Eigenmodes of an anisotropic dielectric spherical body

Quasi-TE and quasi-TM oscillations of an anisotropic spherical body immersed in an isotropic medium are studied. An investigation of the set of Maxwell’s equations within the spherical body shows that it reduces to two coupled differential equations, which are analyzed theoretically for small values of the anisotropy parameter. An approximate solution to these differential equations is obtained. A dispersion relation determining the frequencies of the resonant oscillations is derived for the boundary conditions imposed on the surface of the spherical body. The effect of anisotropy on the spectral characteristics of the resonant oscillations is examined.     

Influence of a thin surface layer on light scattering by spherical particles

The Mie problem with modified boundary conditions that take into account the influence of a thin surface layer on the scattering of an electromagnetic wave by a spherical particle is considered. Analytical equations are derived for the partial amplitudes of scattered waves and forced oscillations. These equations are applicable in the case of anisotropy and gyrotropy of an optical response from the surface layer.     

Resonant frequencies of azimuthal-homogeneous oscillations of an anisotropic sphere

The anisotropy of parameters is an intrinsic characteristic feature of dielectrics employed in production of high-Q resonators. A theory of azimuthal-homogeneous resonant oscillations in a single-crystal sphere is developed. It is demonstrated that the anisotropy gives rise to TM oscillations of two orders at different frequencies. Oscillations with large polar indices are numerically investigated.     

Wave growth rate in a cylindrical metal waveguide with ion-channel guiding of a relativistic electron beam

This paper addresses the formulae and numerical issues related to the possibility that fast wave may be grown when a relativistic electron beam through an ion channel in a cylindrical metal waveguide.To derive the dispersion equations of the beam-wave interaction,it solves relativistic Lorentz equation and Maxwell’s equations for appropriate boundary conditions.It has been found in this waveguide structure that the TM 0m modes are the rational operating modes of coupling between the electromagnetic modes and the betatron modes.The interaction of the dispersion curves of the electromagnetic TM 0m modes and the upper betatron modes is studied.The growth rates of the wave are obtained,and the effects of the beam radius,the beam energy,the plasma frequency,and the beam plasma frequency on the wave growth rate are numerically calculated and discussed.     

Nonlinear non-spherical oscillations of gas bubble under a periodic variation of ambient liquid pressure

A mathematical model is constructed for the bubble dynamics, in which the interphase surface variation is presented in the form of a series in spherical harmonics, and the equations are written with the accuracy up to the squared amplitude of the distortion of the spherical shape of the bubble. In the oscillation regimes close to periodic sonoluminescence of a single bubble in a standing acoustic wave, the character of air bubble oscillations in water was studied depending on the bubble initial radius and the amplitude of the liquid pressure variation. It was found that non-spherical oscillations of bounded amplitude can take place outside the region of linearly stable spherical oscillations. Both the oscillations with a period equal to one or several periods of the liquid pressure variation and aperiodic oscillations are observed. It is shown that neglecting the distortions in the form of spherical harmonics with large numbers (i > 3) may lead to a change of oscillation regimes. The influence of distortions on the bubble surface shape for the harmonics with i > 8 is insignificant.     

Effect of planar anisotropy on damping decrement of free oscillations of magnetization in garnet-ferrite films

The results of experimental investigation of free oscillations of magnetization in garnet-ferrite films with planar anisotropy are considered. It is shown that the damping decrement of free oscillations increases with effective anisotropy field H _Kp .     

非截面二维光子晶体排列矩形波导的全模式分析

在对周期性结构进行谐波分析的基础上，导出了非截面二维光子晶体排列矩形波导的本征值方程. 基于此方程，可以对该类光子晶体波导的所有可能模式进行分析. 分析认为，非截面二维光子晶体排列矩形波导内能存在的模式包括E_(y)，TE_y，H_(y)和TM_y模式；改变波导高度，可以实现E_(y)模式和H_(y)模式与其他模式通带的完全分离. 然而改变任一结构参数，都不能使E_(y)和H_(y)的各个模式通带，以及E_(y)1模式和H_(y)1模式的通带完全隔离. 波导单模工作的带宽由E_(y)1和E_(y)2模式的低端截止频率决定. 关键词： 波导 光子晶体 本征值方程 模式     

Normal modes and quality factors of shielded composite dielectric spherical resonators

Electromagnetic field analysis of shielded composite dielectric spherical resonator in which the dielectric sphere is composed of two concentric spheres with different dielectric materials has been made. Characteristic equations for the TE_nmℓ and TM_nmℓ modes have been derived. From these characteristic equations, the resonant frequencies and quality factors have been calculated using numerical method. Computations of the resonant frequencies and quality factors have been made for resonators with parameters suitable for the optical and microware regions. In this paper we have presented the analysis and the results obtained from the numerical computations for shielded composite dielectric spherical resonator in which the dielectric sphere is composed of two concentric spheres with different dielectric materials. Starting from the Maxwell’s equations for such a resonators have been derived and resonant frequencies and quality factor’s have been calculated for the TE_nmℓ and TM_nmℓ modes using numerical method.     

