Rigorous, full-vectorial source-type integral equation analysis ofcircularly curved channel waveguides

A source-type integral equation method is presented to determine the propagation constants, the radiation losses, and the electromagnetic field distributions of the discrete (“guided”) modes in circularly curved, integrated optical channel waveguides embedded in a homogeneous background. The method can be extended to the case of a multilayered background, e.g. a ridge waveguide. The source-type integral equation forms an eigenvalue problem, where the electric field strength represents the eigenvector. This problem is solved numerically by applying the method of moments. Numerical results are presented for various rectangular channel waveguides situated in a homogeneous embedding and compared with those of other modeling methods     

Integral equation solution to the guidance and leakage propertiesof coupled dielectric strip waveguides

The guidance and leakage properties of single and coupled dielectric strip waveguides are analyzed using the dyadic Green's function and integral equation formulation. Galerkin's method is used to solve the integral equation for the dispersion relation. The effects of the geometrical and the electrical parameters on the dispersion relation are investigated. A method for predicting the occurrence of leakage is proposed. The properties of the even and the odd leaky modes are also investigated. Results are compared with previous analysis and are shown to be in good agreement     

Electrodynamics boundary problem solution for sectoral coaxial ridged waveguides by integral equation technique

The electrodynamics eigenmodes boundary problem for sectoral coaxial single-ridged waveguides is solved by the integral equation technique utilizing the introduced system of orthogonal basis functions, which correctly take into account the singular field behavior at the ridge. The formulas obtained allow to compute cutoff wave numbers and electric and magnetic fields distributions of TE and TM modes in the presence of the ridge either on the outer or on the inner wall of the waveguide. The analysis of the dependence of cutoff wave numbers convergence on the type and the amount of basis functions and partial modes has been carried out. It is shown that for obtaining 0.1% residual error it is necessary to utilize in two times more unorthogonal basis functions, which correctly take into account singularity at the ridge, than introduced orthogonal basis functions, which correctly take into account singularity at the ridge, and in five times more orthogonal trigonometric basis functions, which don??t take into account singularity at the ridge. Besides the computing time increases in 4 and in 20 times, respectively.     

The novel boundary integral equation method for solving arbitrary cross-section waveguides

A novel method for solving arbitrary cross-sectionn waveguides is presented. The novel method is a modification of the eigen-weighted boundary integral equation method; the EWBIEM is modified by using the eigenfunction of a fictitious regular boundary as weighting function, whose eigenvalue may be the known value, and meanwhile using the domain-bases. To confirm the validity of the novel method, numerical analysis are presented for circular groove guide as an example.     

求解各向异性介质涂覆的薄壳元-边界积分法

为了克服传统有限元－边界积分方法在分析薄涂敷目标时采用四面体单元离散导致未知量非常多及需要大量的计算机存储量的缺点,采用薄壳单元（SHELL）与边界积分方法相结合分析各向异性涂敷目标的电磁特性.薄壳单元可以大大减少未知量数目,并可将体积分转化为面积分,使计算量大为减少.用薄壳元－边界积分方法考察了不同厚度及媒质涂敷时对电磁散射特性的影响,证明了该方法是精确的,在减少未知量、存储量和计算时间上具有极大的优势.     

Volterra integral equations for nonstationary electromagnetic processes in time-varying dielectric waveguides

Time-domain Volterra integral equations are obtained for the electromagnetic fields in longitudinal uniform dielectric waveguides with time-varying media in their core. Resolvent operators are constructed for the case when the core permittivity changes abruptly in time and new features are observed in the consequent field transients in comparison with those occurring in a simple unbounded space.     

Green's function in the spectral domain for biaxial and uniaxial anisotropic planar dielectric structures

Green's function solutions of the biaxial and uniaxial anisotropic layered-medium planar-structure is formulated in terms of Maxwell's equations. Diagonalized biaxial and uniaxial permittivity tensors in the coordinate system of interest are treated. The Green's function is found in the double Fourier transformed domain for three longitudinal-to-an-axis coupled electric-magnetic field sets applied to a simple layered structure. The approach is applicable to structures having discontinuities in two orthogonal planar directions such as patch radiators or resonators. Spectral Green's function is usable in method-of-moment calculations assisted by Galerkin's method.     

