Topological bound modes in anti-PT-symmetric optical waveguide arrays

Level pinning of anti-PT-symmetric circuits for efficient wireless power transfer

Wireless power transfer (WPT) technology based on magnetic resonance (a basic physical phenomenon) can directly transfer energy from the source to the load without wires and other physical contacts, and has been successfully applied to implantable medical devices, electric vehicles, robotic arms and other fields. However, due to the frequency splitting of near-field coupling, the resonant WPT system has some unique limitations, such as poor transmission stability and low efficiency. Here, we propose anti-resonance with level pinning for high-performance WPT. By introducing the anti-resonance mode into the basic WPT platform, we uncover the competition between dissipative coupling and coherent coupling to achieve novel level pinning, and construct an effective anti-parity-time (anti-PT)-symmetric non-Hermitian system that is superior to previous PT-symmetric WPT schemes. On the one hand, the eigenvalue of the anti-PT-symmetric system at resonance frequency is always pure real in both strong and weak coupling regions, and can be used to overcome the transmission efficiency decrease caused by weak coupling, as brought about by, for example, a large size ratio of the transmitter to receiver, or a long transmission distance. On the other hand, due to the level pinning effect of the two kinds of coupling mechanisms, the working frequency of the system is guaranteed to be locked, so frequency tracking is not required when the position and size of the receiver change. Even if the system deviates from the matching condition, an efficient WPT can be realized, thereby demonstrating the robustness of the level pinning. The experimental results show that when the size ratio of the transmitter coil to the receiver coil is 4.29 (which is in the weak coupling region), the transfer efficiency of the anti-PT-symmetric system is nearly 4.3 (3.2) times higher than that of the PT-symmetric system when the matching conditions are satisfied (deviated). With the miniaturization and integration of devices in mind, a synthetic anti-PT-symmetric system is used to realize a robust WPT. Anti-PT-symmetric WPT technology based on the synthetic dimension not only provides a good research platform for the study of abundant non-Hermitian physics, but also provides a means of going beyond traditional near-field applications with resonance mechanisms, such as resonance imaging, wireless sensing and photonic routing.

Different phases in non-Hermitian topological semiconductor stripe laser arrays

As a novel branch of topology, non-Hermitian topological systems have been extensively studied in theory and experiments recently. Topological parity-time (PT)-symmetric semiconductor stripe laser arrays based on the Su-Schreiffer-Heeger model are proposed. The degree of non-Hermicity can be tuned by altering the length of the cavities, and PT symmetry can be realized by patterned electrode. Three laser arrays working in different non-Hermitian phases are analyzed and fabricated. With the increasing degree of non-Hermicity, the peaks of output intensities move from the edge to the bulk. The proposed semiconductor stripe laser array can function as an active, flexible, and feasible platform to investigate and explore non-Hermitian topology for further developments in this field.

Light transfer transitions beyond higher-order exceptional points in parity-time and anti-parity-time symmetric waveguide arrays

We propose two non-Hermitian arrays consisting of N = 2l + 1 waveguides and exhibiting parity-time (P T) or anti-P T symmetry for investigating light transfer dynamics based on Nth-order exceptional points (EPs). The P T-symmetric array supports two Nth-order EPs separating an unbroken and a broken phase with real and imaginary eignvalues, respectively. Light transfer dynamics in this array exhibits radically different behaviors, i.e. a unidirectional oscillation behavior in the unbroken phase, an edge-towards localization behavior in the broken phase, and a center-towards localization behavior just at Nth-order EPs. The anti-P T-symmetric array supports also two Nth-order EPs separating an unbroken and a broken phase, which refer however to imaginary and real eigenvalues, respectively. Accordingly, light transfer dynamics in this array exhibits a center-towards localization behavior in the unbroken phase and an origin-centered oscillation behavior in the broken phase. These nontrivial light transfer behaviors and their controlled transitions are not viable for otherwise split lower-order EPs and depend on the underlying SU(2) symmetry of spin-l matrices.

Observation of One-Dimensional Dirac Fermions in Silicon Nanoribbons

Dirac materials, which feature Dirac cones in the reciprocal space, have been one of the hottest topics in condensed matter physics in the past decade. To date, 2D and 3D Dirac Fermions have been extensively studied, while their 1D counterparts are rare. Recently, Si nanoribbons (SiNRs), which are composed of alternating pentagonal Si rings, have attracted intensive attention. However, the electronic structure and topological properties of SiNRs are still elusive. Here, by angle-resolved photoemission spectroscopy, scanning tunneling microscopy/spectroscopy measurements, first-principles calculations, and tight-binding model analysis, we demonstrate the existence of 1D Dirac Fermions in SiNRs. Our theoretical analysis shows that the Dirac cones derive from the armchairlike Si chain in the center of the nanoribbon and can be described by the Su-Schrieffer-Heeger model. These results establish SiNRs as a platform for studying the novel physical properties in 1D Dirac materials.

