The far field asymptotics in the problem of diffraction of an acoustic plane wave by an impedance cone

The work deals with the far field asymptotics of the classical solution for the problem of diffraction by an impedance cone. The incident acoustic plane wave completely illuminates the semi-infinite conical surface. The scattered field contains different components in the asymptotics, namely, the spherical wave from the vertex of the cone, the reflected waves, and, under some conditions, also the surface waves of Rayleigh type. We give integral representations for the scattering diagram of the spherical wave. The uniform (with respect to the observation direction) asymptotic expression for the wave field is also addressed and described by the parabolic cylinder ansatz. Dedicated to the memory of Vladimir Borovikov     

An analytic representation for the potential of a uniform elliptic cone

In view of the fact that various gravitating and charged bodies may have singular points on their surface, the problem of the effect of these singularities in the mass distribution on the behavior of potential arises. The analytic representation for gravitational and electrostatic potentials of a uniform elliptic cone in terms of ordinary integrals is derived. Generally, these integrals are somewhat more complicated than the elliptic ones; however, they reduce to elementary functions in the case of a circular cone. The arbitrariness in the way of truncating a cone manifests itself in the possibility of adding various harmonic polynomials. However, the singularity of potential in the vicinity of the vertex of a cone is of an objective and unique character.     

圆柱体的空间圆锥光反射、折射与衍射

用准直或会聚激光束倾斜照射圆柱体时,其反射光、透射光(柱体透明时)、衍射光(柱体较细时)的叠加将形成以光束入射点为顶点的空间圆锥形光面(空间光锥),并且在垂直于柱体轴线方向的观察平面上投影成一圆形光环.空间光锥的形成与所选圆柱体材料及其粗细无关,只要其表面具有一定反射能力即可.空间光锥的锥角等于入射光束主光轴与圆柱体轴线夹角的2倍,与圆柱体和照射光束的直径大小及光波长无关.给出了对光纤及不同直径大小的玻璃和金属圆柱体的实验观察结果,并利用矢量图解法对其进行了详细地理论分析.进而得出,通常所谓单丝衍射图样,实际上是细丝的衍射和其表面的反射光场的叠加图样,对于透明细丝,还包括其透射光场的贡献.圆柱体的这种空间圆锥光反射和衍射原理有可能用于光束定位、成形、表面检测以及三维面形测量等 关键词： 圆柱体 空间光锥 投影光环     

On the characteristic impedance of a coaxial line with elliptic cone outer conductor and angular strip inner conductor

The expressions of the characteristic impedance of a new kinds of transmission lines—elliptic cone coaxial line are derived. The formulas are based on the TEM and the transformation of the sphero-conal coordinate into two dimension plane. Also themethods using the graphical approximation and taking the geometrical average of the upper and lower bounds to the size of the line are put forward to calculate the characteristic impedance — of the elliptic cone coaxial line.     

Formation of a microfiber bundle by interference of three noncoplanar beams

A systematic analysis of interference of three noncoplanar plane waves with identical frequency is provided. This analysis shows that a fiber bundle with spacing of the order of the wavelength, which one may conveniently control by changing the recording geometry, can be formed by this means. The relation between the incident light-wave vectors and the resultant pattern is analyzed. The concept of uniform contrast for an interference pattern is introduced, and the polarization optimization approach for each beam that ensures maximum uniform contrast for each beam is also given.     

Corrections to the Thomson cross section caused by relativistic effects and by the presence of the drift velocity of a classical charged particle in the field of a monochromatic plane wave

An approach to the solution of the relativistic problem of the motion of a classical charged particle in the field of a monochromatic plane wave with an arbitrary polarization (linear, circular, or elliptic) is proposed. It is based on the analysis of the 4-vector equation of motion of the charged particle together with the 4-vector and tensor equations for the components of the electromagnetic field tensor of a monochromatic plane wave. This approach provides analytical expressions for the time-averaged square of the 4-acceleration of the charge, as well as for the averaged values of any quantities periodic in the time of the reference frame. Expressions for the integral power of scattered radiation, which is proportional to the time-averaged square of the 4-acceleration of the charge, and for the integral scattering cross section, which is the ratio of the power of scattered radiation to the intensity of incident radiation, are obtained for an arbitrary inertial reference frame. An expression for the scattering cross section, which coincides with the known results at the circular and linear polarizations of the incident waves and describes the case of elliptic polarization of the incident wave, is obtained for the reference frame where the charged particle is on average at rest. An expression for the scattering cross section including relativistic effects and the nonzero drift velocity of a particle in this system is obtained for the laboratory reference frame, where the initial velocity of the charged particle is zero. In the case of the circular polarization of the incident wave, the scattering cross section in the laboratory frame is equal to the Thompson cross section.     

