Dispersion Branches Research Articles

Transverse Spurious Mode Compensation for AlN Lamb Wave Resonators

Lamb wave modes with type I dispersion characteristics exhibit strong affinity toward multi transverse modes behavior above resonance frequency (f r ) in the AlN Lamb wave resonators (LWRs), especially the high-transduction-efficiency modes: S 0 and S 1 mode. For conventional interdigital transducer (IDT) design, the IDT aperture and IDT gap are the two main factors impacting the transverse mode placements and strengths, according to the wave vector analysis and finite element method (FEM) simulation. Moreover, the convex slowness curve of the Lamb wave modes propagating in AlN platelets allows the waveguiding and weak lateral leakage into busbars by the high-velocity IDT gap region. Apodization, the standard technique to suppress the transverse modes for IDT-excited resonators, suffers from drawbacks, such as additional loss and reduction of the effective coupling coefficient (k eff 2 ). Type I Lamb wave modes in AlN show positive slope in the dispersion branch so that a border region of lower Eigen-resonance frequency is required to form piston mode structure for transverse spurious mode suppression and lateral leakage reduction. Based on dispersion calculations and 2.5D FEM simulations, we demonstrate that by designing the low-velocity border region, such as simply changing the IDT layout, the guiding can be improved and a piston mode can be obtained for the type I Lamb wave modes.

The external circuit effect on the steady states of the Pierce diode

It was found out that the inclusion of a reactive load in the external circuit of a plasma diode with an electron beam can greatly change the modes of its operation. We demonstrated that the presence of an inductance in the external circuit of the Pierce diode leads to appearance of a new dispersion branch. The growth rates and frequencies for this branch are calculated. The frequencies corresponding to unstable states of this branch exceed the plasma frequency. The threshold of instability is shown to shift to smaller inter-electrode distance values with decreasing in the inductance magnitude and can be lower than the threshold of the Pierce diode with a short circuit.

Elastic wave propagation in smooth and wrinkled stratified polymer films

Periodic materials with sub-micrometer characteristic length scale can provide means for control of propagation of hypersonic phonons. In addition to propagation stopbands for the acoustic phonons, distinct dispersive modes can reveal specific thermal and mechanical behavior under confinement. Here, we employ both experimental and theoretical methods to characterize the phonon dispersion relation (frequency versus wave vector). We employed Brillouin light scattering (BLS) spectroscopy to record the phonon dispersion in stratified multilayer polymer films. These films consist of 4–128 alternate polycarbonate (PC) and poly (methyl methacrylate) (PMMA) layers along and normal to the periodicity direction. The distinct direction-dependent phonon propagation was theoretically accounted for, by considering the polarization, frequency and intensity of the observed modes in the BLS spectra. Layer-guiding was also supported by the glass transition temperatures of the PC and PMMA layers. The number of phonon dispersion branches increased with the number of layers but only a few branches were observable by BLS. Introduction of an additional in-plane periodicity, through a permanent wrinkling of the smooth PC/PMMA films, had only subtle consequences in the phonon propagation. Using the frequencies of the periodicity induced modes and momentum conservation equation we were able to precisely back calculate the wrinkle periodicity. However, a wrinkling-induced acoustic stopband utilizing flexible layered materials is still a challenge.

The optical characteristics of the nonlinear optical single crystal CdSiP2 in the terahertz and infrared ranges

Experimental study of mechanisms forming absorption of Terahertz (THz) radiation in the advanced nonlinear-optical crystal CdSiP2 has been performed by backward-wave oscillator, time-domain and infrared spectroscopy. The classical oscillator model and Lyddane–Sachs–Teller relation were used to calculate the dispersion parameters of phonon modes. The spectra of complex permittivity and absorption coefficient have been determined based on the calculated dispersion parameters. The application of the Fresnel formulas for the absorption analysis in the THz region together with the results of the fit of the phonon modes made it possible to obtain quantitative data on the magnitude of the additional radiation losses in the THz range. Additional loss mechanisms give rise to increase the total absorption by at least one order of magnitude compared to the phonon contribution. The increase of the polariton absorption in the low-frequency dispersion branch is typical for crystals with ionic and ion-covalent bond and is composed of extrinsic losses and difference multi-particle processes. The level of total losses in the THz region in CdSiP2 single crystal is comparable to the values in other nonlinear-optical crystals, which makes this material promising for nonlinear-optical conversion of the infrared radiation into the THz region.

