Surface plasmon modes in multi-layer thin-films

The surface plasmon modes in multi-layer thin-film structures of the metal-insulator-metal (MIM) type are modeled using a matrix method for the propagation of electromagnetic waves in stratified media. It is shown that the dispersion relation for the allowed surface plasmon modes is obtained from one of the matrix elements. The fundamental electromagnetic modes are the eigenfunctions of the differential equation for the magnetic field distribution and the eigenvalues are obtained from the dispersion relation. The expansion of an arbitrary wave profile in terms of the eigenfunctions is discussed and applied to the problem of surface plasmons propagating in a structure consisting of seven layers of alternating metal films and dielectrics.     

A new integral equation formulation for an axisymmetric structure

A new method is developed to compute the acoustic field outside an axisymmetric structure from the normal velocity values on the surface. Surface pressure and normal velocity are expanded in a series of functions that are orthonormal on the surface of the structure and have a constant ratio of pressure to normal derivative of pressure at vanishing frequency. The Helmholtz integral equation is next used to compute the field everywhere outside the structure. The method is tested by applying it to scattering from a rigid cylinder with hemispherical endcaps. The series is shown to converge very rapidly.     

利用源强密度声辐射模态重建声场

为了利用声场中少量测点声压数据精确重建复杂结构的辐射声场,提出了源强密度声辐射模态分析理论和声场重建公式.在结构表面定义的空间上,利用以源强密度分布函数为参量的结构辐射声功率泛函表达式定义了一个线性自伴正辐射算子,该算子的特征函数为结构的源强密度声辐射模态.然后通过对矩形平板和带有半球帽的圆柱体的源强密度声辐射模态的分析,证明了源强密度声辐射模态具有空间滤波特性,并利用该性质建立了声场重建公式.球体仿真和平板实验验证了所提出的声场重建方法的可行性和稳健性.基于源强密度声辐射模态的声场重建方法简单,利用较少测点数据就可以获得较高的声场重建精度,特别适合于复杂结构的低频声场重建.     

Shaping the Sensitive Volume of a Single-Sided NMR-Sensor to Profile Cylindrical Samples with High Resolution

This work reports the construction of a single-sided magnet generating a sensitive volume with adjustable curvature. It is useful to profile cylindrical samples with high depth resolution. The sensor geometry is based on the Profile NMR-MOUSE, which generates a parabolic field profile with a quadratic coefficient that decreases with the distance from the magnet surface. Such field profiles approximate cylinder walls within limited angular range with negligible deviation. Then, by varying the working depth, shells of different diameter in the sample can be matched. Simulation and experiments conducted on phantoms confirm that a depth resolution of about 35 μm can be obtained. The sensor was used to profile the structure of a cylindric air spring bellows with high resolution. Besides resolving the fiber layers used to reinforce the rubber matrix, the ingress of hexane was detected via T ₂ changes of the material.     

Eigenvalues and eigenfunctions of a clover plate

We report a numerical study of the flexural modes of a plate using semi-classical analysis developed in the context of quantum systems. We first introduce the Clover billiard as a paradigm for a system inside which rays exhibit stable and chaotic trajectories. The resulting phase space explored by the ray trajectories is illustrated using the Poincare surface of section, and shows that it has both integrable and chaotic regions. Examples of the stable and the unstable periodic orbits in the geometry are presented. We numerically solve the biharmonic equation for the flexural vibrations of the Clover shaped plate with clamped boundary conditions. The first few hundred eigenvalues and the eigenfunctions are obtained using a boundary elements method. The Fourier transform of the eigenvalues show strong peaks which correspond to ray periodic orbits. However, the peaks corresponding to the shortest stable periodic orbits are not stronger than the peaks associated with unstable periodic orbits. We also perform statistics on the obtained eigenvalues and the eigenfunctions. The eigenvalue spacing distribution P(s) shows a strong peak and therefore deviates from both the Poisson and the Wigner distribution of random matrix theory at small spacings because of the C_4v symmetry of the Clover geometry. The density distribution of the eigenfunctions is observed to agree with the Porter-Thomas distribution of random matrix theory. Received 12 February 2001 and Received in final form 17 April 2001     

Structure of Hamiltonian Matrix and the Shape of Eigenfunctions：Nuclear Octupole Deformation Model

The structure of a Hamiltonian matrix for a quantum chaotic system,the nuclear octupole deformation model,has been discussed in detail.The distribution of the eigenfunctions of this system expanded by the eigenstates of a quantum integrable system is studied with the help of generalized Brillouin-Wigner perturbation theory.The results show that a significant randomness in this distribution can be observed when its classical counterpart is under the strong chaotic condition.The averaged shape of the eigenfunctions fits with the Gaussian distribution only when the effects of the symmetry have been removed.     

