The theory of parallel-plate media for microwave lenses

The problem of the reflection and refraction of an electromagnetic plane wave at a plane interface formed by the edges of an infinite set of equidistant parallel metal plates has been studied, the plates being assumed to have no thickness and perfect conductivity. The direction of propagation of the incident wave is assumed to be at right angles to the edges of the metallic plates, and the electric vector is assumed to be parallel to them. The solution presented extends the scope of those already published, in that no restriction has been placed on the number of waves propagated away from the interface in the homogeneous medium; the reciprocal case of a wave incident from the plate medium has also been treated. Further, the mathematical method is simpler than that used in previous solutions. From the formulae derived, curves have been computed of the power-transmission and power-reflection coefficients, together with those of the phase changes across the interface. The formulae have also been tentatively applied to certain lenses, and the resulting curves indicate practical limits to the design of efficient lenses.