Focal shift in metasurface based lenses

In this paper, the focal shift issues of squared metasurface lenses are investigated. Axial intensity distribution formula of the squared planar lens model is obtained by utilizing traditional diffraction theories combining with the Fresnel approximation method. Fresnel integral and Cornu spiral are adopted to obtain the relations between the relative focal shift and Fresnel number, which can be used to predict the shift for different Fresnel numbers. In the far infrared region (at 10.6 mu m), a group of C-shaped nanoantennas are designed to cover the phase shift from 0 to 2 pi and simulations also performed by using finite-difference time-domain (FDTD) method. Several lenses are arranged by those resonators, and simulation results of focusing performance are in good agreement with the theoretical prediction. It's expected that this work will provide a better solution for the design of lens in the infrared integrated optical systems. (C) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement.