各向异性介质中的菲涅耳公式及应用

本文给出了在空气与各向异性介质分界面上反射光、折射光与入射光振幅间的关系及其在测定各向异性介质主折射率中的一个应用。     

Electromagnetic scattering from an inhomogeneous object by raytracing

A shooting and bouncing ray (SBR) formulation is presented for treating the electromagnetic scattering from electrically large, inhomogeneous objects. A dense grid of rays representing the incident plane wave is shot toward the inhomogeneous objects. At the scatterer boundary, reflected rays and refracted rays are generated due to the discontinuity of the medium parameters. The trajectory, amplitude, phase and polarization of the rays inside the inhomogeneous object are traced based on geometrical optics. Whenever the rays cross the scatterer surface, additional reflected/refracted rays are generated and are tracked. This is repeated until the intensities of the refracted/reflected rays become negligible. The contributions of the existing rays to the total scattered field are calculated using the equivalence principle in conjunction with a ray-tube integration scheme. The ray formulation is applied to calculate the backscattering from cylinders and spheres and good agreement with the exact series solutions is observed in the high-frequency range. In addition, the backscattering mechanisms in penetrable objects are interpreted in terms of simple ray pictures     

High frequency fields in the presence of a curved dielectric interface

A high-frequency line source in a dielectric medium that is separated by a concave cylindrical boundary from an exterior medium with lower dielectric constant generates a variety of wave phenomena which have been explored extensively. This problem is reexamined here with a view toward clarifying relevant reflection and transmission characteristics within the framework of ray optics, with emphasis on the more complicated transmitted field. The exterior domain is divided into illuminated and shadow regions separated by the transmitted tangent ray launched by a ray incident at the critical angle. Conventional ray optics is valid far from the tangent ray shadow boundary on the illuminated side. The shadow boundary is surrounded by transition regions wherein Fock type integrals and Weber functions yielding local lateral waves provide alternative representations. On the shadow side, not too far from the shadow boundary, the field can be interpreted via "tunneling" and subsequent radiation along a ray from a virtual caustic to the observer. The tunneling is associated with the initial evanescent decay of the transmitted field excited by a totally reflected incident ray. However, deeper inside the shadow, this mechanism is inapplicable, and the field is expressed either in terms of the Fock integrals or a creeping wave-type residue series. The results are presented in a format that permits insertion into a geometrical theory of diffraction (GTD) user's manual.     

On the tunneling hypothesis for ray reflection and transmission at a concave dielectric boundary

When a ray field is incident on a concave boundary confining a dielectric medium, total reflection is perturbed by leakage due to surface curvature. The resulting modification of the conventional Fresnel ray reflection coefficient, including its uniform transition through critical incidence, has previously been addressed by the so-called "tunneling hypothesis," which is based essentially on the behavior of a corresponding peripherally guided whispering gallery or leaky modal field; the former exhibits evanescent decay (tunneling) away from the boundary in the exterior region but eventually gives rise to radiation from a caustic whereon the modal phase speed equals the speed of light. It is shown here that inferring local ray field properties from global mode field properties has limited validity. The demonstration is based on a rigorous analysis of the two-dimensional Green's function for a circular boundary. Asymptotic solutions are constructed for the various ray-optical domains, and for the transition regions near caustics and especially near the critically refracted ray. Examination of the reflected and transmitted fields reveals that the tunneling hypothesis holds only near the critically refracted ray. Elsewhere, the transmitted ray field may deviate markedly from that predicted by the tunneling model. The results clarify not only the ray field behavior but also the mechanism of local energy reflection and transmission for a nonplanar interface.     

Rays, Beams, and Modes Pertaining to the Excitation of Dielectric Waveguides

The two-dimensional problem of excitation of an inhomogeneous dielectric layer by a Gaussian beam is considered, with emphasis on useful representations that treat the field either in terms of multiple reflections or in terms of guided modes. A recently developed method is employed whereby the beam fields are generated from line source fields by assigning a complex value to the source coordinates. When applied to the asymptotic solution for the line source field, this procedure furnishes a simple and quantitative relation between line-source-excited ray optics and paraxial beam optics. It also clarifies the role of lateral ray and beam shifts for reflection at a boundary with incidence-angle-dependent reflection coefficient, especially when multiply reflected fields are converted into modal form. Results are given for beams which are reflected at both boundaries, reflected at one boundary and refracted before reaching the other boundary, and trapped by refraction without reaching either boundary. In the first case, conversion to modal form is more convenient at large distances whereas in the latter case, paraxial beam tracking is preferable.     

Scattering of electromagnetic waves by an anisotropic plasma-coated conducting cylinder

This paper considers the scattering of electromagnetic waves by an infinitely long anisotropic plasma-coated conducting cylinder. The source is assumed to be a magnetic current filament which gives rise to an incident magnetic field with only an axial component. Complete expressions for the scattered electric and magnetic fields are obtained. Scattering by an anisotropic plasma column and that by an isotropic plasma-coated conducting cylinder are special cases of the present problem.     

