NETWORK ANALYSIS OF EIGENVALUE PROBLEM FOR MULTILAYER DIELECTRIC WAVEGUIDE CONSISTING OF ARBITRARY NUMBER OF LAYERS

In this paper,the eigenvalue problem of a multilayer dielectric waveguide consisting of arbitrarynumber of layers is solved by the microwave network method.A general program with the function of com-puter graphics has been developed for analyzing the dispersion characteristics and the electromagnetic fielddistributions of an N layer dielectric waveguide.As an example of practical applications,the procedure ofmode conversion and mode separation in dielectric branching waveguides is vividly demonstrated throughanalyzing the field distributions of asymmetric multilayer dielectric structures and the general rules of modeconversion are discussed.     

任意多层介质波导本征值问题的网络分析

本文用微波网络的方法求解了任意多层介质波导的本征值问题;编制了一个分析N层介质波导色散特性和电磁场分布,并具有计算机图形功能的通用程序。通过对非对称多层介质波导场分布的实例分析,形象地说明了介质分支波导中模式转换和分裂的过程,并讨论了模式转换的一般规则。     

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.     

Numerical analysis of dispersion characteristics of rectangular waveguides filled with arbitrary block-shaped dielectrics

The dispersion characteristics of rectangular waveguides filled with arbitrary block-shaped dielectrics are calculated by the method of finite element. A generalized program is given for the hybrid dominant and higher order modes. More than ten different rectangular waveguides loaded with various dielectric distributions have been investigated, and the results verify the reliability of the program. In particular, the useful bandwidth of the waveguide filled with I-shaped dielectric is analyzed in detail. The dispersion curves given in this paper are useful for analyzing and designing related microwave components of current interest.     

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。     

A Method Extending the Boundary Condition for Analyzing Guided Modes of Dielectric Waveguides of Arbitrary Cross-Sectional Shape

A method based on the extended boundary condition method is presented for analyzing guided modes of dielectric waveguides of arbitrary cross-sectional shape. Numerical integration needed in this method is only over the boundary periphery line of the waveguide. Nevertheless, it is applicable to the waveguides with any refractive index difference between core and cladding ranging from negligibly small to considerably large difference, as well as to certain types of waveguide with inhomogeneous core. Approximate formulas for the case of weakly guiding are also derivable from the general basic set of equations presented. Numerical examples are given to verify the usefulness and accuracy of this method.     

Analysis of propagation characteristics of whispering gallery modes in a dielectric disk or a curved rectangular dielectric waveguide

The finite-element method is applied to the analysis of whispering gallery modes in curved optical waveguides. Numerical examples for whispering gallery modes in a dielectric disk with rough boundaries are given. It is demonstrated that the whispering gallery modes and the normal guided modes in a curved rectangular dielectric waveguide are analyzed consistently with this approach, and that the normal guided mode approaches the whispering gallery mode with the increase of waveguide width. The minimum width of the rectangular waveguide needed to support a whispering gallery mode is evaluated.<>     

Optical surface wave mode converters and modulators utilizing static strain-optic effects

Periodic perturbations of dielectric waveguides can be obtained by an evaporated SiO2thin film grating through the static strain-optic effect. These waveguides are applied to TE-TM mode converters and modulators in Ti-diffused LiNbO3waveguides. Using a coupling length of 3 mm in an optical surface waveguide, we have demonstrated a TE-TM mode conversion efficiency of 80 percent and a TE-TM mode modulator with 100 percent modulation with an applied field of 2 V/μm. A theoretical analysis of a reflector for a semiconductor laser waveguide is also described.     

Approximate Scalar Finite-Element Analysis of Anisotropic Optical Waveguides with Off-Diagonal Elements in a Permittivity Tensor

An approximate scalar finite-element program for the analysis of anisotropic optical waveguides having a permittivity tensor with nonzero off-diagonal elements is described. In this approach, the nonphysical spurious solutions which are included in the solutions of the earlier vectorial finite-element method in an axial-components formulation do not appear. Numericaf examples On an anisotropic dielectric rectangular wave-guide composed of a uniaxial medium are given. Our results for the waveguide whose optic axis lies in the plane ( xy-plane) normal to the direction (z-axis) of propagation agree well with the results of the vectorial wave analysis using the variational method. We also demonstrate the application of this approach by analyzing the anisotropic dielectric rectangular waveguide whose optic axis lies in the xz - or yz -plane.     

任意截面波导的模式截面场的数值分析

给出了任意截面波导的传输特性的时域差分（FDTD）数值方法的一般分析方法,首次提出了用数值方法建立任意截面波导中各模式横向场分量截面场分布的方法,为证明这种方法的有效性,计算了常用空气填充的Ka波段矩形波导中主模（H10模）和一次高阶模式H20模的截止波长和Ey场分量,其与理论值的安全一致性表明所提出的方法是正确的。作为应用例子给出了一种新型的五边形波导的最低四个模式的传播常数及主模式和第一高次模的电场在波导横截面的场分布图。     

Theory and Applications of Coupled Optical Waveguides Involving Anisotropic or Gyrotropic Materials

Coupled optical waveguides consisting of two isotropic dielectric slab waveguides coupled through anisotropic or gyrotropic materials inserted between them, are treated theoretically in detail. The properties of reciprocal and nonreciprocal TE-TM mode conversion and a nonreciprocal phase shift for TM modes are shown. As an example of application of this type of coupled waveguide, a nonreciprocal optical integrated circuit (IC) mode converter is proposed. It is shown that a circulator and an isolator which require neither mode separators nor mode filters can be constructed by utilizing the proposed nonreciprocal mode converter. The numerical design examples are also given.     

