Diffraction grating with varying slit width: Quasi-periodic homogenization and its numerical implementation

Optimization of plasmonic metasurfaces: A homogenization-based design

“…When the meta-atoms have characteristics varying spatially along the metasurface, which is the case for practical applications, periodic homogenization has to be adapted and this has lead to locally periodic (a.k.a. quasiperiodic) homogenization [21,22]. As we shall see in the present study, this results in effective jump conditions which have almost the same structure as in the periodic case but involving spatially varying susceptibility tensors.…”

“…( 20) and ( 21) can be solved analytically (see Appendix A for the normal incidence case). For non constant susceptibilities, the effective transition conditions can be implemented in the Finite Element Method (FEM) [13] or with modal methods [22] and used as a mean to simplify the simulation of quasi-periodic metasurfaces since the meta-atoms geometries does not need to be meshed. Such an implementation then requires the weak formulation verified by the effective field.…”

“…In section 2, we adapt this two-scale homogenization approach to the locally-periodic case, when the properties of the meta-atoms are allowed to vary slowly along the metasurface. Note that such homogenization has been developed fairly recently for non resonant acoustic metasurfaces [24,22] but the resonant case, although technically not more difficult, has not be addressed. The optimization procedure, performed on the resulting homogenized metasurface, is detailed in section 3.…”

Homogenized transition conditions for plasmonic metasurfaces

“…Recent realizations built on this vision with the idea that if each pixel can be controlled independently, it becomes possible to realize programmable metasurfaces at the subwavelength pixel level [43][44][45] (not yet deeply subwavelength). By partially relaxing the periodicity assumption, such systems can be modeled with our approach [46]. Extensions of the model to other scenarios are also possible.…”