Beyond dipolar Huygens' metasurfaces for full-phase coverage and unity transmittance

Metasurfaces made from densely packed resonant wavelength-scale particles enable abrupt modulation of impinging electromagnetic radiation within an ultrathin surface. Combining duality symmetry of particles and rotational symmetry of their arrangement led to the development of Huygens' metasurfaces with perfect transmission. However, so far, when identical particles are considered, only their dipolar multipolar contributions are engineered. There, the achievable phase coverage at a fixed wavelength when modifying the period is smaller than 2p, being a clear limitation for applications. To lift such limitation, we consider dipolar-quadrupolar Huygens' metasurfaces. They consist of scatterers that require a dipolar and a quadrupolar term to capture their response. We show that such metasurfaces offer access to the desired 2pphase coverage while preserving the perfect efficiency when the conditions of duality and symmetry continue to be met. We also propose core-multishell and disk-multiring particles made from realistic materials to meet the requirements and that can be used to build such metasurfaces. Our results are important as a theoretical basis for large-scale fabrications in imaging and integrated optics.