Crossing of the Branch Cut: The Topological Origin of a Universal 2π‐Phase Retardation in Non‐Hermitian Metasurfaces

Abstract Full wavefront control by photonic components requires that the spatial phase modulation on an incoming optical beam ranges from 0 to 2π. Because of their radiative coupling to the environment, all optical components are intrinsically non‐Hermitian systems, often described by reflection and transmission matrices with complex eigenfrequencies. Here, it is shown that parity or time symmetry breaking—either explicit or spontaneous—moves the position of zero singularities of the reflection or transmission matrices from the real axis to the upper part of the complex frequency plane. A universal 0 to 2π‐phase gradient of an output channel as a function of the real frequency excitation is thus realized whenever the discontinuity branch bridging a zero and a pole, that is, a pair of singularities, is crossing the real axis. This basic understanding is applied to engineer electromagnetic fields at interfaces, including, but not limited to, 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.