Combating the effects of disorder on light transport in micro- and nano-integrated photonic devices is of major importance from both fundamental and applied viewpoints. In ordinary waveguides, imperfections and disorder cause unwanted back-reflections, which hinder large-scale optical integration. Topological photonic structures, a new class of optical systems inspired by quantum Hall effect and topological insulators, can realize robust transport via topologically-protected unidirectional edge modes. Such waveguides are realized by the introduction of synthetic gauge fields for photons in a two-dimensional structure, which break time reversal symmetry and enable one-way guiding at the edge of the medium. Here we suggest a different route toward robust transport of light in lower-dimensional (1D) photonic lattices, in which time reversal symmetry is broken because of the {\it non-Hermitian} nature of transport. While a forward propagating mode in the lattice is amplified, the corresponding backward propagating mode is damped, thus resulting in an asymmetric transport that is rather insensitive to disorder or imperfections in the structure. Non-Hermitian transport in two lattice models is considered: a tight-binding lattice with an imaginary gauge field (Hatano-Nelson model), and a non-Hermitian driven binary lattice. In the former case transport in spite of disorder is ensured by a mobility edge that arises because of a non-Hermitian delocalization transition. The possibility to observe non-Hermitian delocalization induced by a synthetic 'imaginary' gauge field is suggested using an engineered coupled-resonator optical waveguide (CROW) structure.
The phenomenon of chiral-symmetry protected thermalization gap in Hermitian photonic systems is counterintuitive as it implies that the photon coherence can be continuously improved by disorders towards an asymptotic limit. We show that the phenomenon disappears in time-independent, non-Hermitian photonic systems even when the chiral symmetry is well preserved. In fact, the degree of thermalization generally increases with the disorder strength, in agreement with intuition. As non-Hermitian characteristics (e.g., weak gain and loss) can be expected in realistic physical situations, the phenome…
Discrete-time photonic quantum walks on a synthetic lattice, where both spatial and temporal evolution of light is discretized, have provided recently a fascinating platform for the observation of a wealth of non-Hermitian physical phenomena and for the control of light scattering in complex media. A rather open question is whether invisible potentials, analogous to the ones known for continuous optical media, do exist in such discretized systems. Here it is shown that, under certain conditions, slowly-drifting Kramers-Kronig potentials behave as invisible potentials in discrete-time photonic …
In the past decade, the concept of parity-time ($\mathcal{PT}$) symmetry, originally introduced in non-Hermitian extensions of quantum mechanical theories, has come into thinking of photonics, providing a fertile ground for studying, observing, and utilizing some of the peculiar aspects of $\mathcal{PT}$ symmetry in optics. Together with related concepts of non-Hermitian physics of open quantum systems, such as non-Hermitian degeneracies (exceptional points) and spectral singularities, $\mathcal{PT}$ symmetry represents one among the most fruitful ideas introduced in optics in the past few yea…
In this paper, a non-Hermitian two-dimensional photonic crystal flat lens is proposed. The negative refraction of the second band of photonic crystal is utilized to realize super-resolution imaging of the point source. Based on the principles of non-Hermitian systems, a negative imaginary part is introduced into the imaging frequency, in which case the imaging intensity and resolution are improved. The results indicate that the non-Hermitian system provides a new method to improve the imaging performance of the photonic crystal lens.
Zitterbewegung (ZB) is a phenomenon in relativistic quantum systems where the electron wave packet exhibits a trembling or oscillating behavior during its motion, caused by its interaction or coupling with the negative energy state. To directly observe ZB in electronic systems is difficult, due to the challenges associated with the atomic scale wavelength of the electron. Photonic systems offer an alternative paradigm. We exploit the concept of pseudo parity-time (pseudo PT ) symmetry to study ZB in non-Hermitian quantum systems implemented as an experimentally feasible optical waveguide array…
Spatiotemporal Topological Phase Transition in non-Hermitian Photonic System
Key Laboratory of Multiscale Spin Physics (Ministry of Education), Applied Optics Beijing Area Major Laboratory, School of Physics and Astronomy, Beijing Normal University（多尺度自旋物理教育部重点实验室，应用光学北京地区重大实验室，北京师范大学物理与天文学院）
Non-Hermitian skin effect denotes the exponential localization of a large number of eigen-states in a non-Hermitian lattice under open boundary conditions. Such a non-Hermiticity-induced skin effect can offset the penetration depth of in-gap edge states, leading to counterintuitive delocalized edge modes, which have not been studied in a realistic photonic system such as photonic crystals. Here, we analytically reveal the non-Hermitian skin effect and the delocalized edge states in Maxwell's equations for non-Hermitian chiral photonic crystals with anomalous parity-time symmetry. Remarkably, w…
