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The ability to detect the polarization information of light is often crucial for various applications in optical systems. However, conventional polarization-sensitive photodetectors struggle to simultaneously achieve a wide band coverage and high-precision detection, severely hindering the development of polarization detectors. In this study, a reflective metasurface with full-Stokes detection capabilities over a wide range is proposed. It integrates four linear polarization filters and two circular polarization filters operating in the near-infrared region. By dynamically adjusting the refractive index of the liquid crystal covering the detector surface, high performance full-Stokes parameter detection can be achieved between 730-770 nm with detection error below 0.07. Therefore, this study provides a design approach for the potential application of Stokes polarization detection over a broadband spectrum.

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Non-Hermitian matrices are ubiquitous in the description of nature ranging from classical dissipative systems, including optical, electrical, and mechanical metamaterials, to scattering of waves and open quantum many-body systems. Seminal line-gap and point-gap classifications of non-Hermitian systems using K-theory have deepened the understanding of many physical phenomena. However, ample systems remain beyond this description; reference points and lines do not in general distinguish whether multiple non-Hermitian bands exhibit intriguing exceptional points, spectral braids and crossings. To address this we consider two different notions: non-Hermitian band gaps and separation gaps that crucially encompass a broad class of multi-band scenarios, enabling the description of generic band structures with symmetries. With these concepts, we provide a unified and comprehensive classification of both gapped and nodal systems in the presence of physically relevant parity-time (PT) and pseudo-Hermitian symmetries using homotopy theory. This uncovers new stable topology stemming from both eigenvalues and wave functions, and remarkably also implies distinct fragile topological phases. In particular, we reveal different Abelian and non-Abelian phases inPT-symmetric systems, described by frame and braid topology. The corresponding invariants are robust to symmetry-preserving perturbations that do not induce (exceptional) degeneracy, and they also predict the deformation rules of nodal phases. We further demonstrate that spontaneousPTsymmetry breaking is captured by Chern-Euler and Chern-Stiefel-Whitney descriptions, a fingerprint of unprecedented non-Hermitian topology previously overlooked. These results open the door for theoretical and experimental exploration of a rich variety of novel topological phenomena in a wide range of physical platforms.

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Non-Hermitian degeneracies, also known as exceptional points (EPs), have presented remarkable singular characteristics such as the degeneracy of eigenvalues and eigenstates and enable limitless opportunities for achieving fascinating phenomena in EP photonic systems. Here, the general theoretical framework and experimental verification of a non-Hermitian metasurface that holds a pair of anti-chiral EPs are proposed as a novel approach for efficient terahertz (THz) switching. First, based on the Pancharatnam-Berry (PB) phase and unitary transformation, it is discovered that the coupling variation of ±1 spin eigenstates will lead to asymmetric modulation in two orthogonal linear polarizations (LP). Through loss-induced merging of a pair of anti-chiral EPs, the decoupling of ±1 spin eigenstates are then successfully realized in a non-Hermitian metasurface. Final, the efficient THz modulation is experimentally demonstrated, which exhibits modulation depth exceeding 70% and Off-On-Off switching cycle less than 9 ps in one LP while remains unaffected in another one. Compared with conventional THz modulation devices, the metadevice shows several figures of merits, such as a single frequency operation, high modulation depth, and ultrafast switching speed. The proposed theory and loss-induced non-Hermitian device are general and can be extended to numerous photonic systems varying from microwave, THz, infrared, to visible light.

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This work comprehensively investigates the non-Hermitian skin effect (NHSE) in a spinless Bernevig-Hughes-Zhang -like model in one dimension. It is generally believed that a system with non-reciprocal hopping amplitudes demonstrates NHSE. However, we show that there are exceptions, and more in-depth analyses are required to decode the presence of NHSE or its variants in a system. The fascinating aspects of our findings, depending on the inclusion of non-reciprocity in the inter-orbital hopping terms, concede the existence of conventional NHSE or NHSE at both edges and even a surprising absence of NHSE. The topological properties and the (bi-orthogonal) bulk-boundary correspondence, enumerated via computation of the (complex) Berry phase and spatial localization of the edge modes, highlight the topological phase transitions occurring therein. Further, to facilitate a structured discussion of the non-Hermitian model, we split the results intoPTsymmetric and non-PTsymmetric cases with a view to comparing the two.

