The existence of surface electromagnetic waves in the dielectric-metal interface is due to the sign change of real parts of permittivity across the interface. In this work, we demonstrate that the interface constructed by two semi-infinite photonic crystals with different signs of the imaginary parts of permittivity also supports surface electromagnetic eigenmodes with real eigenfrequencies, protected by $ PT $ symmetry of such loss-gain interface. Using a multiple scattering method and full wave numerical methods, we show that the dispersion of such interface states exhibit unusual features such as zig-zag trajectories or closed-loops. To quantify the dispersion, we establish a non-Hermitian Hamiltonian model that can account for the zig-zag and closed-loop behaviour for arbitrary Bloch momentums. The properties of the interface states near the Brillouin zone center can also be explained within the framework of effective medium theory. It is shown that turning points of the dispersion are exceptional points (EPs), which are characteristic features of non-Hermitian systems. When the permittivity of photonic crystal changes, these EPs can coalesce into higher order EPs or anisotropic EPs. These interface modes hence exhibit and exemplify many complex phenomena related to exceptional point physics.
We demonstrate theoretically the electric tunability due to coalescence of exceptional points in PT-symmetric waveguides bounded by imperfect conductive layers. Owing to the competition effect of multimode interaction, multiple exceptional points and PT phase transitions could be attained in such a simple system and their occurrences are strongly dependent on the boundary conductive layers. When the conductive layers become very thin, it is found that the oblique transmittance and reflectance of the same system can be tuned between zero and one by a small change in carrier density. The results…
In non-hermitian systems, the particular position at which two eigenstates coalesce under a variation of a parameter in the complex plane is called an exceptional point. A non-perturbative theory is proposed which describes the evolution of modes in 2D open dielectric systems when permittivity distribution is modified. We successfully test this theory in a 2D disordered system to predict the position in the parameter space of the exceptional point between two Anderson-localized states. We observe that the accuracy of the prediction depends on the number of localized states accounted for. Such …
Exceptional points, with simultaneous coalescence of eigen-values and eigen-vectors, can be realized with non-Hermitian photonic systems. With the enhanced response, exceptional points have been proposed to improve the performance of photonic sensing. Recently, there are intense debate about the actual sensing advantage of exceptional points. The major concern is that intrinsic noise is also amplified at exceptional points. Here, we aim to clarify the contribution of exceptional points for photonic sensing. This is achieved by analyzing the condition to realize divergent quantum Fisher informa…
Exceptional points as branch singularities describe peculiar degeneracies of non-Hermitian systems that do not obey energy conservation. This work shows that exceptional points can emerge in a topological photonic system, for example, the topological photonic waveguide coupled with two degenerate counter-propagation topological whispering gallery modes. Such a photonic architecture is designed by crystal-symmetry-protected topological photonic insulators based on air rods in conventional dielectric materials. The relevant exceptional point reveals the breaking of the parity-time symmetry, refl…
We report a planar 1D photonic bandgap waveguide exhibiting four second-order exceptional points (EP2s). The interactions between the selective pairs of supported quasi-guided TE modes are modulated by spatial distribution of transverse in-homogeneous gain-loss profile.
