The relationship between acoustic radiation modes and structural modes and its applications

Both acoustic radiation modes and structural modes play an important role in the field of structure-borne sound, however, little work has been done for inherent relations between these two kinds of modes. This paper is focused on the relationship between the radiation modes and structural modes and its physical mechanisms. First, a governing equation for relating the radiation mode and structural mode is given based on the characteristics of the modes. Then, using the symmetric or anti-symmetric properties of two kinds of modes, the corresponding relations are presented. And then, numerical examples are given to verify the theoretical investigations, and it has been shown that, for a simply supported rectangular panel vibrating at low frequencies, the first radiation mode is dominant corresponding to (odd, odd) structural modes; the following radiation modes are respectively dominant corresponding to (even, odd), (odd, even), and (even, even) structural modes. Finally, such relations are applied to active acoustic structural control and provide a direct help for the design of active control strategy and arrangement of the secondary forces.     

Ultra-wideband optical diode based on photonic crystal 90° bend and directional coupler

We propose an ultra-wideband optical diode device based on two-dimensional square-lattice photonic crystals. For the device,the odd mode is completely transmitted in one direction and converted to the fundamental even mode,but completely reflected in the other direction. The operation bandwidth of the device is preserved within a rather wide range of frequencies,which is over 6.5% of the central frequency. A directional coupler and 90° bend are utilized as the composite function device with mode filter and mode converter. It is possible that the photonic crystal device can help to construct on-chip optical logical devices and benefit greatly to the optical systems with multiple spatial modes.     

Competition of the multiple Grtler modes in hypersonic boundary layer flows

Competition of multiple Grtler modes in hypersonic boundary layer flows are investigated with the local and marching methods.The wall-layer mode(mode W)and the trapped-layer mode(mode T)both occur in the compressible boundary layer where there exists a temperature adjustment layer near the upper edge.The mode T has the largest growth rate at a lower Grtler number while the mode W dominates at larger Grtler numbers.These two modes are both responsible for the flow transition in the hypersonic flows especially when Grtler number is in the high value range in which the crossover of these two modes takes place.Such high Grtler numbers are virtually far beyond the neutral regime.The nonparallel base flows,therefore,cease to influence the stability behavior of the Grtler modes.The effects of the Mach number on the multiple Grtler modes are studied within a chosen Mach number of 0.95,2,4 and 6.When the flow Mach number is sufficiently large,e.g.,Ma 4,the growth rate crossover of the mode T and mode W occurs both in the conventional G-βmap as well as on the route downstream for a fixed wavelength disturbance.Four particular regions(Region T,T-W,W-T and W)around the crossover point are highlighted with the marching analysis and the result matches that of the local analysis.The initial disturbance of a normal mode maintains the shape in its corresponding dominating region while a shape-transformation occurs outside this region.     

WG-Like Modes Selectivity in a Square Cavity with Posts

We investigate the characteristics of Whispering-Gallery（WG）-like modes in a square cavity with posts by employing the two-dimensional （2D） finite-difference time-domain （FDTD） technique combined with the effective index method. The results indicate that the posts can result in mode selection in the WG-like modes. The WG-like modes with odd mode numbers are not much sensitive to the sizes of the posts. However, the quality factor （i.e. Q-factor） of the WG-like modes with even mode numbers decreases sharply with the increasing size of the posts. The decreasing Q-factor is attributed to mode leakage and scattering loss due to the presence of the post. The mode selection increases the mode spacing of square cavity twice in an optimized structure.     

The surface plasmon polariton dispersion relations in a nonlinear-metal-nonlinear dielectric structure of arbitrary nonlinearity

The analytic surface plasmon polaritons(SPPs) dispersion relation is studied in a system consisting of a thin metallic film bounded by two sides media of nonlinear dielectric of arbitrary nonlinearity is studied by applying a generalised first integral approach.We consider both asymmetric and symmetric structures.Especially,in the symmetric system,two possible modes can exist:the odd mode and the even mode.The dispersion relations of the two modes are obtained.Due to the nonlinear dielectric,the magnitude of the electric field at the interface appears and alters the dispersion relations.The changes in SPPs dispersion relations depending on film thicknesses and nonlinearity are studied.     

