Study of focal shift effect in planar GaN high contrast grating lenses

In this paper, systematical study on the focal shift phenomenon in planar lenses based on GaN high contrast gratings was performed using finite element method (FEM). Influence of parameters including device size, designed focal length, total phase difference on the focusing performance is presented. It shows that the focal shift is mainly determined by the Fresnel number of the lens, which is nearly equal to the total phase difference divided by π. The influence of the lens size and designed focal length can be attributed to the change of Fresnel number. Theoretical analysis based on diffraction theory is employed to predict the focal shift, which is in accordance with the numerical simulation.