In-plane vibration of thin elliptic plates submitted to uniform pulsed microwave irradiations

The technique of acoustic generation by microwave excitation in structures is applied here to study the in-plane vibration of full or hollowed elliptic plates. The absorption of pulsed microwave irradiations by a material causes a sudden rise of its temperature and the generation of an acoustic wave by thermoelastic effect. A semi-analytic theoretical model is developed to predict the in-plane displacement fields in elliptic thin plates submitted to a uniform temperature rise. It is assumed that the isotropic and viscoelastic plate constitutive material is submitted to a thermoelastic excitation under a plane stress state. The wave equations that govern the Helmholtz displacement potentials are resolved in an elliptic cylindrical system of coordinates by means of infinite angular and radial Mathieu functions series. The displacement field is finally obtained by taking into account the zero stress conditions on the boundaries of the plates. The comparison between the theoretical and the experimental responses of full and hollowed elliptic plates shows a good agreement that permits the validation of the developed model.     

Radar cross sections of conducting elliptic cylinders embedded in strong continuous random media

The radar cross section (RCS) of a conducting elliptic cylinder in a strong continuous random medium is analysed numerically for E-wave and H-wave incidences, by solving the wave scattering as a boundary value problem. The numerical analysis shows that the spatial coherence of an incident wave on the cylinder has an important effect on the RCS, besides the well known effect of double passage, and that the spatial coherence effect depends on the curvature of the elliptic surface illuminated by an incident wave and the size of the ellipse.     

衍射问题一级近似的微扰理论

作者应用微扰理论首先导出了顶角接近π的平面扇形导体衍射场与θ接近π/2的橢锥导体衍射场的微扰项之表达式,因此,对其相应的简单问题——导体半平面屏的衍射与导体平面的反射,也得到了相应的微扰项之表达式。然后,按照文献[10]中所提出的原理,以内接多边形代替一般形状的导体薄片,以许多内接小橢锥面组成的曲面代替一般形状的导体表面,分别将上述微扰对多边形各顶点及曲面各内接锥顶求和。在极限情况下,求和变为积分,从而分别导出了任意形状的导体薄片(因而导体平面屏上的开孔)与导体表面衍射的一级衍射场,它们是对几何光学场的一     

Radar cross sections of conducting elliptic cylinders embedded in strong continuous random media

Abstract

The radar cross section (RCS) of a conducting elliptic cylinder in a strong continuous random medium is analysed numerically for E-wave and H-wave incidences, by solving the wave scattering as a boundary value problem. The numerical analysis shows that the spatial coherence of an incident wave on the cylinder has an important effect on the RCS, besides the well known effect of double passage, and that the spatial coherence effect depends on the curvature of the elliptic surface illuminated by an incident wave and the size of the ellipse.     

Large complete band gap in two-dimensional phononic crystal slabs with elliptic inclusions

Phononic band structure with periodic elliptic inclusions for the square lattice is investigated based on the plane wave expansion method. The numerical results show the systems composed of tungsten (W) elliptic rods embedded in a silicon (Si) matrix can exhibit a larger complete band gap than the conventional circular phononic crystal (PC) slabs. The phononic band structure of the plate-mode waves and the width of the first complete band gap can be tuned by varying the ratio of the minor axis and the major axis, the orientation angle of the elliptic rods and the thickness of the PC slabs. We also study the band structure of plate-mode waves propagating in two-dimensional (2D) slabs with periodic elliptic inclusions coated on uniform substrate.     

Biconical antenna and V-conical antenna with elliptic cross section

The methods of coodinates transfomation and conformal maping are applied to the problem of ra diation from a biconical antenna and V-conical an tenna with elliptic cross section. The infinite el liptic cone geometry can be transformed into two dimentions plane under the assumption of pure TEM spherical wave. The Closed-form solutions for the fields, currents, and characteristic parameters are obtained.     

Radiative transfer in a multi-layer medium subject to Fresnel boundary and interface conditions and uniform illumination by obliquely incident parallel rays

The ADO (analytical discrete ordinates) method, a pre-processing procedure, and the break-point analysis developed for azimuthally symmetric problems in a previous work are generalized and used to solve a radiative-transfer problem defined by a finite, plane–parallel, multi-layer medium subject to Fresnel boundary and interface conditions and uniform illumination in the form of obliquely incident parallel rays. Illumination is modeled by Dirac distributions in each of the two angles (polar and azimuthal) that define the direction of propagation of the incident rays. Accurate numerical results are tabulated for two sets of test problems.     