Symmetry in electron and ion dispersion in 1D Vlasov-Poisson plasma

Using a Vlasov-Poisson model which treats both electrons and ions on the same physics footing or symmetrically in terms of kinetics, we demonstrate perhaps for the first time that the hitherto separate normal mode branches of electrons (or “Thumb curve”) and ions (or the “Teardrop curve”) are “continuously” connected branches of a general symmetric dispersion. Our findings are obtained using a dispersion relation analysis and verified using a driven nonlinear Vlasov Poisson solver. A simple explanation is suggested in terms of the real part of the plasma dispersion function obtained for arbitrary ratios of ion to electron masses and temperatures. It is demonstrated that the “Thumb” and “Teardrop” curves are recovered from the general symmetric dispersion at appropriate limits.

Evidence for dynamic kagome ice

The search for two-dimensional quantum spin liquids, exotic magnetic states remaining disordered down to zero temperature, has been a great challenge in frustrated magnetism over the last few decades. Recently, evidence for fractionalized excitations, called spinons, emerging from these states has been observed in kagome and triangular antiferromagnets. In contrast, quantum ferromagnetic spin liquids in two dimensions, namely quantum kagome ices, have been less investigated, yet their classical counterparts exhibit amazing properties, magnetic monopole crystals as well as magnetic fragmentation. Here, we show that applying a magnetic field to the pyrochlore oxide Nd2Zr2O7, which has been shown to develop three-dimensional quantum magnetic fragmentation in zero field, results in a dimensional reduction, creating a dynamic kagome ice state: the spin excitation spectrum determined by neutron scattering encompasses a flat mode with a six arm shape akin to the kagome ice structure factor, from which dispersive branches emerge.

Surface-Radiative Modes and Longitudinal Excitons in the Spectra of Exciton–Polariton Luminescence

Low-temperature (T = 2 K) spectra of exciton–polariton luminescence in the vicinity of the exciton resonance frequency An = 1 of CdS crystals are studied with allowance for the damping ℏΓ of mechanical excitons. The results of numerical calculations of the partial and interference contributions of bulk and surface-radiative spectral modes in the geometry of the radiation of additional waves into a vacuum with s and p polarizations are analyzed. It is shown that the contributions of purely longitudinal excitons and their interference with polaritons of the upper dispersion branch in luminescence in the vicinity of longitudinal frequency ωL are small (∼10−30%). Nevertheless, these contributions should be taken into account to achieve a quantitative agreement with the experiment; they determine the formation of an additional AL. line under oblique radiation.

First-principles study of spin-wave dispersion in Sm(Fe1−xCox)12

We present spin-wave dispersion in Sm(Fe1−xCox)12 calculated from first-principles. Anisotropy in the lowest branch of the spin-wave dispersion around the Γ point is discussed. It is shown that spin-waves propagate more easily along a∗-axis than along c∗-axis, especially in SmFe12. We also compare values of the spin-wave stiffness with those obtained from an experiment. The calculated values are in good agreement with the experimental values.

The Main Lateral Mode Approximation of a Film Bulk Acoustic Resonator With Perfect Metal Electrodes.

Using first principles and the constitutive equations of a piezoelectric crystal, we solve the 2-D problem inside a three-layer film bulk acoustic resonator (FBAR) in order to study the dispersion and parasitic lateral modes' characteristic of the structure. In our main lateral mode approximation, described here in detail, we construct the acoustic wave by combining the ideal "piston" mode and the main dispersion branch lateral mode. By limiting our analysis to the practical range of frequencies near the series resonance of the stack, where the lateral component $k_{x}$ of the ${k}$ vector is small, we find analytical expressions for the FBAR acoustic wave and for the dispersion of the three-layer stack. When lateral boundary conditions are added to the acoustic problem of a laterally finite resonator, we employ our theory to estimate the amplitude and the propagation of the lateral modes and then compare the theoretical predictions with the measurements of fabricated FBARs and finite-element simulation results. We are able to distinguish between a "clamped" and a "quasi-free" lateral interface by comparing the amplitude strength of the lateral modes produced, and we discuss how optimum lateral boundaries can be engineered with perimeter frames for realistic resonators.