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     

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。     

Simulation of polarization converter formed by poling-inducedpolymer waveguides

A polarization converter using electrooptic (EO) polymer waveguides is proposed and it is simulated by a full vectorial beam propagation method (VBPM) for anisotropic medium. First, an efficient structure of poling electrodes is proposed for the fabrication of TE-mode poling-induced waveguides in EO polymer. For given electrode structures of both TE-mode and TM-mode waveguides, poling-induced dielectric tensors are calculated by the finite-element method to provide refractive index distribution, data for VBPM simulation. It is shown numerically that the poled TE and TM mode waveguides work efficiently as the corresponding polarization filters. Then, new poling electrodes are suggested to fabricate a waveguide device formed by connecting the TE and TM mode waveguides adiabatically with a slowly varying structure. This waveguide device has the optic axis slowly rotating as one moves along the propagation direction, so that it will act as polarization converter. VBPM simulation shows that the polarization of the guided mode rotates following the optic axis distribution. Polarization conversion is demonstrated successfully with high conversion efficiency and low excess loss     

Numerical Solution of Dielectric Loaded Waveguides: II---Modal Approximation Technique

A numerical method is described for the solution of the electromagnetic fields in dielectric loaded waveguides. The method uses the cutoff modes of the waveguide, obtained by finite-element analysis, to determine by matrix methods the fields above cutoff. A theoretical comparison with the conventional finite-element method is given and a general, highly efficient computer program for the analysis of dielectric loaded waveguides by the new method is described. Dispersion curves and contour plots obtained from the program are shown for several geometrical configurations, and these results are compared with analytic values and those obtained by the conventional finite-element method.     

Electromagnetic coupling of coplanar waveguides and microstriplines to highly lossy dielectric media

The spectral-domain technique is utilized to analyze the coupling characteristics of coplanar waveguides and microstrip lines coupled with multilayer lossy dielectric media. Numerical results illustrating the dispersion characteristics of coplanar and microstrip lines, as well as the various electric field components coupled to highly lossy dielectric media, are presented. It is shown that the presence of a superstrate of lossless dielectric between the coplanar waveguide and the lossy medium plays a key role in setting up an axial electric field component that facilitates leaky-wave-type coupling to the lossy medium. The thickness of the superstrate relative to the gap width in the coplanar waveguide is important in controlling the magnitude of this axial electric field component. The coupling characteristics of the microstrip and coplanar lines are compared, and results generally show improved coupling if coplanar waveguides are utilized. Values of the attenuation constant α are higher for coplanar waveguide than for microstrip line, and for both structures α decreases with frequency     

Coupling characteristics of two rectangular dielectric waveguides laid in different layers

The coupling characteristic of rectangular dielectric waveguides which lay in different, parallel layers and one waveguide crossed over the other one are studied. Step-like approximation and the variational method are used for calculating the coupling coefficient which varies with axial distancez. Electromagnetic field expression for the dielectric waveguide mode of rectangular cross section is newly introduced and used. Calculated coupling characteristics are compared with experimental results carried on 50 GHz band. The principle of crossed waveguides leads us to the new design concept of "multilayered integrated circuit."     

Finite-Difference Analysis of Rectangular Dielectric Waveguide Structures

A class of dielectric waveguide structures using a rectangular dielectric strip in conjunction with one or more layered dielectrics is analyzed with a finite-difference method formulated directly in terms of the wave equation for the transverse components of the magnetic field. This leads to an eigenvalue problem where the nonphysical, spurious modes do not appear. Moreover, the analysis inclndes hybrid-mode conversion effects, such as complex waves, at frequencies where the modes are not yet completely bound to the core of the highest dielectric constant, as well as at frequencies below cutoff. Dispersion characteristic examples are calculated for structures suitable for millimeter-wave and optical integrated circuits, such as dielectric image lines, shielded dielectric waveguides, insulated image guides, ridge guides, and inverted strip, channel, strip-slab, and indiffused inverted ridge guides. The numerical examples are verified by results available from other methods.     

The Method of Calculation of Open and Closed Waveguides,Which Is Based on the Modified Method of Discrete Sources

The problem of calculation of eigenmode characteristics is considered for 3D open dielectric waveguides and waveguides with the anisotropic impedance boundary condition. An efficient algorithm is proposed for finding eigenmodes of waveguides having different cross-sections. It is based on the solution of the auxiliary problem of diffraction of the field of a filamentous source located inside the waveguide. The method is tested using weakly directing dielectric waveguides having circular and elliptical sections and a waveguide with the two-sheeted section. The results of calculation of dielectric waveguides obtained with the help of the proposed method, the method of finite elements, and the method of the integral equation over the waveguide section are compared. The circular and elliptical waveguides and the waveguide having a two-sheeted section with an anisotropic impedance are also investigated. The calculation results are compared with the results obtained with the use of the method of separation of variables and the Galerkin method.     

An efficient full-vectorial finite-element modal analysis ofdielectric waveguides incorporating inhomogeneous elements acrossdielectric discontinuities

A new vectorial finite-element method (FEM) free of spurious modes is proposed for analyzing optical waveguides with sharp corners in the cross section. The method is formulated in terms of the transverse field components H_x and H_y or E_x and E_y , and it explicitly shows the relationships between the semivectorial and the full-vectorial wave equations. In this method, we introduce the distribution concept and an inhomogeneous element to describe the field across the dielectric interface, and the error in the numerical solution caused by the dielectric discontinuity is reduced. We show how the width of such inhomogeneous elements and the number of nodes would affect the numerical result and its convergent rate using the dielectric-loaded rectangular waveguide, the channel waveguide, and the rib waveguide as analysis examples. For the dielectric-loaded rectangular waveguide, we compare our results with the exact solutions. For the rib waveguide, we compare our results with previously published data based on other methods. Also, field convergence near the corners is discussed