Inverse design of poles and zeros: tailoring phase control in metasurfaces

We develop a physically interpretable inverse-design framework for generalized Huygens metasurfaces, using prescribed scattering poles and zeros to engineer resonance interference and transmission-phase control. Compared with direct optimization of transmission or reflection coefficients, this approach offers a physically transparent route to rationally controlling resonance properties, including linewidth and group delay, while reducing computational cost. The resulting designs demonstrate how near-unity transmission and $2\pi$ phase excursion can arise from resonance interference. These signatures of the Kerker effect extend beyond the conventional alignment of electric and magnetic dipole resonances to other mechanisms, including guided-mode resonances and quasi-bound states in the continuum. We further optimize the Kerker condition across a continuum of refractive-index states in a reconfigurable phase change material metasurface, enabling high-transmission $2\pi$ phase tuning. Our results establish a versatile and practical approach to metasurface phase control through the targeted design of scattering poles and zeros.