Accurate characterization of 3D dispersion curves and mode shapes of waves propagating in generally anisotropic viscoelastic/elastic plates

We investigate wave propagation in generally anisotropic viscoelastic plates. The generally anisotropic material system has 21 independent complex coefficients in its stiffness matrix when viscoelasticity is taken into account. The dispersion equation is obtained in the form of determinant vanishing in the complex domain based on the straightforward derivation. An accurate root-searching in the dispersion equation for arbitrary ranges of frequencies and complex wavenumbers, however, is very difficult, if not impossible. In this paper, a novel algorithm is introduced to calculate the 3D dispersion curves. An approximate solution in the low attenuation range via the semi-analytical finite element (SAFE) method is also used to compare and validate the introduced algorithm. Using this algorithm, various peculiar wave features are then investigated in details. These include the attenuation jump and branches exchange in viscoelastic model caused by conversion of wave mode shapes, and the veering of dispersion branches in the corresponding elastic medium. The general anisotropic (viscoelastic/elastic) models are further compared with the isotropic ones to identify the similarity and difference on wave features between them. The proposed accurate algorithm along with the observed features should be particularly useful in nondestructive evaluations via waves in viscoelastic/elastic plates and structures.

Coexistence of Polaronic States and Superconductivity in Iron-Pnictide Compound Ba2Ti2Fe2As4O**Supported by the National Basic Research Program of China under Grant Nos 2013CB921700, 2015CB921300 and 2015CB921301, the National Natural Science Foundation of China under Grant Nos 11234014, 11622435, 11274362, 11674371 and 11474340, the National Key Research and Development Program of China under Grant Nos 2016YFA0300300, 2016YFA0300600, 2016YFA0401000 and 2016YFA0400902, the Open

The electronic structure of iron-pnictide compound superconductor Ba2Ti2Fe2As4O, which has metallic intermediate Ti2O layers, is studied using angle-resolved photoemission spectroscopy. The Ti-related bands show a ‘peak-dip-hump’ line shape with two branches of dispersion associated with the polaronic states at temperatures below around 120 K. This change in the spectra occurs along with the resistivity anomaly that was not clearly understood in a previous study. Moreover, an energy gap induced by the superconducting proximity effect opens in the polaronic bands at temperatures below Tc (∼21 K). Our study provides the spectroscopic evidence that superconductivity coexists with polarons in the same bands near the Fermi level, which provides a suitable platform to study interactions between charge, lattice and spin freedoms in a correlated system.

Resolving biomolecular motion and interactions by R2 and R1ρ relaxation dispersion NMR.

Among the tools of structural biology, NMR spectroscopy is unique in that it not only derives a static three-dimensional structure, but also provides an atomic-level description of the local fluctuations and global dynamics around this static structure. A battery of NMR experiments is now available to probe the motions of proteins and nucleic acids over the whole biologically relevant timescale from picoseconds to hours. Here we focus on one of these methods, relaxation dispersion, which resolves dynamics on the micro- to millisecond timescale. Key biological processes that occur on this timescale include enzymatic catalysis, ligand binding, and local folding. In other words, relaxation-dispersion-resolved dynamics are often closely related to the function of the molecule and therefore highly interesting to the structural biochemist. With an astounding sensitivity of ∼0.5%, the method detects low-population excited states that are invisible to any other biophysical method. The kinetics of the exchange between the ground state and excited states are quantified in the form of the underlying exchange rate, while structural information about the invisible excited state is obtained in the form of its chemical shift. Lastly, the population of the excited state can be derived. This diversity in the information that can be obtained makes relaxation dispersion an excellent method to study the detailed mechanisms of conformational transitions and molecular interactions. Here we describe the two branches of relaxation dispersion, R2 and R1ρ, discussing their applicability, similarities, and differences, as well as recent developments in pulse sequence design and data processing.

