An accurate design of graphene oxide ultrathin flat lens based on Rayleigh-Sommerfeld theory

Guiyuan Cao,Xiaosong Gan,Baohua Jia,Han Lin

doi:10.29026/oea.2018.180012

Abstract

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.

Highlights

Flat lenses made of ultrathin materials have the advantages of astigmatism and coma aberrations free, which are otherwise common problems for conventional curved surface lenses, especially when the numerical aperture (NA) is high[1]
It is noticed that the experimental results and the simulations using the RS diffraction theory match well, while the focal length calculated by the Fresnel diffraction theory is significantly different from the others
We have developed a design method based on the RS diffraction theory, which is able to accurately design graphene oxide (GO) lenses with arbitrary focal length and diameter without the optimization process for the first time

Summary

Introduction

Flat lenses made of ultrathin materials have the advantages of astigmatism and coma aberrations free, which are otherwise common problems for conventional curved surface lenses, especially when the numerical aperture (NA) is high[1]. To promote practical GO lens applications, it is necessary to develop a theoretical modeling method that is able to accurately calculate the focusing process of GO lenses with arbitrary NA and focal lengths with high speed and efficiency and low computational cost. Such a model can be applicable to other ultrathin lens with high NA and large focal length. During the conversion[31,32], the GO film shows three continuously tunable physical property variations: the reduction of film thickness, the increase of refractive index and the decrease of transmission These three property variations provide the required phase and amplitude modulation in designing a GO lens.

Results and discussion

Experimental results

Conclusion