Infrared wave interaction with an electron in the rectangular and circular plasma waveguide

In this article, the effect of the electron collision frequency with background ions on TM mode field components, the trajectory, and the electron energy gain in interaction infrared radiation with collisional plasma is studied. The field components of the TM mode in the rectangular and circular collisional plasma waveguides are obtained. The deflection angle and acceleration gradient of an electron in the fields associated with a transverse magnetic (TM) wave propagating inside a plasma waveguide for TM mode is studied. The relativistic momentum and energy equations for an electron are solved, which was injected initially along the propagation direction of the infrared. The results for collisionless and collisional plasma are graphically represented. Finally, the results for rectangular and circular waveguides are compared.     

Localized spin-wave resonance modes of ferromagnetic microstrips in the field of a magnetic probe

Some results of the micromagnetic modeling of forced magnetization oscillations in planar microstrips of NiFe with easy plane anisotropy and Co/Pt with perpendicular easy axis anisotropy in the field of a magnetic spherical probe are considered. It has been shown that the probe field provokes the appearance of a hedgehog–antivortex coupling state in the NiFe strips, due to its lateral components and a skyrmion magnetization state in the Co/Pt layer. These effects destroy spatial magnetization oscillations in the microstrips and lead to the appearance of additional resonances in the spectrum of oscillations corresponding to the modes localized in the probe field.     

Mode theory of three-layer cylindrical waveguides and its application to aurum(Au)/polystyrene(PS)-coated terahertz hollow waveguides

In this paper, we present a generic mode theory for the three-layer cylindrical waveguides consisting of three arbitrary material mediums. Based on derived eigenvalue equations of the TE, TM, and hybrid modes, the mode conditions of metal/dielectric-coated terahertz hollow waveguides are extracted. In addition, we quantitatively describe both the effective refractive indexes and the loss characteristics of the aurum/polystyrene-coated terahertz hollow waveguides operating at the TE₀₁, TM₀₁, and HE₁₁ modes. It is indicated that the loss coefficient of the TE₀₁ mode can be much lower than that of the TM₀₁, and HE₁₁ modes, and, especially, can tend to that of the terahertz wave in air. So the TE₀₁ mode is very significant for the hollow waveguides in term of low loss propagating of the terahertz wave. We expect these results to enable a variety of new long-distance THz applications in sensing, detecting and communicating.     

Collisional Effects on the TM Modes in Parallel Plane Wave Guide Filled with Plasma

The reflection coefficient (C_R) and the transmission coefficient (C_T) of the TM modes in a half space (z < 0) parallel plane wave guide filled with homogeneous, collisional and moving plasma are derived and discussed. It is observed that C_R and C_T are modified depending upon the collision frequency of the electrons as well as that of the ions. There is a remarkable change in C_R due to ion-neutral collisions when the plasma moves against the direction of the TM modes.     

Relative anisotropies of plane waves and guided modes in thin orthorhombic plates: Implication for texture characterization

The angular dependences of the long wavelength velocities of S₀ and SH₀ modes of orthorhombic (orthotropic) plates are compared to those of the velocities of corresponding plane waves. To first order in the anisotropy, many of the phenomena are as expected. The absolute velocities and anisotropy of the SH₀ plate modes are identical to those for plane SH waves and the absolute velocities of the S₀ modes propagating along symmetry axes are reduced from the longitudinal plane wave velocities by an amount explained by the change from the plane strain to the plane stress condition. However, for certain classes of materials such as metal polycrystals, the anisotropy of the S₀ mode can be substantially different from that of the longitudinal plane waves. This effect is explained through an expansion of the crystallite orientation distribution function in terms of generalized spherical harmonics. Implications of the results for the ultrasonic measurement of preferred grain orientation (texture) in polycrystals is indicated.     

Reflection of elastic waves in a crystal of Heusler alloy Ni<Subscript>2</Subscript>MnGa in the phase transition range

The reflection of longitudinal and transverse acoustic waves from the free surface of the ferromagnetic shape memory alloy Ni₂MnGa that is located in the ranges of the premartensite and martensite phase transformations is considered. The propagation directions and amplitudes of the waves reflected in the (001) plane of the crystal are determined. They acquire the character of substantially quasi-longitudinal and quasi-transverse vibrations rather than being pure modes. The angles of wave reflection and conversion are shown to be effectively controlled by temperature and a magnetic field due to the colossal acoustic anisotropy of the crystal over the wide range of its phase transitions. Beginning from a certain critical angle of incidence of a quasi-transverse wave, the quasi-longitudinal wave having appeared upon reflection becomes an accompanying surface vibration, and it can be emitted into the bulk of the crystal when the phase transition point is approached. Two angles of full conversion of an incident quasi-longitudinal wave into a quasi-transverse wave are established, and their temperature dependences are found. Trivisonno’s experimental data for the ultrasound velocity and absorption in an Ni₂MnGa crystal are used to numerically estimate these acoustic effects.     

