Surface integral formulation for calculating conductor anddielectric losses of various transmission structures

The power-loss method, along with a surface integral formulation, has been used to compute the attenuation constant in microstrip and coplanar structures. This method can be used for the analysis of both open and closed structures. Using the surface equivalence principle, the waveguide walls are replaced by equivalent electric surface currents and dielectric surfaces are replaced by equivalent electric and magnetic surface currents. Enforcing the appropriate boundary condition, and E-field integral equation (EFIE) is developed for these currents. Method of moments with pulse expansion and point matching testing procedure is used to transform the integral equation into a matrix one. The relationship between the propagation constant and frequency is found from the minimum eigenvalue of the moment matrix. The eigenvector pertaining to the minimum eigenvalue gives the unknown electric and magnetic surface currents     

Conductor loss in hollow waveguides using surface integralformulation

The power-loss method along with a surface integral formulation is used to compute the attenuation constant in hollow waveguides of arbitrary cross-section. An E-field integral equation is developed for the surface electric currents which is transformed into a matrix equation using the method of moments. An iterative technique, i.e. Muller's method, is used to obtain the relation between the propagation constant and frequency. The attenuation constants have been calculated and formulated for various waveguides and are in good agreement with published data     

Full vectorial finite-element-based imaginary distance beampropagation solution of complex modes in optical waveguides

In this paper, we address accurate computation of complex propagation constants and field distributions of different modes, in general, lossless and lossy optical dielectric waveguides. Using the vector finite-element formulation of the beam propagation method combined with the imaginary distance propagation technique, sequence of both the guided and leaky modes can be accurately calculated. To show the versatility and numerical precision of the proposed technique, we compute the modes of three different three-dimensional (3-D) waveguide structures and compare the results against those of other, different, vector formulations. Further, we present the design of a higher order mode filtering device, based on a 3-D leaky mode optical waveguide     

An integral equation analysis of an infinite array of rectangulardielectric waveguides

An integral equation analysis is applied to the study of the propagation characteristics of an infinite array of dielectric waveguides. The geometry under study is assumed to be rectangular. To find the Green's function of the structure, the Floquet theorem is applied such that the mutual coupling between dielectric waveguide elements is effectively included in the analysis. The effect of the coupling on the propagation characteristics of a dielectric waveguide is studied by varying the size of the Floquet cell. The validity of this analysis to simulate the case of an open dielectric waveguide is confirmed by a comparison with previous results, this in spite of the fact that radiation and leaky wave modes are not accounted for. The complex modes due to the periodicity of the structure are found and their properties are described. The analysis presented, with minor modification, can deal with the problems of dielectric image lines, or dielectric-loaded metallic waveguides     

An Exact Calculation for a T-Junction of Rectangular Waveguides Having Arbitrary Cross Sections

An exact method is developed for the calculation of the electrical performance of the rectangular waveguide T-junction. This method is used to find the equivalent circuit of a rectangular waveguide T-junction in which both cross-sectional dimensions of the side waveguide are different from the cross-sectional dimensions of the through waveguide. The theoretical calculations for a particular T-junction of this type are verified by experimental measurements. In this method the electrical performance is analyzed by using equivalent-circuit concepts applied to waveguide modes to calculate an admittance matrix relating propagating and cutoff waveguide modes to each other. Then the cutoff modes are terminated in their characteristic impedance, and an equivalent admittance matrix of the junction is found relating only the propagating modes in each waveguide to each other. The anlysis is valid when any number of modes can propogate in the waveguides forming the junction. The Inversion of an infinite matrix is required; however, any desired accuracy can be obtained by considering a matrix of finite but sufficient size or equivalently by considering a sufficient number of cutoff modes.     

Numerical solution of integral equations for dielectric objects ofprismatic shapes

A numerical method to investigate scattering from dielectric geometries of prismatic shapes has been developed. The surface integral equations are formulated by Schelkunoff's equivalence principle in terms of equivalent surface electric and magnetic currents. To solve these integral equations for the unknown currents, the object's cross-section is mapped onto a circle. In the transformed space, Fourier type entire-domain basis functions are used in the cross section and triangular subdomain basis functions are selected along the generating curve to represent the currents. A moment method is then used to reduce the integral equations to a matrix equation to compute the current coefficients. It is found that the transformation of the object's surface to a circular shape improves the convergence of the current mode in the cross-section. However, the current modes are coupled on the surface and the matrix equation includes all the modes     

Impedance boundary method of moments for accurate and efficientanalysis of planar graded-index optical waveguides

