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采用本征模式的数值打靶方法研究了离散阿尔芬本征模在DⅢ-D高性能运行条件下的物理特性,包括负磁剪切位形、高性能加热、正反中性束注入、内部输运垒以及高自举电流和甚高约束运行状态对这种阿尔芬模式的影响。在DⅢ-D托卡马克装置负磁剪切位形及先进运行状态实验参数下这些离散阿尔芬本征模存在于宽的径向区域,且具有广泛的本征频谱;高性能加热、同向中性束注入以及内部输运垒的存在有利于产生多个较深的气球模驱动势阱,由之得以很好地形成这种阿尔芬束缚态本征模;在高自举电流和甚高约束运行条件下这些离散阿尔芬本征模束缚态能够在更广的径向区域存在,且可具有较高的本征频率。另外,参照DⅢ-D装置放电实验数据的时间演变情况,这些离散阿尔芬本征模能在很宽的运行参数范围内出现,使之成为该类大型托卡马克实验中可能广泛存在的潜在不稳定性。     

Effects of including the counterrotating term and virtual photons on the eigenfunctions and eigenvalues of a scalar photon collective emission theory

We find eigenmodes of an integral equation describing N 2-level atoms interacting with a scalar field, one atom being initially excited. Neglect of virtual field quanta would replace the correct kernel by its real part. This has serious consequences both for small and large samples.     

Imaging ripples on phononic crystals reveals acoustic band structure and Bloch harmonics

Broadband surface phonon wave packets on a phononic crystal made up of a microstructured line pattern are tracked in two dimensions and in real time with an ultrafast optical technique. The eigenmode distribution and the 2D acoustic band structure are obtained from spatiotemporal Fourier transforms of the data up to 1 GHz. We find stop bands at the zone boundaries for both leaky-longitudinal and Rayleigh waves, and show how the structure of individual acoustic eigenmodes in k space depends on Bloch harmonics and on mode coupling.     

Dielectric properties of ice and liquid water from first-principles calculations

We present a first-principles study of the static dielectric properties of ice and liquid water. The eigenmodes of the dielectric matrix E are analyzed in terms of maximally localized dielectric functions similar, in their definition, to maximally localized Wannier orbitals obtained from Bloch eigenstates of the electronic Hamiltonian. We show that the lowest eigenmodes of E (-1) are localized in real space and can be separated into groups related to the screening of lone pairs, intra-, and intermolecular bonds, respectively. The local properties of the dielectric matrix can be conveniently exploited to build approximate dielectric matrices for efficient, yet accurate calculations of quasiparticle energies.     

Excitation of eigenmodes at gyroelectromagnetic gratings in conical mounting

We study the diffraction of electromagnetic waves at periodically corrugated isotropic–gyroelectromagnetic surfaces, in the index-matching situation, when the plane of incidence forms an arbitrary angle with the main section of the grating (“conical mounting”). It is shown that, under these conditions, eigenmodes can be excited at certain angles of incidence, which can be calculated. We analyze the variation of the position of the anomalies when the orientations of the plane of incidence and of the optic axis are varied. We also show the dependence of the maximum reflected power as a function of the groove height-to-period ratio.     

Homogenization of magnetodielectric photonic crystals

We calculate the low-frequency index of refraction of a medium which is homogeneous along axis z and possesses a periodic dependence of the permittivity epsilon(r) and permeability micro(r) in the x-y plane (2D magnetodielectric photonic crystal). Exact analytical formulas for the effective index of refraction for two eigenmodes with vector E or H polarized along axis z are obtained. We show that, unlike nonmagnetic photonic crystals where the E mode is ordinary and the H mode is extraordinary, now both modes exhibit extraordinary behavior. Because of this distinction, the magnetodielectric photonic crystals exhibit optical properties that do not exist for natural crystals. We also discuss the limiting case of perfectly conducting cylinders and clarify the so-called problem of noncommuting limits, omega-->0 and epsilon--> infinity.     

Combined modes of a two-layer fluid and a solid block in an infinite waveguide

It is shown that a waveguide in the form of a channel of infinite length filled by a two-layer heavy fluid with a free surface can have nonpropagating waves (trapped vibrational modes) along with traveling waves. These waves are localized in the region of a dynamic inclusion, i.e., a solid block (massive die) on the bottom of the channel. The appearance of such waves is due to the presence of a real discrete frequency spectrum of eigenmodes, which is located on the axis of the continuous spectrum corresponding to the divergent waves in the fluid. A relation between the geometric parameters of the channel and the characteristics of the fluid and the solid block for which such a spectrum exists is found for cases with fluids of similar density in the waveguide. Zh. Tekh. Fiz. 68, 15–19 (March 1998)     

Why are the eigenmodes of stable laser resonators structurally stable?