Determination of the in-plane anisotropy field in hexagonal systems via rotational magnetization: Theoretical model and Monte Carlo simulations

The magnetic anisotropy field in thin films with in-plane uniaxial anisotropy can be deduced from the VSM magnetization curves measured in magnetic fields of constant magnitudes. This offers a new possibility of applying rotational magnetization curves to determine the first- and second-order anisotropy constant in these films. In this paper we report a theoretical derivation of rotational magnetization curve in hexagonal crystal system with easy-plane anisotropy based on the principle of the minimum total energy. This model is applied to calculate and analyze the rotational magnetization process for magnetic spherical particles with hexagonal easy-plane anisotropy when rotating the external magnetic field in the basal plane. The theoretical calculations are consistent with Monte Carlo simulation results. It is found that to well reproduce experimental curves, the effect of coercive force on the magnetization reversal process should be fully considered when the intensity of the external field is much weaker than that of the anisotropy field. Our research proves that the rotational magnetization curve from VSM measurement provides an effective access to analyze the in-plane anisotropy constant K ₃ in hexagonal compounds, and the suitable experimental condition to measure K ₃ is met when the ratio of the magnitude of the external field to that of the anisotropy field is around 0.2. Supported by the National Natural Science Foundation of China (Grant Nos. 90505007 and 10774061) Recommended by LI FaShen     

Analysis for the new type long-pulsed and high efficient microwave amplifier—magnicon

This paper begins with the cylindrical cavity field expression of the rotating TM_n10 mode in magnicon, and obtains its dissipated power, cold quality formula and so on, which are different from those in the static state TM_n10. Furthermore starting from the dynamics equations, the passive deflect cavity electron velocity and position solution, as well as the interact instantaneous power solution between electron and wave have been solved. The cylindrical coordinate electron energy dynamics equation in the output cavity, and the modification of terminal parameter formula for relativity have also been discussed. This work is supported by the Sic. & Tech. Funds of CAEP.     

Optical parametric amplification beyond the slowly varying amplitude approximation

The coupled-wave equations describing optical parametric amplification (OPA) are usually solved in the slowly varying amplitude (SVA) approximation regime, in which the second-order derivatives of the signal and idler amplitudes are ignored and in fact the electromagnetic effects due to exit face of the medium is not involved. Here, an analytical plane-wave solution of these coupled-wave equations in a non-absorbing medium is presented. The solutions are derived beyond the SVA approximation up to order of κ/k (coupling constant over the wave number). The intensity distributions of the signal and the idler waves show a periodic behavior about their corresponding distributions of SVA-adapted solution. This behavior can be explained by the interference of the forward propagating signal (idler) wave and the corresponding backward one resulted from the reflection by the end face of the medium. Furthermore, this interference pattern in the medium can in turn serve as a periodic source for the next generations of the signal and idler waves. Therefore, the superposition of the waves, generated from different points of this periodic source, at the exit face of the medium shows an oscillatory behavior of the transmitted signal (idler) wave in terms of normalized coupling constant, κL. This study also shows that this effect is more considerable for high intensity pump beam, high relative refractive index and short length of the nonlinear medium.      

Resonant generation of plasma oscillations by a plane gravitational wave

An exact solution of the universal Maxwell equations linearized in the amplitude of the induced field is found with the help of a previously found exact solution of the kinetic equation with a model collision integral. Two oscillation modes arise under the action of a gravitational wave in a plasmalike medium: an undamped wave with the frequency of the gravitional wave and a damped one with the plasma frequency. When these frequencies coincide, a resonance arises, as a result of which the amplitude of the electric oscillations increases sharply.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 74–77, January, 1985.     

Exact 3D elasticity solution for free vibrations of an eccentric hollow sphere

An exact three-dimensional elastodynamic analysis for describing the natural oscillations of a freely suspended, isotropic, and homogeneous elastic sphere with an eccentrically located inner spherical cavity is developed. The translational addition theorem for spherical vector wave functions is employed to impose the zero traction boundary conditions, leading to frequency equations in the form of exact determinantal equations involving spherical Bessel functions and Wigner 3j symbols. Extensive numerical calculations have been carried out for the first five clusters of eigenfrequencies associated with both the axisymmetric and non-axisymmetric spheroidal as well as toroidal oscillation modes for selected inner-outer radii ratios in a wide range of cavity eccentricities. Also, the corresponding three-dimensional deformed mode shapes are illustrated in vivid graphical forms for selected eccentricities. The numerical results describe the imperative influence of cavity eccentricity, mode type, and radii ratio on the vibrational characteristics of the hollow sphere. The existence of “multiple degeneracies” and the trigger of “frequency splitting” are demonstrated and discussed. The accuracy of solution is checked through appropriate convergence studies, and the validity of results is established with the aid of a commercial finite element package as well as by comparison with the data in the existing literature.