Fig. 1: A super metalens for the multifaceted control of focal points along any 3D curved trajectory.

a Schematic of the proposed super metalens for generating focal points with customized linear polarization states along a 3D Pappus spiral. When the metalens is illuminated with a linearly polarized light beam with continuously variant wavelengths, the focal points with predesigned linear polarization states are generated along the Pappus spiral. The linear polarization directions of focal points (denoted with orange arrows) can be dynamically modulated by continuously changing incident linear polarization. The color gradient of focal points on the transmission side represents the continuous change in the wavelength with a step size of 1 nm. b Different 3D spiral curves with perspective on yz-plane, including a cylindrical helix with a constant pitch, a conical spiral, and a Pappus spiral. The radius R remains constant in the first case, while it varies in the second and third cases. c A magnified view of a segment of the 3D curve shown in (b). The designed focal points in a 3D space include a continuous wavelength range and polarization rotation angles. Each wavelength corresponds to a focal point. The compression of a 3D spiral is controlled with the number of focal points and longitudinal separation Δz. The color bar and orange arrows represent the operating wavelength range (500–700 nm) and linear polarization rotation angle range (0–π), respectively