The continuous refractive beamforming surface for far-field with robustness and high efficiency

We propose a continuous refractive beamforming surface for far-field with a freeform surface and non-one-to-one ray mapping, realizing the high efficiency and robustness of the XY position. We developed a new iterative optimization algorithm. The major tasks in each optimization step are updating the ray emission angles and surface reconstruction. The update of the ray emission angles is performed by the Monge-Ampère equation considering target and tentative far-field intensity distributions. The surface reconstruction is realized by minimizing the loss function consisting of the reconstruction error and regularization terms concerning the surface's height and curvature. We also developed a manufacturing process for the freeform surface, which was very close to the design, by providing manufacturing feedback. This manufacturing process consists of the mastering process by a laser grayscale lithography, mold manufacturing process by a Ni electroforming, and producing element process by an imprinting process.