The snell and fresnel relationships for electromagnetic waves with the constant linear polarization

General conditions for the existence of plane electromagnetic waves with a single nonzero electric-field component (TE waves) in an anisotropic medium are established. A transformation that makes it possible to derive similar formulas for TM waves (plane electromagnetic waves with a single nonzero magnetic-field component) from the formulas expressing the properties of TE waves is considered. A general numerical algorithm is developed for calculating the amplitudes (with allowance for phases) of the TE waves formed when an external TE wave propagates through a system of plane-parallel plates consisting of media supporting TE waves. Formulas are obtained for the solution of the particular problem on the transmission of a TE wave through a plane interface between two media supporting TE waves. A series of relationships that can be interpreted as generalizations of the Snell and Fresnel relationships for media of the considered type are derived. Formulas for the transmission, reflection, and refraction coefficients are obtained. The existence conditions for TE (TM) surface waves are derived. A numerical method is proposed for computing the spectra of such surface waves formed on the interface between two media. For isotropic media, analytic expressions for the spectra of surface waves are derived. It is shown that the obtained formulas are similar to the known formulas for surface TM waves in dielectrics but, in addition, make it possible to take into account both the permittivities and permeabilities of the media.     

左手系材料对称平板结构中的波导模

考虑由左手系材料作覆层衬底的对称波导系统,研究了TE线性极化波在该波导中的传播特性.利用直接图解法对各种波导模式进行了详细地判别,结果表明快波、慢波均可以在该波导中传播,两者的模式特征与传统介电波导及左手波导均存在较大差异.分析了导波的色散关系并定性地讨论了群速度随频率的变化规律.揭示了在一定条件下,该波导系统既可以支持前向线性TE波的传播也可以支持反向线性TE波的传播,且支持低阶快波偶模式和慢波奇模式传播的频率段相对狭窄.     

Reflection by a Sinusoidally Modulated Surface Reactance at Oblique Incidence

The reflection characteristics of the TM and the TE surface waves by a weak sinusoidal modulation of the surface reactance are investigated for the oblique incidence in which the wavevectors are not aligned with the grating vector. A superposition of TM and TE wave fields is needed for the fulfillment of the required boundary conditions. For both the TM and the TE surface waves, the Brewster phenomenon of total transmission occurs at the angle of incidence theta=theta/sub B/ = 45°. A modulation in the surface reactance, in general, causes the TE surface waves to be more efficiently reflected than the TM surface waves.     

Fundamental and Higher Mode Inversion of Dispersed GPR Waves Propagating in an Ice Layer

Dispersion of ground-penetrating radar (GPR) waves can occur when they are trapped in a layer. In this paper, we analyze the modal propagation of GPR pulses through a layer of ice that is overlying water. Dispersed transverse electric (TE) waves that are trapped in the waveguide have larger amplitudes than the critically refracted waves that travel through air, whereas the transverse magnetic (TM) critically refracted waves traveling through air are more dominant than the trapped dispersed TM waves. This can be explained by the leaky waveguide behavior of the ice layer. The reflection coefficients for the waves incident on the ice-water interface show that the TM modes are more leaky than the TE modes. Still, clear dispersion is observed in both cases, which depends on the permittivity and thickness of the ice. Similar to inversion of dispersed Rayleigh waves, these parameters can be estimated by calculating phase-velocity spectra, picking dispersion curves, and inverting the dispersion curves using a combined local and global minimization procedure. Synthetic data show several higher order modes of which separate and combined inversions return the input modeling parameters accurately. Experimental data acquired on a frozen lake show strong dispersion for the TE and TM modes. The phase-velocity spectra of the field data show three TE and four TM modes of which separate and combined inversion of different modes return similar values for the ice thickness and known permittivity of ice. Due to the more leaky behavior of the TM modes, the TE inversion is better constrained and more suitable for inversion.     

An effect of excitation of a transverse magnetic creeping wave when a transverse electric wave crosses the line of the coincidence of propagation constants

Transverse electromagnetic electric (TE) and transverse magnetic (TM) creeping waves on a surface with an anisotropic impedance boundary condition are considered. An asymptotic theory is developed for creeping waves. The theory is valid near the line where the attenuation parameters of two different types of waves coincide and, therefore, standard asymptotics are inapplicable. Asymptotic formulas describing physical effects that occur when a creeping wave propagates across the degeneracy line are derived. It is found that, behind the degeneracy line, a propagating TE wave excites a TM wave with a small amplitude (of order O(k ^−1/6)) and a propagating TM wave excites a TE wave.     

