TE/TM decomposition of electromagnetic sources

Three methods are given by which bounded electromagnetic sources can be decomposed into two parts radiating transverse electric (TE) and transverse magnetic (TM) fields with respect to a given constant direction in space. The theory applies source equivalence and nonradiating source concepts, which lead to decomposition methods based on a recursive formula or two differential equations for the determination of the TE and TM components of the original source. Decompositions for a dipole in terms of point, line, and plane sources are studied in detail. As an application of the point decomposition method, it is demonstrated that the general exact image expression for the Sommerfold half-space problem, previously derived through heuristic reasoning, can be more straightforwardly obtained through the decomposition method     

Time-domain TE/TM decomposition of electromagnetic sources

Theory for the decomposition of electromagnetic sources with arbitrary time dependence into parts radiating transverse electric (TE) or transverse magnetic (TM) fields with respect to a given constant direction in space is developed. The theory is a generalization of that given earlier by the author (1988) for time-harmonic sources. Three different decomposition methods, which for a point source can be expressed in terms of point sources, line sources, and plane sources, are given. As a check it is demonstrated that for time-harmonic time dependence of the original source, the previously derived decomposition expressions are obtained as special cases     

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.     

Eigenfunctions and dyadic Green’s functions of electromagnetic field in regular boundary conditions

Universal form of theM andN vector wave functions and its normalized integrate constants for the regular boundary conditions in Cartesian, cylindrical and spherical coordinates are given, and the cerresponding dyadic Green’s functions are obtained.     

Fractal surfaces and electromagnetic extended boundary conditions

In this paper, we employ the extended boundary condition method with the Weierstrass-Mandelbrot (WM) fractal function to model and solve a relevant electromagnetic scattering problem. The key point of the procedure is the property of the WM to be an almost periodic function. This allows to generalize techniques employed for periodic problems and to express the field by means of a superposition of Floquet modes. The procedure is devised for the general case of dielectric surfaces. Criteria for assessing the validity of the method are discussed and provided. Validity of the method is confirmed by numerical results     

Determination of the TE and TM modes in arbitrarily shaped waveguides using a hypersingular boundary element formulation

In this paper a procedure based on the hypersingular element method is applied to find the TE and TM modes in arbitrarily shaped waveguides. To show the accuracy of this method, various examples are solved and the results are compared to those analytical, when there is an analytical solution, and those presented in the literature. The proposed method did not present spurious modes, and in all the examples presented showed excellent results considering a reasonable number of elements in the boundary.     

Superabsorption-a method to improve absorbing boundary conditions[electromagnetic waves]

The authors propose a technique, which they call superabsorption, for improving absorbing boundary conditions in finite-difference time-domain methods. This method can be applied to every known absorbing boundary condition and greatly reduces the numerical error caused by the boundary reflection. The principle and analysis of the superabsorption method are presented. Numerical tests indicating the improvements obtained on many absorbing boundary conditions are reported     

Comparative evaluation of a novel series approximation for electromagnetic fields at dielectric corners with boundary element method applications

This paper presents a series solution for the longitudinal electromagnetic fields at arbitrary dielectric corners. We apply versions of the method that are up to sixth-order accurate to our recently proposed full vector boundary element method (BEM) mode solver. Our results indicate that our previous formulation models corner fields with high precision.     

High-power TE11 and TM11 circular polarizers in oversized waveguides at 70 GHz

Elliptical deformation of oversized, smooth-wall circular waveguides can produce choosable elliptical or circular polarization from a linearly polarized TE11 or TM11 mode used as intermediate linearly polarized modes in TEO1 to HE11 mode conversion sequences in electron cyclotron resonance heating (ECRH) of magnetically confined thermonuclear fusion plasmas with high-power gyrotrons. Mode coupling in elliptically distorted overmoded circular waveguides has been studied theoretically and experimentally in order to optimize TE11 (and TM11) polarizers (I.D.=27.79 mm) for the 1 MW/70 GHz long-pulse (3s) ECRH system on the Garching Stellarator W VII-AS. Coupling coefficients for ellipticity coupling of non-degenerate modes are given (coupled-mode differential equations formalism). The polarization converters essentially consist of smooth-wall circular waveguides which are gradually squeezed. A sine-squared function of the length coordinate is used to get an almost elliptical crosssection in the middle and circular cross sections at both ends. Arbitrary elliptical polarization states can be generated introducing an extremely low level (<<1%) of undesired spurious modes. Well defined differential phase characteristics have been achieved.     

