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# Crossing of the branch cut: the topological origin of a universal 2{\pi}-phase retardation in non-Hermitian metasurfaces

preprint

posted on 2023-01-12, 15:03 authored by Rémi Colom, Elena Mikheeva, Karim Achouri, Jesus Zuniga-Perez, Nicolas Bonod, Olivier J. F. Martin, Sven Burger, Patrice GenevetFull 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, we show that Parity-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, i.e 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.