Momentum-resolved EELS and CL study on 1D-plasmonic crystal prepared by FIB method.

We investigate a one-dimensional plasmonic crystal (1D PlC) using momentum-resolved electron energy loss spectroscopy (EELS) and cathodoluminescence (CL) techniques, which are complementary in terms of available optical information. The PlC sample is fabricated from large aluminum grains through the focused ion beam (FIB) method. This approach allows curving nanostructures with high crystallinity, providing platforms for detailed analysis of plasmonic nanostructures using both EELS and CL. The momentum-resolved EELS visualizes dispersion curves outside the light cone, confirming the existence of the surface plasmon polaritons (SPP) and local modes, while the momentum-resolved CL mapping analysis identified these SPP and local modes. Such synergetic approach of two electron-beam techniques offers full insights into both radiative and non-radiative optical properties in plasmonic or photonic structures.

Rayleigh wave propagation in centrosymmetric materials with micro-stiffness, flexoelectric and micro-inertia effects.

A theoretical investigation of Rayleigh waves propagation in polarized media has been carried out using a reformulated flexoelectric theory for isotropic dielectrics with micro-inertia effect. Within this non-classical theory, the internal energy density is the functional of the strain tensor, dilatation gradient, deviatoric part of stretch gradient and rotation gradient tensors, polarization vector, and polarization gradient. The obtained system of governing equations additionally contains three material length-scale parameters to account the micro-stiffness effect, one material constant to capture the micro-inertia effect, two flexoelectric constants to describe the flexoelectric effect and three length scale parameters related to the polarization gradient. To solve the coupled governing equations, the method of Lamé-type potentials for mechanical displacement and electric polarization vectors is used. The influences of various factors such as micro-stiffness, flexoelectricity, electric quadrupoles and micro-inertia effects on the phase velocity of the Rayleigh waves in a homogeneous isotropic half-space are studied. It is found that above effects become significant with the increase of the wavenumber. This study can be important for the investigation of high frequency surface acoustic waves in dielectric materials.

Dispersion of elastic waves in the three-layered inhomogeneous sandwich plate embedded in the Winkler foundations.

This research article investigates the behavior of elastic waves in an inhomogeneous isotropic three-layered sandwich plate with soft-core and stiff-skin layers embedded in Winkler foundations, using anti-plane shear motion. The study establishes the exact antisymmetric dispersion relation, low-frequency spectrum, and overall cut-off frequency of the wave propagation. A shortened polynomial dispersion relation is developed for the long-wave low-frequency regime by considering the contrasting material setup and compared with the exact dispersion relation. This article also provides exact and asymptotic formulas for stresses and displacements in each layer of the plate, as well as approximate one-dimensional equations of motion. The results suggest that the approximate equations of motion for the three-layered sandwich plate are valid throughout the entire low-frequency range, despite the presence of Winkler foundations on both sides of the plate. This research is significant as it provides insights into the behavior of waves in composite materials and can be used to improve the design of sandwich structures used in various engineering applications. Additionally, the findings that the approximate equations of motion for the three-layered sandwich plate are valid throughout the low-frequency range, despite the presence of Winkler foundations, can help simplify calculations and make the design process more efficient.

Refraction, beam splitting and dispersion of GHz surface acoustic waves by a phononic crystal.

We exploit a time-resolved ultrafast optical technique to study the propagation of point-excited surface acoustic waves on a microscopic two-dimensional phononic crystal in the form of a square lattice of holes in a silicon substrate. Constant-frequency images and the dispersion relation are extracted, and the latter measured in detail in the region around the phononic band gap. Mode conversion and refraction at the interface between the phononic crystal and surrounding non-structured silicon substrate is studied at constant frequencies. Symmetric phonon beam splitting, for example, is shown to lead to a striking Maltese-cross pattern when phonons exit a square region of phononic crystal excited near its center.

Optimization of Coherent Dynamics of Localized Surface Plasmons in Gold and Silver Nanospheres; Large Size Effects.

