Maximum power transfer between two planar apertures in the Fresnel zone

Abstract
This paper is concerned with the problem of finding the illuminations on two planar antennas (directed toward each other) which maximize the efficiency of the power transfer between them. The two apertures are generally different and their separation, sizes, and shapes are arbitrary (with the exception of some symmetry requirements). It is shown that the optimal phase distributions are such that the two antennas are focused on each other. The optimal amplitude distributions are equal to the field patterns of the mode with minimum diffraction loss in two confocal resonator mirrors, whose separation, sizes, and shapes are equal to those of the apertures in question. For the particular case of rectangular antennas, the optimal amplitude distributions are given by Prolate Spheroidal Wave Functions. The Power Transfer Coefficient between two equal square apertures has been calculated for optimal and uniform (focused and unfocused) illuminations. For moderate to small separations the optimal illuminations yield a very significant increase of the efficiency of the power transfer.

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