In non-Hermitian quasicrystals, mobility edges (ME) separating localized and extended states in complex energy plane can arise as a result of non-Hermitian terms in the Hamiltonian. Such ME are of topological nature, i.e. the energies of localized and extended states exhibit distinct topological structures in the complex energy plane. However, depending on the origin of non-Hermiticity, i.e. asymmetry of hopping amplitudes or complexification of the incommensurate potential phase, different winding numbers are introduced, corresponding to different transport features in the bulk of the lattice…
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）
A hallmark of topological band theory in periodic media is that bulk properties are not affected by boundary conditions. Remarkably, in certain non-Hermitian lattices the bulk properties are largely affected by boundaries, leading to such major effects as the non-Hermitian skin effect and violation of the bulk-boundary correspondence. Here we unveil that non-unitary discrete-time quantum walks of photons in systems involving gain and loss show rather generally non-Bloch parity-time ($\mathcal{PT}$) symmetry breaking phase transitions, and suggest a bulk probing method to detect such boundary-d…
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 ga…
Parity-time ($\mathcal{PT}$) symmetry, originally conceived for non-Hermitian open quantum systems, has opened an excitingly new avenue for the coherent control of light. By tailoring optical gain and loss in integrated photonic structures, $\mathcal{PT}$ symmetric non-Hermitian photonics has found applications in many fields ranging from single mode lasing to novel topological matters. Here we propose a new paradigm towards non-Hermitian photonics based on the charge-parity ($\mathcal{CP}$) symmetry that has the potential to control the flow of light in an unprecedented way. In particular, we…
Observation of non-Hermitian point gap in photonic crystals
Institute of Science Tokyo（科学技術大学）；Department of Physics, Institute of Science Tokyo（科学技術大学物理学科）；Institute of Industrial Science, The University of Tokyo（东京大学工业科学研究所）；NTT Basic Research Laboratories, NTT Corporation（日本电信电话株式会社基础研究中心）；Nanophotonics Center, NTT Corporation（日本电信电话株式会社纳米光子学中心）
Chirality is ubiquitous from microscopic to macroscopic phenomena in physics and biology, such as fermionic interactions and DNA duplication. In photonics, chirality has traditionally represented differentiated optical responses for right and left circular polarizations. This definition of optical chirality in the polarization domain includes handedness-dependent phase velocities or optical absorption inside chiral media, which enable polarimetry for measuring the material concentration and circular dichroism spectroscopy for sensing biological or chemical enantiomers. Recently, the emerging f…
Recent studies of disorder or non-Hermiticity induced topological insulators inject new ingredients for engineering topological matter. Here we consider the effect of purely non-Hermitian disorders, a combination of these two ingredients, in a 1D coupled-cavity array with disordered gain and loss. Topological photonic states can be induced by increasing gain-loss disorder strength with topological invariants carried by localized states in the complex bulk spectra. The system showcases rich phase diagrams and distinct topological states from Hermitian disorders. The non-Hermitian critical behav…
We present an analytical study of the mode degeneracy in non-Hermitian photonic crystals (PC) with $C_{4v}$ symmetry, from the perspective of the coupled-wave-theory (CWT). The wave couplings and leakages within the non-Hermitian PCs are depicted, and the condition of accidental triple degeneracy is derived which leads to a Dirac-cone like dispersion. We prove that, similar to the real Dirac-cone, the Dirac-cone like band in non-Hermitian PC possesses good linearity and isotropy in the vicinity of the $Γ$ point. Moreover, some topological transit of the band may occur when the parameters adiab…
Incoherence-assisted mode excitation in non-Hermitian resonant systems
CREOL, The College of Optics and Photonics, University of Central Florida（中佛罗里达大学光学与光子学院）；Department of Electrical and Computer Engineering, Saint Louis University（圣路易斯大学电气与计算机工程系）
We show that two-dimensional non-Hermitian photonic crystals made of lossy material can exhibit non-trivial point gap topology in terms of topological winding in its complex frequency band structure. Such crystals can be either made of lossy isotropic media which is reciprocal, or lossy magneto-optical media which is non-reciprocal. We discuss the effects of reciprocity on the properties of the point gap topology. We also show that such a non-trivial point gap topology leads to non-Hermitian skin effect when the photonic crystal is truncated. In contrast to most previous studies on point gap t…
In this study, we propose the application of non-Hermitian photonic crystals (PCs) with anisotropic emissions. Unlike a ring of exceptional points (EPs) in isotropic non-Hermitian PCs, the EPs of anisotropic non-Hermitian PCs appear as lines symmetrical about the $Γ$ point. The non-Hermitian Hamiltonian indicates that the formation of EPs is related to the non-Hermitian strength. The real spectrum appears in the $Γ$Y direction and has been validated as the complex conjugate medium (CCM) by effective medium theory (EMT). But for the $Γ$X direction, EMT indicates that the effective refractive in…