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Exceptional points (EPs), known as non-Hermitian singularities, have been observed and investigated in parity-time symmetric metasurfaces. However, the chirality and tunability in non-Hermitian metasurfaces still need to be explored. Here, we propose a dynamic topological metasurface with the meta-atom consisting of two orthogonally oriented nanorods, which are placed on the phase change material Ge2Sb2Te5 (GST) and SiO2 dielectric layer, respectively. When GST is converted from the amorphous state (a-GST) to the crystalline state (c-GST), an EP can be dynamically switched from the "ON" state to the "OFF" state in a parameter space. Moreover, based on the topologically protected phase and amplitude modulations of the cross-polarization component, the phase-only hologram and amplitude-only hologram are engineered in the a-GST case and concealed in the c-GST case. Finally, we explore the 2D-chiral symmetry of meta-atoms and further propose two spin-selective meta-deflectors and a hybrid meta-deflector operating with arbitrary polarizations. The GST-based hybrid metasurface offers richer possibilities to realize various wavefront controls.

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This research introduces a novel methodology of harnessing liquids to facilitate the realization of parity-time (PT)-symmetric optical waveguides on highly integrated microscale platforms. Additionally, we propose a realistic and detailed fabrication process flow, demonstrating the practical feasibility of fabricating our optofluidic system, thereby bridging the gap between theoretical design and actual implementation. Extensive research has been conducted over the past two decades on PT-symmetric systems across various fields, given their potential to foster a new generation of compact, power-efficient sensors and signal processors with enhanced performance. Passive PT-symmetry in optics can be achieved by evanescently coupling two optical waveguides and incorporating an optically lossy material into one of the waveguides. The essential coupling distance between two optical waveguides in air is usually less than 500 nm for near-infrared wavelengths and under 100 nm for ultraviolet wavelengths. This necessitates the construction of the coupling region via expensive and time-consuming electron beam lithography, posing a significant manufacturing challenge for the mass production of PT-symmetric optical systems. We propose a solution to this fabrication challenge by introducing liquids capable of dynamic flow between optical waveguides. This technique allows the attainment of evanescent wave coupling with coupling gap dimensions compatible with standard photolithography processes. Consequently, this paves the way for the cost-effective, rapid and large-scale production of PT-symmetric optofluidic systems, applicable across a wide range of fields.

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Ultrafast all-optical modulation with optically resonant nanostructures is an essential technology for high-speed signal processing on a compact optical chip. Key challenges that exist in this field are relatively low and slow modulations in the visible range as well as the use of expensive materials. Here we develop an ultrafast all-optical modulator based on MAPbBr3 perovskite metasurface supporting exciton-polariton states with exceptional points. The additional angular and spectral filtering of the modulated light transmitted through the designed metasurface allows us to achieve 2500% optical signal modulation with the shortest modulation time of 440 fs at the pump fluence of ∼40 µJ/cm2. Such a value of the modulation depth is record-high among the existing modulators in the visible range, while the main physical effect behind it is polariton condensation. Scalable and cheap metasurface fabrication via nanoimprint lithography along with the simplicity of perovskite synthesis and deposition make the developed approach promising for real-life applications.