Noble metal nanoparticles have attracted attention in recent years due to a number of their exciting applications in plasmonic applications, e.g., in sensing, high-gain antennas, structural colour printing, solar energy management, nanoscale lasing, and biomedicines. The report embraces the electromagnetic description of inherent properties of spherical nanoparticles, which enable resonant excitation of Localized Surface Plasmons (defined as collective excitations of free electrons), and the complementary model in which plasmonic nanoparticles are treated as quantum quasi-particles with discrete electronic energy levels. A quantum picture including plasmon damping processes due to the irreversible coupling to the environment enables us to distinguish between the dephasing of coherent electron motion and the decay of populations of electronic states. Using the link between classical EM and the quantum picture, the explicit dependence of the population and coherence damping rates as a function of NP size is given. Contrary to the usual expectations, such dependence for Au and Ag NPs is not a monotonically growing function, which provides a new perspective for tailoring plasmonic properties in larger-sized nanoparticles, which are still hardly available experimentally. The practical tools for comparing the plasmonic performance of gold and silver nanoparticles of the same radii in an extensive range of sizes are also given.

A Poisson scaling approach to backward wave propagation in a tube.

A mathematical analysis of wave propagation along an elastic cylindrical tube is presented, with the aim of determining the range of Poisson's ratio for which backward wave propagation (i.e. at negative group velocity) can occur near the ring frequency. This range includes zero Poisson's ratio and a surrounding interval of positive and negative values, whose width depends on the thickness of the tube. The whole range of Poisson's ratio is considered, so that the work applies to modern materials, e.g. composites. All results are presented in simple analytic form by means of a dominant balance in parameter space. The identification of this balance, which is unique, is a main new result in the paper, which makes possible a new type of shell theory based on 'Poisson scaling'. The mathematical approach is deductive from the equations of motion, rather than being based on kinematic hypotheses. A key finding, accessible via the Poisson scaling, is that the regime of negative group velocities extends to high wavenumbers, while being confined to a narrow band of frequencies. Thus responses localized in space are possible for near-monochromatic forcing, an important fact for nonlinear theories of tube dynamics near the ring frequency. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'.

The Effect of Micro-Inertia and Flexoelectricity on Love Wave Propagation in Layered Piezoelectric Structures.

The non-classical linear governing equations of strain gradient piezoelectricity with micro-inertia effect are used to investigate Love wave propagation in a layered piezoelectric structure. The influence of flexoelectricity and micro-inertia effect on the phase wave velocity in a thin homogeneous flexoelectric layer deposited on a piezoelectric substrate is investigated. The dispersion relation for Love waves is obtained. The phase velocity is numerically calculated and graphically illustrated for the electric open-circuit and short-circuit conditions and for distinct material properties of the layer and substrate. The influence of direct flexoelectricity, micro-inertia effect, as well as the layer thickness on Love wave propagation is studied individually. It is found that flexoelectricity increases the Love-wave phase velocity, while the micro-inertia effect reduces its value. These effects become more significant for Love waves with shorter wavelengths and small guiding layer thicknesses.

Impact of Nonlocality on Group Delay and Reflective Behavior Near Surface Plasmon Resonances in Otto Structure.

In this work, we study the effects of nonlocality on the optical response near surface plasmon resonance of the Otto structure, and such nonlocality is considered in the hydrodynamic model. Through analyzing the dispersion relations and optical response predicted by the Drude's and hydrodynamic model in the system, we find that the nonlocal effect is sensitive to the large propagation wavevector, and there exists a critical incident angle and thickness. The critical point moves to the smaller value when the nonlocal effect is taken into account. Before this point, the absorption of the reflected light pulse enhances; however, the situation reverses after this point. In the region between the two different critical points in the frequency scan calculated from local and nonlocal theories, the group delay of the reflected light pulse shows opposite behaviors. These results are explained in terms of the pole and zero phenomenological model in complex frequency plane. Our work may contribute to the fundamental understanding of light-matter interactions at the nanoscale and in the design of optical devices.

A review on partial-wave dynamics with chiral effective field theory and dispersion relation.