The photonic spin Hall effect (SHE), featured by a spin-dependent transverse shift of an impinging optical beam driven by its polarization handedness, has many applications including precise metrology and spin-based nanophotonic devices. It is highly desirable to control and enhance the photonic SHE. However, such a goal remains elusive, due to the weak spin-orbit interaction of light, especially for systems with optical loss. Here we reveal a flexible way to modulate the photonic SHE via exceptional points, by exploiting the transverse shift in a parity-time (PT) symmetric system with balance…
Non-Hermitian systems with parity-time (PT) symmetric complex potentials can exhibit a phase transition when the degree of non-Hermiticity is increased. Two eigenstates coalesce at a transition point, which is known as the exceptional point (EP) for a discrete spectrum and spectral singularity for a continuous spectrum. The existence of an EP is known to give rise to a great variety of novel behaviors in various fields of physics. In this work, we study the complex band structures of one-dimensional photonic crystals with PT symmetric complex potentials by setting up a Hamiltonian using the Bl…
Non-Hermitian systems have recently attracted significant attention in photonics. One of the hallmarks of these systems is the possibility of realizing asymmetric mode switching and omnipolarizer action through the dynamic encirclement of exceptional points (EP). Here, we offer a new perspective on the operating principle of these devices, and we theoretically and experimentally show that asymmetric mode switching and omni-polarizer action can be easily realized with the same performance and limitations, using simple configurations that emulate the physics involved in encircling EPs without th…
We propose a novel inverse-design method that enables brute-force discovery of photonic crystal (PhC) structures with complex spectral degeneracies. As a proof of principle, we demonstrate PhCs exhibiting third-order Dirac points formed by the \emph{accidental} degeneracy of modes of monopolar, dipolar, and quadrupolar nature. We show that under suitable conditions, these modes can coalesce and form a third-order exceptional point (EP3), leading to diverging Petermann factors. We show that the spontaneous emission (SE) rate of emitters at such EP3s, related to the local density of states, can …
Many novel properties of non-Hermitian systems are found at or near the exceptional points-branch points of complex energy surfaces at which eigenvalues and eigenvectors coalesce. In particular, higher-order exceptional points can result in optical structures that are ultrasensitive to external perturbations. Here we show that an arbitrary order exceptional point can be achieved in a simple system consisting of identical resonators placed near a waveguide. Unidirectional coupling between any two chiral dipolar states of the resonators mediated by the waveguide mode leads to the exceptional poi…
Chiral exceptional points (CEPs) have been shown to emerge in traveling wave resonators via asymmetric back scattering from two or more nano-scatterers. Here, we provide a new perspective on the formation of CEPs based on the coupled oscillator model. Our approach provides an intuitive understanding for the modal coalescence that signals the emergence of CEPs, and emphasizes the role played by dissipation throughout this process. In doing so, our model also unveils an otherwise unexplored connection between CEPs and other types of exceptional points associated with parity-time symmetric photon…
We investigate the rich physics of photonic molecule lasers using a non-Hermitian dimer model. We show that several interesting features, predicted recently using a rigorous steady state ab-initio laser theory (SALT), can be captured by this toy model. In particular, we demonstrate the central role played by exceptional points in both pump-selective lasing and laser self-terminations phenomena. Due to its transparent mathematical structure, our model provides a lucid understanding for how different physical parameters (optical loss, modal coupling between microcavities and pump profiles) affec…
We investigate the properties of multidimensional parity-time symmetric periodic systems whose non-Hermitian periodicity is an integer multiple of the underlying Hermitian system's periodicity. This creates a natural set of degeneracies which can undergo thresholdless $\mathcal{PT}$ transitions. We derive a $\mathbf{k} \cdot \mathbf{p}$ perturbation theory suited to the continuous eigenvalues of such systems in terms of the modes of the underlying Hermitian system. In photonic crystals, such thresholdless $\mathcal{PT}$ transitions are shown to yield significant control over the band structure…
