Fig. 4 shows the efficiency-optimal normalized amplitude distributions at the transmitting antenna and the corresponding normalized power density distributions in the receiving antenna plane. One can see that because of the power density maximum being shifted away from the beam center, the antennas with radial polarization have antenna power coefficients 1.5-2.5 times greater than antennas with uniform polarization (Fig. 3-6). Therefore, if the maximum value of power density at the antenna is limited, more power can be transmitted and received with radial polarization. Also note that the sharp minimum at the beam center (Fig. 6) can be used to improve beam pointing of the transmitting antenna to the receiving one. Amplitude-phase Distribution Synthesis Method This section describes the synthesis method for amplitude and phase field distributions at the transmitting antenna. The main idea of the method is as follows. The field distribution at the transmitting antenna (a complex function) is expanded in a series of real partial distributions with complex coefficients. Various types of polarization can be described by an appropriate choice of partial distributions. Hence the synthesis problem becomes that of finding unknown complex coefficients providing the optimal characteristics. To find the unknown coefficients the method of penalty functions [11] can be used. The main formulae used for calculating and optimizing the SPS characteristics are given below. The SPS transmitting antenna can be considered as a circular aperture with a continuous field distribution because the dimensions of radiation modules are much less than the antenna radius. The power density distribution in the receiving aperture plane has the form: The function F(u), accurate up to the constant multiplier, coincides with the radiation pattern of the transmitting antenna and is expressed by:
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