180 research outputs found
PT-Symmetric Nonlinear Metamaterials and Zero-Dimensional Systems
A one dimensional, parity-time ()-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 -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 ( 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 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 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 phase in higher-dimensional
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.Comment: 10 pages, 11 figs, subm. to Applied Physics A for the Proceedings of
the META13 Conferenc
SQUID Metamaterials on a Lieb lattice: From flat-band to nonlinear localization
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 crossing the Dirac points. It is demonstrated
numerically that localized states can be excited in the system when it is
initialized with single-site excitations; depending on the amplitude of those
initial states, the localization is either due to the flat-band or to nonlinear
effects. Flat-band localized states are formed in the nearly linear regime,
while localized excitations of the discrete breather type are formed in the
nonlinear regime. These two regimes are separated by an intermediate turbulent
regime for which no localization is observed. Notably, initial single-site
excitations of only edge SQUIDs of a unit cell may end-up in flat-band
localized states; no such states are formed for initial single-site excitations
of a corner SQUID of a unit cell. The degree of localization of the resulting
states is in any case quantified using well-established measures such as the
energetic participation ratio and the second moment.Comment: 11 pages, 9 figure
Superconducting Metamaterials
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 further specificity and functionality. SQUID-based MMs are both
theoretically investigated but also fabricated and analyzed experimentally in
many labs and exciting new phenomena have been found both in the classical and
quantum realms. The SQUID is a unique nonlinear oscillator that can be
manipulated through multiple external means. This flexibility is inherited to
SQUID-based MMs, i.e. extended units that contain a large arrangement of
SQUIDs. Such an assembly of weakly coupled nonlinear oscillators presents a
nonlinear dynamics laboratory where numerous complex spatio-temporal phenomena
may be explored. We focus primarily on SQUID-based MMs and present basic
properties related to their individual and collective responses to external
drives. We start by showing how a SQUID-based system acts as a genuine MM,
demonstrate that the Josephson nonlinearity leads to wide-band tunability,
intrinsic nonlinear as well as flat band localization. We explore further
properties such as multistability and self-organization and the emergence of
chimera states. We then dwell into the truly quantum regime and explore the
interaction of electromagnetic pulses with superconducting qubits where the
coupling between the two yields self-induced transparency and superradiance. We
thus attempt to present the rich behavior of coupled superconducting units and
point to their basic properties and practical utility.Comment: review article, to appear in Physics Reports: 84 pages, 36 figures,
350 reference
Topological split-ring resonator based metamaterials with symmetry relying on gain and loss
A one-dimensional metamaterial with parity-time () symmetry that
relies on balanced gain and loss is introduced, comprising of magnetically
coupled split-ring resonators (SRRs). A particular topology that combines a
non-trivial (topological) dimer configuration with a trivial (non-topological)
dimer configuration which are separated by a central SRR with neither gain or
loss, is investigated. By focusing on the dynamical aspects of such a
topological metamaterial (PTMM), the existence of {\em
topologically protected interface states} which are localized at the central
SRR is demonstrated numerically. The solution of the corresponding {\em
quadratic eigenvalue problem} reveals that the protected state is actually a
robust eigenmode of the topological PTMM, whose eigenvalue is isolated in the
middle of the gap (mid-gap state) of the two-band frequency spectrum. Direct
numerical simulations have been further used to determine the robustness and
dynamic stability of these states in the parameter space of the {\em
dimerization strength} and the {\em gain-loss coefficient}.Comment: 8 pages, 7 figures, 45 references. Accepted by Physical Review B as
Regular Articl
Multistable Dissipative Breathers and Novel Collective States in SQUID Lieb Metamaterials
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 unstable solutions in a narrow frequency
band around resonance. These breathers are very weakly interacting with each
other, while multistability regimes with different number of simultaneously
stable breathers persist for substantial intervals of frequency, flux field
amplitude, and coupling coefficients. Moreover, the emergence of chimera states
as well as novel temporally chaotic states exhibiting spatial homogeneity
within each sublattice of the Lieb lattice is demonstrated.Comment: 11 pages, 9 figures, submitted to Physical Review
SQUID Metamaterials: Tuneability and Multistability
An overview of several dynamic properties of SQUID metamaterials is given in
the presence of both constant and alternating magnetic field. The total current
as a function of the driving frequency exhibits hysteretic effects which are
favored by low levels of disorder. Multistability in the current states leads
to multiple magnetic responses with different value of magnetic permeability.
SQUID metamaterials exhibit wide-band tuneability which is periodic with the
applied constant magnetic field; the numerical calculations reproduce fairly
well recent experimental results. Current work also reveals the possibility for
wave transmission through nonlinear bands, which is briefly discussed.Comment: META 2014 Conference, 20-23 May 2014, Singapore [3 pages, 3 figures
Gain-Driven Discrete Breathers in PT-Symmetric Nonlinear Metamaterials
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.Comment: 5 pages, 7 figure
Coupled nonlinear Schroedinger field equations for electromagnetic wave propagation in nonlinear left-handed materials
For an isotropic and homogeneous nonlinear left-handed materials, for which
the effective medium approximation is valid, Maxwell's equations for electric
and magnetic fields lead naturally, within the slowly varying envelope
approximation, to a system of coupled nonlinear Schroedinger equations. This
system is equivalent to the well-known Manakov model that under certain
conditions, is completely integrable and admits bright and dark soliton
solutions. It is demonstrated that left- and right-handed (normal) nonlinear
mediums may have compound bright and dark soliton solutions, respectively.
These results are also supported by numerical calculations.Comment: 5 pages, 5 figures. Accepted by Physical Review E (in production
Discrete breathers in nonlinear magnetic metamaterials
Magnetic metamaterials composed of split-ring resonators or 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 localized modes, both in the energy-conserved and the dissipative
system. We analyze discrete single and multibreather excitations, as well as a
special breather configuration forming a magnetization domain wall and
investigate their mobility and the magnetic properties their presence induces
in the system.Comment: 4 pages, 6 figures, Physical Review Letters, accepte
Dissipative discrete breathers in rf SQUID metamaterials
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 analyze several discrete breather excitations, both in one and
two dimensions, which are subjected to unavoidable losses. These losses,
however, are counter-balanced by an external flux source leading to linearly
stable discrete breather structures up to relatively large coupling parameters.
We show that DDB excitations may locally alter the magnetic response of array
from paramagnetic to diamagnetic or vice versa, and that they are not destroyed
by increasing the dimensionality.Comment: 9 pages, 13 figures, submitted to Nonlinear Phenomena in Complex
System
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