Artificial magnetic conductors based on capacitive gratings

New realizations of artificial magnetic conductors (AMCs) based on two or more closely spaced capacitive gratings whose period is small relative to the wavelength are proposed. Simple formulas are derived for estimation of the resonance frequencies and frequency bands in which the proposed structures behave as AMCs. Angular dependencies of the resonance frequencies are found for TE and TM waves. Propagation conditions for surface waves are considered. It is shown that, at resonance frequencies, such structures support only slow TM waves with small values of the slowing factor. It is confirmed experimentally that such structures behave as AMCs in a wide interval of the angles of incidence of TE and TM waves.     

矩形波导中主模电磁波传播特性研究

矩形波导主模电磁波是波导传输中使用最多的模式。为了能深入了解其传播特征。从波导的截至波长入手,讨论了电磁波单模传播的条件。得出结论：主模传播需要电磁波波长和波导尺寸之间满足一定关系。推导出主模电磁波的场方程,利用该场方程,结合一定尺寸的矩形波导管,模拟出一定频率的主模电磁波分布图,进而总结了主模电磁波传播的主要特征。这...     

New results for the properties of TE surface waves in absorbinglayers

TE surface waves in absorbing layers with high losses are studied. All basic characteristics of these waves are analyzed. They include attenuation and propagation constants, electric and magnetic losses, complex Brewster angles, phase and amplitude fronts of Brillouin waves inside layers, phase and energy velocities. New phenomena of the upper frequency cutoff and merging of higher order modes are demonstrated. In addition, the excitation of TE surface waves in thin absorbing layers is investigated and the launching efficiency is computed     

用二维矢量FD—TD法分析平面光波导模场分布

本文用二维矢量时域有限差分（FD－TD）法分析了平面光波导基模（TE0模）和高阶模（TE1模）的模场分布情况,分析基模时用了5种不同形态的光谱作为激励,所得的光场分布在光场传播达到稳定后完全相同,所得TE0模和TE1模的二维稳态模场分布结果均与解析法讨论的结果一致。     

含单负材料对称三层平板波导的模式特性

由电磁场的波动方程和边界条件建立了单负材料作为芯层的对称三层平板波导的模式本征方程,用图解法研究其色散特性。研究发现,单负介质波导不支持快波的传播,只支持表面波的传播。在负磁材料平板波导中只存在TE表面模,不存在TM表面模。分析了在负磁材料平板波导中TE模受磁导率的比值-μ2／μ1和波导参数的影响,给出了横向场分布图。在-μ2/μ1〈1时,偶对称只有TE0表面模存在,奇对称只有TE1表面模存在,高阶模式并不存在,且两种模式都没有低频截止;-μ2/μ1〉1时,TE1表面模始终不出现;TE0模的存在与否和波导参数有关,在一定条件下TE0模可出现双模并存。给出的结果可望对表面波器件的设计提供理论基础。     

基于十字形的改进新型频率选择表面

通过对传统的十字单元进行改进,设计了两种新型单元的频率选择表面( FSS)。利用谱域分析法,从理论上分析了传统十字单元和新型单元FSS,研究了TE 波入射时角度变化和大角度入射下极化方式变化对中心频率的影响。仿真结果表明：在TE 波从 0°～60°以不同角度入射时,传统十字单元的中心频率漂移为420 MHz,两种新型单元中心频率的漂移量分别为180MHz 和210MHz, 减少了1/2 以上;在45°不同极化方式的波入射时,传统十字单元中心频率的漂移量为990MHz,两种新型单元的漂移量为150MHz 和120MHz,减少了2/3 以上。与传统十字单元相比,两种新型FSS 单元均能实现TE 波入射时的角度稳定性和大角度入射时的良好的极化稳定性,为FSS 在天线雷达领域中的应用提供了基础。     

Finite-element formalism for nonlinear slab-guided waves

A unified computer-aided numerical approach, based on the finite-element method, is developed for analyzing optical waves guided by dielectric slab waveguiding structures with arbitrary nonlinear media. In the formulations, both TE and TM polarizations are considered. For the TM case, the biaxial nature of nonlinear refractive index is considered without any approximation. Numerical results are presented for nonlinear TE and TM waves propagating in symmetric slab waveguides. The dependence of dispersion relations on the refractive-index profile of the film is examined     