Electron on a cylinder with topological defects in a homogeneous magnetic field

In this work we study the effects of the geometry and topology of a cylinder on the energy levels of an electron moving in a homogeneous magnetic field. We consider the existence of topological defects as a screw dislocation and a disclination. When we take the region of movement as the full cylindrical surface, we find that, by increasing the strength of the screw dislocation, the dispersion on the electronic energy levels is affected and monotonically increasing. For an electron moving in an almost flat region we show that the dispersion on the Landau levels decrease monotonically as we increase the strength of the screw dislocation. The lowest Landau level can reach a zero value, leaving the energy of the system solely given by the geometry of the cylinder, which does not depend on the magnetic field. In both situations, as we change the deficit angle of the disclination, we observe that the energy levels are shifted and the magnitude of such shift depends on the magnetic field. The Landau levels for a flat sample are recovered in the limit of an infinite cylinder radius.     

Diffraction of Electromagnetic Waves by an Anisotropic Cylindrical Inhomogeneity in a Planar Waveguide

We consider diffraction of electromagnetic waves by an anisotropic cylindrical inhomogeneity located in a planar waveguide with perfectly conducting walls. Anisotropy is allowed for by using the uniaxial-crystal approximation. A rigorous analytical solution is represented in the form of double sums over eigenfunctions of a planar waveguide with perfectly conducting walls and azimuthal eigenfunctions of a cylinder. Different components of the intensity of the electric field scatttered by an anisotropic inhomogeneity are numerically calculated. The influence of the anisotropy and sizes of the inhomogeneity on the scattered field is analyzed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 7, pp. 605–615, July 2005.     

关于量子口袋动力学

将MIT边条件用于运动和变形中的口袋,讨论了口袋的动力学:包括变动中口袋内的单夸克和单胶子波函数;夸克──胶子场的量子化和由夸克──胶子系统推动的口袋运动的动力学及其量子化、发现:变动中的口袋内胶子场为符合MIT边条件必须包含纵场成份:夸克数算符和胶子数算符成为非(?)密的;口袋作为一个整体的动力学类似于强子场论的动力学,例如仍可沿用强子场论中的自由强子传播子而将强子内部的夸克──胶子结构反映到顶点的非定域化上,这样就完成了量子口袋动力学的一个理论框架,使得可以在按动力学结构将口袋模型重新参数化后,在夸克──胶子和强子的两个不同层次上统一研讨强子物理和核物理。 量子口袋动力学也是变动中的容器内的量子场沦以及容器内的场与容器表面耦合的量子理论的例子。     

Magnetoexcitons in nanostructures exhibiting cylindrical symmetry

The problem of an exciton in the cylindrical nanostructure exposed to an external static magnetic field is investigated. The theoretical model assumes anisotropic masses which are different inside and outside the nanostructure. The confinement potential has finite value at the boundaries and magnetic field is parallel to the axis of the cylinder. The screened Coulomb interaction between an electron and a hole is assumed. The consistent mathematical procedure is developed to calculate the magnetoexciton eigenfunctions and eigenenergies. Our method applies to the systems exhibiting cylindrical symmetry where, due to confinement effects accompanied by the e-h Coulomb interaction, the separation of relative- and center-of-mass motion is not possible. Numerical calculations have been performed for the quantum disk, the cylinder and the quantum rod. The magnetic field dependent energy spectrum and corresponding wave functions, expressed in terms of known one-particle electron and hole eigenfunctions, are calculated. Additionally, we point out the different role of Coulomb interaction in every case.     

