Graphene oxide (GO) ultrathin flat lenses have provided a new and viable solution to achieve high resolution, high efficiency, ultra-light weight, integratable and flexible optical systems. Current GO lenses are designed based on the Fresnel diffraction model, which uses a paraxial approximation for low numerical aperture (NA) focusing process. Herein we develop a lens design method based on the Rayleigh-Sommerfeld (RS) diffraction theory that is able to unambiguously determine the radii of each ring without the optimization process for the first time. More importantly, the RS design method is able to accurately design GO lenses with arbitrary NA and focal length. Our design is experimentally confirmed by fabricating high NA GO lenses with both short and long focal lengths. Compared with the conventional Fresnel design methods, the differences in ring positions and the resulted focal length are up to 13.9% and 9.1%, respectively. Our method can be further applied to design high performance flat lenses of arbitrary materials given the NA and focal length requirements, including metasurfaces or other two-dimensional materials.

In this work, an all-fiber-based mode converter for generating orbital angular momentum (OAM) beams is proposed and numerically investigated. Its structure is constructed by cascading a mode selective coupler (MSC) and an inner elliptical cladding fiber (IECF). OAM modes refer to a combination of two orthogonal LPlm modes with a phase difference of ±π/2. By adjusting the parameters and controlling the splicing angle of MSC and IECF appropriately, higher-order OAM modes with topological charges of l = ±1, ±2, ±3 can be obtained with the injection of the fundamental mode LP01, resulting in a mode-conversion efficiency of almost 100%. This achievement may pave the way towards the realization of a compact, all-fiber, and high-efficiency device for increasing the transmission capacity and spectral efficiency in optical communication systems with OAM mode multiplexing.