Symmetric Eigenmodes Research Articles

Topological band gaps and edge modes materialized by symmetric silicon-on-insulator photonic crystal slabs in the mid-IR range

We successfully fabricated silicon-on-insulator (SOI) photonic crystal (PhC) slabs in which electromagnetic topological band gaps and edge modes were materialized for symmetric transverse-electric-like modes. Because the structure of our specimens can be regarded as symmetric about the horizontal middle plane of the PhC slab, their symmetric and antisymmetric eigenmodes were rigorously separated, so we could achieve genuine photonic band gaps for the former. We fabricated those specimens by electron beam lithography of the top Si layer of SOI wafers and successive plasma-enhanced chemical vapor deposition of a ${\mathrm{SiO}}_{2}$ capping layer. We confirmed the complete common band gap of topologically trivial and nontrivial PhCs and the topological edge modes on the boundary between them by angle-resolved reflection spectroscopy in the mid-infrared range. This is an observation of the common band gap and edge modes that materialized in symmetric PhC slabs without a membrane structure, that is, without the etching of a sacrificial layer under the PhC to increase the refractive-index contrast and the width of the common band gap.

Equivalent Electromechanical Model for Quartz Tuning Fork Used in Atomic Force Microscopy.

Quartz tuning forks (QTFs) are self-sensing and possess a high quality factor, allowing them to be used as probes for atomic force microscopes (AFMs) for which they offer nano-scale resolution of sample images. Since recent work has revealed that utilizing higher-order modes of QTFs can offer better resolution of AFM images and more information on samples, it is necessary to understand the relationship between the vibration characteristics of the first two symmetric eigenmodes of quartz-based probes. In this paper, a model that combines the mechanical and electrical characteristics of the first two symmetric eigenmodes of a QTF is presented. Firstly, the relationships between the resonant frequency, amplitude, and quality factor between the first two symmetric eigenmodes are theoretically derived. Then, a finite element analysis is conducted to estimate the dynamic behaviors of the analyzed QTF. Finally, experimental tests are executed to verify the validity of the proposed model. The results indicate that the proposed model can accurately describe the dynamic properties of a QTF in the first two symmetric eigenmodes either under electrical or mechanical excitation, which will provide a reference for the description of the relationship between the electrical and mechanical responses of the QTF probe in the first two symmetric eigenmodes as well as the optimization of higher modal responses of the QTF sensor.

One-dimensional -symmetric eigenmodes in k-wave number Scarf II potential with defocusing nonlinearity

The stationary states and dynamical evolution of one-dimensional eigenmodes in self-defocusing nonlinear Kerr medium under transverse parity-time () symmetric k-wave number Scarff-II potential have been analysed. We study the effect of the coefficient of the imaginary component of the -symmetric potential on the eigenvalue spectra of the ground and first excited states in linear and nonlinear models. Symmetric eigenmodes with real eigenvalues are obtained in the unbroken regime in both models. The linear stability analysis shows that the solutions are stable in the unbroken regime. The stable propagation of the solutions in linear and nonlinear media supported by -symmetric k-wave number Scarff-II potential is also investigated. The comparison of the solutions in the presence and the absence of nonlinearity reveals that in the self-defocusing Kerr medium nonlinearity suppresses the region of -symmetry. The influence of the width of the complex k-wave number Scarff-II potential and the depth of the real potential function on the -symmetry breaking have also been analysed.

Low-Frequency, Open, Sound-Insulation Barrier by Two Oppositely Oriented Helmholtz Resonators.

