Localized Eigenmodes Research Articles

Localization and increased damping in irregular acoustic cavities

The present study is concerned with the properties of 2D shallow cavities having an irregular boundary. The eigenmodes are calculated numerically on various examples, and it is shown first that, whatever the shape and characteristic sizes of the boundary, irregularity always induces an increase of localized eigenmodes and a global decrease of the existence surface of the eigenmodes. Besides, irregular cavities are shown to exhibit specific damping properties. As expected, the increased damping, compared to a regular cavity, is related first to the larger perimeter to surface ratio. But more interestingly, there is a specific enhancement of the dissipation for those modes that are localized near the boundary, modes which are favored by the geometric irregularity.

Localized vibrational modes in optically bound structures

We show, through analytical theory and rigorous numerical calculations, that optical binding can organize a collection of particles into extended, periodic one-dimensional lattices. These lattices, as well as other optically bound structures, are shown to exhibit spatially localized vibrational eigenmodes. The origin of localization here is distinct from the usual mechanisms such as disorder, defect, or nonlinearity but is a consequence of the long-ranged nature of optical binding. For an array of particles trapped by an interference pattern, the stable configuration is often dictated by the external light source, but we observed that interparticle optical binding forces can have a profound influence on the dynamics.

On ion cyclotron emission in toroidal plasmas

A detailed study of ion cyclotron interactions in a toroidal plasma has been carried out in order to elucidate the role of toroidal effects on ion cyclotron emission. It is well known that non-relaxed distribution functions can give rise to excitation of magnetosonic waves by ion cyclotron interactions when the distribution function increases with respect to the perpendicular velocity. We have extended and clarified the conditions under which even collisionally relaxed distribution function can destabilize magnetosonic eigenmodes. In a toroidal plasma, cyclotron interactions at the plasma boundary with ions having barely co-current passing orbits and marginally trapped orbits can cause destabilisation by the strong inversion of the distribution function along the characteristics of cyclotron interaction by neo-classical effects. The unstable interactions can further be enhanced by tangential interactions, which can also prevent the interactions from reaching the stable part of the characteristics, where they interact with trapped orbits. Conditions on the localization of the magnetosonic eigenmodes for unstable excitation are analysed by studying the anti-Hermitian part of the susceptibility tensor of thermonuclear alpha-particles. The pattern of positive and negative regions of the anti-Hermitian part of the susceptibility tensor of thermonuclear alpha-particles is, in general, consistent with the excitation of edge localized magnetosonic eigenmodes, even though the eigenmodes are usually not localized in the major radius and for distribution functions that have relaxed to steady state.

Localized electromagnetic eigenmodes in three-dimensional metallic photonic fractals

The existence of localized electromagnetic eigenmodes in a three-dimensional metallic fractal of stage three was verified theoretically for the first time. Eigenfrequencies and the field distribution of the localized modes were successfully calculated by the numerical simulation of dipole radiation based on the finite-difference time-domain method. The 90° light-scattering spectra agreed well with the eigenfrequencies and satisfied the selection rule due to the symmetry of the eigenmodes.

Localization of scalar and fermionic eigenmodes and confinement

We discuss the localization of eigenmodes of the covariant lattice Laplacian and overlap Dirac operator in lattice SU(2) gluodynamics. It occurs that the localization properties of the eigenmodes for fundamental scalars and fermions are different in confining configurations and in those from which confining disorder was eliminated by center-vortex removal. Localization of eigenmodes on subspaces of dimension less than four indicates the existence of the low dimensional structures in the confining vacuum.

LCAO approximation for scaling properties of the Menger sponge fractal

The electromagnetic eigenmodes of a three-dimensional fractal called the Menger sponge were analyzed by the LCAO (linear combination of atomic orbitals) approximation and a first-principle calculation based on the FDTD (finite-difference time-domain) method. Due to the localized nature of the eigenmodes, the LCAO approximation gives a good guiding principle to find scaled eigenfunctions and to observe the approximate self-similarity in the spectrum of the localized eigenmodes.

Electromagnetic eigenmodes of a three-dimensional photonic fractal

The eigenfrequency, field distribution, and quality factor of localized electromagnetic eigenmodes of the Menger sponge fractal were calculated by numerical simulation of dipole radiation based on the finite-difference time-domain method. The Menger sponge of stage three with a dielectric constant of 8.8 that is composed of an epoxy resin and fine particles of metal dioxides was assumed for a specimen. Due to the cubic symmetry of the fractal structure, each eigenmode was attributed to one of the irreducible representations of the ${O}_{h}$ point group. The highest quality factor of 840 was found for an ${E}_{u}$ mode.