The description of strong interaction physics of low-lying resonances is out of the valid range of perturbative QCD. Chiral effective field theories (EFTs) have been developed to tackle the issue. Partial wave dynamics is the systematic tool to decode the underlying physics and reveal the properties of those resonances. It is extremely powerful and helpful for our understanding of the non-perturbative regime, especially when dispersion techniques are utilized simultaneously. Recently, plenty of exotic/ordinary hadrons have been reported by experiment collaborations, e.g. LHCb, Belle, and BESIII, etc. In this review, we summarize the recent progress on the applications of partial wave dynamics combined with chiral EFTs and dispersion relations, on related topics, with emphasis onππ,πK,πNandK̄Nscatterings.

Is the existence of a J/ψJ/ψ bound state plausible?

In a recent measurement LHCb reported pronounced structures in the J/ψJ/ψ spectrum. One of the various possible explanations of those is that they emerge from non-perturbative interactions of vector charmonia. It is thus important to understand whether it is possible to form a bound state of two charmonia interacting through the exchange of gluons, which hadronise into two pions at the longest distance. In this paper, we demonstrate that, given our current understanding of hadron-hadron interactions, the exchange of correlated light mesons (pions and kaons) is able to provide sizeable attraction to the di-J/ψ system, and it is possible for two J/ψ mesons to form a bound state. As a side result we find from an analysis of the data for the ψ(2S)→J/ψππ transition including both ππ and KK¯ final state interactions an improved value for the ψ(2S)→J/ψ transition chromo-electric polarisability: |αψ(2S)J/ψ|=(1.8±0.1)GeV-3, where the uncertainty also includes the one induced by the final state interactions.

Impact of the Interband Transitions in Gold and Silver on the Dynamics of Propagating and Localized Surface Plasmons.

Understanding and modeling of a surface-plasmon phenomenon on lossy metals interfaces based on simplified models of dielectric function lead to problems when confronted with reality. For a realistic description of lossy metals, such as gold and silver, in the optical range of the electromagnetic spectrum and in the adjacent spectral ranges it is necessary to account not only for ohmic losses but also for the radiative losses resulting from the frequency-dependent interband transitions. We give a detailed analysis of Surface Plasmon Polaritons (SPPs) and Localized Surface Plasmons (LPSs) supported by such realistic metal/dielectric interfaces based on the dispersion relations both for flat and spherical gold and silver interfaces in the extended frequency and nanoparticle size ranges. The study reveals the region of anomalous dispersion for a silver flat interface in the near UV spectral range and high-quality factors for larger nanoparticles. We show that the frequency-dependent interband transition accounted in the dielectric function in a way allowing reproducing well the experimentally measured indexes of refraction does exert the pronounced impact not only on the properties of SPP and LSP for gold interfaces but also, with the weaker but not negligible impact, on the corresponding silver interfaces in the optical ranges and the adjacent spectral ranges.

Effect of periodic corrugation on Lamb wave propagation in PMN-PT single crystal bilayer plates.

Propagation characteristics of Lamb waves in a bilayer plate comprised of a PMN-PT single crystal layer and an elastic layer were investigated in this study. The profiles of the bilayer plate's upper and lower surfaces and the common interface between the PMN-PT and elastic layers were assumed to be periodic corrugation instead of perfect planes. The PMN-PT single crystal was poled along the [0 1 1]c direction with macroscopic symmetry of orthonormal mm2. The dispersion relations of Lamb waves for electrically open and electrically short boundary conditions were derived in the closed form. The effects of the related corrugation parameters and thickness ratios of the PMN-PT single crystal layer to the elastic layer on the phase velocity were assessed using the numerical results. The parameters of the amplitudes and wavenumbers related to the periodic corrugation played key roles in the propagation and dispersion behaviors of the Lamb waves. The phase velocity increased, especially in a lower wavenumber range when the upper or lower surfaces were considered corrugated contours. However, the phase velocity decreased when the common interface was treated as a corrugated configuration. The smaller thickness ratio produced higher phase velocity. These results can provide some fundamental characteristics for the design and application of acoustic wave devices fabricated with PMN-PT single crystals, especially for improving the efficiency and sensitivity.