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Acoustic metasurfaces are at the frontier of acoustic functional material research owing to their advanced capabilities of wave manipulation at an acoustically vanishing size. Despite significant progress in the last decade, conventional acoustic metasurfaces are still fundamentally limited by their underlying physics and design principles. First, conventional metasurfaces assume that unit cells are decoupled and therefore treat them individually during the design process. Owing to diffraction, however, the non-locality of the wave field could strongly affect the efficiency and even alter the behavior of acoustic metasurfaces. Additionally, conventional acoustic metasurfaces operate by modulating the phase and are typically treated as lossless systems. Due to the narrow regions in acoustic metasurfaces' subwavelength unit cells, however, losses are naturally present and could compromise the performance of acoustic metasurfaces. While the conventional wisdom is to minimize these effects, a counter-intuitive way of thinking has emerged, which is to harness the non-locality as well as loss for enhanced acoustic metasurface functionality. This has led to a new generation of acoustic metasurface design paradigm that is empowered by non-locality and non-Hermicity, providing new routes for controlling sound using the acoustic version of 2D materials. This review details the progress of non-local and non-Hermitian acoustic metasurfaces, providing an overview of the recent acoustic metasurface designs and discussing the critical role of non-locality and loss in acoustic metasurfaces. We further outline the synergy between non-locality and non-Hermiticity, and delineate the potential of using non-local and non-Hermitian acoustic metasurfaces as a new platform for investigating exceptional points, the hallmark of non-Hermitian physics. Finally, the current challenges and future outlook for this burgeoning field are discussed.

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In light of a general scenario of a two-level non-Hermitian PT-symmetric Hamiltonian, we apply the tetrad-based method to analyze the possibility of analogue Hawking radiation. We carry this out by making use of the conventional null-geodesic approach, wherein the associated Hawking radiation is described as a quantum tunneling process across a classically forbidden barrier on which the event horizon imposes. An interesting aspect of our result is that our estimate for the tunneling probability is independent of the non-Hermitian parameter that defines the guiding Hamiltonian.

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The spectral properties of gap electroacoustic waves in aPT-symmetric structure of piezoelectrics of symmetry class 6 mm separated by a gap are theoretically investigated. The spectra were calculated for lead germanate (non-zero transverse piezoactivity) and barium titanate (symmetry class 4 mm-zero transverse piezoactivity). It has been established that at a certain level of losses and gain in piezoelectrics, the symmetric and antisymmetric modes intersect. The intersection point determines the singular point of thePT-symmetric structure. Beyond this point, there is a violation of the symmetric and antisymmetric distribution of electric fields in the gap of the slotted structure of two identical piezoelectrics, which is confirmed by the calculation of the electric field profiles. It is shown that the dependence of the amplitude on the frequency at an exceptional point has an extremely narrow resonance peak, which opens up the possibility of creating supersensitive sensors based onPT-symmetric physical structures.

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Non-Hermitian systems have been widely explored in platforms ranging from photonics to electric circuits. A defining feature of non-Hermitian systems is exceptional points (EPs), where both eigenvalues and eigenvectors coalesce. Tropical geometry is an emerging field of mathematics at the interface between algebraic geometry and polyhedral geometry, with diverse applications to science. Here, we introduce and develop a unified tropical geometric framework to characterize different facets of non-Hermitian systems. We illustrate the versatility of our approach using several examples and demonstrate that it can be used to select from a spectrum of higher-order EPs in gain and loss models, predict the skin effect in the non-Hermitian Su-Schrieffer-Heeger model, and extract universal properties in the presence of disorder in the Hatano-Nelson model. Our work puts forth a framework for studying non-Hermitian physics and unveils a connection of tropical geometry to this field.

