Complex eigenvalues of two-dimensional slotted metallic elliptic cavities

Highly accurate calculations of the complex eigenvalues of natural TM- and TE-oscillations which may be excited in a two-dimensional (2D) elliptic cavity with a variably located longitudinal slit are reported. The algorithm is obtained by regularisation of the integral equations obtained from the single-and double-layer potential representations, respectively. The final form is a Fredholm matrix equation of second kind. Its solution is obtained by the truncation method which rapidly converges as the truncation order increases. The high accuracy of the method is assessed by comparison with the eigenvalues for the closed cavity computed from exact solutions in terms of special functions. A novel study of the evolution of the complex eigenvalues and the corresponding modes as a longitudinal slit of increasing width is opened is reported.