Theory of polarization-dependent amplification in a slab waveguidewith anisotropic gain and losses

We analyze the waveguiding properties of a semiconductor slab waveguide amplifier in which the gain (i.e., the permittivity) in the quantum well (QW) is taken to be anisotropic. Losses may be present simultaneously in the cladding layers. Using scattering theory, a rigorous integral equation is derived. Our model incorporates the two main causes of polarization sensitivity of the amplification, viz. 1) waveguiding and 2) the anisotropic light-matter interaction in the QW. It is determined how much anisotropy is needed in the QW to get a polarization-insensitive amplification. Also, reflection coefficients and TE/TM mixing are studied. A comparison between the exact results and the Born approximation is made. A Green's tensor for a layered structure with losses is derived     

Calculation of bending losses in dielectric waveguides usingeigenmode expansion and perfectly matched layers

In this letter, we present a different approach to accurately calculate the bending losses in curved dielectric waveguides. It is based on the well-known conformal transformation of the index profile and on vectorial eigenmode expansion, but this time with perfectly matched layer (PML) boundary conditions to accurately model radiation losses. The modal spectrum of these waveguides in the presence of PML is discussed and the method is validated by comparing it to previously published results     

The impact of CMP and underlying back-end topographical features on losses in deposited dielectric waveguides

The bending losses in rectangular dielectric waveguides deposited on a chemical mechanical polished (CMP) surface above the metal interconnect/interlayer dielectric stack of a processed Si wafer are modeled and estimated. CMP efficiently removes local topography and microroughness, but leaves long-range surface profile undulations due to variations in the metal pattern density. These surface undulations are then transferred to the waveguides deposited on this surface. A beam propagation method (BPM) waveguide simulation program and an equation for bending loss developed by Marcuse have been used to examine the bending losses seen by waveguides deposited on such a surface. In order to simplify the simulation of the bending losses of the waveguides, the undulations are modeled as a series of arcs, which is shown to be a good approximation. It was determined that under typical conditions, the bending losses may be ignored as they are less than 0.1 dB/cm, which is below the range of typical propagation losses for a straight guide.     

A comparison of spherical wave boundary value matching versus integral equation scattering solution for a perfectly conducting body

A spherical-wave expansion (SPEX) technique for calculating the scattering from a smooth perfectly conducting body is presented. Sample case results are compared with the well-known Lawrence Livermore National Laboratory Numerical Electromagnetics code (NEC), which is based on the integral equation formulation. The internal fields are computed for both results using a third surface current integration program, which is totally independent of both SPEX and NEC. The internal fields, which would be zero for a perfect solution, are much more sensitive to the currents than the scattered fields. The SPEX solution, which uses fewer unknowns and less computer time than NEC, also produces a lower internal field. The SPEX technique also allows a direct check on satisfaction of the boundary condition at any set of points on the surface, independent of the points used to obtain the solution. This provides a valuable built-in test feature for quickly validating results, which is one of the most attractive features of the technique.     

An integral equation method for the evaluation of conductor anddielectric losses in high-frequency interconnects

An integral equation method is developed to solve for the complex propagation constant in multilayer planar structures with an arbitrary number of strip conductors on different levels. Both dielectric losses in the substrate layers and conductor losses in the strips and ground plane are considered. The Green's function included in the integral equation is derived by using a generalized impedance boundary formulation. The microstrip ohmic losses are evaluated by using an equivalent frequency-dependent impedance surface which is derived by solving for the fields inside the conductors. This impedance surface replaces the conducting strips and takes into account the thickness and skin effect of the strips at high frequencies. The effects of various parameters such as frequency, thickness of the lines, and substrate surface roughness on the complex propagation constant are investigated. Results are presented for single strips, coupled lines, and two-level interconnects. Good agreement with data available in the literature is shown     

Extended boundary condition integral equations for perfectly conducting and dielectric bodies: Formulation and uniqueness

The equivalence theorem is used to derive novel generalized boundary condition (GBC) integral equations for the tangential components of the electric and magnetic fields on the interfaces of a finite number of dielectric or conducting scatterers. Closed surface, plane, and line extended boundary conditions (EBC) equivalent to the GBC are introduced. The GBC integral equations can now be replaced by any of these EBC integral equations whose solutions are unique and easy to obtain numerically using the moment method. A perfectly conducting sphere and a dielectric sphere in the electrostatic field of two equal and opposite point charges are presented as simple examples of the general procedure.     