In this work, a low-frequency, open, sound-insulation barrier, composed of a single layer of periodic subwavelength units (with a thickness of λ/28), is demonstrated both numerically and experimentally. Each unit was constructed using two identical, oppositely oriented Helmholtz resonators, which were composed of a central square cavity surrounded by a coiled channel. In the design of the open barrier, the distance between two adjacent units was twice the width of the unit, showing high-performance ventilation, and low-frequency sound insulation. A minimum transmittance of 0.06 could be observed around 121.5 Hz, which arose from both sound reflections and absorptions, created by the coupling of symmetric and asymmetric eigenmodes of the unit, and the absorbed sound energy propagating into the central cavity was greatly reduced by the viscous loss in the channel. Additionally, by introducing a multilayer open barrier, a broadband sound insulation was obtained, and the fractional bandwidth could reach approximately 0.19 with four layers. Finally, the application of the multilayer open barrier in designing a ventilated room was further discussed, and the results presented an omnidirectional, broadband, sound-insulation effect. The proposed open, sound-insulation barrier with the advantages of ultrathin thickness; omnidirectional, low-frequency sound insulation; broad bandwidth; and high-performance ventilation has great potential in architectural acoustics and noise control.

A fundamental understanding of the unstable eigenmodes of double tearing instabilities in a shear slab geometry

Two types of unstable eigenmodes of resistive tearing instabilities, namely, symmetric and anti-symmetric modes, in a double current sheet configuration are analyzed by means of both an eigenvalue solver and initial value simulation. It has been clearly identified that these two types of eigenmodes are different from the two independent single tearing modes even though the symmetric eigenmode in a double current sheet configuration shares the same properties of the single tearing mode near each current sheet. In the case with finite separation Δx between two current sheets, an arbitrary phase disturbance between two current sheets can lead to “phase instability,” i.e., the transition from the symmetric mode to the anti-symmetric mode. For a large Δx limit, both anti-symmetric and symmetric modes share the same properties of the single tearing mode. Thus, the superposition of two independent single tearing modes with arbitrary phases and arbitrary amplitudes at two current sheets can become the linear combination of symmetric and anti-symmetric eigenmodes. The same growth rate/eigenvalue of symmetric and anti-symmetric eigenmodes infers that an arbitrary superposition of two independent single tearing modes is still the eigenmode of the double current sheet configuration.

Double magnonic chains of particles: Spin waves slowing and snaking

We calculated the dispersion relations for magnon waves in a single and two adjacent periodic chains of spherical magnetic particles magnetized along the chain axis. Dipole-dipole coupling between point magnetic moments in a chain and between chains was taken into account. A weak coupling between local magnetic moments at separate particles in a chain leads to formation of narrow transmittance band, which results in a low group velocity of the spin waves. The group velocity can be controlled by the chain parameters. In the case of double magnon chains, a transmittance band splits into two sub-bands corresponding to symmetric and anti-symmetric eigenmodes. Interference between them results in spin wave snaking between the two chains. This effect is field-dependent that makes possible application of double chains of magnetic particles in magnonic switch.

Identifying eigenmodes of averaged small-amplitude perturbations to turbulent channel flow

Eigenmodes of averaged small-amplitude perturbations to a turbulent channel flow – which is one of the most fundamental canonical flows – are identified for the first time via an extensive set of high-fidelity graphics processing unit accelerated direct numerical simulations. While the system governing averaged small-amplitude perturbations to turbulent channel flow remains unknown, the fact such eigenmodes can be identified constitutes direct evidence that it is linear. Moreover, while the eigenvalue associated with the slowest-decaying anti-symmetric eigenmode mode is found to be real, the eigenvalue associated with the slowest-decaying symmetric eigenmode mode is found to be complex. This indicates that the unknown linear system governing the evolution of averaged small-amplitude perturbations cannot be self-adjoint, even for the case of a uni-directional flow. In addition to elucidating aspects of the flow physics, the findings provide guidance for development of new unsteady Reynolds-averaged Navier–Stokes turbulence models, and constitute a new and accessible benchmark problem for assessing the performance of existing models, which are used widely throughout industry.