Rayleigh wave propagation in a homogeneous centrosymmetric flexoelectric half-space.

Although Rayleigh waves are a research topic of constant interest, research on Rayleigh waves in flexoelectric materials is still lacking. This study reports the influences of flexoelectricity, strain gradient elasticity, micro-inertia effect and surface effect on Rayleigh waves in a homogeneous centrosymmetric flexoelectric material half-space. The nonclassical governing equations and boundary conditions are deduced with Hamilton's principle. Our findings suggest that the influence of flexoelectricity on the phase velocity depends on the flexoelectric coefficients. Strain gradient elasticity and surface elasticity can increase the phase velocity, while micro-inertia effect can decrease the phase velocity. Besides, these influences become significant for Rayleigh waves with high frequencies and short wavelengths. A mathematical foundation may be established to measure the material properties on the basis of the relationships among the material parameters, the phase velocity and the wave number. Moreover, the current work might provide guidance in developing small-scale acoustic wave devices operating at high frequencies.

Dynamic characterization of a periodic microstructured flexural system with rotational inertia.

We consider the propagation of waves in a flexural medium composed of massless beams joining a periodic array of elements, elastically supported and possessing mass and rotational inertia. The dispersion properties of the system are determined and the influence and interplay between the dynamic parameters on the structure of the pass and stop bands are analysed in detail. We highlight the existence of three special dynamic regimes corresponding to a low stiffness in the supports and/or low rotational inertia of the masses; to a high stiffness and/or high rotational inertia regime; and to a transition one where dispersion degeneracies are encountered. In the low-frequency regime, a rigorous asymptotic analysis shows that the structure approximates a continuous Rayleigh beam on an elastic foundation. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 1)'.

Electron spill-out effects in plasmon excitations by fast electrons.

A new non-retarded hydrodynamic approach to the interaction between a fast electron and a diffuse metal-vacuum interface is presented. The metal is characterized by the parameters of a dispersive bulk dielectric function which slowly fade at the interface. The response of the medium is described by the induced charge density, which is self-consistently calculated. This formalism is applied to the study of the energy loss spectrum (EELS) experienced by a fast electron passing by a metal-vacuum interface. In the case of a sharp interface analytical expressions for the loss probability, fully equivalent to that of the Specular Reflection Model (SRM), are found. In an Al interface the effects of the electron density spill-out (modeled according to Lang-Kohn density) on both the longitudinal (EELS) and transverse components of the momentum transfer are studied. The influence of the interface profile on the surface plasmon dispersion in EELS is also discussed, showing that in agreement with previous theoretical and experimental works the dispersion of surface plasmon turns out to be much weaker than the one calculated in the SRM. A possible extension of the theory to study interfaces between transition metals and insulators is also discussed.

Dispersive and effective properties of two-dimensional periodic media.

We consider transverse propagation of electromagnetic waves through a two-dimensional composite material containing a periodic rectangular array of circular cylinders. Propagation of waves is described by the Helmholtz equation with the continuity conditions for the tangential components of the electric and magnetic fields on the boundaries of the cylinders. We assume that the cell size is small compared with the wavelength, but large compared with the radius a of the inclusions. Explicit formulae are obtained for asymptotic expansion of the solution of the problem in terms of the dimensionless magnitude q of the wavevector and radius a. This leads to explicit formulae for the effective dielectric tensor and the dispersion relation with the rigorously justified error of order O((q 2 + a 2)5/2).

Influence of post-deposition annealing on structural, morphological and optical properties of copper (II) acetylacetonate thin films.

