Theory of coupled open resonators

A theory of coupled open resonators with an inclined beam splitter is constructed on the basis of numerical solution of integral equations with allowance for ohmic and diffraction losses caused by finiteness of mirror sizes. High selectivity of longitudinal modes is shown to be possible with the effective extraction in the form of a wave beam and excess of the useful radiation power over the internal loss.     

Effect of a longitudinal wave on the self-resonant motion of electrons

The effect of the longitudinal component of an electromagnetic wave on the self-resonant motion of electrons in waveguides is considered. The equation of motion for electrons in a plane, longitudinal-transverse, circularly polarized wave has been solved by the method of successive approximations with allowance for the longitudinal integral of motion present in such a wave. The expansion parameter is the ratio of the amplitudes of the longitudinal and transverse components of the wave. For the case n < 1 the longitudinal field of the wave does not change the nature of the electron motion, but only induces weak oscillations about a solution that does not include the longitudinal field. For n > 1 with spontaneous phasing of the electrons a criterion is obtained for neglecting the effect of the longitudinal field, and numerical estimates are given.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 66–71, September, 1978.     

Enhanced angular selectivity in volume holograms with speckle reference waves

A speckle-multiplexing scheme with enhanced angular selectivity for holographic storage is proposed. Angular selectivity in the proposed holographic storage system is theoretically and experimentally investigated. We find the effect of speckle reference wave on angular selectivity strongly depends on the techniques to perform multiplexing for holographic storage. Angular selectivity of a holographic storage system can be effectively enhanced as long as angular deviation of reading wave induces a lateral displacement of the speckle pattern on the hologram plane. When angular deviation of reading wave only induces a speckle wavefront tilt on the hologram plane, the speckle wave is not helpful to enhance the angular selectivity and the angular selectivity becomes to depend on material thickness (Bragg condition) only.     

Coherent waves in a multiply scattering poro-elastic medium obeying Biot's theory

Twersky's theory is generalized to multiple scattering by a uniform random distribution of cylinders in a poro-elastic medium. The high-frequency regime only, where no dispersion effects occur in the absence of scatterers, is investigated in the frame of Biot's theory. The scatterers lie within a slab of the host medium, and an incident wave gives rise to a fast longitudinal coherent wave, a slow longitudinal one, as well as a shear one in the slab. The dispersion equations of those three coherent waves are derived. The shear coherent wave propagates independently of the other two, while the longitudinal coherent waves obey a coupled dispersion equation involving conversion terms. Numerically speaking, coupling effects are significant only when forward scattering by a single cylinder of the fast wave into the slow one (or the slow wave into the fast) is larger than forward scattering with no conversion.     

Generation of elastic stress waves at a corner junction of square rods

Fourier techniques are used to predict the transmitted and reflected waves at an L-joint in rods of square cross-section. The expressions for both longitudinal and flexural wave components are derived for a variable angle of connection for the rods. These components are evaluated for a 90° angle of connection and an arbitrary longitudinal input pulse. The predicted waves are compared with experimental results at a number of locations away from the joint for an input pulse with wavelengths which are large compared with the cross-sectional dimensions of the rods. Good agreement is obtained for all waves. For the flexural wave this agreement is shown to improve with distance from the joint. This confirms the adequacy of elementary and Timoshenko beam theory to describe the longitudinal and flexural wave motions respectively. The results demonstrate the applicability of Fourier techniques to the solution of stress wave propagation in rods.     

Heating of gadolinium plasma ions by the ion cyclotron resonance method

Resonance rf heating of gadolinium plasma ions is calculated in the configuration when an electric field travels along a permanent magnetic field and simultaneously rotates in the direction normal to the latter. Two model functions are taken as initial ion distribution functions over longitudinal velocities: one is a linear function of the velocity in the low velocity range and the other is a shifted semi-Maxwellian function. The ion transverse velocity distribution function is calculated under the assumption that the initial “transverse” distribution function is Maxwellian with a temperature of 5 eV. Ion fluxes toward collector plates are calculated by integrating the total distribution function over the allowed ranges of longitudinal and transverse velocities and transverse coordinates of the guiding center of the ions before the collector. The calculation is performed as applied to the ¹⁵⁷Gd target isotope and its two nearest neighbors. The effect of the longitudinal temperature on the width of the heating efficiency resonance line and of the longitudinal magnetic field on the ion heating selectivity is studied. Also, the influence of the longitudinal wavenumber of the warming traveling electric field on the selectivity of an ion cyclotron resonance reactor is investigated. The heating efficiency is estimated from the frequency dependence of the fraction of ions heated to an energy above a given value.     

