CLOSED-FORM LOW-FREQUENCY SOLUTIONS FOR ELECTROMAGNETIC-WAVES THROUGH A FREQUENCY SELECTIVE SURFACE

A simple closed-form approximate solution is given to the problem of transmission of a low-frequency electromagnetic wave through a frequency selective surface (FSS). The FSSs considered are periodic metal plates (or their complementary apertures) sandwiched between dielectric slabs. At low frequencies, the induced currents on the metal plates may be approximated by a known function with a constant coefficient to be determined by the boundary conditions. Based on such a one-mode approximation, a closed-form solution for the scattered field is derived for FSS with multiple narrow rectangular slots, with a single wide rectangular aperture, and a circular aperture. When compared with the available exact solutions, the one-mode approximation is found valid when the period a of the FSS is such that a/ lambda is small enough that no grating lobe appears (e. g. , a less than lambda for normal incidence) where lambda is the wavelength.