In this study, the effect of thermal annealing under vacuum conditions on structural, morphological and optical properties of thermally evaporated copper (II) acetylacetonate, cu(acac)2, thin films were investigated. The copper (II) acetylacetonate thin films were deposited using thermal evaporation technique at vacuum pressure ~1 × 10-5 mbar. The deposited films were thermally annealed at 323, 373, 423, and 473 K for 2 h in vacuum. The thermogravimetric analysis of cu(acac)2 powder indicated a thermal stability of cu(acac)2 up to 423 K. The effects of thermal annealing on the structural properties of cu(acac)2 were evaluated employing X-ray diffraction method and the analysis showed a polycrystalline nature of the as-deposited and annealed films with a preferred orientation in [1¯01] direction. Fourier transformation infrared (FTIR) technique was used to negate the decomposition of copper (II) acetylacetonate during preparation or/and annealing up to 423 K. The surface morphology of the prepared films was characterized by means of field emission scanning electron microscopy (FESEM). A significant enhancement of the morphological properties of cu(acac)2 thin films was obtained till the annealing temperature reaches 423 K. The variation of optical constants that estimated from spectrophotometric measurements of the prepared thin films was investigated as a function of annealing temperature. The annealing process presented significantly impacted the nonlinear optical properties such as third-order optical susceptibility χ(3) and nonlinear refractive index n2 of cu(acac)2 thin films.

Space-time structure and wavevector anisotropy in space plasma turbulence.

Space and astrophysical plasmas often develop into a turbulent state and exhibit nearly random and stochastic motions. While earlier studies emphasize more on understanding the energy spectrum of turbulence in the one-dimensional context (either in the frequency or the wavenumber domain), recent achievements in plasma turbulence studies provide an increasing amount of evidence that plasma turbulence is essentially a spatially and temporally evolving phenomenon. This review presents various models for the space-time structure and anisotropy of the turbulent fields in space plasmas, or equivalently the energy spectra in the wavenumber-frequency domain for the space-time structures and that in the wavevector domain for the anisotropies. The turbulence energy spectra are evaluated in different one-dimensional spectral domains; one speaks of the frequency spectra in the spacecraft observations and the wavenumber spectra in the numerical simulation studies. The notion of the wavenumber-frequency spectrum offers a more comprehensive picture of the turbulent fields, and good models can explain the one-dimensional spectra in the both domains at the same time. To achieve this goal, the Doppler shift, the Doppler broadening, linear-mode dispersion relations, and sideband waves are reviewed. The energy spectra are then extended to the wavevector domain spanning the directions parallel and perpendicular to the large-scale magnetic field. By doing so, the change in the spectral index at different projections onto the one-dimensional spectral domain can be explained in a simpler way.

On periodic geophysical water flows with discontinuous vorticity in the equatorial f-plane approximation.

We are concerned here with geophysical water waves arising as the free surface of water flows governed by the f-plane approximation. Allowing for an arbitrary bounded discontinuous vorticity, we prove the existence of steady periodic two-dimensional waves of small amplitude. We illustrate the local bifurcation result by means of an analysis of the dispersion relation for a two-layered fluid consisting of a layer of constant non-zero vorticity γ1 adjacent to the surface situated above another layer of constant non-zero vorticity γ2≠γ1 adjacent to the bed. For certain vorticities γ1,γ2, we also provide estimates for the wave speed c in terms of the speed at the surface of the bifurcation inducing laminar flows.This article is part of the theme issue 'Nonlinear water waves'.

Competition of energy between active transport and vesicle fusion at the origin of intracellular gradient fields.

It has been reported that the ionic patterns of hyphal growth can be explained by a weakening of the active transport at the tip at the expense of other biosynthesis processes, from which results energy transport from the proximal cells to the apical ones (Potapova et al. 1988). We present here a theory to support this hypothesis, whose extent is much more general than the initial frame where it has been formulated. It can be summarized in two basics mechanisms, one coupling active transport of the plasma membrane, electric potential and vesicle fusion, the other coupling the Ca2+-ATPase of the endoplasmic reticulum and vesicle fusion. For some values of parameters introduced in the theory, the uniform state of the cell becomes unstable, at the origin of intracellular gradient fields. Theoretical ionic patterns are spontaneously produced, which can be satisfactorily compared to several observed in and around tip-growing cells.