Surface plasmon tunneling through a touching gold nanocylinder array on a thin gold film

The optical property of a structure composed of a touching gold nanocylinder array on a thin gold film is investigated using finite-difference time-domain (FDTD) method. It is discovered that the transmission behavior can be tuned by tuning the geometry of the structure. As the film thickness increases, the transmission mode associated with the localized surface plasmon resonance blue shifts accompanied with a decrease of magnitude and full width at half maximum, and a second transmission appear due to the interaction of the plasmons on the cylinder with their images induced on the film. The localized waveguide resonance diminishes but the second resonance peak is intensified and broadened noticeably with the separation of the cylinder array and film increase. The cylinder radius size influences the localized surface plasmon resonance mode obviously. These results may be helpful for the design of a novel optical device.     

Improved fictitious charge method for calculations of electric potential and field generated by point-to-plane electrodes

In the framework of standard tip-to-plane electrode geometry favorable to corona streamer discharge development at atmospheric pressure, this work is devoted to the improvement of fictitious charge method for calculations of electric potential and field repartition when the tip is powered by a DC voltage. It is in fact dedicated to implement the image charge method (generally used in plane-to-plane electrodes) in the case of a point-to-plane geometry. The numerical method is based on the solution an open system of n equations with m unknowns (n >> m) where m is the number of fictitious charges and n the number of contours at the surface of the tip electrode defining the boundary conditions. This numerical technique can accurately interpolate the shape of the electrode tip whatever its geometry and hence allows us to accurately calculate the electric potential and field even at a position very close to the electrode. It is noteworthy that the solution of such open system of equations cannot be obtained from conventional techniques (Cramer, Gauss, matrix inversion, etc.). We used the method of least squares which enables us to close the equation systems and to find the optimal solution fulfilling all the required boundary conditions. The present method is therefore based on the coupling between the conventional method of fictitious charges using image charge method and the optimization by the Least Squares Method. The results of simulation show that the punctual fictitious charges have given the most accurate results when the electrode has symmetry of revolution like the present geometry of a pen shape anode cylinder ended by a sharp tip set in front of cathode plane.     

First-order optical systems with real eigenvalues

It is shown that a lossless first-order optical system whose real symplectic ray transformation matrix can be diagonalized and has only real eigenvalues, is similar to a separable hyperbolic expander in the sense that the respective ray transformation matrices are related by means of a similarity transformation. Moreover, it is shown how eigenfunctions of such a system can be determined, based on the fact that simple powers are eigenfunctions of a separable magnifier. As an example, a set of eigenfunctions of a hyperbolic expander is determined and the resemblance between these functions and the well-known Hermite-Gauss modes is exploited.     

The continuum gauge field-theory model for low-energy electronic states of icosahedral fullerenes

The low-energy electronic structure of icosahedral fullerenes is studied within the field-theory model. In the field model, the pentagonal rings in the fullerene are simulated by two kinds of gauge fields. The first one, non-abelian field, follows from so-called K spin rotation invariance for the spinor field while the second one describes the elastic flow due to pentagonal apical disclinations. For fullerene molecule, these fluxes are taken into account by introducing an effective field due to magnetic monopole placed at the center of a sphere. Additionally, the spherical geometry of the fullerene is incorporated via the spin connection term. The exact analytical solution of the problem (both for the eigenfunctions and the energy spectrum) is found.     

Average scattered field from a random PEC cylinder buried below a slightly rough surface

Scattering from a perfect electric conducting cylinder with random radius buried below a half space dielectric homogenous interface is studied. The cylindrical wave scattered by cylinder is expanded in terms of plane wave spectrum. Small perturbation method is used to study the interaction of each plane wave with the interface. The zeroth order term yields solution for a flat interface, whereas scattering from a rough surface is given by first-order term. Results are obtained for both TM and TE polarizations. Analytical expressions of the average scattered field are obtained and verified using numerical evaluation. Different scattering scenarios are simulated by varying the distribution of the radius. It is observed that average scattering cross section of an ensemble with normal/uniform distribution is almost equal to that of a cylinder with mean radius.     