Atmospheric oscillations provide simultaneous measurement of neutron star mass and radius

ABSTRACT Neutron stars with near-Eddington observable luminosities were shown to harbour levitating atmospheres, suspended above their surfaces. We report a new method to simultaneously measure the mass and radius of a neutron star based on oscillations of such atmospheres. In this paper, we present an analytic derivation of a family of relativistic, oscillatory, spherically symmetric eigenmodes of the optically and geometrically thin levitating atmospheres, including the damping effects induced by the radiation drag. We discover characteristic maxima in the frequencies of the damped oscillations and show that from a measurement of the frequency maximum and of the luminosity one can determine the mass and radius of the neutron star. In addition to the stellar parameters, observation of the variation of the oscillation frequencies with flux would allow us to estimate the stellar luminosity and therefore the distance to the source with an accuracy of a few per cent. We also show that the ratio of any two undamped eigenfrequencies depends only on the adiabatic index of the atmosphere, while for the damped eigenfrequencies, this ratio varies with the luminosity. The damping coefficient is independent of the mode number of the oscillations. Signatures of the dynamics of such atmospheres will be reflected in the source’s X-ray light curves.

Study of encapsulated microbubble cluster based on association schemes perspective

Ultrasound contrast agents have been recently utilized in therapeutical implementations for targeted delivery of pharmaceutical substances. Radial pulsations of a cluster of encapsulated microbubbles under the action of an ultrasound field are complex and highly nonlinear, particularly for drug and gene delivery applications with high acoustic pressure amplitudes. In this paper, based on Qin-Ferrara’s model (Qin and Ferrara, 2010), the complete synchronization and cluster formation in targeted microbubbles network are studied. Also, association schemes as a novel approach are suggested for finding a relationship between coupled microbubbles elements which are immersed in blood or surrounding soft tissue. A significant advantage of this method is that the stability of the synchronized state (or symmetric eigenmode of mutual bubble oscillation) with respect to another state (another eigenmode) can now predict. More interestingly, we find a significant relationship between an isolated and multiple microbubbles. The results show that the problem of studying the dynamics of encapsulated microbubble cluster at synchronization state is dependent on the dynamical characteristics of isolated cases, shell thickness, density. Also, the distance between microbubbles has an important role in their synchronous modes.

Dynamics of periodic ribbed plates with inner resonance: Analytical homogenized model and dispersion features

The dynamic behavior of a periodic ribbed plate with local resonance is investigated. The behavior of the cell made of a beam clamped along a plate edge analyzed through multi-scale asymptotic method enables to derive the governing equations of the effective mechanical behavior. This approach allows obtaining a full homogenized analytical model that provides a relevant representation of the flexural and torsional mechanisms at both global and local scales. The complex dynamic behavior is shown to encompass several mechanisms associated with enriched kinematics. Two types of flexural and torsional waves are evidenced and governed by two distinct differential equations that describes (i) waves where both beam and plate moves, and (ii) guided waves where the plate only is set in motion. The inner resonance of the plate induces unconventional dispersion features, with singularities associated either with the symmetric eigenmodes for the bending waves or the antisymmetric modes for the torsional waves. The guided waves are alternatively related to the symmetric and antisymmetric modes of the bended plate and are propagative above the corresponding eigenfrequencies. The predictions of the homogenized model are successfully compared to numerical calculations conducted using Wave Finite Element based methods, for two realistic examples of ribbed plates. The study provides design rules to tailor ribbed plate panels having specific atypical features in a given frequency range.

Limits of imaging with multilayer hyperbolic metamaterials.

The multilayer hyperbolic metamaterials are known to be capable of imaging with sub-wavelength resolution. In this work performance of these "hyperbolic lenses" is analyzed in depth by employing commonly used transfer matrix method as well as the eigen-mode approach, the latter offering a clear physical insight into the operation of hyperbolic imagers and revealing their fundamental limitations. The resolution of multilayer structures is shown to decrease with the number of layers not only due to increased loss but also because of the severe suppression of large spatial frequencies caused by the cancellation between symmetric and antisymmetric eigen-modes. Additionally, the resolution is strongly affected by the granularity and fill ratio. In the end, hyperbolic metamaterials can create an image with subwavelength resolution only at very close distance to the object and hence limiting their utility.

