Semi-Analytical Diffraction Synthesis of Cylindrical Reflector Beam Splitters

The authors present a numerical synthesis of a 2-D shaped reflector operating as a splitter of an E-polarized wave beam. The implemented method is based on a singular integral equation (SIE), which is descretized with the method of discrete singularities (MDS). Due to high efficiency and controlled accuracy, the SIE-MDS serves as a core of a computer optimization routine. The new point is that they derive an additional SIE for the gradient of the objective function, which is the deviation of the near field from a prescribed function on some contour. The method applying such a semianalytical gradient is more efficient and more accurate than finding the gradients numerically by finite differences