Gap solitons in a medium with third-harmonic generation

We find two-component optical solitons in a nonlinear waveguide with a Bragg grating, including Kerr effects and third-harmonic generation (THG). The model may be realized in temporal and in spatial domains. Two species of fundamental gap solitons (GSs) are found. The first ("THG-gap soliton") has the bulk of its energy at the fundamental frequency (FF) and a lesser part in the third-harmonic (TH) band. The FF part of the soliton is always single humped; the TH part may be single or double humped. Stability domains for quiescent and moving THG-gap solitons strongly shrink with increase of velocity. The second species is the usual ("simple") GS, sitting entirely in the TH band. More complex solutions are also found, in the form of a bound state of a THG-gap soliton and two simple GSs, with a finite binding energy. When a THG-gap soliton is unstable, the instability is oscillatory. It may ultimately cause the THG-gap soliton to throw off some radiation and evolve into a localized structure with the FF and TH components out of phase, with or without internal oscillations. Stable solitons feature an excited state (i.e., they support a localized eigenmode).

Light scattering and transmission spectra of the Menger sponge fractal

Selection rules for light scattering and transmission by the Menger sponge fractal were derived by the group theory based on the symmetry of its localized electromagnetic eigenmodes. The light scattering and transmission spectra were calculated by the finite-difference time-domain method and compared with the eigenfrequencies of the localized modes obtained from the dipole radiation spectra. Their correspondence is quite good and supports the accuracy of the numerical calculation and the correctness of the selection rules.

Femtosecond Imaging of Surface Plasmon Dynamics in a Nanostructured Silver Film

Light interacting with nanostructured metals excites the collective charge density fluctuations known as surface plasmons (SP). Through excitation of the localized SP eigenmodes incident light is trapped on the nanometer spatial and femtosecond temporal scales and its field is enhanced. Here we demonstrate the imaging and quantum control of SP dynamics in a nanostructured silver film. By inducing and imaging the nonlinear two-photon photoemission from the sample with a pair of identical 10-fs laser pulses while scanning the pulse delay, we record a movie of SP fields at a rate of 330-attoseconds/frame.

Mobility edge in lattice QCD

We determine the location $\lambda_c$ of the mobility edge in the spectrum of the hermitian Wilson operator on quenched ensembles. We confirm a theoretical picture of localization proposed for the Aoki phase diagram. When $\lambda_c>0$ we also determine some key properties of the localized eigenmodes with eigenvalues $|\lambda|<\lambda_c$. Our results lead to simple tests for the validity of simulations with overlap and domain-wall fermions.

The analysis of space–time structure in QCD vacuum, I: localization vs global behavior in local observables and Dirac eigenmodes

The structure of QCD vacuum can be studied from first principles using lattice-regularized theory. This line of research entered a qualitatively new phase recently, wherein the space–time structure (at least for some quantities) can be directly observed in configurations dominating the QCD path integral, i.e., without any subjective processing of typical configurations. This approach to QCD vacuum structure does not rely on any proposed picture of QCD vacuum but rather attempts to characterize this structure in a model-independent manner, so that a coherent physical picture of the vacuum can emerge when such unbiased numerical information accumulates to a sufficient degree. An important part of this program is to develop a set of suitable quantitative characteristics describing the space–time structure in a meaningful and physically relevant manner. One of the basic pertinent issues here is whether QCD vacuum dynamics can be understood in terms of localized vacuum objects, or whether such objects behave as inherently global entities. The first direct studies of vacuum structure strongly support the latter. In this paper, we develop a formal framework which allows to answer this question in a quantitative manner. We discuss in detail how to apply this approach to Dirac eigenmodes and to basic scalar and pseudoscalar composites of gauge fields (action density and topological charge density). The approach is illustrated numerically on overlap Dirac zero modes and near-zero modes. This illustrative data provides direct quantitative evidence supporting our earlier arguments for the global nature of QCD Dirac eigenmodes.

90-degree light scattering by the Menger sponge fractal

Selection rules for the 90 degrees light scattering by the Menger sponge fractal were derived by the group theory based on the symmetry of its localized electromagnetic eigenmodes. The light scattering spectra were calculated by the finite-difference time-domain method and compared with the eigenfrequencies of the localized modes obtained from the dipole radiation spectra. Their correspondence is quite good and supports the accuracy of the numerical calculation and the correctness of the selection rules. It was also shown that the scattering spectra are background free and the quality factor of the localized modes can be obtained from the spectral width of the scattering peaks. Thus the 90 degrees light scattering is a powerful method for the investigation of the Menger sponge fractal.

