Non-Hermitian systems with complex-valued energy spectra provide an extraordinary platform for manipulating unconventional dynamics of light. Here, we demonstrate the localization of light in an instantaneously reconfigurable non-Hermitian honeycomb photonic lattice that is established in a coherently-prepared atomic system. One set of the sublattices is optically modulated to introduce the absorptive difference between neighboring lattice sites, where the Dirac points in reciprocal space are extended into dispersionless local flat bands. When these local flat bands are broad enough due to larger loss difference, the incident beam is effectively localized at one set of the lattices with weaker absorption, namely, the commonly seen power exchange between adjacent channels in photonic lattices is effectively prohibited. The current work unlocks a new capability from non-Hermitian two-dimensional photonic lattices and provides an alternative route for engineering tunable local flat bands in photonic structures.
The presence of topological edge modes at the interface of two perturbed honeycomb photonic crystals with $C_6$ symmetry is often attributed to the different signs of Berry curvature at the K and K$'$ valleys. In contrast to the electronic counterpart, the Chern number defined in photonic valley Hall effect is not a quantized quantity but can be tuned to finite values including zero simply by changing geometrical perturbations. Here, we argue that the edge modes in photonic valley Hall effect can exist even when Berry curvature vanishes. We numerically demonstrate the presence of the zero-Berr…
In this paper, the photonic quantum spin Hall effect (PQSHE) is realized in dielectric two-dimensional (2D) honeycomb lattice photonic crystal (PC) by stretching and shrinking the honeycomb unit cell. Combining two honeycomb lattice PCs with a common photonic band gap (PBG) but different band topologies can generate a topologically protected edge state at the combined junction. The topological edge states and their unidirectional transmission as the scatterers with triangular, pentagonal, and heptagonal shapes are researched. Meanwhile, the unidirectional transmission in an inverted Ω-shaped w…
We report on transport properties of the super-honeycomb lattice, the band structure of which possesses a flat band and Dirac cones, according to the tight-binding approximation. This super-honeycomb model combines the honeycomb lattice and the Lieb lattice and displays the properties of both. The super-honeycomb lattice also represents a hybrid fermionic and bosonic system, which is rarely seen in nature. By choosing the phases of input beams properly, the flat-band mode of the super-honeycomb will be excited and the input beams will exhibit strong localization during propagation. On the othe…
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.
We study topological states of honeycomb photonic crystals in absence of inversion symmetry using plane wave expansion and finite element methods. The breaking of inversion symmetry in honeycomb lattice leads to contrasting topological valley indices, i.e., the valley-dependent Chern numbers in momentum space. We find that the topological corner states appear for 60$^\circ$ degree corners, but absent for other corners, which can be understood as the sign flip of valley Chern number at the corner. Our results provide an experimentally feasible platform for exploring valley-dependent higher-orde…
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…
We study, theoretically and experimentally, optical properties of different types of honeycomb photonic structures, known also as `photonic graphene'. First, we employ the two-photon polymerization method to fabricate the honeycomb structures. In experiment, we observe a strong diffraction from a finite number of elements, thus providing a unique tool to define the exact number of scattering elements in the structure by a naked eye. Then, we study theoretically the transmission spectra of both honeycomb single layer and 2D structures of parallel dielectric circular rods. When the dielectric co…
We consider light propagation through a ballistic amplifying photonic honeycomb lattice below the lasing threshold. Two sublattices of the system are formed by the wave-guides with different complex dielectric permittivities, which results in the non-Hermitian Dirac equation for electromagnetic field. We reveal that there exists a critical length of the amplifying region for which the photonic lattice exhibits an amplifier to generator transition. The transmission and reflection probabilities at the normal angle of incidence are strongly enhanced at a critical length of the system. We also com…
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…
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…
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…
We experimentally reveal the emergence of edge states in a photonic lattice with orbital bands. We use a two-dimensional honeycomb lattice of coupled micropillars whose bulk spectrum shows four gapless bands arising from the coupling of $p$-like photonic orbitals. We observe zero-energy edge states whose topological origin is similar to that of conventional edge states in graphene. Additionally, we report novel dispersive edge states that emerge not only in zigzag and bearded terminations, but also in armchair edges. The observations are reproduced by tight-binding and analytical calculations.…