Controlling Level Splitting by Strong Coupling of Surface Plasmon Resonances with Rhodamine-6G on a Gold Grating

Strongly coupled system is known to pose challenges, particularly those involving multitude of levels as in molecules. Surface plasmons offer intense and localized electromagnetic fields, wherein molecules placed in such environment exhibit generic features of strongly coupled system. We demonstrate the control over the splitting of surface plasmon polaritons dispersion branches in strong coupling regime within the absorption and fluorescence bands of Rhodamine-6G molecules placed on top of gold grating structures. The enhanced electromagnetic near-fields of surface plasmon polaritons excited on top of gold gratings have been calculated by numerical simulation and various aspects related to the coupling have been captured by modelling the Rhodamine-6G molecule as a theoretical three level Λ–system which support the experimentally observed variation in splitting with varying periods of gratings. The plasmonically enhanced electromagnetic field plays the role of a control field applied across one leg of the Λ–system. Experimentally measured spectral features, including level splitting and dispersions of the strongly coupled system of molecule-gold grating are consistently described by the model for a variety of samples, with different periodicities, different molecule-grating separations obtained through a dielectric spacer layer, and coupling to higher order diffraction modes of the grating.

Phonon-induced renormalization of the electron spectrum of biased bilayer graphene

The effect of the electron-phonon interaction on the electron subsystem of the bilayer graphene has been investigated in the case when there is a potential bias between the graphene layers. The electron-phonon interaction has been shown to lead to increasing of the curvature of the lower dispersion branch of the conduction band of the bigraphene in the vicinity of the Dirac point. The latter corresponds to the decreasing of the absolute value of the electron effective mass. The corresponding correction to the effective mass has been calculated. Dependence of this correction on the bias has been investigated. Influence of such effect on the bigraphene conductivity is discussed.

Dispersion transitions and pole-zero characteristics of finite inertially amplified acoustic metamaterials

This work presents a comprehensive analysis of wave dispersion patterns and band gap formation associated with Inertially Amplified Acoustic Metamaterials (IAAM). The findings explain the different mechanisms by which inertial amplification affect wave dispersion in the individual IAAM cell as well as the evolution of such effects in finite configurations of these cells. Derived expressions for acoustic wave dispersion in IAAMs reveal unique features including flat dispersion branches with zero group velocity and a transition from a metamaterial (local resonance) to a phononic behavior that is directly related to the location and magnitude of the inerter elements. Using a closed-form transfer function approach, the translation of such effects to IAAM realizations with a known number of cells is interpreted from the pole-zero distributions of the resultant finite structures. It is also shown that band gaps are not always necessarily enlarged in the presence of inertial amplification. Comparing with benchmark conventional acoustic metamaterials, the conditions leading up to favorable as well as inferior IAAM designs are fully derived. Finally, an alternative resonator-free acoustic metamaterial is presented and shown to exhibit local resonance effects under appropriately tuned conditions.

The gaseous plasmonic response of a one-dimensional photonic crystal composed of striated plasma layers

We present simulations of the response of a one-dimensional striated plasma slab to incident electromagnetic waves that span regions both above and below the plasma frequency, ωp. Photonic bandgap modes are present throughout these regions, and volume and surface plasmon modes facilitate the response below ωp, where the dielectric constant, εp < 0. In the vicinity of ωp, most apparently, when ωp is in proximity of the lattice frequency, there is a feature for transverse magnetic (TM) polarization that is associated with the emergence of new dispersion branches. Also for TM polarization, a very low frequency mode emerges outside of the light line. Both these features are plasmonic and are attributed to the excitation of symmetric and asymmetric surface plasmon polaritons (SPPs) at the plasma-dielectric interface of the multi-layer plasma slabs. The features seen in the bandgap maps near ωp reveal the possible presence of Fano resonances between the symmetric branch of the SPP and the Bragg resonance as a narrow stop band (anti-node) is superimposed on the otherwise broad transmission band seen for transverse-electric polarization. We provide renderings that allow the visualization of where the transmission bands are and compute the transmittance and reflectance to facilitate the design and interpretation of experiments. The transmission bands associated with photonic bandgap modes above the plasma frequency are rather broad. The plasmonic modes, i.e., those associated with εp ≤ 0, can be quite narrow and are tuned by varying the plasma density, affording an opportunity for the application of these structures as ultra-narrow tunable microwave transmission filters.

