Power transfer efficiency between focused circular antennas with Gaussian illumination in Fresnel region

The power transfer efficiency between two circular aperture antennas in the Fresnel region is obtained analytically and explicitly. They are focused at each other and illuminated as a simple Gaussian taper. Two apertures also have generally different sizes and unequal illuminations. It is shown that the Gaussian distribution is close to the optimum, which is derived from the theory of the confocal optical resonators. The effect of the deviation of the illumination from the optimum upon the efficiency is numerically evaluated. The result shows that the reduction of the efficiency for a constant deviation increases as the Fresnel number decreases. The dissimilarity of both aperture illuminations also reduces the efficiency. The qualitative trend is such that the larger the dissimilarity, the smaller the efficiency. When the order of dissimilarity is small or the taper of the aperture is large, the efficiency can be approximately predicted by assuming equal illumination with the geometrical mean of the two illuminations. A simplified approximate efficiency which can be applied to the greatly tapered illumination is also derived.