Redirection and splitting of sound waves by a periodic chain of thin perforated cylindrical shells

A line of perforated cylindrical shells in air is practically transparent for sound since each individual unit is a weak scatterer. However, strong scattering occurs due to the coupling to the acoustic eigenmodes of the chain. Here we develop an analytical theory of sound transmission and scattering at a linear chain of perforated shells and predict strong anomalous effect for oblique incidence. The chain eigenmodes are weakly decaying, with symmetric profile and anomalous dispersion, or with antisymmetric profile and normal dispersion, and their excitation leads to deep minima in the transmission and 90̊-redirection of the external sound. At normal incidence, only the symmetric eigenmode can be excited, otherwise both modes are excited at close frequencies. Moreover, the wave which resonates with the normal-dispersion mode is redirected along the “right” direction, whereas the wave resonating with the anomalous-dispersion mode is redirected in the “wrong” direction. Thus, a periodic chain of perforated shells may serve not only as a 90̊-redirecting antenna but also as a splitter of sound waves with close frequencies. For example, an acoustic signal containing two frequencies around 3 kHz can be split into monochromatic components propagating in opposite directions along the chain, if the beat frequency is ≈500 Hz.

Nonlinear Analysis of Two-layer Fluid Sloshing in a Rectangular Tank Subjected to Width Direction Excitation

This paper describes a nonlinear theory to describe oscillations of two liquid layers formed in a rectangular tank. Nonlinear equations based on the variational principle and the Galerkin method are used, which are written in a form of direct expanding in eigenmodes. Analysis using the equations is described under the experimental conditions reported in a previous study. Both the experiment and the analysis demonstrate a “peculiar oscillation” in which the interface of the two liquids oscillates at 1/5 to 1/7 of the excitation frequency in a particular excitation frequency range. By observing the nonlinear force time series, four eigenmodes are identified to be mainly relevant to the oscillation. An amplitude equation analysis was applied to the four relevant eigenmodes. It was found that this “peculiar oscillation” is one of summed and differential harmonic oscillations (combination oscillation) in which one asymmetric and one symmetric eigenmode excite each other through the mediation of other two asymmetric eigenmodes.

Surface plasmon enhancement of spontaneous emission in graphene waveguides

This work analyzes the spontaneous emission of a single emitter placed near the graphene waveguide formed by two parallel graphene monolayers, with an insulator spacer layer. In this case, the eigenmodes supported by the structure, such as surface plasmon and wave guided modes, provide decay channels for the electric dipole placed close to the waveguide. We calculated the contribution to the decay rate of symmetric and antisymmetric eigenmodes as a function of frequency and the orientation of the emitter. Our results show that the modification of the spontaneous emission due to excitation of guided modes is much lower than the corresponding decays through the excitation of symmetric and antisymmetric surface plasmons, for which, the spontaneous emission is dramatically enhanced. As a consequence of the high confinement of surface plasmons in the graphene waveguide, we found that the decay rate of the emitter with vertical orientation (with respect to graphene sheets) is twice the corresponding decay of the same emitter with parallel orientation in the whole frequency range where surface plasmon modes exist. Differently from metallo-dielectric structures, where structural parameters determine the range and magnitude of this emission, our work shows that, by dynamically tuning the chemical potential of graphene, the spectral region where the decay rate is enhanced can be chosen over a wide range.

Coil Block Designs With Good Homogeneity for MRI Magnets Based on SVD Eigenmode Strengths

This paper describes an improved method to determine coil block (CB) placements with good homogeneities for magnetic resonance imaging magnets. Each magnet has a main coil (MC) for strong magnetic fields in a volume of interest and a shield coil (SC) to make the magnetic fields weak outside the magnet. The CB placements are done in three steps and at every step, the SC magnetic moments are tuned. In step 1, approximate placements are done with axially distributed circular filament loop currents. According to the distribution, rough placements of CBs are done for the MC. In step 2, the CB cross-sectional shapes and positions are optimized to get good homogeneity with real numbers of winding turns. In step 3, the CB shapes are approximated with integer numbers of winding turns and conductor sizes, and the CB positions are tuned to get as good homogeneities as the step 1 result. In all steps, optimizations are done through truncated singular value decompositions. In steps 2 and 3, the placements are done with respect to eigenmode strengths, which are obtained in step 1. For a magnet with six MC-CBs, seven symmetric eigenmode strengths are tuned. The CB placements for magnets can be obtained with good homogeneities and integerized CB winding turns using the method.