Optical resonators are usually examined wave optically. We consider geometrical imaging in stable canonical resonators. We show that, with important exceptions related to eigenmode degeneracy, stable resonators generally image all transverse planes into each other. This insight leads to an intuitive understanding of important properties of the corresponding eigenmodes, most notably their well-known structural stability, i.e., the property that the eigenmodes retain their shape on propagation.     

Extremely low optical transmittance in the stopbands of photonic crystals

We demonstrate extremely low transmittance characteristics of photonic crystals (PhCs) with a finite thickness in specific photonic bandgaps (PBGs) through numerical simulation, and clarify its origin. Some of the PhCs support decaying Bloch eigenmodes, whose propagation constant (real part of the Bloch wavenumber) as well as their decay constant (imaginary part) changes with frequency inside the bandgap. Such a class of modes can interfere destructively at the exit end of the crystal depending on their round-trip phase change, which creates comb-like valleys in their transmission spectra.     

Energy Decay for the Damped Wave Equation Under a Pressure Condition

We establish the presence of a spectral gap near the real axis for the damped wave equation on a manifold with negative curvature. This result holds under a dynamical condition expressed by the negativity of a topological pressure with respect to the geodesic flow. As an application, we show an exponential decay of the energy for all initial data sufficiently regular. This decay is governed by the imaginary part of a finite number of eigenvalues close to the real axis.     

Direct computation of higher-order propagation modes using the imaginary-distance beam propagation method

In this paper we present an extension to the standard method of eigenmode-extraction using the imaginary-distance beam propagation method. We show that it is possible to directly extract higher-order propagation modes of arbitrary shaped waveguide structures by propagating the field along the imaginary axis when the parameters are chosen in an appropriate manner. This method requires an assumption of the propagation constant of the eigenmode. In many cases this value can be determined using fast approximate techniques like the effective index method. Additionally, the approximate mode shape may be introduced as a starting condition and can further accelerate the extraction of the eigenmode. The overall number of propagation steps needed to extract multiple eigenmodes is then significantly smaller than in the case when extracting the modes sequentially with the former method.     

Detection of the high eigenmodes of spin diffusion in porous media

The dynamics of spin diffusion in a fluid is governed by the Torrey-Bloch equations, and the solution is often expressed mathematically in an eigenmode expansion. We report an experimental demonstration of the excitation and detection of a wide range of eigenmodes in porous media by exploring the inhomogeneous internal magnetic field in the pore space. The nodal character of the eigenfunctions of the high eigenmodes was clearly observed. The methodology of excitation and detection of the high eigenmodes may be used to better characterize pore geometry.     

Trapped modes in finite quantum waveguides

The eigenstates of an electron in an infinite quantum waveguide (e.g., a bent strip or a twisted tube) are often trapped or localized in a bounded region that prohibits the electron transmission through the waveguide at the corresponding energies. We revisit this statement for resonators with long but finite branches that we call ??finite waveguides??. Although the Laplace operator in bounded domains has no continuous spectrum and all eigenfunctions have finite L ₂ norm, the trapping of an eigenfunction can be understood as its exponential decay inside the branches. We describe a general variational formalism for detecting trapped modes in such resonators. For finite waveguides with general cylindrical branches, we obtain a sufficient condition which determines the minimal length of branches for getting a trapped eigenmode. Varying the branch lengths may switch certain eigenmodes from non-trapped to trapped or, equivalently, the waveguide state from conducting to insulating. These concepts are illustrated for several typical waveguides (L-shape, bent strip, crossing of two strips, etc.). We conclude that the well-established theory of trapping in infinite waveguides may be incomplete and require further development for applications to finite-size microscopic quantum devices.     

Modal interference and dynamical instability in a solid-state slice laser with asymmetric end-pumping

We observed complicated emission patterns consisting of different transverse modes and associated intensity pulsations at beat frequencies between pairs of transverse eigenmodes in a solid-state thin-slice Fabry-Perot laser with asymmetric end-pumping. The dependence of transverse patterns and pulsation frequencies on pump power has been demonstrated. The interference among nonorthogonal transverse eigenmodes, which are formed in a deformed Fabry-Perot microcavity possessing an asymmetric, gradient refractive-index potential for optical waves, is proposed for explaining observed instabilities. Intensity modulations have been remarkably reproduced by numerical simulations of model equations.     