The effect of material stresses on electromagnetic boundary conditions

The appearance of a layer of charge or current on the boundary of a material usually implies that a discontinuity in an electromagnetic field occurs at that boundary. The converse is not necessarily true. The reaction of the electromagnetic field to the charge or current layer is a stress communicated across the boundary. Determination of the charge or current on a boundary must take all the stresses and electromechanical interactions at the boundary into account. Calculating surface currents or charges derived from electromagnetic field quantities alone, ignoring mechanical stresses, may lead to wrong answers at material boundaries. In short, the occurrence of charge or current on material in the presence of an electromagnetic field is intimately related to momentum conservation. A postulate equivalent to identifying the Poynting vector with energy flow is introduced, linking surface currents and charges to momentum balance at the surface. A formally correct method for calculating surface currents and charges based on momentum balance is described.     

On combined source solutions for bodies with impedance boundary conditions

Numerical solutions to the impedance boundary condition (IBC) combined source integral equation (CSIE) for scattering from impedance spheres are presented. The CSIE formulation is a well-posed alternative to the IBC electric and magnetic field integral equations which can be contaminated by spurious resonant modes. Compared with the IBC combined field integral equation (CFIE), CSIE solutions have the same accuracy when the combined source coupling admittance is chosen to be the same value as the combined field coupling admittance. However, the CSIE formulation is better suited than the CFIE for creating a general purpose computer code capable of handling aperture radiation problems and/or a scatterer which has a spatially varying surface impedance.     

FDTD simulation of TE and TM plane waves at nonzero incidence in arbitrary Layered media

Plane wave scattering is an important class of electromagnetic problems that is surprisingly difficult to model with the two-dimensional finite-difference time-domain (FDTD) method if the direction of propagation is not parallel to one of the grid axes. In particular, infinite plane wave interaction with dispersive half-spaces or layers must include careful modeling of the incident field. By using the plane wave solutions of Maxwell's equations to eliminate the transverse field dependence, a modified set of curl equations is derived which can model a "slice" of an oblique plane wave along grid axes. The resulting equations may be used as edge conditions on an FDTD grid. These edge conditions represent the only known way to accurately propagate plane wave pulses into a frequency dependent medium. An examination of grid dispersion between the plane wave and the modeled slice reveals good agreement. Application to arbitrary dispersive media is straightforward for the transverse magnetic (TM) case, but requires the use of an auxiliary equation for the transverse electric case, which increases complexity. In the latter case, a simplified approach, based on formulating the dual of the TM equations, is shown to be quite effective. The strength of the developed approach is illustrated with a comparison with the conventional simulation based on an analytic incident wave specification with half-space, single frequency reflection and transmission for the edges. Finally, an example of a possible biomedical application is given and the implementation of the method in the perfectly matched layer region is discussed.     

Study of Ka-band TM01 to TE11 Mode Converters with Parallel Input and Output Waveguides

Based on the bent waveguide mode coupling theory, a combined TM₀₁-TE₁₁ mode converter with parallel input and output ports is designed by numerical calculation with the phase rematch technology employed. A numerical calculation comparison between the converter and another double-arc TM₀₁-TE₁₁ mode converter with nonparallel input and output ports shows that the former has obvious advantages over the latter in conversion, bandwidth and compact. Good agreement between tests and calculations shows the converter meets the application well.     

