of metamaterials, novel artificial structures that provide full access to all four quadrants of the real permittivity -permeability plane [1]. Recently, there has been increasing interest in synthetic materials with a combined parity -time (PT ) symmetry. Although quantum systems described by PT −symmetric Hamiltonians have been studied for many years ([2] and refs. therein), it was only recently realized that many classical systems are PT −symmetric [3]. Subsequently, the notion of PT symmetry has been extended to dynamical lattices, particularly in optics [4,5]. Soon after that, PT −symmetry breaking was experimentally observed [6][7][8]. Such considerations have been also extended in nonlinear lattices, where the existence of stable discrete solitons [9] and Talbot effects [10] was theoretically demonstrated.Among recent developements in PT −symmetric materials, the application of these ideas in electronic circuits [11] not only provides a platform for testing the new ideas within the framework of easily accessible experimental configurations, but also provides a link to metamaterials. Conventional, metallic metamaterials suffer from high losses that hamper their use in practical applications. However, building metamaterials with PT symmetry, relying on gain and loss, may provide a way out and moreover lead to new extraordinary properties. It is shown that PT −symmetric metamaterials undergo spontaneous symmetry breaking from the exact PT phase (real eigenfrequencies) to the broken PT phase (at least a pair of complex eigenfrequencies), with variation of the gain/loss coefficient. In the presence of nonlinearity, the generation of long-lived excitations in the form of discrete breathers (DBs) [12] is demonstrated numerically in metamaterial models. These novel gain-driven DBs, generated either by proper intialization of the PT metamaterial or purely dynamically through external driving, result from power matching of the input power through the gain mechanism and internal loss.SRR with Loss ...

show abstract

“…Metamaterial Lines.-SQUID metamaterials support flux waves that are capable of transmitting energy, in much the same way as in nonlinear magnetoinductive transmission lines made of conventional (metallic) metamaterials [65], which may function as a frequency-selective communication channel for devices.…”

Section: Energy Transmission Through Squidmentioning

confidence: 99%

Wide-band tuneability, nonlinear transmission, and dynamic multistability in SQUID metamaterials

2014

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Nonlinear Magnetoinductive Transmission Lines

Cited by 23 publications

References 54 publications

Bifurcation Results for Traveling Waves in Nonlinear Magnetic Metamaterials

Bifurcation Results for Traveling Waves in Nonlinear Magnetic Metamaterials

Gain-Driven Discrete Breathers inPT-Symmetric Nonlinear Metamaterials

Wide-band tuneability, nonlinear transmission, and dynamic multistability in SQUID metamaterials

Contact Info

Product

Resources

About