The non-Bloch band theory can describe energy bands in a one-dimensional (1D) non-Hermitian system. On the other hand, whether the non-Bloch band theory can be extended to higher-dimensional non-Hermitian systems is nontrivial. In this work, we construct the non-Bloch band theory in two classes of two-dimensional non-Hermitian systems, by reducing the problem to that for a 1D non-Hermitian model. In these classes of systems, we get the generalized Brillouin zone for a complex wavevector and investigate topological properties. In the model of the non-Hermitian Chern insulator, as an example, we show the bulk-edge correspondence between the Chern number defined from the generalized Brillouin zone and the appearance of the edge states.

Non-Bloch bands in two-dimensional non-Hermitian systems

In this paper, we introduce the concept of dynamical degeneracy splitting to describe the anisotropic decay behaviors in non-Hermitian systems. We demonstrate that systems with dynamical degeneracy splitting exhibit two distinctive features: (i) the system shows frequency-resolved non-Hermitian skin effect; (ii) Green's function exhibits anomalous at given frequency, leading to uneven broadening in spectral function and anomalous scattering. As an application, we propose directional invisibility based on wave packet dynamics to investigate the geometry-dependent skin effect in higher dimensions. Our work elucidates a faithful correspondence between non-Hermitian skin effect and Green's function, offering a guiding principle for exploration of novel physical phenomena emerging from this effect.

Dynamical Degeneracy Splitting and Directional Invisibility in Non-Hermitian Systems

1D chains with non-reciprocal tunneling realizing the non-Hermitian skin effect (NHSE) have attracted considerable interest in the last years whereas their experimental realization in real space remains limited to a few examples. In this work, we propose a new generic way of implementing non-reciprocity based on a combination of the Rashba-Dresshlauss spin-orbit coupling, existing for electrons, cold atoms, and photons, and a lifetime imbalance between two spin components. We show that one can realize the Hatano-Nelson model, the non-Hermitian Su-Schrieffer-Heeger model, and even observe the NHSE in a 1D potential well without the need for a lattice. We further demonstrate the practical feasibility of this proposal by considering the specific example of a photonic liquid crystal microcavity. This platform allows one to switch on and off the NHSE by applying an external voltage to the microcavity.

Non-Hermitian skin effect induced by Rashba-Dresselhaus spin-orbit coupling

Exceptional points and skin effect, as the two distinct hallmark features unique to the non-Hermitian physics, have each attracted enormous interests. Recent theoretical works reveal that the topologically nontrivial exceptional points can give rise to the non-Hermitian skin effect, which is geometry-dependent. However, this kind of novel correspondence between the exceptional points and skin effect remains to be confirmed by experiments. Here, we corroborate the correspondence in a non-Hermitian phononic crystal. The exceptional points connected by the bulk Fermi arcs, and the skin effects with the geometry dependence, are evidenced in simulations and experiments. Our work, building an experimental bridge between the exceptional points and skin effect and uncovering the unconventional geometry-dependent skin effect, expands a horizon in non-Hermitian physics.

Observation of exceptional points and skin effect correspondence in non-Hermitian phononic crystals

We explore absorbing open-boundary modes in non-Hermitian photonic systems. The modes have a continuum spectrum in the infinite-system-size limit and can exhibit the non-Hermitian skin effect. In contrast to the conventional non-Hermitian skin modes under the fixed-end open-boundary condition, the modes concerned exhibit a strongly size-dependent spectrum that gradually converges to the non-Bloch-band dispersion. The modes correspond to the poles of the $S$ matrix and are closely related to the lasing. We demonstrate these properties in a two-dimensional non-Hermitian photonic crystal with gain having a point-(pseudo)gap topology. 

Non-Hermitian skin effect and lasing of absorbing open-boundary modes in photonic crystals

Abstract Skin effect that all eigenmodes within a frequency range become edge states is dictated by the topological properties of complex eigenvalues unique in non-Hermitian systems. The prevailing attempts to realize such a fascinating effect are confined to either one-dimensional or nonreciprocal systems exhibiting asymmetric couplings. Here, inspired by a recent model Hamiltonian theory, we propose a realistic reciprocal two-dimensional (2D) photonic crystal (PhC) system that shows the desired skin effect. Specifically, we establish a routine for designing such non-Hermitian systems via revealing the inherent connections between the nontrivial eigenvalue topology of order-2 exceptional points (EPs) and the skin effects. Guided by the proposed strategy, we successfully design a 2D PhC that possesses the EPs with nonzero eigenvalue winding numbers. The spectral area along a specific wavevector direction is then formed by leveraging the symmetry of the macroscopic geometry and the unit cell. The projected-band-structure calculations are performed to demonstrate that the desired skin effect exists at the specific crystalline interfaces. We finally employ time-domain simulations to vividly illustrate this phenomenon by exciting a pulse at the center of a finite-sized PhC. Our results form a solid basis for further experimental confirmations and applications of the skin effect.

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Geometry-dependent skin effects in reciprocal photonic crystals

Abstract Designing perfect anomalous reflectors is crucial for achieving many metasurface-based applications, but available design approaches for the cases of extremely large bending angles either require unrealistic gain–loss materials or rely on brute-force optimizations lacking physical guidance. Here, we propose a deterministic approach to design passive metasurfaces that can reflect impinging light to arbitrary nonspecular directions with almost 100% efficiencies. With both incident and out-going far-field waves given, we can retrieve the surface-impedance profile of the target metadevice by matching boundary conditions with all allowed near-field modes added self-consistently and then construct the metadevices deterministically based on passive meta-atoms exhibiting local responses. We design/fabricate two proof-of-concept microwave metadevices and experimentally demonstrate that the first one achieves anomalous reflection to a 70° angle with efficiency ∼98%, and the second one can generate multiple reflected beams with desired bending angles and power allocations. Our findings pave the way for realizing high-efficiency wave-control metadevices with desired functionalities.

/pdf/deterministic-approach-to-design-passive-anomalous-f7kuq9k3.pdf

Deterministic approach to design passive anomalous-diffraction metasurfaces with nearly 100% efficiency

Raman‐fluorescence dual‐mode enhanced nanoparticles have enormous potential for bioimaging with combined advantages of sensitivity and speed. This is primarily achieved through a trade‐off between fluorescence quenching and electromagnetic (EM) enhancement on the plasmonic metal surface, as demonstrated in previous research. A strategy that can minimize EM‐field attenuation and temporal photobleaching would be highly desirable. In this study, a novel approach using Raman‐fluorescence enhanced dual‐mode nanoparticles with the near‐infrared fluorescence reporter IR780 directly embedded in the ultra‐high EM fields between gold (Au) nanopetals of various morphology and a silver (Ag) coating without a spacer is presented. The results show these nanoparticles to be single‐nanoparticle Raman sensitive and that they can generate a fluorescence enhancement factor as high as 1113 experimentally and 2000 by numerical simulation. The random morphology of the nanopetals supports broadband resonances for both fluorescence excitation and emission, resulting in nanowatt detectability, the dual‐mode photostability of more than 30 min under continuous laser irradiation, and a long shelf life, making them promising for wide applications in bioimaging with ultra‐brightness, low laser power, and long‐duration monitoring. In summary, they represent a novel strategy for high‐performance Raman‐fluorescence enhancement dual‐mode nanotags.

Zhening Fang

Papers

Geometry-dependent skin effects in reciprocal photonic crystals

Deterministic approach to design passive anomalous-diffraction metasurfaces with nearly 100% efficiency

Ultrahigh Raman‐Fluorescence Dual‐Enhancement in Nanogaps of Silver‐Coated Gold Nanopetals