Complex Reflection Coefficient Synthesis Applied to Dual-Polarized Reflectarrays With Cross-Polar Requirements

An extended formulation of the intersection approach (IA) algorithm is presented to synthesize matrices of complex reflection coefficients for dual-polarized reflectarrays. The synthesis of complex reflection coefficients allows to impose copolar as well as cross-polar specifications, since these coefficients fully characterize the behavior of the unit cell. The implementation of the algorithm is based on the use of the fast Fourier transform (FFT) in both the forward and backward projectors of the IA, allowing for a highly efficient and fast synthesis process of dual-polarized reflectarrays. Although arbitrary restrictions can be enforced in the reflection coefficients, they might not be feasible for passive antennas. Hence, the unit cell is analyzed as a lossless and lossy passive two-port network and the restriction equations are derived for both cases involving amplitudes and phases of the reflection coefficients. The lossless constraints proved to be too restrictive so lossy restrictions should be applied to achieve feasible reflection coefficients for passive array design. Test cases are provided, which confirm that the algorithm is able to synthesize with success radiation patterns with copolar and cross-polar requirements with restrictions applied to the reflection coefficients.