Quantum interference in anti-parity-time symmetric coupled waveguide system

We theoretically demonstrate quantum interference in an anti-parity-time (anti-PT) symmetric system based on coupled waveguides. We calculate the coincidence probability in an input polarization-entangled two-photon state, which can be used to simulate different statistical particles. When the birefringence of the waveguides is negligible, our results indicate that the coincidence probabilities of the bosons and fermions decrease exponentially with the propagation distance in both the unbroken and broken anti-PT symmetry regions owing to the dissipation. Particularly, loss-induced transparency is observed for the bosons. Simultaneously, the statistical rule valid in the Hermitian system is violated and the antibunching of bosons is observed. When the birefringence of the waveguides is considered, the coincidence probability of the bosons and fermions is equalized at the exceptional point (EP), whereas that of the bosons is less(greater) than that of the fermions in the broken(unbroken) anti-PT symmetry region. Additionally, we observe the Hong-Ou-Mandel dip for bosons in the broken anti-PT phase. Our research provides a complementary technique for the manipulation of quantum interference compared with the PT symmetric system and may be applied in building quantum devices with anti-PT symmetric quantum mechanics.

Non-Hermitian flat bands in rhombic microring resonator arrays

We investigate the flat bands in a quasi-one-dimensional rhombic array composed of evanescently coupled microring resonators (MRRs) with non-Hermitian coupling. By changing the relative position of non-Hermitian coupling in each cell, we construct topologically trivial and nontrivial flat bands, where both the real and imaginary parts of energy bands become flat and coalesce into a single band. We show the nontrivial systems are able to support topological boundary modes isolated from the flat bulk bands although there is no band gap. The elusive topology of flat bands can be geometrically visualized by plotting the trajectories of their eigenvectors on Bloch sphere based on Majorana's stellar representation (MSR). Furthermore, we perform a full wave simulation and show the characteristics of flat bands, associated compact localized modes, and boundary modes are reflected from absorption spectra and field intensity profiles. The study may find potential applications in lasers, narrowband filters, and efficient light harvesting.

Square-root non-Bloch topological insulators in non-Hermitian ring resonators

We investigate the topological skin effect in a ring resonator array which can be mapped into the square root of a Su-Schrieffer-Heeger (SSH) model with non-Hermitian asymmetric coupling. The asymmetric coupling is realized by integrating the same amount of gain and loss into the two half perimeters of linking rings that effectively couple two adjacent site rings. Such a square-root topological insulator inherits the properties from its parent Hamiltonian, which has the same phase transition points and exhibits non-Bloch features as well. We show the band closing points for open chain are different from that of periodic chain as a result of the skin effect. Moreover, the square-root insulator supports multiple topological edge modes as the number of band gaps is doubled compared to the original Hamiltonian. The full-wave simulations agree well with the theoretical analyses based on a tight-binding model. The study provides a promising approach to investigate the skin effect by utilizing ring resonators and may find potential applications in light trapping, lasers, and filters.

Tunable Optical Bistability, Tristability and Multistability in Arrays of Graphene

The optical bistability, tristability and multistability are explored in arrays of graphene. The arrays are periodically arranged spatially by single sheets of graphene. Optical bistability could be achieved with a strong enough incident intensity of light wave. The thresholds of optical bistability and the intervals between the upper and lower thresholds change with the surface conductivity of graphene and the incident wavelength. By increasing the intensity of incident light, tristability and multistability can be induced as well. Furthermore, the thresholds of bistability, tristability and multistability can be regulated via the chemical potential of graphene. This study may have potential applications in optical logic gates, all-optical switches and photomemory.

Extended SSH Model in Non-Hermitian Waveguides with Alternating Real and Imaginary Couplings

We studied the topological properties of an extended Su–Schrieffer–Heeger (SSH) model composed of a binary waveguide array with alternating real and imaginary couplings. The topological invariant of the periodic structures remained quantized with chiral symmetry even though the system was non-Hermitian. The numerical results indicated that phase transition arose when the absolute values of the two couplings were equal. The system supported a topological zero mode at the boundary of nontrivial structures when chiral symmetry was preserved. By adding onsite gain and loss to break chiral symmetry, the topological modes dominated in all supermodes with maximum absolute value of imaginary energy. This study enriches research on the SSH model in non-Hermitian systems and may find applications in optical routers and switches.

Exceptional Points in Non-Hermitian Photonic Crystals Incorporated With a Defect

We explored exceptional points (EPs) in one dimensional non-Hermitian photonic crystals incorporated with a defect. The defect was asymmetric with respect to the center. Two EPs could be derived by modulating the normalized frequency and the gain-loss coefficient of defect. The reflection coefficient complex phase changed dramatically around EPs, and the change in complex phase was π at EPs. The electric field of EPs was mainly restricted to the defect, which can induce a giant Goos–Hänchen (GH) shift. Moreover, we found a coherent perfect absorption-laser point (CPA-LP) in the structure. A giant GH shift also existed around the CPA-LP. The study may have found applications in highly sensitive sensors.

