The use of FDTD for the analysis of magnetoplasma channelwaveguides

The finite-difference time-domain (FDTD) method is used for the analysis of magnetoplasma rectangular channel waveguides. Single and parallel-coupled waveguides are considered. The effect of varying the amplitude and the orientation of the bias magnetic field B₀ on the dispersion characteristics of the first modes is examined. However, the FDTD formulation, does not excite evanescent modes for a sufficiently long time interval, particularly when in the presence of the propagating or dynamic modes. As a result, the nonreciprocal properties of these structures, primarily associated with the evanescent modes, could not be investigated     

Modification of Marcatili's method for the calculation ofanisotropic rectangular dielectric waveguides

Mareatili's method for the calculation of rectangular dielectric rod waveguides has been modified for uniaxial anisotropic dielectric materials. The averaging method without guessing the field distribution has been used to derive the equations. Experimental results for an anisotropic sapphire waveguide show a good agreement with those calculated using the approach developed here     

A variational vector finite difference analysis for dielectricwaveguides

A numerical technique based on the finite difference method is developed for the analysis of lossless dielectric waveguides. This method is a variational approach which uses all three components of the magnetic field vector, allowing for the enforcement of the divergence condition. The dispersion characteristics and field distributions for dielectric waveguides are accurately computed. Comparisons are made between the magnetic vectorial finite difference method and a finite element method incorporating the same functional     

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.     

部分填充电各向异性介质波导的直线法

文本引用直线法,分析了一般的部分填充电各向异性介质的波导的色散特性。波动方程仅在一个方向上进行离散化,这样就产生了微分——差分方程,可以解析求解。并推导出了一般的色散特性方程。最后,为了证实本方法的有效性,对各向同性介质波导进行了计算并与精确解进行了比较,结果极为一致。同时,对部分填充电各向异性介质波导进行了计算。     

Characteristics of waveguides filled with homogenous lossy anisotropic drifting plasma†

In this paper the dispersion relation for rectangular waveguides filled with homogeneous lossy drifting plasma under the influence of infinite longitudinal magnetic field is derived and discussed. The properties of TE modes are found to be the same as those of air-filled guides. However, uniaxial anisotropic drifting lossy plasma has a significant effect on the propagation characteristics of TM modes. A comparison of the effects and physical significance of the changes due to isotropic and anisotropic plasma models is discussed.     

Finite-element solution of anisotropic waveguides with arbitrary tensor permittivity

An improved vector finite-element method has been used for the solution of general anisotropic waveguide problems. This method is formulated in terms of all three components of the magnetic field and is valid for arbitrary tensor permittivity. In the improved finite-element analysis, the spurious nonphysical solutions do not appear when the effective refractive index is larger than 1. Therefore, this method is very useful for the analysis of the surface-wave modes of optical waveguides. To show the validity and usefulness of the improved finite-element method, computed results are illustrated for anisotropic rectangular waveguides with optic axis in any orientation and gyrotropic rectangular waveguides.     

An efficient high-order mixed-edge rectangular-element method forlossy anisotropic dielectric waveguides

A new efficient high-order mixed-edge rectangular element method is proposed for the analysis of lossy anisotropic dielectric waveguides. The space construction of the high-order mixed-edge rectangular element is investigated and the explicit form of the shape function is given. The high-order mixed-edge element yields higher accuracy and faster convergence than the lowest order mixed-edge rectangular elements without spurious solutions, and is more efficient compared to the high-order covariant projection element. The computations of the propagation constants in the rectangular waveguide and the slab loaded waveguide show that the accuracy of this high-order mixed-edge element is about one order higher than that of the lowest order one, and the nodes used in the calculation are only two-thirds as many as those used in the high-order covariant projection element having the same accuracy. The calculations of the dispersion curves for the dominant mode in the waveguide loaded with the lossy anisotropic dielectric block verify the accuracy and efficiency of the present method     

Full vectorial finite element formalism for lossy anisotropicwaveguides

An efficient computer-aided solution procedure based on the finite-element method is developed for solving general waveguiding structures containing lossy, anisotropic materials. In this procedure a formulation in terms of the transverse magnetic field component is adopted and the eigenvalue of the final matrix equation corresponds to the propagation constant itself. Thus one avoids the unnecessary iterations which arise when using complex frequencies. To demonstrate the strength of the presented method, numerical results are shown for a rectangular waveguide filled with lossy anisotropic dielectric with off-diagonal elements in a permittivity tensor and compared with those obtained by the telegrapher equation method. The results are in excellent agreement both for phase and for attenuation     

Transversely anisotropic curved optical fibers: variationalanalysis of a nonstandard eigenproblem

A novel variational functional is introduced for the analysis of curved open and closed waveguides. The theory is based on the variational principle for nonstandard eigenvalue problems. The present method is valid for the arbitrary waveguide cross section and arbitrary radius of curvature for closed waveguides; for open guides, the radius should be sufficiently large, because the method predicts the real part of the propagation constant, not the imaginary part, which gives the attenuation in curved open structures. The dielectric medium can be homogeneous or nonhomogeneous with transverse and/or longitudinal anisotropy. As an example of the method, curved isotropic and anisotropic single-mode fibers with two different kinds of anisotropy models are studied. The analysis includes field distributions, changes in the dispersion curves due to reformed geometry, and birefringence characteristics in curved anisotropic fibres     

Improved Finite-Element Formulation in Terms of the Magnetic Field Vector for Dielectric Waveguides

An improved finite-element method for the analysis of dielectric waveguides is formulated in terms of all three components of the magnetic field H. In this approach, the spurious, nonphysical solutions do not appear anywhere above the "air-line," and therefore the present formulation is very useful for the analysis of the surface-wave modes of dielectric waveguides. The application of this improved finite-element method to the dielectric waveguides with perfect electric and magnetic conductors is also discussed. In particular, the discussion is how to use the conditions on a boundary surface of a perfect electric or magnetic conductor whose normal direction is not coincident with the direction of a coordinate axis. Application of these boundary conditions for perfect conductors to the dielectric waveguides with planes of symmetry reduces the matrix size. The strength of this approach to boundary conditions is not just the economical use of computer memory but the elimination of spurious solutions through rigorous enforcement of boundary conditions as well.     

Vectorial wave analysis of dielectric waveguides for optical-integrated circuits using equivalent network approach

A vectorial wave analysis of the propagation characteristics of open dielectric waveguides for optical-integrated circuits using an equivalent network approach is presented. In this approach, all of the contributions from the discrete and continuous parts of the spectrum and from the TE-TM coupling, which are neglected in the earlier equivalent network approach, are taken into account. To show the validity and usefulness of this formulation, examples are computed for optical strip waveguides, rib waveguides, rectangular dielectric waveguides, embossed waveguides, and embedded waveguides.     

Covariant-projection quadrilateral elements for the analysis ofwaveguides with sharp edges

Covariant-projection elements are shown to be a good way of finding the dispersion characteristics of arbitrarily shaped waveguides. They have been demonstrated to produce no spurious modes, and because only tangential continuity is imposed between elements, either the electric field or the magnetic field may be calculated in the presence of dielectric and magnetic materials. Waveguides with sharp metal edges may be analyzed more efficiently than with other methods. Results are presented for a rectangular waveguide half loaded with dielectric, a double-ridged waveguide, a shielded microstrip line, and coupled microstrip lines on a cylindrical substrate. The matrices generated are sparse. and the number of zero eigenvalues produced is predictable. It therefore seems likely that the algebraic problem can be solved by sparse techniques, which would make the method applicable to even more complicated geometries at a modest computational cost     

New Waveguide Structures for Millimeter-Wave and Optical Integrated Circuits

Some new dielectric waveguide structures suitable for millimeter-wave and optical integrated circuits are presented. A method of analyzing wave propagation in these guides is developed by assuming simple field distribution and approximating the various regions of the guides in terms of effective dielectric constants. The mathematical formulation utilized results in simple eigenvalue equations from which the dispersion characteristics of the waveguides are readily obtained. Experimental results are described and the agreement between theory and experiment is shown to be quite good.     

非均匀介质填充波导本征值问题的有限元分析

本文讨论了用有限元法求解非均匀介质填充波导本征值问题的具体过程。给出了有关的计算公式和程序。作为例子,对条形介质填充矩形波导主模场结构的分析和色散特性的计算,获得了与解析解十分一致的结果,从而证实了所述程序的可靠性。     

A scalar variational conformal mapping technique for weakly guiding dielectric waveguides

A novel approach of combining the finite-element method with the conformal mapping technique is proposed for solving the scalar variational formulas for weakly guiding dielectric waveguides. This approach avoids spurious modes and gives satisfactory results even for modes near cutoff, requiring less computer memory and time. Various specific dielectric structures, such as the rectangular guide, channel guide, and rib guide, are considered to estimate the error associated with the scalar formulation relative to the vectorial formulation. The efficiency of this approach is demonstrated with an analysis of a directional coupler whose coupling properties are described by means of numerical results such as propagation constants, field distributions, etc.     

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.     

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 arbitrary number of layers is solved by the microwave network method. A general program with the function of computer graphics has been developed for analyzing the dispersion characteristics and the electromagnetic field distributions of an N layer dielectric waveguide. As examples of practical applications of the program, first, the dispersions and field patterns for the planar waveguides with refractive index of parabolic and exponential profiles are analyzed. Secondly, the procedure of mode conversion and mode separation in dielectric branching waveguides is vividly demonstrated through analyzing the field distributions of asymmetric multilayer dielectric structures and the general rules of mode conversion are discussed. The examples show that the present method possesses the advantages of versatility, rapidity, simplicity and accuracy.     

A scalar variational analysis of rectangular dielectric waveguidesusing Hermite-Gaussian modal approximations

A scalar variational analysis of rectangular dielectric waveguides using Hermite-Gaussian modal approximations is presented. The technique analyzes waveguides by finding a closed-form, approximate solution to the given problem. We begin with an assumed, closed-form field solution, with unknown parameters which can be chosen to best match the assumed field to the actual field solution using variational principles. The values of the unknown parameters of the assumed field are determined by solving a set of simultaneous equations, not by a search method. As a result, this analysis method is computationally fast. Another benefit is that this method gives best-fit, closed-form modal approximations