Microwave transmission through a series of inclined gratings

A polarisation cascade matrix is derived which describes the transmission of an arbitrary elliptically polarised wave through an inclined grating of parallel wires. The terms of the matrix are the well established complex reflection and transmission coefficients for a linearly polarised wave incident on a single grating. Hence the matrix can be adapted for gratings with wires or strips of non-circular cross-section. The product of a series of matrices representing a series of gratings whose wires are at different angles to a fixed direction gives the total complex transmission and reflection coefficients. The results are shown to be in agreement with previously published work on a double-grating system, and are experimentally verified for a series of five gratings. These results confirm that such a series of gratings can be used to design broadband polarisation rotators for linear polarisation. A similar matrix analysis can be applied, for wider wire spacings, to the design of broadband circular or elliptical polarisers or analysers. A sharp resonance reflection condition, which occurs when the gratings are separated by half a wavelength, can have applications as a frequency filter.