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

Full wavefront control by photonic components requires that the spatial phase modulation on an incoming optical beam ranges from 0 to 2 pi. 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 2 pi-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.