Efficient optimization of large reflectarrays using continuous functions

Two new efficient optimization schemes for direct optimization of printed reflectarrays are presented. Instead of optimizing directly on the geometry of the array elements, continuous function are envoked to represent the aperture field from which the geometry of the array elements are determined. In this way, the sharp transitions in the geometrical variation of the array elements can be sufficiently reproduced and gives designs that are comparable to those obtained where the array elements are directly optimized. The first scheme uses complex spline representation (CSR) whereas the second uses Fourier series representation (FSR). To demonstrate the two schemes, an offset 50 × 50 square wavelengths pencil beam reflectarray is considered. It is shown that the CSR and FSR schemes are capable of yielding designs with the same performance as that obtained where the array elements are directly optimized, and that the optimization time can be reduced by a factor of 6.