Fano Resonance by Symmetry Breaking Stub in a Metal-Dielectric-Metal Waveguide

The coupling of a stub obliquely intersected with a metal-dielectric-metal plasmonic waveguide is investigated by using the finite difference in time domain method. Results show that an odd mode, except for the usual even mode, is excited in the stub due to the symmetry breaking of the oblique intersection. Moreover, the results show that tile quality factor of the odd mode is very high in comparison with that of the usual even mode, which is then explained by the symmetry breaking of the oblique stub intersection. The superposition of the even and the odd mode generates a Fano shaped spectrum with a very narrow linewidth. The effect of metallic loss and compensation are also discussed. Both the stub and the waveguide are compact in size, and simple in structure, which are beneficial for the achievements of narrow band filtering, sensing, lasing, and nonlinearity enhancement.     

Comparison of ITG and TEM Microturbulence in DⅢ-D Tokamak

Microturbulence excited by ion temperature gradient(ITG)-dominant and trapped electron mode(TEM)-dominant instabilities is compared in the fusion plasmas using gyrokinetic simulations based on the realistic equilibrium data from DⅢ-D discharges.Collisions make a difference between two plasmas and give rise to similar results to those found in previous research experiments[Chin.Phys.Lett.35(2018)105201].The mode structures and frequency spectrum of the most unstable modes characterized by the ITG-dominant and TEM-dominant instabilities are excited in the lower and higher T. plasmas in the linear simulations.In the nonlinear simulations,contour plots of the perturbed potential are shown in the saturated stage,with the radial correlation lengths being microscopic on the order of the ion thermal gyroradius ρi in both the ITG and the TEM microturbulences.The dominant mode wavelengths of the perturbed potential increase when evolving from linear to nonlinear stages in both simulations, with the fluctuation energy spreading from the linearly dominant modes to the nonlinearly dominant modes.The radial correlation lengths are about 4ρi and the electron density fluctuation intensities are about 0.85% in the nonlinear saturated stage,which are in agreement with the experimental results.     

The dispersion relations for surface plasmon in a nonlinear-metal-nonlinear dielectric structure

In the asymmetric and symmetric nonlinear-metal-nonlinear dielectric structures, this paper studies the analytic dispersion relation for surface plasmon in a system consisting of a thin metallic film covered on two sides media of intensity-dependent refractive indexes by applying a generalised first integral approach. Especially in the symmetric waveguide structure, two possible modes can exist: the odd mode and the even mode. The dispersion relations of the two modes are obtained. Due to the nonlinear dielectric, the squared magnitude of the electric field at the interface appears and alters the dispersion relations. Numerical results are compared to those from a certain approximate treatment.     

Inversion of Rayleigh Wave in a Stratified Half Space

Inversion of Rayleigh waves is studied for the first time by using the genetic algorithm based on the intensities of the fundamental and/or higher modes. The relations of all modes to the medium structure are investigated. It is emphasized that the higher modes and mode jumping should be considered in the inversion when the low-velocity     

Characteristics of nonlinear evolution of wavepackets in boundary layers

The nonlinear evolution of a finite-amplitude disturbance in a 3-D supersonic boundary layer over a cone was investigated recently by Liu et al.using direct numerical simulation(DNS).It was found that certain small-scale 3-D disturbances amplified rapidly.These disturbances exhibit the characteristics of second modes,and the most amplified components have a welldefined spanwise wavelength,indicating a clear selectivity of the amplification.In the case of a cone,the three-dimensionality of the base flow and the disturbances themselves may be responsible for the rapid amplification.In order to ascertain which of these two effects are essential,in this study we carried out DNS of the nonlinear evolution of a spanwise localized disturbance(wavepacket) in a flat-plate boundary layer.A similar amplification of small-scale disturbances was observed,suggesting that the direct reason for the rapid amplification is the three-dimensionality of the disturbances rather than the three-dimensional nature of the base flow,even though the latter does alter the spanwise distribution of the disturbance.The rapid growth of 3-D waves may be attributed to the secondary instability mechanism.Further simulations were performed for a wavepacket of first modes in a supersonic boundary layer and of Tollmien-Schlichting(T-S) waves in an incompressible boundary layer.The results show that the amplifying components are in the band centered at zero spanwise wavenumber rather than at a finite spanwise wavenumber.It is therefore concluded that the rapid growth of 3-D disturbances in a band centered at a preferred large spanwise wavenumber is the main characteristic of nonlinear evolution of second mode disturbances in supersonic boundary layers.     

The reflection of the Lamb wave in a semi-infinite plate

The Lamb wave technique is used in the detection of internal defects inplates.The reflection of the Lamb wave at the free edge of the plate has been shownto be rather complicated.The reflected wave is usually composed of infinite numberof Lamb wave modes even in the case of incidence of one pure mode.The analysisof the reflection problem is complicated in nature as the orthogonality relations ofthe eigen modes of the Lamb wave concern both the stresses and displacements.Weadopt the principle of the least squares as a new approach to simplify the analysis,inwhich the eigen-modes are taken as the trial function.It seems to be simple and effective.In most cases a good enough result can be obtained on using an 8-bitmicrocomputer.Here the coefficients of the various reflected modes are calculated,some interesting phenomena on the mode conversion are indicated and the condi-tions on the pure mode reflection are given.     

Resonant Modes of L-Shaped Gold Nanoparticles

We analyze the electric field modes excited in resonant L-shaped gold nanoparticles using a finite-difference time domain method. Compared to a single gold nanorod, both the odd and even modes of the L-shaped nanoparticles can be excited due to the symmetry breaking. The nanoparticles with equal and unequal arms have different dependence of field enhancement and mode on the incident polarization.     

The phenomenon of even bulk modes variance in a ferromagnetic A--A bilayer system

The eigenproblems of spin waves in a symmetrical ferromagnetic bilayered system with periodic boundary conditions are solved using the interface-rescaling approach (IRA). The results show that interface coupling between two sublayers would not change the excitation energy of odd bulk modes, but change excitation energy of even bulk modes. We call this peculiar phenomenon the phenomenon of even bulk mode variance (PEBMV). There are two kinds of mechanisms which cause PEBMV: phase reversal and phase translation of the magnon at the interface, corresponding, respectively, to the antiferromagnetic and ferromagnetic interface coupling cases. PEBMV embodies the selective effect of the interface on different bulk magnons.     

Attachment Instabilities of SF6 Inductively Coupled Plasmas under Different Coupling Intensities

Characteristics of attachment instabilities in SF6 inductively coupled plasmas are experimentally studied under different coupling intensities. Experimental results show that the instabilities only occur in H modes operating in positive feedback regions. Both the sudden mode transitions and the instabilities are influenced by the coupling intensities. With increasing absorbed power, weak and middle coupling discharges can sequently undergo sudden mode transitions and attachment instabilities. In strong coupling discharges, the sudden mode transitions disappear and only attachment instabilities exist. The strong and weak coupling discharges are the most stable and unstable, respectively.     

