Design and Analysis of Binary Fan-out Gratings based on Step-Transition Perturbation Approach

Nowadays, diffractive optical elements are used for a variety of applications because of their high design flexibility, compact size, and mass productivity. At the same time, they require having high and complex optical functionalities such as a large number of diffraction orders and a wide diffraction angle, which is beyond the limits of scalar paraxial diffraction domain. We propose a stable and fast gradient-based optimization algorithm based on step-transition perturbation approach applied to design binary diffractive elements with small and many features for being performed in a large number of diffraction orders and wide diffraction angles. Using our optimization, we obtained high-performance elements than using optimization based on purely scalar theory. In addition, it needs much less calculation time than parametric optimization based on rigorous diffraction theory. Upon verification with the experimental results, we observed that our gradient-based optimization method is valid for 1-by-117 fan-out grating with some small features (on the order of the illumination wavelength) and about 22 degrees full pattern diffraction angle.