Finite element analysis of lossy dielectric waveguides

This paper presents a full-wave analysis of lossy dielectric waveguides using a hybrid vector finite element method. To avoid the occurrences of spurious modes in the formulation, edge elements and first-order nodal finite element basis functions are used to span the transverse and the z components of the electric field, respectively. Furthermore, the direct matrix solution technique with minimum degree of reordering has been combined with the modified Lanczos algorithm to solve for the resultant sparse generalized eigenmatrix equation efficiently     

Full-wave high-order FEM model for lossy anisotropic waveguides

Anisotropic lossy waveguides are analyzed by applying the finite-element method with higher order interpolatory vector elements. The problem is formulated in terms of the electric field only. The transverse vector component of the electric field is numerically represented by higher order curl-conforming interpolatory vector functions, whereas the longitudinal component of the field is represented by higher order scalar basis functions. Due to the better interpolatory capabilities of the expansion functions, the metallic and material losses are modeled with a higher precision with respect to that provided by the other available numerical models. Furthermore, the use of higher order elements permits the correct modeling of the discontinuity of the normal field component at the interfaces between different materials     

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     

Coupled-mode analysis of anisotropic dielectric planar branching waveguides

We present a theoretical study of mode propagation in anisotropic planar branching waveguides consisting of isotropic and anisotropic layers. The characteristic equation of anisotropic five-layered structure is introduced to calculate the propagation constants and field patterns of the branching-waveguide modes. Coupled-mode analysis shows that the normalized parameter is effective for the evaluation of mode-coupling effects in the anisotropie branching waveguides as well as in the isotropic branching waveguides.     

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     

The method of lines for the analysis of lossy planar waveguides

The method of lines is extended to calculate the losses of waveguide structures. Ohmic losses in metallizations (with frequency-dependent, extremely high dielectric constants) and dielectric losses are simultaneously considered. Despite the high ratios of the dielectric constants of the metallizations and the dielectrics, the analysis and numerical treatment are carried out accurately. Using nonequidistant discretizations the results are computed efficiently, and an approximate value of the propagation constant close to the exact value is found by extrapolation. The phase constant deviates less than 0.5%. The attenuation may deviate up to 2%. The advantages of the method of lines are a small computation time and, due to the analytical solutions of the fields in one direction, a very good approach to the fields inside the strip as well as to the strong fields directly adjacent at the edges. The results for a single microstrip line are shown and compared with those of other authors     

Dispersion characteristics of asymmetric coupled anisotropic dielectric waveguides using FDFD

The formulation is developed in the frequency domain and the finite difference method is used for the numerical solution of the scalar wave equation, written in terms of the transverse components of the magnetic field. As a result a conventional eigenvalue problem is obtained without the presence of spurious modes due to the implicit inclusion of the divergence of the magnetic field equal to zero. The formulation is developed to include biaxial anisotropic dielectrics with an index profile varying arbitrarily in the cross section of the waveguide under analysis. This formulation is then applied to the analysis of the influence on the dispersion characteristics of the dimensions of asymmetric coupled rectangular uniaxial anisotropic dielectric waveguides. As expected, the reduction of the height or the width of one of the rectangular dielectric waveguides causes the dispersion curves to move towards higher frequencies.     

Circular waveguides with anisotropic walls

First, the wave propagation in circular waveguides with the boundary condition E? = H? = 0 is investigated, and the use of these guides for producing circularly polarised waves is described. Secondly, a similar investigation is made for corrugated guides. Their propagation characteristics are compared.     

Multiple scattering among vias in lossy planar waveguides using SMCG method

Large-scale full-wave multiple scattering among cylindrical vias in planar waveguides is modeled using the Foldy-Lax equation. The formulation includes the skin effects of the conducting power/ground plane. Numerical solution of the Foldy-Lax equation with large number of unknowns is computed efficiently using the sparse-matrix canonical-grid method. In this method, interactions among vias are decomposed into the strong interactions part and the weak interactions part. The calculation of the weak part is carried out using two-dimensional (2-D)-fast Fourier transform (FFT) by translating the locations of the vias onto the uniform grids. The final solution of the Foldy-Lax equations is calculated by an iterative method. The results show O (N log N) CPU efficiency and O (N) memory efficiency. This makes large scale via problems possible for computer simulation.     