Effect of oriented crystalline converter temperature on spectrometer response

Cooling of a 1-mm crystalline tungsten converter oriented along the ??111?? axis situated in front of an electromagnetic spectrometer of thickness 25X ₀, recording showers of 28-GeV electrons, to a temperature of 77 K results in a decrease of the crystal radiation length by ??30%, shifts the cascade curve of the shower development in the spectrometer by ??7%, and improves the spectrometer energy resolution by ??5% in comparison with similar parameters of the spectrometer at a crystal temperature of 293 K.     

Structure of a nonparaxial gaussian beam near the focus: III. Stability,eigenmodes, and vortices

Exact analytical structurally stable solutions of the Maxwell equations for singular mode beams propagating in free space or a uniform isotropic medium are obtained. Approximate boundary conditions are chosen in the form of the requirement that in the paraxial approximation the fields of nonparaxial mode beams in the waist plane are transformed into the fields of eigenmodes and vortices of weakly guiding optical fibers with the axial symmetry of refractive index. It is shown that optical vortices, in spite of a rather complex structure of field distribution, do not experience substantial changes in the beam form and reproduce, in general features, the field of paraxial vortices. Linear perturbations of the characteristic parameters of mode beams do not change the structure of their electromagnetic field. Nonparaxial singular beams have one more important property, in addition to the fact that the structure of these beams in the paraxial approximation is similar to the structure of the fields of eigenmodes in a fiber. The propagation constants of eigenmodes of a fiber exactly coincide (in the first approximation of perturbation theory) with the projection of the wave vector of a mode beam on the optical axis (an analog of the propagation constant). The possibility of the paraxial transition for nonparaxial mode beams with arbitrary values of azimuthal and radial indices is shown. The properties of nonparaxial modes are illustrated by numerous examples. The solutions obtained and the results of their analysis can be used for exact matching optical fibers and laser beams in various applications.     

TM–TE hybridization and tunable refraction in magnetophotonic crystals

In the present work we study the photonic band structure (PBS) and the polarization state of the Bloch eigenmodes of a two-dimensional magnetophotonic crystal (MPC) with square lattice formed from magneto-optically (MO) active cylinders. The refraction of light at the boundary of the MPC is analyzed. We found that both—the PBS and eigenmodes of the MPC—are most significantly altered by the MO activity in the vicinity of the degeneracies. For this case we demonstrated the possibility of an abrupt change in the propagation direction of light by the application of a magnetic field. For the Bloch wave vectors and frequencies corresponding to non-degenerate branches, the alteration of the PBS is shown to be negligible and eigenmodes almost completely coincide with linearly TE- and/or TM-polarized eigenmodes of the non-magnetic photonic crystal.     

Mixed quantum mechanical periodic and potential wall problem

We consider the Schrödinger equation with an even-square integrable potential of period one on the negative real axis and a wall potential of heighta > 0 on the positive real axis. The spectrum of this Schrödinger equation is determined and it is proved that bounded solutions never exist if the energyE < a is lying in a gap of the periodic spectrum.     

On the generation of solitons and breathers in the modified Korteweg-de Vries equation

We consider the evolution of an initial disturbance described by the modified Korteweg-de Vries equation with a positive coefficient of the cubic nonlinear term, so that it can support solitons. Our primary aim is to determine the circumstances which can lead to the formation of solitons and/or breathers. We use the associated scattering problem and determine the discrete spectrum, where real eigenvalues describe solitons and complex eigenvalues describe breathers. For analytical convenience we consider various piecewise-constant initial conditions. We show how complex eigenvalues may be generated by bifurcation from either the real axis, or the imaginary axis; in the former case the bifurcation occurs as the unfolding of a double real eigenvalue. A bifurcation from the real axis describes the transition of a soliton pair with opposite polarities into a breather, while the bifurcation from the imaginary axis describes the generation of a breather from the continuous spectrum. Within the class of initial conditions we consider, a disturbance of one polarity, either positive or negative, will only generate solitons, and the number of solitons depends on the total mass. On the other hand, an initial disturbance with both polarities and very small mass will favor the generation of breathers, and the number of breathers then depends on the total energy. Direct numerical simulations of the modified Korteweg-de Vries equation confirms the analytical results, and show in detail the formation of solitons, breathers, and quasistationary coupled soliton pairs. Being based on spectral theory, our analytical results apply to the entire hierarchy of evolution equations connected with the same eigenvalue problem. (c) 2000 American Institute of Physics.     

Longitudinal development of electromagnetic showers in directional spectrometer

The length of the longitudinal development of the electromagnetic shower induced by electrons with an energy of 26 GeV in a directional spectrometer consisting of a crystalline tungsten converter oriented along the ??111?? axis and a composite Cherenkov shower spectrometer is shorter in comparison with the length of the standard shower development by 20?C30% at a converter thickness from 2.7 to 8.4 mm.