An impedance boundary method of moments (IBMOM) is proposed to accurately and efficiently compute the propagation characteristics including the number of guided modes of general graded-index dielectric slab waveguide structures. The method is based on Galerkin's procedure in the method of moments and employs the exact impedance boundary condition at the interfaces between the graded-index region and constant-index cladding. Legendre polynomials are utilized in the field expansion. Computational results are shown for waveguides with various inhomogeneous refractive index profiles. The results indicate that typically five Legendre polynomials are sufficient for accurate solutions of the dominant TE and TM modes in optical waveguides having a finite region of inhomogeneous refractive index. Diffused optical waveguides with untruncated index profiles as well as coupled dielectric waveguides can be accurately analyzed using ten Legendre polynomials     

条形介质加载型表面等离子体波导传输特性的研究

采用二维时域有限差分(FDTD)法,分析对比了 介质-金属(IM)结构和金属-介质-金属(MIM) 结构波导对光波传输特性的影响,以及通过对IM结构的尺寸、折射率进行优化得到最佳传 输长度。数值 结果表明,IM结构波导能使光波传输距离更长。对IM波导结构研究发现,当介质层厚为 300nm,金属 层厚为200nm时,传输效果最佳。基于这个参数的IM结构,计算介质 层折射率对IM波导光传输特性的影响发现,介质层折射率为1.5时, 在模场约束较好的情况下,传输损耗降低,表面等离 子体波的传输长度最长。整体优化后的条型波导可以实现最大传输距离为37μm。这一设计和优化波导结构 参数的方法不仅拓宽了介质加载型表面等离子体激元(SPP)波导结构的理论基础,在纳米光 学集成器件研究上也具有一定的应用潜能。     

Waves and Evanescent Fields in Rectangular Waveguides Filled with a Transversely Inhomogeneous Dielectric

A numerical-calculation method for rectangular waveguides containing a transversely inhomogeneous dielectric is presented. The method is not restricted to the cutoff case or to special inhomogeneities. The relative permittivity of the dielectric can be an arbitrary function of the cross-sectional coordinates. The electric-and magnetic-field strengths, the dispersion characteristics of the propagating modes, and the attenuation constants of the evanescent modes result from the solution of a matrix eigenvalue problem with typically 8000 matrix elements. Propagating and evanescent modes in a waveguide containing a longitudinal semicircular dielectric rod are calculated as examples. The accuracy of the calculation method is confirmed by measurements and by calculating a special example with an exactly known solution. The error of the field intensities is typically 5 percent; the error of the dispersion characteristics and of the attenuation constants is typically 0.5 percent.     

Multilayer waveguides: efficient numerical analysis of generalstructures

An efficient numerical method for accurately determining the real and/or complex propagation constants of guided modes and leaky waves in general multilayer waveguides is presented. The method is applicable to any lossless and/or lossy (dielectric, semiconductor, metallic) waveguide structure. The method is based on the argument principle theorem and is capable of extracting all of the zeros of any analytic function in the complex plane. It is applied to solving the multilayer waveguide dispersion equation derived from the well known thin-film transfer matrix theory. Excellent agreement is found with seven previously published results and with results from two limiting cases where the propagating constants can be obtained analytically     

Equivalent network approach for multistep discontinuities inelectron waveguides

An analysis method is described for multistep discontinuities in electron waveguides composed of semiconductor heterostructures. The method is based on a rigorous mode-matching procedure that takes into account the effects of external finite potential and spatially varying effective mass. Stress is placed on network representations to establish physical pictures of the quantum effects and to yield insight; in addition, a systematic microwave network approach is employed. The equivalent network representation is given for the waveguide modes propagating normally to the step discontinuity, and the mode-matching procedure is described for the boundary-value problem of the step discontinuity. Combining the above two procedures, the super-cascade matrix formulation is carried out, from which the reflection and transmission characteristics of multistep discontinuities in electron waveguides can be estimated. In order to show the validity and usefulness of this approach, examples are computed for constriction structures composed of three-layered electron waveguides     

任意块状介质填充矩形波导色散特性的数值分析

本文给出了一个用有限元法计算任意块状介质填充矩形波导的孪生波主模和高次模色散特性的标准程序。使用该程序,对十余种不同结构、不同介质加载矩形波导色散特性的计算,证实了所述程序的可靠性,文中对工字形介质填充波导的有用带宽作了详细的分析。本文所提供的各种色散特性曲线可供分析和设计有关微波元件时参考。     

A novel design and analysis of low loss abrupt bends of dielectricslab waveguides

On the basis of the well-known laws of reflection and refraction of the plane electromagnetic waves, a concept for designing very low loss nonadiabatic junctions between tilted straight sections of dielectric waveguides is investigated. Combining the ray representation of the propagating modes with the equivalent source formulation of the dielectric waveguide excitation problem, a simple and accurate 2-D theory for treating such bends in slab waveguides is developed. Numerical results for typical cases are explained along with some new junctions for achieving large angle redirection of guided waves with very low bending loss     

