A metalens is a difficult structure to design and simulate using photonic simulation algorithms, since its overall size is very large and contains many nano-structures. To simulate the nano-structures, a rigorous algorithm such as FDTD must be used. However, FDTD is computationally expensive, requiring substantial computer resources. The largest metalens that can be directly simulated in most labs through FDTD is only tens of micrometers in diameter, much smaller than what is needed .
In practice, however, direct FDTD simulation of the entire metalens is fortunately not required. In this paper, we demonstrate an approach that decomposes the metalens into simpler elements that can be solved individually. A rigorous algorithm such as FDTD, or alternatively RCWA, is used to calculate the phase shift of the individual unit nano-cells, from which a phase mask for the complete metalens is constructed. More efficient algorithms, such as Beam Propagation Method (BPM) or Beam Synthesis Propagation (BSP), are then used to simulate the propagation through the metalens. For the propagation, we will use both BPM and BSP on the same metalens structures for cross-validation.