We report the realization of a synthetic magnetic field for photons and polaritons in a honeycomb lattice of coupled semiconductor micropillars. A strong synthetic field is induced in both the s and p orbital bands by engineering a uniaxial hopping gradient in the lattice, giving rise to the formation of Landau levels at the Dirac points. We provide direct evidence of the sublattice symmetry breaking of the lowest-order Landau level wavefunction, a distinctive feature of synthetic magnetic fields. Our realization implements helical edge states in the gap between n=0 and n=1 Landau levels, expe…
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…
We establish experimentally a photonic super-honeycomb lattice (sHCL) by use of a cw-laser writing technique, and thereby demonstrate two distinct flatband line states that manifest as noncontractible-loop-states in an infinite flatband lattice. These localized states (straight and zigzag lines) observed in the sHCL with tailored boundaries cannot be obtained by superposition of conventional compact localized states because they represent a new topological entity in flatband systems. In fact, the zigzag-line states, unique to the sHCL, are in contradistinction with those previously observed in…
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）
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…
We clarify theoretically that the topological ring-cavity (TRC) modes propagating along the interface between two honeycomb-type photonic crystals distinct in topology can be exploited for achieving stable single-mode lasing, with the maximal intensity larger than a whispering-gallery-mode counterpart by order of magnitude. Especially, we show that the TRC modes located at the bulk bandgap center benefit maximally from the gain profile since they are most concentrated and uniform along the ring cavity, and that, inheriting from the Dirac-like dispersion of topological interface states, they ar…
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, …
The Fano resonance with a distinctive ultra-sharp, asymmetric line shape and high quality factor Q, is a widely occurring phenomena that has a large variety of optical, plasmonic and microwave manifestations. In this paper, we explore the characteristic robustness of the Fano resonance mode, which is topologically protected by manufacturing band inversion induced by breaking the mirror symmetry of a two-dimensional honeycomb photonic crystal (HPC), associated with C_6 point group symmetry. So the dark and bright topological edge modes appear in the band gap made by opening of the Dirac cone. D…
Non-Hermitian Interaction between Light and Photonic Time Crystal Beyond the Floquet Quasinormal Mode Approximation
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；State Key Laboratory for Mesoscopic Physics and Frontiers Science Center for Nano-optoelectronics, School of Physics, Peking University（北京大学物理学院介观物理国家重点实验室及纳米光电子前沿科学中心）
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…
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…
Non-Hermitian photonic systems are known to exhibit unique phenomena, where non-Hermiticity is typically introduced by material loss or gain. Here, we propose and experimentally demonstrate unidirectional phenomena solely based on radiation. Our design is on the basis of a double-lattice photonic crystal that has a linear dispersion with a single exceptional point, where the magnitudes of Hermitian and non-Hermitian couplings are cancelled out in one direction. Based on this concept, we realize a unidirectional waveguide which shows perfect radiation when light is incident from one side, and s…
The toolbox quantities used for manipulating the flow of light include typically amplitude, phase, and polarization. Pseudospins, such as those arising from valley degrees of freedom in photonic structures, have recently emerged as an excellent candidate for this toolbox, in parallel with rapid development of spintronics and valleytronics in condensed-matter physics. Here, by employing symmetry-broken honeycomb photonic lattices, we demonstrate valley-dependent wavepacket self-rotation manifested in spiraling intensity patterns, which occurs without any initial orbital angular momentum. Theore…
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…
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…
We present a $\mathbf{k} \cdot \mathbf{p}$ theory of photonic crystals containing gain and loss in which the gain and loss are added to separate primitive cells of the underlying Hermitian system, thereby creating a supercell photonic crystal. We show that the supercell bands of this system can merge outward from the degenerate contour formed from folding the bands of the underlying Hermitian system into the supercell Brillouin zone, but that other accidental degeneracies in the band structure of the underlying Hermitian system do not yield band merging behavior. Finally, we show that the moda…
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…
Two-dimensional (2D) coupled resonant optical waveguide (CROW), exhibiting topological edge states, provides an efficient platform for designing integrated topological photonic devices. In this paper, we propose an experimentally feasible design of 2D honeycomb CROW photonic structure. The characteristic optical system possesses two-fold and three-fold Dirac points at different positions in the Brillouin zone. The effective gauge fields implemented by the intrinsic pseudo-spin-orbit interaction open up topologically nontrivial bandgaps through the Dirac points. Spatial lattice geometries allow…
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 …
