Understanding resonant metasurfaces from the perspective of topological photonics

Full wavefront control by photonic components requires that the spatial phase modulation on an incoming optical beam ranges from 0 to 2π. All optical components are intrinsically non-Hermitian, often described by reflection and transmission matrices with complex eigenfrequencies. We discovered that crossing the discontinuity branch bridging a Zero and a Pole along the real frequency axis provides a universal 0 to 2π spectral phase variation of an output channel as a function of the real frequency excitation. This basic understanding is applied to engineer electromagnetic fields at metasurfaces. Non-Hermitian topological features associated with exceptional degeneracies or branch cut crossing are shown to play a surprisingly pivotal role in the design of resonant photonic systems.