Modal analysis of kagome-lattice structures

The first few lowest order circularly symmetric electromagnetic eigenmodes of a full kagome lattice are compared to those of a kagome lattice with a hexagonal defect. This analysis offers important insights into the physics behind the waveguiding properties of hollow-core fibers with a kagome-lattice cladding.

Optimal excitation of the Bloch modes of coupled resonator optical waveguides

When light is injected into a microring-based coupled resonator optical waveguide (CROW), it usually excites one of the whispering gallery modes (WGMs) in each microring. Because the WGMs are not, in fact, the actual eigenmodes of the structure, the modal dispersion accompanied by such excitation schemes is expected to limit the device performance, especially for wide bandwidth and large time delay applications. To overcome this problem, an alternative method of exciting the CROW, via a Y power splitter exciting the symmetric eigenmode rather than a WGM, is proposed and studied in detail. The impact of fabrication tolerances and errors for silicon-on-insulator(SOI) are explored and analyzed. It is shown that this approach can significantly improve the performance of a CROW delay line in terms of eye-closure penalty and delay-bandwidth product.

Near- and far-field properties of plasmonic oligomers under radially and azimuthally polarized light excitation.

We present a comprehensive experimental and theoretical study on the near- and far-field properties of plasmonic oligomers using radially and azimuthally polarized excitation. These unconventional polarization states are perfectly matched to the high spatial symmetry of the oligomers and thus allow for the excitation of some of the highly symmetric eigenmodes of the structures, which cannot be excited by linearly polarized light. In particular, we study hexamer and heptamer structures and strikingly find very similar optical responses, as well as the absence of a Fano resonance. Furthermore, we investigate the near-field distributions of the oligomers using near-field scanning optical microscopy (NSOM). We observe significantly enhanced near-fields, which arise from efficient excitation of the highly symmetric eigenmodes by the radially and azimuthally polarized light fields. Our study opens up possibilities for tailored light-matter interaction, combining the design freedom of complex plasmonic structures with the remarkable properties of radially and azimuthally polarized light fields.

Effects of classical nonlocality on the optical response of three-dimensional plasmonic nanodimers

We examine the optical scattering from a variety of axially symmetric plasmonic nanoparticle dimers separated by nanoscale gaps, quantifying the role of classical nonlocality on their optical properties. Due to the rotational symmetry of the analyzed structures, a high degree of accuracy is achieved using a computational approach termed 2.5D modeling, in which a small number of simulations on a two-dimensional domain can replace a memory- and time-intensive simulation on a three-dimensional domain. We find that scattered light from dimers consisting of nanoparticles with flat surfaces, such as nanodisks, exhibits pronounced spectral shifts due to the nonlocality of the electron fluid; these significant shifts persist even at relatively large (>1 nm) gap dimensions, where quantum tunneling effects are believed to be negligible. The 2.5D modeling technique accurately incorporates all responses due to any nonaxially symmetric eigenmodes of the system, such as dipolar and quadrupolar modes, thereby providing a complete characterization of the system for any excitation.

Origins of magnetic damping measurement variations using ferromagnetic resonance for nano-sized devices

It is shown that ferromagnetic resonance measured in larger thin films yield varying results for damping in nanosized devices. Results are shown to critically depend on magnetic parameters, scalar and vector. Results here also explain why different experiments have concluded different size-dependent trends measuring damping with in-plane devices. The observed variation is due, in part, to a crossover in the dominant eigen-mode and unique eigen-mode evolution. However, antithesizing in-plane devices, we find that for out-of-plane magnetization, distinct symmetric eigen-modes demonstrates ideal stability, leading to no variation in apparent damping, suggesting a better measurement configuration using larger samples.