Focusing by an anisotropic plasma interface

When an electromagnetic source confined in a homogeneous, anisotropic plasma half space radiates into the exterior medium, focusing effects may occur wherein the influence of the plane interface bounding the plasma is similar to that of an optical lens. The existence and location of the caustics and focus depends on the various plasma parameters, in particular on the strength and orientation of the externally applied magnetic field, and the refractive index curves for the medium may be used advantageously for the prediction of their properties. After a qualitative discussion pertaining to the general gyrotropic case, a detailed field evaluation for line source and dipole excitation is carried out for the special problem of uniaxial anisotropy, corresponding to an infinitely strong external magnetic field. In this instance, the ray system and the caustics may be described in simple terms and expressions are given for the fields inside or outside the focusing region.     

微极广义磁热弹性固体界面上波的传播

给出了微极广义热弹性固体的一般控制方程；研究了在定常磁场作用下具有均匀初始温度的两理想接触微极弹性介质平面分界面上磁热弹性波的传播特性；给出了分别在缺少磁场、热场作用或不同广义热传导理论下反射或折射热波、纵向位移波、耦合横向和微旋转波与入射纵向位移波的振幅比随入射角变化的关系曲线，讨论了热松弛及磁场对振幅比的影响。结果表明：热松弛时间及磁场对振幅比均有显著影响，改变热松弛时间或磁场强度可以明显改变波的传播形式。     

各向异性介质涂覆PEC平板的反射场分析

利用射线级数法分析各向异性介质涂覆PEC平板反射场。该分析引入Chew使用的状态向量来表征场,利用传输矩阵表征各向异性涂覆层中的电磁波经过了一次下行路径和上行路径之后幅值和相位产生的变化。将涂覆层表面总场表示成一个射线级数。每项级数分别判定成入射场、单次反射场及n次反射场,并通过涂覆层顶层和底层表面上的边界条件进行约束。从实际应用的角度考虑,对n次反射场之和的贡献选取截断次数,并验证了截断次数选取的合理性。文中的算例和分析说明了射线级数法的有效性及所得反射场的合理性。     

Electromagnetic waves in a suddenly created magnetized Lorentzmedium (transverse propagation)

The interaction of electromagnetic waves in a suddenly created Lorentz medium with impressed steady uniform magnetic field is considered. It was shown that for the case of the incident electric field normal to the static magnetic field, the source wave splits into six new extraordinary waves whose frequencies are different from the incident waves. Three of those six new waves are transmitted waves, and the other three are reflected waves. The dispersion relation, power transmission, and reflection coefficients are derived and discussed     

On waves in an anisotropic plasma imbedded in a moving dielectric medium

The governing equations for electromagnetic fields in an anisotropic plasma imbedded in a moving dielectric medium are obtained. Examination of the wave and dispersion equations yields information on the elliptically or linearly polarized waves which may exist when the external magnetic field is parallel or perpendicular to the direction of motion, respectively.     

The Radiation Properties of a Parallel-Plane Waveguide in a Transversely Magnetized, Homogeneous Plasma

The Wiener-Hopf technique is used to study the radiation from a parallel-plane waveguide embedded in a homogeneous anisotropic plasma in which the external magnetic field is perpendicular to the direction of propagation and parallel to the perfectly conducting planes of the guide. The incident field in the guide is a TEM wave, which propagates in the positive z direction. The parallel-plane guide terminates at z = 0, causing a reflected field in the waveguide, a radiation field, and a surface wave that is guided along the outer surface of one of the perfect conductors. Expressions are found for these field components, and the results are discussed for the different frequency ranges.     

Impedance of a short horizontal dipole over a ground plane covered with an anisotropic plasma

Impedance of a short dipole antenna placed parallel over a ground plane covered with an anisotropic plasma has been studied by the quasistatic approximation with emphasis on the effects of image displacement for arbitrary inclinations of the static magnetic field. As the image location can move with the operating frequencies, the reflected characteristic conical surfaces can create oblique resonance anomalies, depending upon source dimensions and source location. While an oblique resonance occurs when the characteristic conical surface coincides with the dipole axis, another anomaly occurs when the reflected cone grazes the dipole ends.     

Excitation of Plasma Waves in an Unbounded Homogeneous Plasma by a Line Source

The radiation characteristics of a line source of magnetic current embedded in a homogeneous electron plasma of infinite extent are investigated for the case in which a uniform magnetic field is impressed externally throughout the medium in the direction of the source. The single-fluid theory of magnetohydrodynamics is employed. A very simple model is assumed for the plasma. Under this assumption, it is found that there are two modes of propagation of waves of small amplitude. By examining the behavior of these modes in the limiting cases of vanishing external magnetic field or infinite source frequency, they are identifiable as the modified forms of the usual plasma and optical modes which exist in an isotropic electron plasma. The dispersion relations for these two modes are discussed. The power radiated in each of the two modes is also evaluated. It is found that the power radiated in the optical mode is always lower than that due to the line source in free space, whereas the power radiated in the plasma mode is higher than that value for certain ranges of the source frequency.     

Massively parallel computational simulations in light scattering

Described is the Connection Machine, a massively parallel SIMD (single instruction multiple data) computer of 64K processors, used to simulate optical scattering and absorption phenomena where the scattering objects are much larger than the wavelength of the incident light. One processor of the connection machine is assigned to an individual incident ray. The processor tracks the ray through the object system noting the multiple reflections and refractions which occur. The results calculated are the vectors of the outgoing rays which are leaving the object system environment. As each of the interactions of each incident ray are independent of those of all other rays, 64K incident rays can be tracked at a time. The classic communication bottleneck between processors on SIMD machines is nonexistent in this case. Using a stochastic approach, a Monte Carlo technique is used whereby each ray is either reflected or refracted based on probabilities. The object is represented by a collection of small facets enabling almost any shaped object or objects to be modeled from any orientation. The limit on the complexity of the object system is limited only by the size of the host memory of the Connection Machine. The algorithm is such that it runs in linear time to the number of facets which are used to represent the system     

On Radial Transmission Line Representations of Electromagnetic Fields in an Anisotropic Moving Medium

The problems of electromagnetic waves in moving isotropic or uniaxial mediums have been dealt with by numerous authors. Chawla and Unz considered the fields in a moving anisotropic plasma, and Chen and Cheng analyzed waves in an isotropic plasma in a moving dielectric medium. In this note we consider electromagnetic fields in a moving anisotropic medium and propose the network formulation of electromagnetic fields in the moving medium in the radial cylindrical coordinate. The method is an extension of the transmission line representation of electron beams on infinite magnetic fields. We can apply these results to the cases of any magnetic field intensity and, further, solve the complex problems for a stationary anisotropic plasma by a similar method.     

别汉棱镜角度误差对光轴一致性影响的研究

在周视扫描成像系统中,需要通过特定光学元件进行消像旋。别汉棱镜是最常用的消像旋元件之一,由于棱镜的角度误差对系统光轴的影响较大,因此对别汉棱镜的角度误差要求非常严格。本文通过分析推导反射光线、折射光线以及三维坐标系旋转的矢量形式表达式,建立了别汉棱镜的角度误差模型,在此基础上分析了入射光轴经别汉棱镜折反射之后出射光轴的方向向量,并且基于Matlab实现了从别汉棱镜出射的光轴的方向向量及其相对于入射光轴偏差的计算。通过与光线追迹仿真结果和实验结果进行对比,验证了所建立模型以及分析计算过程的正确性,解释了在棱镜胶合过程中出现四个十字叉丝的问题,对棱镜的加工具有指导作用,同时提高了胶合效率和棱镜的光轴一致性精度。     

Forbidden directions for TM waves in anisotropic conducting media

We investigate the wave propagation properties of nonuniform plane waves in an (unbounded homogeneous) anisotropic conducting material. Such waves (for which amplitudes vary across surfaces of constant phase) characterize the refracted field in an imperfect dielectric, like the earth when a uniform electromagnetic plane wave is incident from the air. The results, presented in terms of polar diagrams of the attenuation, slowness, energy velocity, and quality factor predict the existence of “stopbands” beyond a given degree of nonuniformity (i.e., combinations of propagation and attenuation directions where there is no wave propagation). This is a peculiar, effect due to the joint presence of anisotropy and conductivity that may have application in the design of synthetic materials acting as absorbers of electromagnetic radiation     

Complex ray analysis of beam transmission through two-dimensional radomes

Assessment of the radiation characteristics of certain types of radome covered antennas poses the problem of transmission of amplitude tapered large-aperture fields through a curved dielectric layer. Modeling the amplitude taper by a Gaussian, the incident illumination can be generated by a source at a complex coordinate location. The radome problem is then addressed by tracing complex ray fields from the complex source point through the complex extension of the radome configuration to the real location of the observer. No integrations over equivalent apertures are required here. The complex ray tracing has been performed for conventional complex geometric trajectories as well as more accurate trajectories with lateral shifts at the radome interfaces, and takes into account multiple reflections inside the radome. As previously for real rays, the multiple internally reflected complex rays can be combined into a "collective ray" that is weighted with a curvature and (or) taper corrected slab transmission coefficient. Numerical calculations for various two-dimensional circular cylindrical and wedge-tapered prototypes and various beam illuminations demonstrate the feasibility of the complex ray method, the efficiency of the collective ray concept, and the adequacy of the ray model without lateral shifts for the radome application.     

Propagation of electromagnetic pulse having a Gaussian envelope in longitudinally inhomogeneous anisotropic ionized media

For radio-wave communication with ionospheric propagation, it is useful to study the distortion of signals propagating through a plasma medium. The problem is discussed of finding the distortion of a pulse after it has propagated through a longitudinally inhomogeneous anisotropic ionized medium whose electron density varies linearly in one direction. As a model of the incident pulse source, the Gaussian envelope carrier pulse is considered. Dependence of the electromagnetic pulse distortion upon the duration of the pulse, the gradient of the electron density, the magnetostatic field, and the carrier frequency is mathematically studied in detail.