硅包层质子交换条形光波导的频率响应

退火质子交换工艺已成为一种制备低损耗铌酸锂光波导的重要技术.但目前对该类光波导传输特性的研究还不多.利用半矢量光束传播法,对硅包层X切退火质子交换铌酸锂条形光波导的频率响应特性进行了数值分析.给出了几种波导结构参数下的计算结果.结果表明,波导传输模式的衰减特性与波长相关.波导的衰减特性,可以通过调整波导表面中心处折射率增量,硅包层厚度,及缓冲层的折射率和厚度来控制.硅包层光波导可以用来制作光频滤波器.     

Full vectorial finite-element solution of nonlinear bistable optical waveguides

The accurate computation of the propagation constants and field distributions of different modes in nonlinear optical dielectric waveguides is addressed in this paper. Using the vector finite-element formulation of the beam propagation method, combined with the imaginary distance propagation technique, both linear and nonlinear modes can be accurately calculated. The proposed technique is applied to obtain the fundamental TE nonlinear mode of a strip-loaded waveguide, and the excellent agreement seen with published results shows its high numerical precision.     

Analysis of leaky modes by a modified finite-element method

The finite-element method with integral boundary conditions is used to investigate leaky modes (quasi-eigenmodes) of open dielectric waveguides. Dispersion characteristics and field distributions in double-layer and multilayer circular waveguides are calculated. The influence of uniform deformations of the waveguide cross section on the properties of these modes is studied.     

Broadside coupled strip inset dielectric guide and its directionalcoupler application

A theoretical and numerical method is presented for the analysis of broadside-coupled strip inset dielectric guide. The method of analysis is based on an integral equation formulation and Galerkin's procedure. Besides propagation constants for two fundamental and higher order modes, the characteristic impedances for the two fundamental modes are calculated using the total propagating power and the longitudinal strip currents. The propagation characteristics of the two fundamental modes are then used to compute 4-port circuit parameters that are essential for accurate analysis and design of coupled line circuits. The effects of various structural parameters on the S-parameters are investigated and it is found that this broadside coupled strip IDG structure is useful for the realization of the directional couplers. Examples of strong and weak directional couplers are given. Furthermore, the propagation constants and S-parameters of coaxially excited coupled strips are measured, and are in good agreement with the theoretical analysis     

A Combined Method for Dielectric Waveguides Using the Finite-Element Technique and the Surface Integral Equations Method

A combined method employing a finite-element technique in the H/sub x/ - H/sub y/ formulation and the surface integral equations method is proposed to treat the propagation characteristics of inhomogeneous waveguides with single or multiple claddings. The significant features of this combined method are that it does not suffer from any kind of spurious modes, which have been troublesome in applying the finite-element technique to waveguides and it is also capable of treating the cutoff frequencies of arbitrarily shaped, inhomogeneous dielectric waveguides with a single cladding, which is perhaps original. Furthermore, the proposed method is convenient in treating propagation constants close to cutoff and in handling coupled waveguides. Numerical results of inhomogeneous elliptical waveguides, diffusion waveguides, and the corresponding directional couplers are presented, including the cutoff frequencies of the elliptical waveguides.     

Full-Wave Modal Analysis of Slow-Wave Periodic Structures Loaded With Elliptical Waveguides

In this paper, a novel full-wave method for the modal characterization of periodic structures loaded with elliptical waveguides is presented. This method relies on an integral equation formulation solved via the method of moments, which finally leads to the solution of a standard eigenvalue problem. The required modal spectrum of elliptical waveguides is determined through the boundary integral-resonant mode expansion technique. For validation purposes, the proposed analysis method is first successfully applied to periodic waveguide structures already considered in the technical literature. Then, our new algorithm is used to compute the related Brillouin diagrams and the interaction impedance of new periodic structures loaded with elliptical waveguides. Not only the main interacting mode (such as the $TM_{01}$ mode) is studied, but higher-order Floquet modes are also considered. These results have potential applications as slow-wave structures for high-power microwave devices and possibly filtering structures at millimeter-wave frequencies.      

非线性平板介质波导传输特性的网络分析

本文提出了分析包含非线性介质的层状介质波导特性的等效传输线方法。通过把线性和非线性介质分别用等效传输线表示,从而把非线性介质这一复杂的电磁场问题等价成一个电路问题求解。其本征方程可以利用横向谐振原理得到。本文最后分析了层状介质波导包含饱和和非饱和非线性介质时TE模的传播功率与归一化传播常数之间的关系。所获得的结果与有关文献符合得相当好。