Design method for continuous phase plate enabling wide-angle beam shaping

A continuous phase plate (CPP) is a beam-shaping element characterized by a quasi-random continuous surface that robustly achieves the target far-field intensity distribution despite changes in incident light conditions. In this study, we present what we believe to be a novel optimization algorithm for designing CPPs. In each iteration step, the transmission directions of light rays are calculated using a rigorous formulation beyond the small-angle approximation. These transmission directions are then refined by solving the standard Monge-Ampère equation, ensuring that the 2D histogram better matches the target distribution. The updated height profile is obtained by solving the surface reconstruction problem with or without regularization concerning surface curvature and height variation. Our method enables the design of compact CPPs for wide-angle beam shaping with controlled manufacturability.