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, 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 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, 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.

Non-Hermitian chiral degeneracy of gated graphene metasurfaces

“…For the exploration of non-Hermitian physics and the application of EP-enabled functionalities, metasurfaces 22,23,[27][28][29] are now being considered one of the most versatile platforms because their constituent metaatoms are inherently constructed from lossy coupled subwavelength-scale resonators. Generally, any change in the polarisation state of light transmitted through the non-Hermitian metasurface can be characterised by a non-Hermitian Jones matrix that plays the role of an effective Hamiltonian [28][29][30][31][32][33] .…”

Uniform Huygens Metasurfaces with Postfabrication Phase Pattern Recording Functionality

“…We have demonstrated in our previous work that Huygens metasurfaces behavior is governed by the positions in the complex frequency plane of topological phase singularities (zeros and poles of the transmission coefficient), special points in the complex frequency plane that are turning metasurface optical transmission into zero or infinity, respectively, with the phase value wrapping around the singular point . These two types of singularities have the opposite topological charge ±1; they exist in pairs of the opposite charge and can annihilate when they superimpose.…”

“…It has recently been proposed theoretically that a full 2π resonant phase gradient can be produced in metasurfaces by breaking symmetries . Parity-time breaking in reflection or time-reversal symmetry breaking in transmission are shown to relax the restrictions on the values of system eigenfrequencies of different types.…”

“…In transmission, explicit time-reversal symmetry breaking requires gain-loss engineering, which is not technologically relevant to this problem. The other solution is spontaneous symmetry breaking, which relies on the interaction of two transmission zeros associated with two resonant modes, the effect demonstrated in Huygens metasurfaces . Therefore, in transmission, our choice is limited to Huygens metasurfaces that have been, and still are, receiving tremendous attention due to their ability to reach high efficiencies combined with a full 2π phase coverage for arbitrary wavefront shaping .…”

Derivation of the Transient and Steady Optical States from the Poles of the S‐Matrix

“…Let us emphasize that the S-and T-matrix formalism is very general [10,35,[55][56][57][58] and that the singularity expansion method can be applied to 2D [40] and 3D scatterers, [49,59] and also periodic structures such as diffraction gratings or metasurfaces. [8,60] The method derived in this work is therefore general and can be applied to other geometries of photonic cavities.…”