Over the past decade, parity-time ($\mathcal{PT}$)-symmetric Hamiltonians have been experimentally realized in classical, optical settings with balanced gain and loss, or in quantum systems with localized loss. In both realizations, the $\mathcal{PT}$-symmetry breaking transition occurs at the exceptional point of the non-Hermitian Hamiltonian, where its eigenvalues and the corresponding eigenvectors both coincide. Here, we show that in lossy systems, the $\mathcal{PT}$ transition is a phenomenon that broadly occurs without an attendant exceptional point, and is driven by the potential asymmet…
A long existing issue for microdisk lasers is the small spontaneous emission coupling rate (β) in microdisk,. We found that it is due to the coupling of emitter spontaneous emission into competing Fabry-Perot (FP) modes in the microdisk cavity. Based on this analysis, we propose a new type of photonic crystal microdisk (PCM) laser to drastically suppress the photonic density of states in the vertical FP modes. As a result, we obtained a three fold increase of β than previously reported highest β of 0.15 at room temperature. The spontaneous emission control in truncated photonic crystals become…
This paper theoretically and numerically studies the response characteristics of non-Hermitian resonant photonic systems operating near an exceptional point (EP), where two resonant eigenmodes coalesce. It is shown that a system near an EP can exhibit a non-Lorentzian frequency response, whose line shape and intensity strongly depend on the modal decay rate and coupling parameters for the input waves, unlike a normal Lorentzian response around a single resonance. In particular, it is shown that the peak intensity of the frequency response is inversely proportional to the fourth power of the mo…
Unconventional Weyl points with topological charges higher than 1 can transform into various complex unconventional Weyl exceptional contours under non-Hermitian perturbations. However, theoretical studies of these exceptional contours have been limited to tight-binding models. Here, we propose to realize unconventional Weyl exceptional contours in photonic continua -- non-Hermitian anisotropic chiral plasma, based on ab initio calculation by Maxwell's equations. By perturbing in-plane permittivity, an unconventional Weyl point can transform into a quadratic Weyl exceptional circle, a Type-I W…
The H1 photonic crystal cavity supports two degenerate dipole modes of orthogonal linear polarization which could give rise to circularly polarized fields when driven with a $π$/$2$ phase difference. However, fabrication errors tend to break the symmetry of the cavity which lifts the degeneracy of the modes, rendering the cavity unsuitable for supporting circular polarization. We demonstrate numerically, a scheme that induces chirality in the cavity modes, thereby achieving a cavity that supports intrinsic circular polarization. By selectively modifying two air holes around the cavity, the dip…
Exceptional points in non-Hermitian systems have recently been shown to possess nontrivial topological properties, and to give rise to many exotic physical phenomena. However, most studies thus far have focused on isolated exceptional points or one-dimensional lines of exceptional points. Here, we substantially expand the space of exceptional systems by designing two-dimensional surfaces of exceptional points, and find that symmetries are a key element to protect such exceptional surfaces. We construct them using symmetry-preserving non-Hermitian deformations of topological nodal lines, and an…
The fundamental active photonic dimer consisting of two coupled quantum well lasers is investigated in the context of the rate equation model. Spectral transition properties and exceptional points are shown to occur under general conditions, not restricted by PT-symmetry as in coupled mode models, suggesting a paradigm shift in the field of non-Hermitian photonics. The optical spectral signatures of system bifurcations and exceptional points are manifested in terms of self-termination effects and observable drastic variations of the spectral line shape that can be controlled in terms of optica…
Controlling gain and loss of coupled optical cavities can induce non-Hermitian degeneracies of eigenstates, called exceptional points (EPs). Various unconventional phenomena around EPs have been reported, and expected to incorporate extra functionalities into photonic devices. The eigenmode exactly under the EP degeneracy is also predicted to exhibit enhanced radiation. However, such responses have yet to be observed in on-chip lasers, because of both the limited controllability of their gain and loss and the lifting of degeneracy by pump-induced cavity detuning. Here, we report the first non-…