A rigorous time domain analysis of gyrotrons

A self-consistent time domain analysis of gyrotrons is presented which allows studying multi-mode, multi-frequency operation. The electromagnetic field in the gyrotron cavity is expanded with respect to complete sets of eigenfunctions so that space charge effects are included in the analysis. Two improvements of the modal expansion inside gyrotron cavities are suggested which significantly increase the accuracy and the numerical efficiency of this method, namely, the removal of the non-uniform convergence of some field series at the coupling apertures and the estimation of the asymptotic values of some slowly converging series related to the modal analysis by a moderate number of cavity eigenfunctions. Discrete Fourier transform is used to obtain the time dependence of the electromagnetic field. The electron beam is described by a set of relativistic single particles. It is demonstrated that the strong numerical requirements of the suggested method can be overcome by using a vector computer. Two gyrotrons are investigated, namely, a low Q 35 GHz TE₀₁- and a 150 GHz TE₀₃-gyrotron. Both oscillation build-up and steady state operation are investigated including mode competition and window reflections. The simulations show that the assumption of a monofrequent steady state operation of gyrotrons, which is made by the commonly used frequency domain methods, is not always justified.     

Use of a generalized method of eigenmodes in the theory of lasers

An analysis is made of the application a generalized method of eigenmodes, which is used in steady-state diffraction problems to the theory of lasers. In the study of open laser cavities the use of this method makes it possible to avoid difficulties associated with the exponential growth of the field at infinity. The generalized method developed previously for solving steady-state diffraction problems is extended to the case of non-steady-state narrow-band processes to construct in the ordinary way the equations describing the operation of the laser. The only difference is that the field is expanded in the eigenfunctions that are orthogonal in the region occupied by the active medium. This eliminates the difficulties associated with the behavior of the mode field at infinity. In addition, in a number of cases the generalized eigenfunctions (modes) correspond considerably better to the field distribution in the operating laser. Zh. Tekh. Fiz. 67, 46–49 (June 1997)     

Continuous-distribution puddle model for conduction in trilayer graphene

Influence of the weak electric field on the electronic structure of the Fibonacci superlattice is considered. The electric field produces a nonlinear dynamics of the energy spectrum of the aperiodic superlattice. Mechanism of the nonlinearity is explained in terms of energy levels anticrossings. The multifractal formalism is applied to investigate the effect of weak electric field on the statistical properties of electronic eigenfunctions. It is shown that the applied electric field does not remove the multifractal character of the electronic eigenfunctions, and that the singularity spectrum remains non-parabolic, however with a modified shape. Changes of the distances between energy levels of neighbouring eigenstates lead to the changes of the inverse participation ratio of the corresponding eigenfunctions in the weak electric field. It is demonstrated, that the local minima of the inverse participation ratio in the vicinity of the anticrossings correspond to discontinuity of the first derivative of the difference between marginal values of the singularity strength. Analysis of the generalized dimension as a function of the electric field shows that the electric field correlates spatial fluctuations of the neighbouring electronic eigenfunction amplitudes in the vicinity of anticrossings, and the nonlinear character of the scaling exponent confirms multifractality of the corresponding electronic eigenfunctions.     

Shape-dependence of magnetotransport through quantum dots

Magnetotransport through quantum dot structures is investigated numerically via a scattering matrix technique. The results for two typical structures show that the magnetoconductance is strongly dependent on the quantum dot geometry. For the symmetric quantum dot structure, it is found that the magnetoconductance profiles exhibit irregular structures and the magnetic field plays a similar role to that of disorder in the electron transport. For the T-shaped quantum dot structure, the oscillations in the conductance are found to be completely suppressed and the quantized conductance plateaus are recovered in a strong magnetic field, which is attributed to the asymmetry of the structure geometry with respect to the right- and left-moving edge states.     

Calculated signal-to-noise ratio of MRI detected with SQUIDs and Faraday detectors in fields from 10 microT to 1.5 T

We examine the calculated signal-to-noise ratio (SNR) achievable with different MRI detection modalities in precession fields ranging from 10 microT to 1.5 T. In particular, we compare traditional Faraday detectors with both tuned and untuned detectors based on superconducting quantum interference devices (SQUIDs). We derive general expressions for the magnetic field noise due to the samples and the detectors, and then calculate the SNR achievable for a specific geometry with each modality with and without prepolarization. We show that each of the three modalities is superior in one of the three field ranges. SQUID-based detection is superior to conventional Faraday detection for MRI in precession fields below 250 mT for a 65 mm diameter surface coil placed a distance of 25 mm from the voxel of interest embedded in a cylinder of tissue 50 mm tall and of radius 50 mm. This crossover field, however, is sensitive to the geometry.