Overview
Metalenses are macroscopic optical elements comprised of nano-scale building blocks, the meta-atoms. The numerical aperture of a metalens NA is restricted by the excitation wavelength λ and the minimal meta-atom unit cell size \(l_{unit}\), such that
$$\ NA≤\frac{λ}{\ 2 l_{unit}}\ $$
As several millions of unit cells can be used to constitute a single metalens, the computation of its response can span several length scales posing a challenge to the respective simulation. As a result, one needs to consider a trade-off between speed and accuracy. We offer three different solutions to simulate metalenses depending on the requirements of accuracy and computation speed, respectively.
Metalens Analysis
Full FDTD (Small-Scale Metalens – Field Propagation)
This is the most expensive as well as the most accurate type of metalens simulation that we offer. The interaction between the individual meta-atoms is calculated in the full metalens FDTD simulation. Given that this approach makes the fewest approximations it is the most physically accurate approach validating these devices; however, as with all numerical methods this level of accuracy comes at the price of high memory and CPU time consumption. This approach is best suitable for small-scale metalenses. If the lens diameter is at the mm-scale, users may need to make sure the PC is powerful enough or consider the other faster approaches. Bypassing traditional workstations, Ansys Lumerical products function with multiple machines (a cluster) to enable high-performance computing (HPC) (Introduction to High-Performance Computing with Lumerical).
Meta-atom field stitching (Small-Scale Metalens – Field Propagation)
A less expensive approach compared to the full metalens FDTD simulation is the meta-atom field stitching approach. For a given metalens design, the individual meta-atom response is laid out on the metalens design grid and stitched together to form the overall metalens response. In this case, we pre-calculate the individual meta-atom response using RCWA. As such, we assume periodic boundary conditions for each meta-atom i.e., local periodic approximation (LPA). Thus, the coupling between different neighboring meta-atoms is not reflected accurately. The approximation is most likely to break down if neighboring meta-atoms are vastly dissimilar. This can be the case, if the phase response changes abruptly. Deviations between the full metalens FDTD simulation and the meta-atom field stitching approach are likely to occur.
Ray-tracing (Large-Scale Metalens – Ray Propagation)
This is the least expensive but also with the lowest level of detail due to the metalens dimensions simulation we offer. If one is not interested in the full wave nature of the light response, this might be the approach of choice. To this end, we combine the nanoscale results from Ansys Optics RCWA with Zemax Optics Studio’s ray tracing. Similar to the meta-atom field stitching approach, the individual meta-atom response is pre-calculated in RCWA. Together with a metalens design scheme it is passed to Zemax Optics Studio. Hence, this approach also makes use of the LPA. Instead of calculating the response for the entire metalens only the response surrounding each ray hitting the metalens is used. The response at each ray location is interpolated from the surrounding meta-atom responses. This approach can be highly sensitive to abrupt changes in the meta-atom phase. Note that in this approach, the behavior of the outermost boundary cells of the metalens (up to four unit cells) is not defined.
Related applications
Ansys has developed different applications utilizing metalenses within optical systems, these are listed below:
- Eye tracking optical system with a metalens, we demonstrate the simulation of an eye-tracking system that utilizes the latest optical technologies of a metalens and a system of pancake lenses.