Implementation of anisotropic PML for frequency domain FEM solution of discontinuity in dielectric waveguide

The anisotropic Perfectly Matched Layer(PML) absorbing boundary condition is implemented in a 2-D finite element formulation to solve dielectric waveguide discontinuity problems. The choice of parameters of anisotropic PML has been investigated. Using the boundary truncating technique, the solution process of Finite-Element Method (FEM) has been greatly simplified compared with other hybrid methods. The required computational resources have also significantly declined since the anisotropic PML interface can be placed much closer to the scatterer compared to other well known artificial boundary.     

Integral equation formulation for inhomogeneous anisotropic mediaGreen's dyad with application to microstrip transmission linepropagation and leakage

A straightforward numerical technique based on the equivalence principle is presented to determine the complete spectral Green's dyad for inhomogeneous anisotropic media. This method is relevant to guided-wave problems where propagation characteristics are desired in the axial transform domain. Spectral Green's components are determined from a one-dimensional polarization-type integral equation. This method is very simple and versatile, and can be used to model continuously varying or stratified dielectric media with permittivity dyads of the most general form. As an application, a microstrip transmission line residing on a generally orientated uniaxial and biaxial substrate is considered, and new results for higher-order mode leakage are presented     

Full-wave boundary integral equation method for suspended planartransmission lines with pedestals and finite metallizationthickness

A boundary integral equation method is proposed for the full-wave analysis of suspended planar transmission lines with pedestals and/or finite metallization thickness. Coupled boundary integral equations are formulated on equivalent magnetic currents only on the apertures of subregions using the Green's identity of the second kind. Because it is possible to take a large number of terms in the series expansion of Green's functions in each subregion independently from the order of resulting matrices, this approach can avoid the relative convergence problem. Numerical results for suspended coplanar waveguides are found to have a stable convergence property and to be in excellent agreement with other available theoretical results. Numerical data reveal the effects of conductor thickness and aperture width on the transmission properties of suspended planar transmission lines with pedestals     

导体-介质组合体散射分析两种积分方程法比较

采用耦合积分方程和单积分方程两种方法,分析了三维导体-介质组合体目标的电磁散射问题.与传统的耦合积分方程法相比,单积分方程法使介质体表面的未知量数目减少一半,并且能获得更快的迭代解.讨论了导体-介质交界线上RWG基函数的正确处理问题.对介质锥-导体柱组合体、导体-介质组合球和某导弹模型的雷达截面(RCS)进行了计算和比较,验证了两种积分方程方法的正确性,且数值结果表明单积分方程法更加有效.     

Resonant solutions involved in the integral equation approach to scattering from conducting and dielectric cylinders

Resonant solutions involved in the integral equation formulation for analyzing the scattering problems and the elimination of these erroneous solutions are investigated. The parameter ranges where the resonant solutions are mixed into the correct ones and the degree of errors caused by the resonant solutions are checked on through numerical computation of matrix condition numbers and scattering cross sections for dielectric cylinders of square cross section with side width/wavelength ratio being less than about 1.27. As a method of removing the resonant solutions, the method taking some lower order equations of the so-called "extended boundary condition (EBC) method" into consideration is proposed.     

多层鳍线本征模的精确有效和完备求解

对多层鳍线现有的奇异积分方程法进行了如下改进：１）适当选择导体带所在平面切向电场和表面电流的线性组合,以使得导出奇异积分方程的级数具有很快的收敛特性;２）对于附加的边界条件,利用其级数的渐近特性来加速其收敛;３）给出系统计算任意阶特征矩阵元素的解析方法,以避免数值积分或对无穷级数求和;４）为完备地求解本征模的传播常数,构造了一个解析函数,保留特征矩阵行列式的所有零点,但消除其所有奇点．采用本文的奇异积分方程法,首次精确有效完备地求解了鳍线中的大量本征模．     

Accurate and efficient computation of dielectric losses inmulti-level, multi-conductor microstrip for CAD applications

An approach to accurate and efficient computation of dielectric losses in complex microstrip structures is proposed. It can be used in lieu of lossy, full-wave solutions to provide accurate and efficient data for the CAD of multilevel, multiconductor MIC and MMIC structures. Results that are as accurate as lossy full-wave techniques over a wide range of frequencies, including the dispersive region, are obtained. In addition to providing accurate results, the method is up to three times faster, depending on the number and type of substrates or superstrates. Results for various multiconductor, multilevel structures that compare well with the lossy, full-wave approach and require significantly less computer time to compute are shown