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The synergy between non-Hermitian concepts and topological ideas have led to very fruitful activity in the recent years. Their interplay has resulted in a wide variety of new non-Hermitian topological phenomena being discovered. In this review, we present the key principles underpinning the topological features of non-Hermitian phases. Using paradigmatic models-Hatano-Nelson, non-Hermitian Su-Schrieffer-Heeger and non-Hermitian Chern insulator-we illustrate the central features of non-Hermitian topological systems, including exceptional points, complex energy gaps and non-Hermitian symmetry classification. We discuss the non-Hermitian skin effect and the notion of the generalized Brillouin zone, which allows restoring the bulk-boundary correspondence. Using concrete examples, we examine the role of disorder, describe the Floquet engineering, present the linear response framework, and analyze the Hall transport properties of non-Hermitian topological systems. We also survey the rapidly growing experimental advances in this field. Finally, we end by highlighting possible directions which, in our view, may be promising for explorations in the near future.

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Efficient control of integrated light sources is crucial to advancing practical applications of nanophotonics. Despite the success of microlasers, their sophisticated nanostructures are not applicable in nanolasers. The situation for bottom-up-synthesized nanolasers becomes more challenging due to the constraints of fixed cavity shapes and fragile material stability. Here, the physics of exceptional points (EPs) is employed, and a strategy is demonstrated to precisely tune the lasing actions in lead halide perovskite nanorods. By placing a nanoparticle to the boundary of a square nanocavity, it is shown that EPs regularly and controllably emerge as a function of the nanoparticle position. Consequently, both the internal lasing actions and their far-field radiation can be completely reversed with a tiny displacement of <100 nm. The new strategy for controlling lasing actions in nanocavities is confirmed with numerical simulations and lasing experiments. This research can also bring new avenues for ultrasensitive position sensing.

Asunto(s)

RESUMEN

Exceptional points (EPs) are spectral degeneracies of non-Hermitian (NH) systems where eigenvalues and eigenvectors coalesce, inducing unique topological phases that have no counterpart in the Hermitian realm. Here we consider an NH system by coupling a two-dimensional semiconductor with Rashba spin-orbit coupling (SOC) to a ferromagnet lead and show the emergence of highly tunable EPs along rings in momentum space. Interestingly, these exceptional degeneracies are the endpoints of lines formed by the eigenvalue coalescence at finite real energy, resembling the bulk Fermi arcs commonly defined at zero real energy. We then show that an in-plane Zeeman field provides a way to control these exceptional degeneracies although higher values of non-Hermiticity are required in contrast to the zero Zeeman field regime. Furthermore, we find that the spin projections also coalescence at the exceptional degeneracies and can acquire larger values than in the Hermitian regime. Finally, we demonstrate that the exceptional degeneracies induce large spectral weights, which can be used as a signature for their detection. Our results thus reveal the potential of systems with Rashba SOC for realizing NH bulk phenomena.

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The present work addresses the distinction between the topological properties ofPTsymmetric and non-PTsymmetric scenarios for the non-Hermitian Su-Schrieffer-Heeger model. The non-PTsymmetric case is represented by non-reciprocity in both the inter- and the intra-cell hopping amplitudes, while the one withPTsymmetry is modeled by a complex on-site staggered potential. In particular, we study the loci of the exceptional points, the winding numbers, band structures, and explore the breakdown of bulk-boundary correspondence (BBC). We further study the interplay of the dimerization strengths on the observables for these cases. The non-PTsymmetric case denotes a more familiar situation, where the winding number abruptly changes by half-integer through tuning of the non-reciprocity parameters, and demonstrates a complete breakdown of BBC, thereby showing non-Hermitian skin effect. The topological nature of thePTsymmetric case appears to follow closely to its Hermitian analogue, except that it shows unbroken (broken) regions with complex (purely real) energy spectra, while another variant of the winding number exhibits a continuous behavior as a function of the strength of the potential, while the conventional BBC is preserved.

