3.3 Improvement of the cross-polarization performance through direct optimization

The third and final stage is optional and consists in improving the crosspolarization performance of the synthesized reflectarray by directly optimizing its layout using a FW-LP tool. This is especially important for applications with tight cross-polarization requirements, such as space missions [2], since the layout obtained in the previous stage most likely will only comply with copolar specifications. As a starting point, the layout obtained in the previous stage is employed. Also, the copolar specification masks are maintained to keep the copolar pattern within specifications while the cross-polarization performance is improved.

There are a number of approaches that can be followed in this stage depending on the application. A common approach in the literature is to directly minimize the crosspolar component of the far field [19, 20]. This is done by applying Eq. (2) for the crosspolar pattern masks in the forward projector of the generalized IA. Another approach is to impose Eqs. (6) and (7) in order to maximize the XPDmin or the XPI. This is especially convenient for space applications in which cross-polarization requirements are specified by those parameters [17].

Nevertheless, this stage requires the use of a FW-LP tool to obtain the full matrix of reflection coefficients in Eq. (10) in order to correctly characterize the crosspolar radiation pattern. Thus, the improvement in cross-polarization performance will be slower than the POS in the first stage.
