A class of dielectric waveguide structures using a rectangular dielectric strip in conjunction with one or more layered dielectrics is analyzed with a finite-difference method formulated directly in terms of the wave equation for the transverse components of the magnetic field. This leads to an eigenvalue problem where the nonphysical, spurious modes do not appear. Moreover, the analysis inclndes hybrid-mode conversion effects, such as complex waves, at frequencies where the modes are not yet completely bound to the core of the highest dielectric constant, as well as at frequencies below cutoff. Dispersion characteristic examples are calculated for structures suitable for millimeter-wave and optical integrated circuits, such as dielectric image lines, shielded dielectric waveguides, insulated image guides, ridge guides, and inverted strip, channel, strip-slab, and indiffused inverted ridge guides. The numerical examples are verified by results available from other methods.

Finite-Difference Analysis of Rectangular Dielectric Waveguide Structures

Maxwell's equations can be cast into a basic differential operator equation, the curlcurl equation, which lends itself easily to variational treatment. Various forms of this equation are associated with problems of practical importance. The formulation includes the treatment of loss-free anisotropic media. The boundary conditions associated with electromagnetic-field problems are treated in detail and the uniqueness of the solution is discussed. A functional is derived for the curlcurl equation in Cartesian and cylindrical coordinates.

Vector Variational Formulation of Electromagnetic Fields in Anisotropic Media

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. >

Review of finite element methods for microwave and optical waveguides

An efficient method for calculating the dispersion characteristics of planar waveguide structures is presented, of which the principle is known as the ‘method of lines’ in mathematical literature. The wave equation is discretized in only one direction, and the resulting differential-difference equation can be solved analytically. As an example of application the phase constant and the characteristic impedance of microstrips with tuning septums are calculated.

A new technique for the analysis of the dispersion characteristics of planar waveguides

The vector parasite problem is studied in the context of finite-element solutions of Maxwell's equations for driven boundary-value problems. An expanded weak form which combines the divergence equation with the conventional weak form of the double-curl equation is introduced. This form is related to penalty methods where the penalty or weighting factor varies with the dielectric constant. The resulting algebraic system is identical to the Galerkin-Helmholtz operator on homogeneous subregions. Normal and tangential boundary conditions arise in terms of the divergence and curl of the field on the boundary which can be reexpressed as equivalent charges and currents. Computational results show the occurrence of two distinct types of parasitic modes in driven problems and their elimination with the formulation presented. Practical observations concerning the conditions which provoke spurious modes in these problems are reported. Spurious solutions arise from improper or unphysical boundary conditions, and the importance of careful specification of boundary-value problems is illustrated. Most conceptual difficulties with boundary conditions per se are removed when hybrid methods are used to couple the interior finite-element solution to the exterior problem. which focuses attention on the physics of the source distribution. >

Elimination of vector parasites in finite element Maxwell solutions

By means of finite difference methods, dispersion curves are obtained for the fundamental and higher order hybrid modes in both single and coupled microstrip. Structures of realistic proportions are investigated by the use of a graded finite difference mesh. Variational methods are used in deriving the finite difference equations. The higher order modes are found to be similar to LSM slab line modes. A spurious nonphysical class of solutions is found to exist in this and similar formulations, the characteristics of which are described.

Computer Analysis of the Fundamental and Higher Order Modes in Single and Coupled Microstrip

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Computer Analysis of the Fundamental and Higher Order Modes in Single and Coupled Microstrip