The computational analysis of nanophotonic devices is usually carried out via the standard finite element method (FEM). However, FEM requires meshes that are fitted to the devices’ boundaries, so making changes to the geometry (and thus the mesh) results in an inefficient process at best. Such an approach is therefore at odds when conducting design, which requires the analysis of multiple device geometries until reaching a satisfactory solution. Computational design tools such as topology optimization are often used, but the use of density-based representations of geometry inevitably leads to other issues—e.g., pixelized fuzzy boundaries with “gray material” (that does not correspond to dielectric nor vacuum) have an adverse effect on the devices’ interaction with electromagnetic waves. In this paper we propose an interface-enriched generalized finite element method (IGFEM) for the analysis of two-dimensional electromagnetic scattering and eigenvalue problems. IGFEM enables the use of finite element meshes that are completely decoupled from the problem's geometry. The analysis procedure is further coupled to a level set description of topology, resulting in a versatile enriched approach to topology optimization; this level set-based interface-enriched topology optimization procedure is devoid of the issues mentioned above regarding density-based methods, and yields crisp “black-and-white” designs that are devoid of jagged fuzzy edges. We first demonstrate that the analysis procedure achieves the same convergence rate as that of standard FEM using geometry-fitted meshes. We then compare the convergence properties of IGFEM with Nitsche's method on a problem containing an embedded straight interface. Finally, we conduct topology optimization for designing both a 2-D metalens and a 2-D reflector, maximizing their ability to focus light onto a target point.

In the future, automated cars may feature external human–machine interfaces (eHMIs) to communicate relevant information to other road users. However, it is currently unknown where on the car the eHMI should be placed. In this study, 61 participants each viewed 36 animations of cars with eHMIs on either the roof, windscreen, grill, above the wheels, or a projection on the road. The eHMI showed ‘Waiting’ combined with a walking symbol 1.2 s before the car started to slow down, or ‘Driving’ while the car continued driving. Participants had to press and hold the spacebar when they felt it safe to cross. Results showed that, averaged over the period when the car approached and slowed down, the roof, windscreen, and grill eHMIs yielded the best performance (i.e., the highest spacebar press time). The projection and wheels eHMIs scored relatively poorly, yet still better than no eHMI. The wheels eHMI received a relatively high percentage of spacebar presses when the car appeared from a corner, a situation in which the roof, windscreen, and grill eHMIs were out of view. Eye-tracking analyses showed that the projection yielded dispersed eye movements, as participants scanned back and forth between the projection and the car. It is concluded that eHMIs should be presented on multiple sides of the car. A projection on the road is visually effortful for pedestrians, as it causes them to divide their attention between the projection and the car itself