The phase of each unit nano-cell is critical to metalens performance. Approximate estimation based on the phase shift of the mode guided in an isolated nano-cell is not accurate  because it ignores resonances inside the nano-cell and interference from neighboring nano-cells. In our study, we use RSoft’s FullWAVE (FDTD) and DiffractMOD (RCWA) tools to calculate the phase delay for individual nano-cells with certain lattice patterns. Shown in Figure 1 are the calculated phase shifts as functions of normalized diameter for the nano-pillar and nano-hole (left), and for rectangular and hexagonal lattices of nano-pillars (right) at λ=532nm.
Based on the phase delay curves shown in Figure 1, the diameter of each cell in a metalens can be determined according to the designed phase shift at that particular point. Shown in Figure 2 is the layout of an ideal metalens.
The phase profile of this metalens is shown in Equation 1.
To ensure that the metalens we create is manufacturable, the normalized diameters are chosen in the range of [0.45,0.85], which can provide 360o phase shift. The phase mask of the above metalens is generated and is shown in Figure 3.
For comparison the memory requirements for BPM were 0.19G and FDTD was 55G, and the respective simulation times on a desktop computer were 1.5mins and 130 minutes. Thus, BPM provides similar results to FDTD in significantly faster simulation time.
Because of the huge memory requirements that would be required for FDTD to simulate the large metalens directly, we validate BPM against another propagation algorithm, Synopsys’ CODE V® Beam Synthesis Propagation (BSP) feature. BSP, due to its implementation, does not handle the physical optics simulation of the nano-structures directly. Instead, it treats the metalens as a phase mask, as shown in Figure 3. The BSP result is shown in Figure 5 on the right. It confirms the smallest spot size obtained occurs at L=200µm, in excellent agreement with the BPM result. For this simulation, the BSP simulation takes approximately 3 minutes with 4 GB RAM on a laptop computer.
We have demonstrated an effective approach to designing and simulating practical metalenses by using RSoft’s FullWAVE and/or DiffractMOD to simulate the individual metalens nano-cells and BeamPROP or CODE V's BSP features to simulate the propagation of the light through the whole metalens. The test examples shown here demonstrate that this is a viable approach, and provides both accuracy and efficient use of computational resources.