The theory of propagation of electromagnetic waves in a waveguide with a magnetoactive anisotropic modulated filling

Propagation of electromagnetic waves in a waveguide with an arbitrary cross section is considered. The waveguide is filled with a magnetoactive anisotropic medium periodically modulated in space and time. The wave equations for the potentials of transverse electric (TE) and transverse magnetic (TM) fields are derived. Expressions for the TE and TM waveguide fields observed in the region of weak interaction between the signal wave and the modulation wave are found in the first approximation for small modulation indexes of the filling. The frequency near which strong (resonance) interaction between the signal wave and the modulation wave develops is expressed in an analytic form. The propagation of TE and TM waves in the strong-interaction region is investigated.     

Cyclotron Autoresonance with TE and TM Guided Waves

The electron cyclotron autoresonance is of both theoretical and practical interest for acceleration of charged particles and for generation of microwave radiation in various gyro-devices. In this paper a unified first-principles approach is applied to the analysis of the interaction of gyrating electrons with electromagnetic waves with different characteristic impedance. In contrast to the previous works that consider the underlying autoresonance integral only for the case of plane transverse waves and TE modes our analysis is applied also to TM modes. An approximate constant of motion is derived for the latter case from which it follows that the requirements for autoresonance can be satisfied easily in comparison to the TE modes. Some fundamental relations which follow from the analysis are discussed as well.     

非线性负折射率材料表面TE电磁波的空间稳定特性分析

针对电磁波在正负非线性材料界面处的传播,研究了两种稳定状态下电磁波的物理特性。理论分析和数值计算表明,该界面处电磁波的传播存在着频率通带,且带宽仅与两种材料的固有属性有关。得出前向表面波和后向表面波均可以在这种非线性导波系统中传播,并且在一定条件下,随着频率的变化,前向表面波和后向表面波可以在两种材料中跃变。推论出两种稳定传播的电磁波场峰值位置随传播功率的变化也能实现在两种材料中跃变,并逐渐向界面靠近,而传播功率较大的稳定态电场峰值几乎靠着界面。     

Field analysis for the cylindrical m.h.d. induction generator

The interaction of a cylindrical conducting fluid stream is analysed in three dimensions using the magnetic vector diffusion equation. The electromagnetic waves in the conducting medium are surface waves and can be separated into TE and TM modes.     

Transverse Magnetic Wave Propagation in Sinusoidally Stratified Dielectric Media

The problem of the propagation of TM waves in a sinusoidally stratified dielectric medium is considered. The propagation characteristics are determined from the stability diagram of the resultant Hill's equation. Numerical results show that the stability diagrams for Hill's equation and those for Mathieu's equation are quite different. Consequently, the dispersion properties of TM waves and TE waves in this stratified medium are also different. Detailed dispersion characteristics of TM waves in an infinite stratified medium and in waveguides filled longitudinally with this stratified material are obtained.     

Propagation in Transversely Magnetized Compressible Plasma Between Two Parallel Planes

The propagation of waves in compressible single fluid macroscopic plasma between two parallel, perfectly conducting planes, with a transverse static magnetic field parallel to the boundaries is investigated. It is shown that the TE waves are not affected by either the static magnetic field or the compressibility of the plasma, while the TM wave will be affected by both.     

含单负材料光子晶体隧穿模的偏振特性

为探讨含磁单负材料光子晶体的偏振特性,构造了由普通材料A(SiO2)和磁单负材料B组成的(AB)3(BA)3对称型一维光子晶体。数值计算结果表明,垂直入射时,原禁带的1 907 nm处出现了一个十分尖锐的隧穿模。对TE波,入射角增加、B介质的介电常数B或几何厚度减少时,禁带边缘蓝移,宽度变窄,隧穿模的透射率和半峰全宽保持不变,但其位置蓝移。上述3个参数分别变化时,TM波的透射谱及隧穿模的变化规律与TE波的相同,只是入射角增加时,TM波禁带长波边缘的蓝移量小于TE波的。隧穿模的这些偏振特性对高品质滤波器的设计具有指导意义。