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An approximate technique for solving eigenvalue equations, the variation-iteration method,is commonly used in theoretics physics. A previous paper presented the application of this method to the scalar case of a dielectric slab loaded rectangular waveguide. This paper presents its extension to the complex vector case of a lossy dielectric insert loaded waveguide. Starting from an initial trial function, iterates are calculated in which the components relative to the unwanted eigenfunctions are eliminated. Both an upper and a lower bound for the unknown eigenvalues are available. Each iterate is the solution of a system of algebraic simultaneous equations. This system is solved by the successive overrelaxation method using an automatically computed optimal accelerating factor. An extrapolation technique further accelerates the convergence. This yields the attenuation and propagation coefficients for the dominant as well as several other modes, together with the electric and magnetic field configurations.

A method has been developed to improve the use of the RayIeigh-Ritz procedure. A criterion is established, which is a measure of the cumulative improvement due to the addition of more and more terms in the series expansion. Without calculating the exact roots of determinantal equations, the convergence is accelerated by skipping unnecessary intermediate steps. The computation time is drastically reduced because the final result is obtained after only a few (not more than 5 to 7) values of determinants of increasing order. Inhomogeneneously loaded waveguides are chosen as an application because the exact solution is available to check the validity of the method. The results obtained with the method described in this paper are compared with other approximate procedures. The comparison shows a definite advantage for the suggested technique.

An approximate technique for eigenvalue equations, the variation-iteration method, is commonly used in theoretical physics. Through an adequate numerical treatment it reduces to the inverse iteration method. It is shown here that this technique is most promising. Starting from an initial trial function, iterates are calculated, in which the components relative to the unwanted true eigenfunctions are eliminated. Both an upper and a lower bound of the unknown eigenvalues are calculated. This leads to an approbate eigenvalue within a specified accuracy with respect to the exact (unknown) eigenvalue. An extrapolation technique further accelerates the convergence. The computation time is shorter than when using the Rayleigh-Ritz procedure. The method is applied here to the dielectric-slab loaded waveguide, because the exact solution is available to check the validity of the method. The influence of the geometry, the dielectric constant, and the frequency is evaluated.