Gap and out-gap breathers in a binary modulated discrete nonlinear Schr�dinger model

We consider a modulated discrete nonlinear Schrodinger (DNLS) model with alternating on-site potential, having a linear spectrum with two branches separated by a ‘forbidden’ gap. Nonlinear localized time-periodic solutions with frequencies in the gap and near the gap -- discrete gap and out-gap breathers (DGBs and DOGBs) -- are investigated. Their linear stability is studied varying the system parameters from the continuous to the anti-continuous limit, and different types of oscillatory and real instabilities are revealed. It is shown, that generally DGBs in infinite modulated DNLS chains with hard (soft) nonlinearity do not possess any oscillatory instabilities for breather frequencies in the lower (upper) half of the gap. Regimes of ‘exchange of stability’ between symmetric and antisymmetric DGBs are observed, where an increased breather mobility is expected. The transformation from DGBs to DOGBs when the breather frequency enters the linear spectrum is studied, and the general bifurcation picture for DOGBs with tails of different wave numbers is described. Close to the anti-continuous limit, the localized linear eigenmodes and their corresponding eigenfrequencies are calculated analytically for several gap/out-gap breather configurations, yielding explicit proof of their linear stability or instability close to this limit.

The coupling of elastic, surface-wave modes by a slow, interfacial inclusion

The coupling of in-plane, elastic, surface waves guided by a homogeneous layer on a similar substrate, but perturbed by the presence of a second, long, slow, interfacial layer, of slowly varying thickness, is studied. By projecting the elastic-wave equations onto a basis of local eigenmodes, an infinite system of coupled-mode equations describing the evolution of the amplitudes of each mode is obtained. Within the equations, the coupling is manifested by the presence of coupling coefficients that depend critically on the difference between the wavenumbers of adjacent modes. This system is truncated and solved by noting under what conditions the modes can be satisfactorily described by a WKBJ approximation (propagating without coupling) and under what conditions they are coupled by adjacent wavenumbers being brought into proximity by the slowly changing propagation environment. The criteria for coupling is that the difference in neighboring wavenumbers be of the same order as the slope of the inclusion. The case of the first three modes is worked out in detail: it is shown how initially modes one and two couple followed by the coupling of modes two and three.

Plasmon localization and local field distribution in metal-dielectric films.

An exact and very efficient numerical method for calculating the effective conductivity and local-field distributions in random R-L-C networks is developed. Using this method, the local-field properties of random metal-dielectric films are investigated in a wide spectral range and for a variety of metal concentrations p. It is shown that for metal concentrations close to the percolation threshold (p=p(c)) and frequencies close to the resonance, the local-field intensity is characterized by a non-Gaussian, exponentially broad distribution. For low and high metal concentrations a scaling region is formed that is due to the increasing number of noninteracting dipoles. The local electric fields are studied in terms of characteristic length parameters. The roles of both localized and extended eigenmodes in Kirchhoff's Hamiltonian are investigated.

Localization and pattern formation in Wigner representation via multiresolution

We present an application of variational-wavelet analysis to quasiclassical calculations of solutions of Wigner equations related to nonlinear (polynomial) dynamical problems. (Naive) deformation quantization, multiresolution representations and variational approach are the key points. Numerical calculations demonstrates pattern formation from localized eigenmodes and transition from chaotic to localized (waveleton) types of behaviour.

Internal localized eigenmodes on spin discrete breathers in antiferromagnetic chains with on-site easy-axis anisotropy

We investigate internal localized eigenmodes of the linearized equation around spin discrete breathers in 1D antiferromagnets with on-site easy axis anisotropy. The threshold of occurrence of the internal localized eigenmodes has a typical structure in parameter space depending on the frequency of the spin discrete breather. We also performed molecular dynamics simulation in order to show the validity of our linear analysis.

Unstable ion-temperature-gradient modes in the Wendelstein 7-X stellarator configuration

The linear stability of the ion-temperature-gradient modes (ITG) in the electrostatic limit is examined in the short wavelength region by using a two fluid reactive model in fully three-dimensional Wendelstein 7-X (W7-X) stellarator [G. Grieger et al., Plasma Physics and Controlled Nuclear Fusion Research, 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 3, p. 525] geometry. The spectrum of stable and unstable modes and their real frequencies and eigenfunctions are calculated. The effects of density gradients, temperature gradients, temperature ratios, wavevector, ballooning angle, curvature and local magnetic shear on the ITG mode are also investigated. The frequency and growth rate of the most unstable ITG mode is calculated and visualized for a specific magnetic flux surface. For the equilibrium under investigation both localized and extended eigenmodes are found. The effect of small and large temperature ratios, small and large density gradients as well as large local magnetic shear are all found to be stabilizing. The highest growth rates are found at the outer part of the surface where the local magnetic shear is small and normal curvature is unfavorable.

Transition of Toroidal Alfven Eigenmode to Global Alfven Eigenmode in CHS Heliotron/Torsatron Plasmas Heated by Neutral Beam Injection.

A transition of a core localized type toroidal Alfven eigenmode with n = 1 toroidal mode number to two n = 1 global Alfven eigenmodes was observed in NBI-heated plasmas in the Compact Helical System (CHS) heliotron torsatron. This transition phenomenon is interpreted based on the temporal evolution of the rotational transform near the plasma center caused by the increase in the beam-driven current.