A full-vectorial beam propagation method for anisotropic waveguides

An extension of the full-vectorial beam propagation method to anisotropic media is presented. Optical waveguides made of anisotropic materials can be modeled and simulated. The polarization dependence and coupling due to both the material and the geometric effects are considered     

Finite element formulation for lossy waveguides

An efficient computer-aided solution procedure based on the finite-element method is developed for solving general waveguiding structures composed of lossy materials. In this procedure, a formulation in terms of the transverse magnetic-field components is adopted and the eigenvalue of the final matrix equation corresponds to the propagation constant itself. Thus, it is possible to avoid the unnecessary iteration using complex frequencies. To demonstrate the strength of the presented method, numerical results for a rectangular waveguide filled with lossy dielectric are presented and compared with exact solutions. As more advanced applications of the presented method, a shielded image line composed of a lossy anisotropic material and a lossy dielectric-loaded waveguide with impedance walls are analyzed and evaluated     

New approach to lossy optical waveguides

We review a method we recently developed to construct Green's function in the paraxial approximation associated with arbitrary graded-index optical elements. We then demonstrate that our formalism may be successfully applied to calculate in an extremely simple fashion the optical losses associated with bent and perturbed optical waveguides.     

Perturbation feedback method for analysing rectangular dielectric waveguides

A simple and accurate method for analysing rectangular dielectric waveguides is proposed. By virtue of a successive perturbation process, propagation constants and field distributions can be calculated with greater accuracy than other approximate approaches.<>     

A modified ray-optic method for arbitrary dielectric waveguides

A modified ray-optic method (MRO) is proposed for evaluating the propagation characteristics of dielectric waveguides with arbitrary refractive index profile. The authors correct the error caused by assuming a constant phase shift for any mode at the turning point on the substrate side. Very simple formulas are given for calculating the dispersion characteristics including those for planar optical waveguides and single-mode fibers. The results are more accurate than those of the ordinary ray-optic method, especially in the near cutoff regions, and agree well with those of the exact numerical methods. A comparison with other analytical and the exact numerical methods shows that the proposed method is simpler than other methods. This method can be extended to other more complicated cases     

Computing the eigenmodes of lossy field-induced optical waveguides

Slab waveguides which achieve lateral confinement in the guiding region by applying a spatially selective electric field across a multiquantum well cladding region are modeled by solving the appropriate Helmholtz equation. Attention is focused on the effects of absorption in the cladding region of the waveguide, which leads to attenuation along the propagation direction. Galerkin's method is utilized to compute exact mode propagation constants and intensities of the fundamental mode. It is found that increased absorption in the cladding layer results in increased lateral extent of the guided mode. At a critical absorption strength, the guided mode becomes unconfined in the lateral direction. This transition can be rationalized in part in terms of the effective index method, which provides a simple approximate way to calculate the characteristics of waveguides with two-dimensional index profiles     

Improved perturbation feedback method for the analysis ofrectangular dielectric waveguides

A simple and accurate method for analyzing rectangular dielectric waveguides is proposed. By investigating some improved equivalent guide models, which can be defined by a successive perturbation feedback process, propagation constants of the original guides can be reasonably obtained with accuracy better than those obtained by applying current approximate approaches, especially when the modes exist at or around the weakly confined region     

Eigen Q-factor of electromagnetic oscillations of E-type in waveguide junction of plane waveguides with anisotropic dielectric

The electrodynamic and numerical analysis of eigen Q-factor of electromagnetic modes of E-type in waveguide junction of plain waveguides, fulfilled with anisotropic dielectric in depending on a permittivity tensor components and dielectric loss have been carried out in the paper. The recommendations on using of waveguide junctions for measurement of dielectric losses of the materials are given.     

Attenuation and wavelength measurement of lossy waveguides

A simple coherent detection system can accurately measure the attenuation and phase constants of an e.m. wave propagating in a lossy waveguide. The main advantages of the system are its great linearity, sensitivity and versatility. This allows precise measurements on a wide variety of waveguides, even when the losses are very large.     

Analysis of lossy dielectric guides by transverse magnetic fieldfinite elements method

Recently a transverse magnetic field formulation of the finite element method for solving lightwave propagation in lossless optical waveguides was demonstrated using only two components of the magnetic field. We extend this formulation to include loss in the waveguides, and compare the results from this formulation with those of other formulations for three different types of waveguides. Our results from the new approach show good agreement with those from previously published data. No perturbation technique is needed to arrive at these results     

Quasi-static analysis of electrooptic modulators by the method oflines

A quasi-TEM analysis using the method of lines is implemented to calculate the electric field anywhere within a layered guided wave structure at appropriately low frequencies. The analysis provides the electric fields and transmission-line parameters for a shielded structure having any number of coplanar electrodes within an arbitrary number of anisotropic dielectric layers, the principal axes of which are parallel to the axes of the structure. The practical application considered is the calculation of the phase shift of a guided optical wave within an electrooptic modulator that has a dielectric buffer layer between the electrodes and electrooptic substrate