Natural history data for young subjects with Sanfilippo syndrome type B (MPS IIIB)

Among the tools of structural biology, NMR spectroscopy is unique in that it not only derives a static three-dimensional structure, but also provides an atomic-level description of the local fluctuations and global dynamics around this static structure. A battery of NMR experiments is now available to probe the motions of proteins and nucleic acids over the whole biologically relevant timescale from picoseconds to hours. Here we focus on one of these methods, relaxation dispersion, which resolves dynamics on the micro- to millisecond timescale. Key biological processes that occur on this timescale include enzymatic catalysis, ligand binding, and local folding. In other words, relaxation-dispersion-resolved dynamics are often closely related to the function of the molecule and therefore highly interesting to the structural biochemist. With an astounding sensitivity of ∼0.5%, the method detects low-population excited states that are invisible to any other biophysical method. The kinetics of the exchange between the ground state and excited states are quantified in the form of the underlying exchange rate, while structural information about the invisible excited state is obtained in the form of its chemical shift. Lastly, the population of the excited state can be derived. This diversity in the information that can be obtained makes relaxation dispersion an excellent method to study the detailed mechanisms of conformational transitions and molecular interactions. Here we describe the two branches of relaxation dispersion, R2 and R1ρ, discussing their applicability, similarities, and differences, as well as recent developments in pulse sequence design and data processing.

The equivalent stiffness of a saturated poroelastic halfspace interacting with an infinite beam under a moving point load

The equivalent stiffness of a saturated poroelastic halfspace that supports an infinite Euler-Bernoulli beam under a moving point load has been investigated in this paper. The smooth contact condition is assumed for the interface of beam and halfspace, however, with an improved continuity condition, i.e. the continuities of contact normal stress and contact vertical displacements are imposed across the width of the beam. The equivalent stiffness of the halfspace has been evaluated using a contour integration approach such that contributions of the Rayleigh pole and the dispersion branches can be explicitly taken into account. Influences of the continuity condition and the permeability on the equivalent stiffness have been studied. It is found that the imaginary part of the equivalent stiffness is nonzero since the viscous coupling between two phases of the saturated halfspace has been considered. This observation fundamentally differentiates the present paper to the work by Shi and Selvadurai (2016) where an infinite permeability has been assumed for the halfspace, i.e. null viscous coupling.

The influence of the surface parameter changes onto the phonon states in ultrathin crystalline films

In this paper, we have analytically investigated how the changes in boundary surface parameters influence the phonon dispersion law in ultrathin films of the simple cubic crystalline structure. Spectra of possible phonon states are analyzed using the method of two-time dependent Green’s functions and for the diverse combination of boundary surface parameters, this problem was presented numerically and graphically. It turns out that for certain values and combinations of parameters, displacement of dispersion branches outside of bulk zone occurs, leading to the creation of localized phonon states. This fact is of great importance for the heat removal, electrical conductivity and superconducting properties of ultrathin films.

The Role of Radiative Surface Modes and Longitudinal Excitons in the Formation of Exciton-Polariton Luminescence Spectra of CdS-Type Crystals

The low-temperature (T = 2 K) exciton-polariton luminescence (EPL) spectra in the vicinity of the exciton-resonance frequency An=1 for CdS-type crystals have been theoretically and experimentally investigated with allowance for the mechanical exciton decay . The results of the numerical calculations of the partial and interference contributions of the bulk and radiative surface spectral modes to the EPL in the geometry of additional s- and p-polarized waves emitted into vacuum are analyzed. It is shown that the contributions of purely longitudinal excitons and their interference with polaritons of the upper dispersion branch near the longitudinal frequency ωL to the EPL are small (∼10% - 30%); nevertheless, they must be taken into account to obtain quantitative agreement with experimental data. Specifically these contributions are responsible for the formation of an additional line (along with the fundamental AT line) in the case of oblique incidence of radiation.