Numerical investigation of separation-induced transition in a lowpressure turbine cascade in a low-disturbance environment

In this paper,the separation-induced transition in an LPT(low-pressure turbine)cascade is investigated at low Reynolds number with DNS(direct numerical simulation).The transition process is accurately predicted giving good agreements between the DNS and experimental results.To illustrate the secondary instability of separation-induced transition in a low-disturbance environment,the results are comprehensively analyzed in both Fourier space and physical space.It is illustrated that the effect of hyperbolic instability dominates around the saddle point of hyperbolic streamlines.This instability mechanism is responsible for the emergence of the streamwise vortices in the braid region.Elongated and intensified because of the“stretching”effect of the background flow,these vortices become the most noticeable characteristic of the flow field.Fundamental modes of small spanwise wavelength are excited in the braid region,so as some low-frequency modes.The elliptical instability plays a minor role than hyperbolic instability.It is also observed that the fundamental mode with a larger spanwise wavelength is unstable in the vortex core which is associated with the deformation of the vortex core via elliptical instability.There is no convincing evidence for the existence of subharmonic instability.     

Guided modes in asymmetric metal-cladding left-handed material waveguides

We investigate guided modes in the asymmetric waveguide structure with a left-handed material (LHM) layer surrounded by air and metal. A graphical method is proposed to determine the guided modes. New properties of the oscillating and surface guided modes, such as absence of the fundamental mode, coexistence of the oscillating and surface guided modes, fast attenuation of the surface guided modes, and mode degeneracy, are analyzed in detail. We also investigate dispersive characteristics of the metal-LHM- air optical waveguide. The propagation constant increases with decreasing slab thickness for the first-order oscillating mode, which is different from that in traditional metal-cladding waveguides.     

Influence of laser mode on splitting beam illumination effect of Dammann grating

The influences of various laser modes on the splitting beam effect of Dammann grating are studied in theory and by numerical simulation. The results show that fundamental mode laser resembles plane wave while high order mode laser differs from plane wave in the splitting beam effect by Dammann grating. Therefore, the fundamental mode laser is more suitable to be the light source to improve the energy efficiency in far-distance image detecting systems, such as laser image ladar, which use Dammann grating in the ilhlmination svstem.     

Propagation properties of electromagnetic fields in elliptic dielectric hollow fibres and their applications

We numerically calculate and analyse the electromagnetic fields, optical intensity distributions, polarization states and orbital angular momentum of some elliptic hollow modes in an elliptic dielectric hollow fiber (EDHF) by using Mathieu functions, and also calculate the optical potential of the blue-detuned _eHE₁₁ mode evanescent-light wave for ⁸⁵Rb atoms, including the position-dependent van der Waals potential, and discuss briefly some potential applications of our EDHF in atom and molecule optics, etc. Our study shows that the vector electric field distributions of the odd modes in the cross section of the EDHF are the same as that of the even modes and with different boundary ellipses by rotating an angle of π/2, and the orbital angular momentum (OAM) of single HE (EH) mode is exactly equal to zero, while that of dual-mode in the EDHF is fractional in h, and has a sinusoidal oscillation as z varies. The EDHF can be used to produce various elliptic hollow beams, even to generate and study various atomic vortices with a fractional charge and its fractional quantum Hall effect in atomic Bose--Einstein condensate, and so on.     

Generation of new longitudinal modes in an amplifying dye solution

A novel phenomenon is reported for the first time that the generation of the newlongitudinal modes in amplifying multi-longitudinal mode laser in a dye amplifier.The newmodes are located on the violet side within the gain band of the amplifing medium.The phe-nomenon is explained by the theory of third-order nonlinear polarization in the case of four-wave resonances.The intensity of the new modes created are comparable with or even higherthan that of the original modes.The effect can be expected to serve as a new method for ex-tention of spectral tuning ranges of laser.     

Intermodal interference of LP01 and LP11 modes inpanda fibers

LP01 and LP11 mode interferences in high-birefringence （Hi-Bi） panda fibers are theoretically and experimentally presented. The propagation characteristics of both the fundamental and second-order modes in Hi-Bi panda fibers are investigated, and the interference output intensity distribution of the LP₀1 and LP₁1 modes in panda fibers are thoroughly examined. An experiment is conducted to verify the feasibility of modal interference sensors. The results show that the two-lobe interference pattern of panda fibers generates energy exchanges when external strain is applied on the fiber. Moreover, Hi-Bi panda fibers can be used to design voltage sensors.