Fa Fernandez

Finite Element Analysis of All Modes in Cavities with Circular Symmetry

A field analysis is presented of all modes in a hollow, conducting cavity with rotational symmetry about an axis. Cavities can be periodic along this axis, and the unit (or single) cell can be of arbitrary longitudinal section, with inhomogeneous dielectric loading. Modes of any angular dependence of arbitrary phase-shift per unit cell are analyzed. The finite element method is applied in the longitudinal plane, and uses a specially developed sparse matrix scheme.

Review of finite element methods for microwave and optical waveguides

The authors review the application of the finite element method to analysis of waveguide problems. They discuss the significance of different variational formulations, the modeling of the infinite domain of open-boundary waveguides, techniques to avoid spurious solutions, and matrix solution techniques. They briefly refer to the application of these techniques to waveguides containing nonlinear materials and to three-dimensional problems. >

Reducing Transmission Losses in Hollow THz Waveguides

Research on reducing material absorption in Terahertz (THz) waveguides has lead to development of guiding structures with transmission losses as low as 1 dB/m. Among waveguides that exhibit low loss at THz frequencies are the dielectric-lined hollow cylindrical metallic waveguides. Loss reduction in this waveguide is attributed to an ideal profile of the dominant hybrid HE11 mode. This mode profile also results in relatively low dispersion and very high coupling efficiency. In this contribution we overview properties of dielectric-lined hollow cylindrical metallic waveguides for THz waves, their design principles and the fabrication process. The impact of the mode profile on losses and dispersion at THz frequencies is confirmed experimentally by THz near-field imaging and THz time-domain spectroscopy and numerically by the finite element method.

Transition, radiation and propagation loss in polymer multimode waveguide bends

Design curves for insertion loss of multimode polymer waveguide 90 masculine bends are reported as a function of bend radius for several waveguide widths. For the first time, to our knowledge, in multimode rectangular waveguides the insertion loss is resolved into its components of transition, radiation and propagation loss, in order of decreasing strength, separating them from input and output coupling loss by calibration and comparison of experimentally measured and beam propagation method (BPM) modeled curves. We used the method of nested bends for the first time in multimode polymer waveguides to calculate the propagation loss on a small substrate without using destructive cut-back. The lowest loss of 0.74 dB occurred for a 50 mum square cross section, Deltan=0.0296, 13.5 mm radius waveguide bend.

Vectorial finite element modelling of 2D leaky waveguides

An accurate finite element method is described for the analysis of leaky optical waveguides with arbitrary cross-section and inhomogeneous anisotropic dielectrics including loss or gain. The method leads to the iterative solution of a nonlinear matrix eigenvalue problem without compromising the sparsity of the resultant matrices which depend only on the mesh topology. >

An efficient finite element solution of inhomogeneous anisotropic and lossy dielectric waveguides

An efficient finite element method is presented for the full wave analysis of dielectric waveguides. This method has four major features: (1) the ability to treat a wide range of dielectric waveguide problems with arbitrarily shaped cross section, inhomogeneity, transverse-anisotropy, and significant loss (or gain); (2) total elimination of spurious solutions; (3) direct solution for the (complex) propagation constant at a specified frequency; and (4) the use of only two components of the magnetic field, thus maximizing the numerical efficiency of solution. The resultant matrix eigenvalue problem is of canonical form and is solved with an efficient method, specially developed for this purpose, taking full advantage of the sparsity of the matrices. Numerical results are shown for a variety of microwave and optical waveguides including anisotropy and losses. These examples also include closed and open structures. The computational results agree very well with analytical and previously published results. >

Measurement of Dielectric Properties of Nematic Liquid Crystals at Millimeter Wavelength

Due to their large birefringence and moderately low loss, liquid crystals (LCs) are a promising dielectric media for development of a variety of reconfigurable millimeter-wave devices. In order to optimize the design of tunable millimeter-wave devices, accurate values of the dielectric and elastic constants, as well as the loss tangents of LCs, are needed. However, characterization of LCs at millimeter-wave frequencies is a very challenging and demanding task. In this work, a transmission line method is used for the broadband characterization of nematic LCs in the frequency range of 30-60 GHz. For this purpose, a unique LC cell is proposed and using this, five different nematic LCs, including E7, K15, E44, E63, and MDA-00-3506, are measured and the values of their electrical and mechanical parameters are extracted. The extraction of these parameters from the measurements involves an optimization using two finite-element computer programs recently developed by the authors for the prediction of the local alignments of LC molecules and the wave propagation within the test cell. The highest values of the dielectric birefringence and the highest values of the loss tangents are recorded for E44 and MDA-00-3506. The loss tangent for all the LCs shows a general downward trend as the frequency increases, which is a useful characteristic in the development of reconfigurable millimeter-wave devices.

Three-Dimensional Modelling of Liquid Crystal Display Cells using Finite Elements

A computer modelling method for the three-dimensional dynamic analysis of liquid crystal display cells is presented. The method is based on a variational approach to the Oseen-Frank free energy formulation considering three elastic constants and uses a vectorial representation of the director field. A simpler approximate form that uses only two elastic constants but is faster to operate is obtained as a by-product of the full three-constant model implementation. The modelling uses finite elements on a mesh of tetrahedral elements for the calculation of directors and electric potentials while finite differences in time are used in the time stepping process. Comparisons are made with results from a 2D dynamic program using a tensor model giving good agreement.

Calculation of Fully Anisotropic Liquid Crystal Waveguide Modes

The accurate analysis of optical waveguides is an important issue when designing devices for optical communication. Waveguides combined with liquid crystals have great potential because they allow waveguide tuning over a wide range using low voltages. In this paper, we present calculations that combine an advanced algorithm for calculating liquid crystal behavior and a finite-element mode solver that is able to incorporate the full anisotropy of the materials. Calculation examples demonstrate the validity of our program.

Vector finite element solution of saturable nonlinear strip-loaded optical waveguides

A numerical solution is given for nonlinear optical waveguides with power confinement in both transverse dimensions. Self-consistent solutions are obtained by using an accurate vector-finite-element formulation along with the penalty technique. Numerical results for the first quasi-transverse-magnetic power-dependent mode are presented for strip-loaded waveguides with saturable self-focusing media. The variations with total power are illustrated for the modal index and for the fraction of the total power carried by different regions, showing interesting abrupt power switching for realistic geometries. It is shown that the switching effect is maintained in the presence of saturation and over a range of two-transverse-dimensions geometries. This switching effect can be controlled with variation of some of the parameters of the guide.<<ETX>>