The effects of gain and loss on the band structures of a bulk topological dielectric photonic crystal (PC) with $C_{6v}$ symmetry and the PC-air-PC interface are studied based on first-principle calculation. To illustrate the importance of parity-time (PT) symmetry, three systems are considered, namely the PT-symmetric, PT-asymmetric, and lossy systems. We find that the system with gain and loss distributed in a PT symmetric manner exhibits a phase transition from a PT exact phase to a PT broken phase as the strength of the gain and loss increases, while for the PT-asymmetric and lossy systems…
The Chern topological numbers of a material platform are usually written in terms of the Berry curvature, which depends on the normal modes of the system. Here, we use a gauge invariant Green's function method to determine from first principles the topological invariants of photonic crystals. The proposed formalism does not require the calculation of the photonic band-structure, and can be easily implemented using the operators obtained with a standard plane-wave expansion. Furthermore, it is shown that the theory can be readily applied to the classification of topological phases of non-Hermit…
We study optomechanical interactions in non-Hermitian photonic molecules that support two photonic states and one acoustic mode. The nonlinear steady-state solutions and their linear stability landscapes are investigated as a function of the system's parameters and excitation power levels. We also examine the temporal evolution of the system and uncover different regimes of nonlinear dynamics. Our analysis reveals several important results: (1) Parity-time ($\mathcal{PT}$) symmetry is not necessarily the optimum choice for maximum optomechanical interaction. (2) Stable steady-state solutions a…
We study the breaking of reciprocity in non-Hermitian coupled photonic waveguides by the simultaneous action of the nonlinear effect of saturable absorption, and the presence of exceptional points. The nonlinear response of such a system is studied in depth, giving physical insight into the operational principles and fundamental limitations, while producing analytical and semi-analytical results for the transmission and nonreciprocal intensity range. We numerically validate the theoretical results and assess important performance metrics for the nonreciprocal operation of such a device. This n…
Programmable Non-Hermitian Synchronization of Light on a Silicon Photonic Processor
KTH Royal Institute of Technology（瑞典皇家理工学院）；University of Michigan（密歇根大学）；University of Vaasa（瓦萨大学）；Institute of Science Tokyo（东京科学大学）；Huazhong University of Science and Technology（华中科技大学）
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…
Here, we develop a gauge-independent Green function approach to characterize the Chern invariants of generic non-Hermitian systems. It is shown that analogous to the Hermitian case, the Chern number can be expressed as an integral of the system Green function over a line parallel to the imaginary-frequency axis. The approach introduces in a natural way the "band-gaps" of non-Hermitian systems as the strips of the complex-frequency plane wherein the system Green function is analytical. We apply the developed theory to nonreciprocal electromagnetic continua, showing that the topological properti…
Zero modes are symmetry protected ones whose energy eigenvalues have zero real parts. In Hermitian arrays, they arise as a consequence of the sublattice symmetry, implying that they are dark modes. In non-Hermitian systems, that naturally emerge in gain/loss optical cavities, particle-hole symmetry prevails instead; the resulting zero modes are no longer dark but feature $π/2$ phase jumps between adjacent cavities. Here we report on the direct observation of zero modes in a non-Hermitian three coupled photonic crystal nanocavity array containing quantum wells. Unlike the Hermitian counterparts…
In this work we propose a general theoretical approach to the modelling of complex dispersion characteristics of leaky optical modes operating in photonic crystal slab composed of two high-index contrast gratings, beyond the protection of the light cone. Opening access of wave-guided resonances to free space continuum provides large amount of extra degrees of freedom for mode coupling engineering. Not only can the two gratings communicate via near field coupling, but they are also allowed to couple via the propagating radiated field. Our analytical model, based on a non-Hermitian Hamiltonian, …
We show the existence of a flat band consisting of photonic zero modes in a gain and loss modulated lattice system, as a result of the underlying non-Hermitian particle-hole symmetry. This general finding explains the previous observation in parity-time symmetric systems where non-Hermitian particle-hole symmetry is hidden. We further discuss the defect states in these systems, whose emergence can be viewed as an unconventional alignment of a pseudo-spin under the influence of a complex-valued pseudo-magnetic field. These defect states also behave as a chain with two types of links, one rigid …
In some non-Hermitian systems, the eigenstates in the bulk are localized at the boundaries of the systems. This is called the non-Hermitian skin effect, and it has been studied mostly in discrete systems. In the present work, we study the non-Hermitian skin effect in a continuous periodic model. In a one-dimensional system, we show that the localization lengths are equal for all the eigenstates. Moreover, the localization length and the eigenspectra in a large system are independent of the types of open boundary conditions. These properties are also found in a non-Hermitian photonic crystal. S…
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）