Low Threshold Optical Bistability in Aperiodic PT-Symmetric Lattices Composited with Fibonacci Sequence Dielectrics and Graphene

We explore the optical bistability in aperiodic parity–time-symmetric (PT-symmetric) photonic lattices that are composed of Fibonacci sequence dielectrics and graphene at terahertz frequencies. Two Fibonacci sequence dielectrics, viz. aperiodic photonic lattices, are utilized for enhancing band-edge resonances and achieving the electric field localization that can enhance the nonlinearity of graphene. Modulating the gain-loss factor of dielectrics in the PT symmetry lattices further strengthens the nonlinearity effect and, consequently, low threshold bistability is realized. The interval between the upper and lower bistability thresholds enlarges as the momentum relaxation time of graphene changes. Moreover, we show that the bistability threshold can also be flexibly tuned by modulating the graphene chemical potential. The study might be applied in photomemories and optical switches.

Plasmonic Jackiw-Rebbi Modes in Graphene Waveguide Arrays

We investigate the topological bound modes of surface plasmon polaritons (SPPs) in a graphene pair waveguide array. The arrays are with uniform inter-layer and intra-layer spacings but the chemical potential of two graphene in each pair are different. The topological bound modes emerge when two arrays with opposite sequences of chemical potential are interfaced, which are analogous to Jackiw-Rebbi modes with opposite mass. We show the topological bound modes can be dynamically controlled by tuning the chemical potential, and the propagation loss of topological bound modes can be remarkably reduced by decreasing the chemical potential. Thanks to the strong confinement of graphene SPPs, the modal wavelength of topological bound modes can be squeezed as small as 1/70 of incident wavelength. The study provides a promising approach to realizing robust light transport beyond diffraction limit.

Unidirectional Invisibility Induced by Complex Anti-Parity–Time Symmetric Periodic Lattices

Complex anti-parity-time symmetric periodic lattices, in a wide frequency band, can act as unidirectional invisible media. The reflection from one end is suppressed while it is enhanced from the other. Furthermore, unidirectional laser points (ULPs) which correspond to the poles of reflection from one end, arise in the parameter space composed of the permittivity and angular frequency. The phase of the reflection coefficient changes sharply near the ULPs. Subsequently, large lateral shift which is proportional to the slope of phase could be induced for the reflected beam. The study may find great applications in unidirectional invisibility, unidirectional lasers and highly sensitive sensors.

High-sensitivity real-splitting anti-PT-symmetric microscale optical gyroscope

Optical gyroscopes measure the angular velocity using the Sagnac effect. However, the resonance splitting due to the Sagnac effect is directly proportional to the linear dimensions of the device. Consequently, integrated optical gyroscopes are still the subject of research. We propose the idea and the design of an anti-parity-time (APT)-symmetric optical gyroscope exhibiting a resonance splitting independent from the dimensions of the device. With a 80  μm×40  μm footprint integrated device, we demonstrated that it is possible to achieve a resonance splitting 10⁶ times higher than the one obtained through the classical Sagnac effect. With respect to the previously proposed parity-time (PT)-symmetric gyroscope, our solution exhibits a real frequency splitting, directly measurable at the output power spectrum. Moreover, it can be kept at its exceptional point more accurately than the PT-symmetric counterpart. Finally, the anti-PT-symmetric gyroscope presented here can detect the sign of the angular velocity differently from the PT-symmetric one.

Coherent Perfect Absorption Laser Points in One-Dimensional Anti-Parity–Time-Symmetric Photonic Crystals

We investigate the coherent perfect absorption laser points (CPA-LPs) in anti-parity–time-symmetric photonic crystals. CPA-LPs, which correspond to the poles of reflection and transmission, can be found in the parameter space composed of gain–loss factor and angular frequency. Discrete exceptional points (EPs) split as the gain–loss factor increases. The CPA-LPs sandwiched between the EPs are proved to be defective modes. The localization of light field and the bulk effect of gain/loss in materials induce a sharp change in phase of the reflection coefficient near the CPA-LPs. Consequently, a large spatial Goos–Hänchen shift, which is proportional to the slope of phase, can be achieved around the CPA-LPs. The study may find great applications in highly sensitive sensors.

Reflection Enhancement and Giant Lateral Shift in Defective Photonic Crystals with Graphene

This study investigates the reflectance of the defective mode (DM) and the lateral shift of reflected beam in defective photonic crystals incorporated with single-layer graphene by the transfer matrix method (TMM). Graphene, treated as an equivalent dielectric with a thickness of 0.34 nm, was embedded in the center of a defect layer. The reflectance of the DM was greatly enhanced as the intraband transition of electrons was converted to an interband transition in graphene. The reflectance of the DM could be further enhanced by increasing the Bragg periodic number. Furthermore, a large lateral shift of the reflected beam could also be induced around the DM. This study may find great applications in highly sensitive sensors.