Generalization of the Hutson and White theory to the case of piezosemiconductors with mixed conductivity

The Hutson-White theory is extended to the case when there are mobile charge carriers of both signs in a piezeosemiconductor. Expressions are obtained for the damping and velocity of the longitudinal sound wave being propagated along the z axis in the piezosemiconductor as a function of the magnitude of the longitudinal electrical field, as well as for the constant current density originating here. It is shown that the acoustic wave changes the conductivity of a piezosemiconductor with mixed conductivity. A method is proposed for determining the mobility simultaneously of both the positive and negative carriers in an intrinsic piezosemiconductor.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 55–58, November, 1984.     

变周期慢波系统内同步问题的研究

由于行波管的工作依赖于其慢波系统中的电子注与沿轴传输交变电磁场之间的相互作用而完成,而这样的相互作用要求沿轴传输的交变电磁场必须与电子注有着近乎同步的速度,所以慢波系统内的同步问题就成了研究行波管的一个很重要的问题.而变周期慢波系统是将一般慢波系统的周期进行变化而形成的,它可以比原周期慢波系统有着更宽的带宽,更高的互作用效率,还可以选择空间谐波.本文分析了变周期慢波系统内的空间谐波,提出了使慢波系统内的一次空间谐波一直与电子注同步所需要满足的原则,最后以变周期折叠波导为例,证明了这个原则. 关键词： 变周期 慢波系统 空间谐波 同步     

The pure-shear mode solidly mounted resonator based on c-axis oriented ZnO film

In this paper, we fabricate a pure-shear mode film bulk acoustic resonator based on c-axis oriented ZnO film. The resonator is consisted of an in-plane electrode, a highly c-axis oriented ZnO film and a SiO₂/W Bragg reflector. The shear mode wave is excited by the lateral electric field. The resonator works in a pure-shear mode with the resonance frequency near 1.5 GHz and the Q-factor of 479 in air. There is no obvious longitudinal mode resonance in the frequency response, which can be explained that the electric field component normal to the surface is very weak and the Bragg reflector has the effective frequency selectivity for the shear mode. Importantly for sensors, the immersion into de-ionized water and glycerol liquid still allows for a Q-factor up to 335 and 220, respectively. This resonator shows the potential as mass loading sensors for biochemical application.     

Relativistic nonlinear waves in a magnetised plasma

Relativistic propagation of a nonlinearly-coupled circularly-polarised electromagnetic wave and a Langmuir wave along the applied magnetic field is considered. Analytical solutions are given or are indicated for some special cases like purely transverse waves and purely longitudinal waves. In the presence of an applied magnetic field, the incident circularly polarised electromagnetic wave is found to propagate further into denser regions of the plasma — a result which is in accord with the so-called inverse Faraday effect. Finally, we shall consider general coupled transverse and longitudinal waves for which we give an approximate solution. We investigate whether this system of coupled waves exhibits any internal resonances and consequent energy exchange between them.     

A slow wave with the structure of an electromagnetic wave in piezoelectric and magnetostrictive media

The propagation of elastic waves in piezoelectric and magnetostrictive materials is considered theoretically. It is shown that an elastic wave in a piezoelectric can create not only a longitudinal electric field parallel to the wave normal (longitudinal piezoactivity) but also a transverse field of electric induction (transverse piezoactivity). The presence of a transverse induction field leads to the appearance of a magnetic field perpendicular to the direction of the wave normal and to the induction vector; therefore, the transverse-piezoactive wave is accompanied by a transverse wave having the structure of an electromagnetic wave and propagating with the speed of sound. Transverse-magnetostrictive elastic waves in magnetostrictive dielectrics are accompanied by a similar wave.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 32–36, October, 1976.     