We demonstrate the existence of exceptional points of degeneracy (EPD) of periodic eigenstates in non-Hermitian coupled chains of dipolar scatterers. Guided modes supported by these structures can exhibit an EPD in their dispersion diagram at which two or more Bloch eigenstates coalesce, in both their eigenvectors and eigenvalues. We show a second-order modal EPD associated with the parity-time ($\cal{PT}$) symmetry condition, at which each particle pair in the double chain exhibits balanced gain and loss. Furthermore, we also demonstrate a fourth-order EPD occurring at the band edge. Such deg…
Transition of Photonic Dissipative Dynamics through the Exceptional Point
Ministry of Industry and Information Technology Key Lab of Micro-Nano Optoelectronic Information System, Guangdong Provincial Key Laboratory of Semiconductor Optoelectronic Materials and Intelligent Photonic Systems, Harbin Institute of Technology, Shenzhen（工业和信息化部微纳光电信息系统重点实验室，广东省半导体光电子材料与智能光子系统重点实验室，哈尔滨工业大学（深圳））；Pengcheng Laboratory（鹏城实验室）；Quantum Science Center of Guangdong-Hongkong Macao Greater Bay Area（粤港澳大湾区量子科学中心）；Collaborative Innovation Center of Extreme Optics, Shanxi University（极端光学协同创新中心，山西大学）；Heilongjiang Provincial Key Laboratory of Advanced Quantum Functional Materials and Sensor devices, Harbin Institute of Technology, Harbin（黑龙江省先进量子功能材料与传感器器件重点实验室，哈尔滨工业大学）
We theoretically investigate the flow of electromagnetic waves in complex honeycomb photonic lattices with local PT symmetries. Such PT structure is introduced via a judicious arrangement of gain or loss across the honeycomb lattice, characterized by a gain/loss parameter γ. We found a new class of conical diffraction phenomena where the formed cone is brighter and travels along the lattice with a transverse speed proportional to Sqrt (γ).
Non-Hermitian (NH) photonics has attracted considerable attention from researchers owing to exotic properties that originate from the parity-time ($\mathcal{PT}$) phase transition and exceptional points (EPs). To date, the $\mathcal{PT}$ phase transition, EPs, and circling around EPs have been investigated in many photonic systems. However, few studies focused on the singular nature of the EP eigenstates of the Hamiltonian matrices. Moreover, the switching of an EP eigenstate based on the sign of the coupling constant and its manifestation in physical phenomena have not yet been investigated. …
Exceptional points (EPs) with a global collapse of pairs of eigenfunctions are shown to arise in two locally-coupled and spatially-extended optical structures with balanced gain and loss. Global collapse at the EP deeply changes light propagation, which becomes very sensitive to small changes of initial conditions or system parameters, similarly to what happens in models of classical or quantum catastrophes. The implications of global collapse for light behavior are illustrated by considering discrete beam diffraction and Bloch oscillation catastrophe in coupled waveguide lattices.
Exceptional points are a ubiquitous concept widely present in driven-dissipative coupled systems described by a non-Hermitian Hamiltonian. It is characterized by the degeneracy of the Hamiltonian's eigenvalues and coalescence of corresponding eigenvectors. Recent developments demonstrated that exceptional points can play an important role in photonics. However, to date, exceptional points have been extensively examined in the systems supporting only a few optical modes, thereby leaving the observation of collective (multimode) effects outside of the scope of study. In the present paper, we ana…
The sensitivity of perturbation sensing can be effectively enhanced with higher-order exceptional points due to the nonlinear response to frequency splitting. However, the experimental implementation is challenging since all the parameters need to be precisely prepared. The emergence of exceptional surface (ES) improves the robustness of the system to the external environment, while maintaining the same sensitivity. Here, we propose the first scalable protocol for realizing photonic high-order exceptional surface with passive resonators. By adding one or more additional passive resonators in t…
Exceptional light propagation via generalized bulk-edge correspondence
Instituto de Ciencia de los Materiales, Universidad de Valencia（瓦伦西亚大学材料科学研究所）；Instituto de Física e Ciencias Aeroespaciais (IFCAE), Universidade de Vigo（维戈大学物理与航空航天科学研究所）
