Jb Davies

Finite-element solution of integrated optical waveguides

A vector H -field finite-element method has been used for the solution of optical waveguide problems. The permittivity of the guiding structures can be an arbitrarily tensor, only limited to being lossless. To extend the domain of the field representation, infinite elements have been introduced. To eliminate spurious solutions and to improve eigenvectors, a penalty function method has been introduced. To show the validity and usefulness of this formulation, computed results are illustrated for step channel waveguide, diffused channel waveguide, anisotropic channel waveguide, and channel waveguide directional couplers.

Finite-Element Analysis of Optical and Microwave Waveguide Problems

A vector H-field formulation is developed for electromagnetic wave propagation for a wide range of guided-wave problems. It is capable of solving microwave or optical waveguide problems with arbitrarily anisotropic materials. We have introduced infinite elements to extend the region of explicit field representation to infirdly, to consider open-type waveguides more accurately. Computed results are given for a variety of optical planar guides, image lines, and waveguides containing skew anisotropic dielectic.

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. >

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. >

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>>

Theoretical and experimental study of nematic liquid crystal display cells using the in-plane-switching mode

In this paper a two-dimensional (2-D) dynamic model, based on a tensor formulation and solved numerically by combining finite elements and finite differences, is proposed and used for analyzing nematic liquid crystal (LC) test cells with interdigital electrodes. We compare theoretical and experimental results concerning the switching behavior, response mechanism, and viewing angle characteristics of nematic LC pixel structures which use the in-plane-switching (IPS) mode. The good agreement observed between theory and experiment in terms of electro-optical properties validates our modeling and demonstrates its potential for design optimization. We show that the proposed LC test cells, using the in-plane-switching mode, ensure switching-ON and -OFF response times of 22 and 28 ms, respectively, and excellent viewing angle characteristics.

Two-dimensional finite-element modeling of nematic liquid crystal devices for optical communications and displays

A two-dimensional finite-element code is presented for the steady-state analysis of liquid crystal structures in nonuniform electric fields. It is based on a free-energy formulation which includes all three elastic constants and can deal with pure nematic, twisted nematic, and cholesteric liquid crystal materials. The enhanced capabilities of our code allow the design of composite structures made of both dielectric and liquid crystal materials and with arbitrary configuration of electrodes. Unwanted effects, such as the formation of disclination lines in the director orientation, can be accurately predicted. The method has been applied for analyzing pure nematic liquid crystal microlenses with variable focal length and twisted nematic liquid crystal cells for display applications. Numerical results show that a careful choice of the device structures can avoid the formation of defects and improve their performance.

Numerical analysis of nonlinear bistable optical waveguides

Numerical solutions illustrating the onset of bistability and hysteresis are presented for the symmetrical step index, asymmetrical step index, and asymmetrical diffused slab nonlinear optical waveguides. Two different numerical techniques have been used independently-a finite-element method and a variational method. Both methods produce numerically stable solutions, and agreement between them is good for both increasing and decreasing total power from below or above the threshold power. The results are compared with analytical solutions for these structures. The onset and the end of the physically unstable solutions regime coincides with the two power thresholds for the increasing and decreasing powers.<<ETX>>

Computation of wave propagation in integrated optical devices using z-transient variational principles

As an alternative to the classical beam propagation method (BPM), a variational method is presented to solve the TE and TM Helmholtz equations in the paraxial approximation for the propagation of polarized beams through optical waveguides. Using the method of local potentials, the paraxial wave equations are first converted into equivalent z-transient variational principles. These functionals are minimized using a combination of the Rayleigh-Ritz finite-element procedure and a Crank-Nicholson-like finite-difference scheme. Solutions for anisotropic materials are obtained by applying standard Galerkin finite-element and finite-difference methods to a variational formulation derived from the coupled TE/TM paraxial Helmholtz equations. >