Kinetic study of instability growth rate in a helicon plasma discharge source

In this work, a kinetic model is developed to study the effects of the radio frequency antenna wavenumber, helicon plasma electron density, as well as their drift velocity and temperature on the instability increment rate of the helicon wave in both longitudinal and transverse directions. The ion acoustic (IA) wave frequencies and wavenumbers of the helicon waves are obtained when the maximum wave energy is deposited on the plasma ions. Moreover, it is shown that, at the IA wavenumber and frequencies, while the longitudinal instability increment rates for both the helicon and IA waves are ignorable, the transverse instability increment rate for both the helicon and IA wave increases. Besides, the longitudinal instability increment rate for the helicon or IA wave has non‐zero resonant frequencies. On the other hand, the transverse instability increment rate of helicon or IA wave can be neglected. Furthermore, it is observed that, while both the imaginary part of longitudinal permittivity and longitudinal instability increment rate are not influenced by the electron temperature, their transverse component increases linearly with the electron temperature. In addition, the imaginary part of transverse permittivity increases almost linearly with the drift velocity of the plasma electrons.     

On the solutions of the coupled system of oscillators and electromagnetic fields excited by an external charge

A systematic study of the longitudinal, transverse and total solutions of a coupled system of oscillators and electromagnetic fields in the presence of an external point charge is carried out. The space-time dependence of the solutions as well as their values in specific cases and asymptotic behavior are analyzed. It is shown that, in general, the longitudinal fields show two well-defined contributions: (a) a symmetric field surrounding the particle and carried convectively which is interpreted as a screening field. (b) an excitation defined in principle in a whole semispace and identified with an oscillator plasma wave which corresponds to the excitation predicted in A. Bohr's microscopic theory of energy losses, although showing somewhat different properties. The transverse solutions appear as differences between the fields given in Fermi's macroscopic theory of energy losses and the longitudinal solutions. Using methods of complex variable theory it is shown how we can separate the total perturbations created by the particle in a medium represented by oscillators into three intimately related contributions: screening, oscillator-plasma excitation and Cherenkov radiation. The space-time configuration of these fields as well as their relation to the longitudinal solutions and their evolution for different ranges of the velocity of the particle is given. The problem of the energy loss associated to the creation of the plasma wave is treated.     

Lattice Waves in Two-Dimensional Hexagonal Quantum Plasma Crystals

Lattice waves including a longitudinal wave and a transverse wave in two-dimensional hexagonal quantum plasma crystals are investigated by using the modified Debye-Hückel screening potential. It is shown that there exists an unstable region of lattice parameters, where the system will melt. The general dispersion relations are derived, and the waves propagating parallel to a primitive translation vector are discussed. We find that both the longitudinal and transverse waves are acoustic-like, and the longitudinal wave has a greater sound speed than that of the transverse wave in the long wavelength limit region.     

Reflecting phase volume holographic grating (PVHG) in LiNbO3

The spectral-angular selectivity of reflecting PVHG in LiNbO 3 and electric control of light diffraction are investigated. It is shown that a PVHG with approximate 7000 lines/mmand thickness spatial frequency 3.7mmhas a spectral selectivity 0.023 nm and angular selectivity that varies in the range from 2 to 50 ang. min, depending on the angle between the beams that record the grating. Application of an 850 V electric field decreases the diffraction effectiveness by one-half for an extraordinary wave and a transverse scheme (the transverse dimension of the PVHG is 5 mm). It is established that the spectral-angular characteristics of reflecting PVHG and electric control of light diffraction can be described within the framework of the theory of coupled wave and the electrooptical effect.Translated from Lazernye Sistemy, pp. 112–120, 1982.     

Coherent waves in a multiply scattering poro-elastic medium obeying Biot's theory

Twersky's theory is generalized to multiple scattering by a uniform random distribution of cylinders in a poro-elastic medium. The high-frequency regime only, where no dispersion effects occur in the absence of scatterers, is investigated in the frame of Biot's theory. The scatterers lie within a slab of the host medium, and an incident wave gives rise to a fast longitudinal coherent wave, a slow longitudinal one, as well as a shear one in the slab. The dispersion equations of those three coherent waves are derived. The shear coherent wave propagates independently of the other two, while the longitudinal coherent waves obey a coupled dispersion equation involving conversion terms. Numerically speaking, coupling effects are significant only when forward scattering by a single cylinder of the fast wave into the slow one (or the slow wave into the fast) is larger than forward scattering with no conversion.     