Bandwidth and Q of antennas radiating TE and TM modes

The time-domain Poynting theorem is used to develop a general expression for the complex Poynting vector applicable to any single-frequency electromagnetic radiation field. It is found that the traditional complex Poynting vector applies to TE or TM fields, which we call simple fields, but that it does not apply to TE and TM fields, which we call compound fields. Either TE or TM fields are generated by most antennas. We show that previously imposed theoretical minimum size-to-wavelength ratios for useful antenna operation apply to simple fields but not always to compound ones. We conclude that electrically small, efficient compound antennas may be possible. As an example, the general form of the Poynting vector is used to analyze a compound source consisting of four antenna elements; idealized, superimposed, properly phased and oriented, coherent, electric and magnetic, dipole and quadrupole radiators. When properly driven, the antenna supports zero reactance on a circumscribing virtual surface of radius a, even in the limit as the radius-to-wavelength ratio of that surface goes to zero. The directivity pattern has a fixed 9 dB gain; the radiative Q of the surface is less and the bandwidth more by a factor of (ka)², where k is the wave number, than for similarly sized radiators of simple fields     

Application of electromagnetic inverse boundary conditions to profile characteristics inversion of conducting spherical shapes

An inverse problem of continuous wave electromagnetic scattering is considered. It is assumed that the incident and the scattered fields are given everywhere and that the material surface properties satisfy the Leontovich boundary condition. Applying the concept of electromagnetic inverse boundary conditions it is shown how the shape and the averaged local surface impedance for spherical monobody and two-body scattering geometries can exactly be recovered. To enable accurate inversion for the multibody or general spherical case, analytical continuation methods in three dimensions are introduced.     

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。     

Partial variational principle for electromagnetic field problems:theory and applications

A partial variation concept is proposed to clarify and extend the ideas and techniques used in variational electromagnetic (VEM) and variation reaction theory (VRT) of recent papers. Based on this concept, a partial variational principle (PVP) is established for handling a general linear time-harmonic interior and/or exterior electromagnetic field problem. This principle is then applied to attack the problem of waves incident on a dielectric discontinuity in a parallel-plate guide. Also included are numerical results and discussions about such waveguide discontinuity problems for illustrating the use of the proposed technique     

Propagation of electromagnetic TE waves in a nonlinear medium with saturation

Propagation of electromagnetic TE waves in a nonlinear dielectric layer with saturation is considered. The layer is located between two isotropic nonmagnetic semi-infinite media with constant electromagnetic parameters. A nonlinear boundary-value problem for the eigenvalues of a second-order ordinary differential equation is studied. The dispersion equation for the eigenvalues of the problem (propagation constants) is derived. Dispersion curves are calculated.     

Analysis of TE and TM modes in DFB lasers by two-dimensional theory

The two-dimensional theory of a distributed feedback (DFB) laser (which was previously presented and applied to the analysis of the laser threshold conditions for the transverse-electric (TE) mode in a simple three-layer waveguide structure) is developed to treat both TE and transverse-magnetic (TM) modes in a four-layer waveguide structure with a thin grating layer, which more closely reflects actual DFB laser structure. The differences between TE and TM modes for the dispersion relations and the laser threshold conditions are clarified. The effects of the waveguide structure (including grating layer thickness, refractive indexes of layers, coupling constant, and corrugation period) on the threshold gains and the gain differences between the two longitudinal modes on both sides of the Bragg frequencies are studied in detail for both TE and TM modes     

Scalar BPM analyses of TE and TM polarized fields in bent waveguides

We have applied the effective index method to reduce the two-dimensional (2-D) refractive index profile into the 1-D refractive index structure and modified the wave equations to obtain the paraxial wave equations. Then, transverse electric (TE) and transverse magnetic (TM) polarized fields in the curved single-mode planar waveguides are analyzed by using the scalar beam-propagation method (BPM) employing the finite-difference method with a slab structure. The bending loss in bent waveguides is analyzed for optical fields obtained from the BPM and comparisons are made between the loss for the waveguides with various radius of curvature and refractive index difference. The outward shift of the optical field, which is generated at the connection between a straight and a bent waveguide, is obtained from the results of calculation of location of the maximum optical intensity. The transition loss can be reduced by introducing an optimized inward offset at a straight-to-bend junction. The birefringence for TE and TM polarized fields in bent waveguides is calculated from the phase difference of the optical fields. The wavelength shift due to the birefringence of TE and TM polarized fields in bent waveguides is also calculated.