A generic photonic coupler with active and lossy parts, gain saturation and asymmetric characteristics is examined. Saturable activity is shown to be able to enhance the overall stability of the steady states, prevent evolution to undesirable unbounded modes and allow for bistable operation in specific regions of parametric space. Both stability and bistability are studied in the phase space of the system, where the basins of attraction of each state are identified, providing an accurate description of the dependence of the electric fields on the initial conditions. Continuous families of exce…
We investigate a parity-time (PT) symmetric system that consists of two symmetrically coupled asymmetric dimers. The enclosed magnetic flux controls the PT phase transition. The system can reenter the exact PT-symmetric phase from a broken PT-symmetric phase with large non-Hermiticity. Two-state coalescence may have one or two defective eigenstates. The topology of exceptional points is reflected by the magnetic flux independent phase rigidity scaling exponents. The topology changes when exceptional points coincide. The geometric phases accumulate when encircling the exceptional points and var…
We investigate spontaneous emission from a quantum emitter located within the mode volume of a microring resonator that features chiral exceptional points. We show that this configuration offers enough degrees of freedom to exhibit a full control to either enhance or suppress the emission process. Particularly, we demonstrate that the Purcell factor can be enhanced by a factor of two beyond its value in an identical microring operating at a diabolic point. Our conclusions, which are derived using a non-Hermitian Hamiltonian formalism, are confirmed by employing full-wave simulations of realist…
By exploring the extraordinary property of exceptional points (EPs) in non-Hermitian systems, we here demonstrate that losses can play constructive roles in controlling bistable states. We experimentally realize the EP in a non-Hermitian meta-molecule of coupled resonators in microwave regime. By increasing the loss, we first observe the bistable state suppression at the weak-dissipative regime, but then the bistable state recovery in strong-dissipative regime. Both the experimental and theoretical analysis demonstrate that the revival of bistable states results from the revival of the field i…
Non-Hermitian Exceptional Topology on a Klein Bottle Photonic Circuit
KTH Royal Institute of Technology（皇家理工学院）；Stockholm University（斯德哥尔摩大学）；Rochester Institute of Technology（罗切斯特理工学院）；Huazhong University of Science and Technology（华中科技大学）
Exceptional points (EPs) are degeneracies in open wave systems with coalescence of at least two energy levels and their corresponding eigenstates. In higher dimensions, more complex EP physics not found in two-state systems is observed. We consider the emergence and interaction of multiple EPs in a four coupled optical waveguides system by non-Hermitian coupling showing a unique EP formation pattern in a phase diagram. In addition, absolute phase rigidities are computed to show the mixing of the different states in definite parameter regimes. Our results could be potentially important for deve…
Exceptional Points in Photonics: From Non-Hermitian Physics to Applications
Harbin Engineering University（哈尔滨工程大学）；ITMO University（ITMO大学）；Siberian Federal University（西伯利亚联邦大学）；LV Kirensky Institute of Physics, Federal Research Center KSC SB RAS（LV基伦斯基物理研究所，俄罗斯科学院西伯利亚分院克拉斯诺亚尔斯克科学中心联邦研究中心）；University of California, Irvine（加州大学尔湾分校）；The Hong Kong University of Science and Technology（香港科技大学）
Non-Hermitian singularities known as exceptional-points (EPs) have been shown to exhibit increased sensitivities but the observation of EPs has so far been limited to wavelength scaled systems subject to diffraction limit. We propose a novel approach to EPs and report their first observation in plasmonics at room temperature. The plasmonic EPs are based on the hybridization of detuned resonances in multilayered plasmonic crystals to reach a critical complex coupling rate between nanoantennas arrays, and, resulting in the simultaneous coalescence of the resonances and loss rates. Because plasmo…
There has been remarkable recent progress in the formation of nano-resonators that support ultra-low-loss, compact dielectric photonic crystals with exceptional high-Q modes that operate at visible or telecom wavelengths. New insights into modal engineering have recently emerged from researchers exploring exotic electronic phases in 2D materials. The phenomenon relates to a twist in the angle between two layers of materials with high periodic spatial ordering, such as graphene. A moire pattern forms, and at a particular magic angle of twist, the electronic behavior significantly changes, enjoy…