椭圆柱体对任意入射极化的电磁波的散射

基于电磁场的多尺度变换理论,得到了以导体椭圆柱为例的电磁波任意极化,任意垂直入射到目标上的散射场的解析式.将所得结果应用于计算圆柱目标的散射场,结果与文献完全一致.对椭圆柱体的散射宽度随入射波方位角,电磁波频率以及目标尺寸的变化进行了仿真.结果表明,在垂直于电磁波的方向上观测时,椭圆柱的垂直尺寸对散射有较大的影响,电磁波水平极化时散射最强.所用算法适用于介质椭圆柱等目标的散射特性研究,所得结果为目标尺寸、形状遥感电磁测量等实际应用提供了理论依据.     

光锥聚光性能分析

推导了光线在光锥中传播的轨迹方程,利用Matlab进行仿真分析,得到了平行光和杂散光入射光锥后的传播情况。结果表明,光锥对大入射角的平行光的聚集能力较好,对杂散光会聚增益较小,在非视线光通信中只适宜作为不同光学元件的结合部。     

超宽谱短脉冲电场标准装置馈电结构

研究了超宽谱脉冲电场产生装置的馈电结构,分析了不同结构参数下馈电点不连续性及其时域响应特性,测试得到了馈电插针在不同插入深度下装置的阻抗匹配特性,结合理论计算和时域有限差分法获取了不同参数下的馈电点处脉冲响应特性,并与实测数据进行了比对。结果表明,当控制馈电结构插针深度为1.0 mm时,其对脉宽0.3~1.5 ns范围内单双极激励脉冲电压反射系数不大于4%。利用D-dot传感器测试了单锥内场脉冲电场波形,结果显示,在单锥TEM室有效时间窗口内,脉冲激励波形与脉冲场测试波形基本一致。     

Dynamic polarization rotation and vector field steering based on phase change metasurface

Polarization rotation and vector field steering of electromagnetic wave are of great significance in modern optical applications. However, conventional polarization devices are bulky, monofunctional and lack of tunability, which pose great challenges to the miniaturized and multifunctional applications. Herein, we propose a meta-device that is capable of multi-state polarization rotation and vector field steering based on phase change metasurface. The supercell of the meta-device consists of four Ge₂Sb₂Te₅ (GST) elliptic cylinders located on a SiO₂ substrate. By independently controlling the phase state (amorphous or crystalline) of each GST elliptic cylinder, the meta-device can rotate the polarization plane of the linearly polarized incident light to different angles that cover from 19.8° to 154.9° at a wavelength of 1550 nm. Furthermore, by merely altering the phase transition state of GST elliptic cylinders, we successfully demonstrated a vector field steering by generating optical vortices carrying orbital angular momentums (OAMs) with topological charges of 0, 1 and −1, respectively. The proposed method provides a new platform for investigating dynamically tunable optical devices and has potential applications in many fields such as optical communications and information processing.     

双折射调谐器设计的等色图原理

提出双折射调谐器设计的等色图方法，给出原理。分析表明当晶片光轴处在以折射光线为轴线、顶角为４５°的圆锥面上时，双折射调谐器具有最快的波长调谐速率；当光轴位于过折射光线并与入射面成４５°或１３５°的平面内时，调谐器抑制非所需波长的能力最强。由此给出光轴相对晶片表面的两个优化取向，对石英晶片它们分别为１８．７１２°和５９．９２２°。文中还给出了三块晶片组合的调谐器的设计例子，对其调谐特性进行了简要的讨论。     

中能重离子反应中的在平面流和椭圆流

利用同位旋相关的量子分子动力学模型研究了⁴⁰Ca+⁴⁰Ca系统在能量从30MeV/u到150MeV/u的在平面流和椭圆流.发现随着入射能量的增加,在平面流出现从负到正的跃迁,而椭圆流则随入射能量的增大而减少并且出现从正到负的跃迁.椭圆流和在平面流对于入射能量和碰撞参数较为敏感,相反对于对称能和核态方程却不太敏感.最后对于不同质量的碎块的依赖性关系我们还作了进一步仔细的研究.     

On the convergence of the amplitude of the diffracted nonstationary wave in scattering by wedges

We make more precise the Limiting Amplitude Principle in the two-dimensional scattering of an incident plane harmonic wave by a wedge. We find the long-time asymptotic regime of convergence of the amplitude of the cylindrical wave diffracted by the vertex of a wedge to the limiting amplitude of the solution to the corresponding stationary problem. The asymptotics turns out to be uniform on compacta and depends on the magnitude of the wedge and the profile of the incident wave. The cases of Dirichlet-Dirichlet and Dirichlet-Neumann boundary conditions are considered.