On the Theory of Self-Resonant Grids

Arnaud and Pelow1* have recently described measurements of the transmission properties of several new types of self-resonant, metal grid structures. These grids, which are readily fabricated by photolithographic techniques, have applications as millimeter-wave quasi-optical filters, or diplexers, in communications satellite antennas and in beam waveguide systems. The grid elements are symmetrical such t h a t the grids may be used with two orthogonal polarizations. In this paper, we derive theoretical expressions for the frequency response of the simplest of the new grids and compare the results with measured data. The grid to be considered here is a periodic array of "Jerusalem" crosses as shown in Fig. la. We wish to determine the grid frequency response in terms of the dimensions of the elements when the planar transmitted wave is incident normally. On account of the complex geometry of the grid elements, an exact treatment as a boundary value problem would be prohibitively difficult. Computer-oriented, numerical techniques 2 - 3 have provided a powerful means of solution for grid structures in the form of arrays of rectangular, or circular, apertures. The successful application of these techniques requires, 4 however, considerable caution in approximating the unknown aperture fields. When the aperture geometry is complicated, as here, this aspect of the numerical approach poses a considerable difficulty. Now, in general, the transmission properties of grid structures can be described 5 in terms of an equivalent impedance, together with a * In eq.