We apply homogeneization theory to devise equivalent interface conditions for the modeling of phase gradient metasurfaces in the frequency-domain. The resulting transmission conditions are closely related to the so-called GSTC (Generalized Sheet Transition Conditions) that are derived from physical principles. Our approach provides a direct link between the coefficient of the susceptibility tensors driving surfacic polarization fields and the structural design of a metasurface with nanostructures. These equivalent boundary conditions are useful for numerical simulations since they reduce the complexity of the meshes at the interfaces and thus the number of degrees of freedom to be solved. This work is conducted in collaboration with Agnès Maurel (ESPCI, Institut Langevin1) and Kim Pham (ENSTA, Institut des Sciences de la Mécanique et Applications Industrielles).

Mesh with (left) and without (right) nanostructures.

Left: solution with homogeneization-based equivalent boundary conditions. Right: reference solution computed on a nanostructured mesh.

Zoom of the reference solution computed on a nanostructured mesh.