O型契伦柯夫器件慢波结构高频特性

理论推导了电磁波在半无限长直波导和均匀慢波结构交界面上的反射系数表达式,得到反射系数模值和相位随电磁波的纵向相移常数和慢波结构末端相位的变化关系。运用传输线理论以及反射系数的理论计算结果,得到了有限长慢波结构的纵向谐振条件,可以分析各种情况下有限长慢波结构的纵向谐振特性。计算了一种有限长慢波结构的纵向谐振频率,理论预测与数值仿真结果基本一致。对于一种非均匀慢波结构的数值计算结果表明,其纵向谐振模式对应的频率、场分布与相应的均匀慢波结构接近,因此仍可根据提出的纵向谐振条件对非均匀慢波结构进行分析。     

Longitudinal waves in carbon nanotubes in the presence of transverse magnetic field and elastic medium

In the present paper, the coupling effect of transverse magnetic field and elastic medium on the longitudinal wave propagation along a carbon nanotube (CNT) is studied. Based on the nonlocal elasticity theory and Hamilton's principle, a unified nonlocal rod theory which takes into account the effects of small size scale, lateral inertia and radial deformation is proposed. The existing rod theories including the classic rod theory, the Rayleigh-Love theory and Rayleigh-Bishop theory for macro solids can be treated as the special cases of the present model. A two-parameter foundation model (Pasternak-type model) is used to represent the elastic medium. The influence of transverse magnetic field, Pasternak-type elastic medium and small size scale on the longitudinal wave propagation behavior of the CNT is investigated in detail. It is shown that the influences of lateral inertia and radial deformation cannot be neglected in analyzing the longitudinal wave propagation characteristics of the CNT. The results also show that the elastic medium and the transverse magnetic field will also affect the longitudinal wave dispersion behavior of the CNT significantly. The results obtained in this paper are helpful for understanding the mechanical behaviors of nanostructures embedded in an elastic medium.     

Influence of the slow wave on the relation between the angular resonances and the leaky guided modes properties for a poroelastic plate embedded in water

A numerical study of the guided modes in a water-saturated poroelastic plate that obeys the Biot theory is presented. In the first part, we study the leaky guided modes and the angular resonances when the slow wave does not propagate. Two types of guided modes exist. The first ones occur from coupling of the fast longitudinal wave with the shear wave; most of them propagate whatever the frequency is, provided that it is not close to their cut-off frequencies. The leaky guided modes of the second type occur from coupling of the two longitudinal waves and the shear wave. These modes do not propagate (they are highly damped) as long as the slow wave remains diffusive. We show that the characteristics of the angular resonances can be linked to the leaky guided waves of the first type in the same way as for an elastic plate. The guided modes of the second type may not be associated to angular resonances. In the second part, we consider a thinner plate in a higher frequency range so that the slow wave can propagate. Once again its influence is studied both on the leaky guided modes and on the angular resonances.     

Evaluation of interface wave velocity, reflection coefficients and interfacial stiffnesses of contacting surfaces

The phase velocity of the antisymmetric-mode interface wave as well as the longitudinal and shear wave reflection coefficients have been measured for contacting poly(methyl methacrylate) (PMMA) surfaces subjected to different contact pressures. It has been found that while the reflection coefficients decrease as the contact pressure is increased, the phase velocity of the interface wave increases from that of the Rayleigh wave toward that of the bulk shear wave. From these measurements, the normal and tangential interfacial stiffnesses of the contacting PMMA surfaces have been evaluated as functions of the contact pressure. As a result, the two independent procedures to evaluate the tangential stiffness, namely, from the interface wave velocity and from the shear wave reflection measurements, have yielded mutually consistent results. Furthermore, it has been found that the tangential/normal stiffness ratio and the shear/longitudinal reflection ratio of the contact interface are consistent with the predictions of an existing theoretical model for kissing bond interfaces.