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Artificial structures provide an efficient method to generate acoustic vortices carrying orbital angular momentum (OAM) essential for applications ranging from object manipulation to acoustic communication. However, their flexibility in terms of chirality control has thus far been limited by the lack of reconfigurability and degrees of freedom like spin-orbit coupling. Here we show that this restriction can be lifted by controlling the individual on-off states of two coherent monopolar sources inside a passive parity-time-symmetric ring cavity at an exceptional point where the counter-propagating waves coalesce into one chiral eigenmode. One of the sources satisfies the chirality-reversal condition, generating a travelling wave field fully decoupled from and opposite to the chiral eigenmode, while the other source is phase-shifted such that the wave generated by the first source can be canceled out, and the remaining sound field circulates in the same direction as the chiral eigenmode. Such non-Hermitian selective excitation enables our experimental realization of acoustic vortex emission with switchable OAM but free of system reconfiguration. Our work offers opportunities for chiral sound manipulation as well as integrated and tunable acoustic OAM devices.

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The conventional non-Hermitian but P T -symmetric three-parametric Bose-Hubbard Hamiltonian H(γ, v, c) represents a quantum system of N bosons, unitary only for parameters γ, v and c in a domain D . Its boundary ∂ D contains an exceptional point of order K (EPK; K = N + 1) at c = 0 and γ = v, but even at the smallest non-vanishing parameter c ≠ ~0 the spectrum of H(v, v, c) ceases to be real, i.e. the system ceases to be observable. In this paper, the question is inverted: all of the stable, unitary and observable Bose-Hubbard quantum systems are sought which would lie close to the phenomenologically most interesting EPK-related dynamical regime. Two different families of such systems are found. Both of them are characterized by the perturbed Hamiltonians H ( λ ) = H ( v , v , 0 ) + λ V for which the unitarity and stability of the system is guaranteed. In the first family the number N of bosons is assumed conserved while in the second family such an assumption is relaxed. Attention is paid mainly to an anisotropy of the physical Hilbert space near the EPK extreme. We show that it is reflected by a specific, operationally realizable structure of perturbations λ V which can be considered small.

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With the corresponding Liouvillian as a starting point, we demonstrate two seemingly new phenomena of the STIRAP problem when subjected to irreversible losses. It is argued that both of these can be understood from an underlying Zeno effect, and in particular both can be viewed as if the environment assists the STIRAP population transfer. The first of these is found for relative strong dephasing, and, in the language of the Liouvillian, it is explained from the explicit form of the matrix generating the time-evolution; the coherence terms of the state decay off, which prohibits further population transfer. For pure dissipation, another Zeno effect is found, where the presence of a non-zero Liouvillian gap protects the system's (adiabatic) state from non-adiabatic excitations. In contrast to full Zeno freezing of the evolution, which is often found in many problems without explicit time-dependence, here, the freezing takes place in the adiabatic basis such that the system still evolves but adiabatically.

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Sets in the parameter space corresponding to complex exceptional points (EP) have high codimension, and by this reason, they are difficult objects for numerical location. However, complex EPs play an important role in the problems of the stability of dissipative systems, where they are frequently considered as precursors to instability. We propose to locate the set of complex EPs using the fact that the global minimum of the spectral abscissa of a polynomial is attained at the EP of the highest possible order. Applying this approach to the problem of self-stabilization of a bicycle, we find explicitly the EP sets that suggest scaling laws for the design of robust bikes that agree with the design of the known experimental machines.

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Controlling the emission and the flow of light in micro- and nanostructures is crucial for on-chip information processing. Here we show how to impose a strong chirality and a switchable direction of light propagation in an optical system by steering it to an exceptional point (EP)-a degeneracy universally occurring in all open physical systems when two eigenvalues and the corresponding eigenstates coalesce. In our experiments with a fiber-coupled whispering-gallery-mode (WGM) resonator, we dynamically control the chirality of resonator modes and the emission direction of a WGM microlaser in the vicinity of an EP: Away from the EPs, the resonator modes are nonchiral and laser emission is bidirectional. As the system approaches an EP, the modes become chiral and allow unidirectional emission such that by transiting from one EP to another one the direction of emission can be completely reversed. Our results exemplify a very counterintuitive feature of non-Hermitian physics that paves the way to chiral photonics on a chip.