Flexible control of multi-focus with geometric phase encoded metalens based on the complex digital addition principle

A transmissive encoding metasurface based on the geometric phase principle is proposed. The encoding unit adopts an anisotropic Si dielectric strip and SiO2 substrate on the upper layer, and realizes the phase modulation of the incident wave in the span of 0–2π on the premise of achieving high polarization conversion efficiency. 1-bit, 2-bit and even multi-bit coding units are constructed by rotating surface units. In order to realize the multi-focus function of imaging space, we propose to introduce the principle of complex code addition into the design of metalens. Compared with traditional scalar encoding, complex encoding reveals the intrinsic connection between different encoded bits, thus closer to the essence of electromagnetism. The multi-angle control of multi-focus in free space is realized by the complex coding of four groups of single-focal metalenses and their addition operations. The multifocal metalens at this time also has the angular characteristics of the previous single focus lens, and multiple angles have no influence on each other. Our proposed complex additive multifocal metalens provides a new idea for future multifocal metalens design, especially the design of polarization-sensitive devices.