We calculated the shielding characteristic of a three-dimensional array of strip conductors by using the electric field integral equation method and its expansion to an array structure. From reflection coefficients, the effective permittivity of the array is calculated. The effective permittivity becomes negative in the frequency range above resonance, in which the electromagnetic waves travel through the material in an evanescent mode and the transmission coefficient becomes very small.

Full-wave FD-TD analysis has been carried out for coaxial probes inserted into waveguides. Both single and symmetrically placed paired coaxial probe structures have been discussed and we have revealed the relation between equivalent circuit parameters and structural parameters of the coaxial probes including cases for large diameter and extension length, which is useful for practical waveguide circuit design. The equivalent circuit parameters calculated from the scattering parameters agreed well with corresponding measured data. From the calculated field in a waveguide, field concentration at sharp edges of probe sole or base, which ought to be taken into account for high power application design has been also discussed. Besides, amplitudes of higher order modes in waveguides excited by coaxial probes or pairs of coaxial probes has been calculated so as to estimate the range beyond which higher order modes decay sufficiently. This estimation is necessary for simple and easy design of probe using circuit theory.

A simple extension to treat evanescent modal excitation at the aperture of a parallel plane waveguide is shown here by GTD diffracted rays with complex propagation angles. Numerical comparison with other solution confirmed that our simple solution can be used for modal excitation estimation below the cut-off frequency.