Lu, Yilong; (1991) The finite element solution of inhomogeneous anisotropic and lossy dielectric waveguides. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

This thesis presents a new variational finite element formulation and its implementation for the analysis of microwave and optical waveguide problem with arbitrarily- shaped cross section, inhomogeneous, transverse-anisotropic, and lossy dielectrics. In this approach, the spurious, nonphysical solutions, which ordinarily appear interspersed with the correct results of earlier vectorial finite element methods and thus have been the most serious problem in finite element analysis of waveguides, are totally eliminated. In this formulation either the propagation constant or the frequency may be treated as eigenvalues of the resulting generalized eigenvalue problem. This formulation also has the capability to find complex modes of lossless waveguides. Furthermore, the numerical efficiency of the solution is maximized since this formulation uses the most economical representation of a problem, in terms of only two vector components. This is achieved without losing the sparsity of the matrices of the resultant eigenvalue equation, which only depends on the topology of mesh used. This property is very important for solving large-size problems by efficient sparse matrix algorithms. In this work, a basic vector wave equation which involves only transverse components of magnetic field is straightforwardly derived from Maxwell equations. This differential equation incorporates the divergence condition V.B = 0 and leads to a canonical form of the resultant eigenvalue equation. The Local Potential Method is used to obtain the variational formulation. When implementing the finite element method, the Rayleigh-Ritz procedure is used to find stationary values of the functional to get the resulting generalized matrix eigenvalue equation. To show the validity and applicability of the method, a series of examples of microwave and optical waveguides including inhomogeneity, anisotropy and loss are studied. These examples show good accuracy and complete absence of spurious modes, demonstrating the effectiveness of the new formulation developed.

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