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     

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     

Finite element analysis for lossy optical waveguides by usingperturbation techniques

A finite element analysis, based on the variational procedure, is used to find the modal loss or gain for both the TE and TM modes with the application of the perturbation technique. Results for the modal gain for the buried heterostructure diode laser are presented, as well as the loss estimation for both the TE and TM modes for the asymmetrical multilayer metal-clad planar optical waveguides. The results obtained agree very well, for a wide range of loss/gain values, with the previously published work using alternative approaches     

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.     

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.     

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.     

Equivalent circuit representation of lossy coplanar waveguides

The study of the dispersion properties of planar transmission lines including metallic losses with the generalized transverse resonance method is formalized in building an equivalent network of the cross-section which specifies the relationships between the tangential components of the fields on each side of the interfaces. Virtual sources represent the trial quantities chosen to describe the problem. With twoport type boundary conditions, the trial quantities are not easily defined from physical considerations, but the virtual sources obey to specific rules. This purpose is illustrated in studying the attenuation in lossy suspended coplanar transmission lines.     

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     

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     

Modeling lossy anisotropic dielectric waveguides with the method oflines

This paper presents a new formulation useful for modeling waveguides constructed from lossy inhomogeneous anisotropic media. Our approach is based on a pair of Sturm-Liouville type wave equations that have been derived to handle inhomogeneous, diagonalized complex permittivity and permeability tensors. The method of lines is then applied to these wave equations, and related field equations, creating an indirect eigenvalue problem that correctly models this class of structure. Some refinements to the method of lines are also proposed, particularly, regarding the construction of the modal matrices found in the eigenvalue problem. Using our approach, modal dispersion curves have been computed for millimeter-wave and optical structures. Comparisons made with results available from the literature validate our approach     

Analysis of lossy planar transmission lines by using a vectorfinite element method

The vector finite element method with hybrid edge/nodal triangular elements is extended for the analysis of lossy planar transmission lines. In order to handle lossy conductor transmission lines, the present approach includes the effect of finite conductivity of a lossy area, and the dissipations in metallic conductors and dielectrics are calculated directly by considering a complex permittivity for the lossy region of interest. A propagation constant formulation is used in the FEM, which avoids spurious solutions absolutely and can handle sharp metal edges in inhomogeneous electromagnetic waveguides. Numerical examples are computed for microstrip lines, finlines, and triplate strip lines. The results obtained agree well with the earlier theoretical and experimental results, and thus show the validity of the method. Also, the current distributions on the lossy microstrip lines with finite strip thickness and isotropic substrates are presented     

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     

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     

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     

Generalisation of the partial-power law (Brown's identity) to waveguides with lossy media

The partial-power law, otherwise known as Brown's identity, which relates the product of the phase velocity of a mode on a lossless waveguide to the time-average power and momentum carried by the mode, is generalised to be applicable to lossy waveguides as well.     

Numerical solution of lossy waveguides: t.l.m. computer program

The transmission-line-matrix method is a time-domain numerical method for solving wave problems. The method uses a mesh of transmission lines to represent a propagation space, and the losses in the space are accounted for by making the transmission lines lossy. Lossy boundaries are simulated by imperfect boundary reflections on the transmission lines. A FORTRAN program implementing this technique is presented.     

Finite element analysis of diffused anisotropic optical waveguides

Results are presented for anisotropic waveguides, with an arbitrary permittivity tensor, being diffused in both the transverse directions and by using the finite element method with the vector H-field formulation for the analysis. The importance of considering the waveguide core dimensions to be greater than the diffusion depth in both the transverse directions, the use of extrapolation techniques and of a symmetry plane for anisotropic waveguides are also discussed     

Semi-vectorial finite element method for arbitrary step-indexoptical waveguides

A simple semi-vectorial finite element method using a new formula is presented which treats only a linearly polarised transversal electric field E_t. The electric field should satisfy the conditions that either E_t or n²E_t is continuous, whether E_t is parallel or perpendicular to the refractive index discontinuous interface in an optical waveguide. This allows accurate and efficient analyses of the polarisation dependence of arbitrary step-index optical waveguides     

Numerical solution of fields in lossy structures using MAGY

Lossy structures are used in vacuum electronic devices to control and suppress modes. Numerical simulation of the effect of these lossy structures is critical to the design and optimization of devices. The gyrotron simulation code MAGY makes use of the generalized telegraphist's equations in which the transverse structure of fields is represented as a sum of local modes of a metallic waveguide. If the wall is not a perfect conductor then sum over modes is not uniformly convergent. We have developed an algorithm to deal with this problem and allow for the simulation of structure with highly lossy walls. The theory and implementation of this algorithm are presented     

Determination of the TE and TM modes in arbitrarily shaped waveguides using a hypersingular boundary element formulation

In this paper a procedure based on the hypersingular element method is applied to find the TE and TM modes in arbitrarily shaped waveguides. To show the accuracy of this method, various examples are solved and the results are compared to those analytical, when there is an analytical solution, and those presented in the literature. The proposed method did not present spurious modes, and in all the examples presented showed excellent results considering a reasonable number of elements in the boundary.