Engineered photonic spin Hall effect of Gaussian beam in antisymmetric parity-time metamaterials

A model of the photonic spin Hall effect(PSHE)in antisymmetric parity-time(APT)metamaterials with incidence of Gaussian beams is proposed here.We derive the displacement expression of the PSHE in APT metamaterials based on the transport properties of Gaussian beams in positive and negative refractive index materials.Furthermore,detailed discussions are provided on the APT scattering matrix,eigenstate ratio,and response near exceptional points in the case of loss or gain.In contrast to the unidirectional non-reflection in parity-time(PT)symmetric systems,the transverse shift that arises from both sides of the APT structure is consistent.By effectively adjusting the parameters of APT materials,we achieve giant displacements of the transverse shift.Finally,we present a multi-layer APT structure consisting of alternating left-handed and right-handed materials.By increasing the number of layers,Bragg oscillations can be generated,leading to an increase in resonant peaks in transverse shift.This study presents a new approach to achieving giant transverse shifts in the APT structure.This lays a theoretical foundation for the fabrication of related nano-optical devices.

基于光学Parity-Time对称微腔结构的大范围电场传感器

为解决传统电场传感器测量范围受限的技术难题,设计了一种基于光学 Parity-Time(PT)对称掺杂电光介质的微腔结构,提出新的电场传感机制.利用传输矩阵方法计算结构的传输谱,发现独特的放大的缺陷模式.缺陷模式的峰值和波长位置均随外电场变化,由此可以利用缺陷模峰值变化和波长位置变化两种机制测量同一电场.测量范围仅受电光介质击穿电场的限制,可以为 0 0.06 V/nm,几乎涵盖了可能的电场环境.对峰值变化传感机制,灵敏度范围 38.042- 47.558 nm/V;对波长变化传感机制,灵敏度范围 18.357-18.642nm/V,在测量范围内平均分辨率为0.00925 V/nm.

Parity-time对称性对电注入半导体激光器的模式控制

非厄米的描述对于开放系统有重要意义,满足parity-time对称性的哈密顿量,其参数在一定范围内可以使能量具有实的本征值.本文通过模拟,研究了损耗大小以及结构对称性对条形波导中的parity-time对称性的影响,并通过实验发现了电注入条件下由parity-time对称破缺导致的脊条波导模式间隔加倍、模式数减半的现象.

Localization and Steering of Light in One-Dimensional Parity-Time Symmetric Photonic Lattices

We theoretically study the propagation dynamics of input light in one-dimensional mixed linear-nonlinear photonic lattices with a complex parity-time symmetric potential. Numerical computation shows simultaneous localization and steering of the optical beam due to the asymmetric scatter and interplay between Kerr-type nonlinearity and PT symmetry. This may provide a feasible measure for manipulation light in optical communications, integrated optics and so on.

Bifurcated overtones of one-way localized Fabry-Pérot resonances in parity-time symmetric optical lattices

Since the first observation of parity-time（PT） symmetry in optics, varied interesting phenomena have been discovered in both theories and experiments, such as PT phase transition and unidirectional invisibility, which turns PT-symmetric optics into a hotspot in research. Here, we report on the one-way localized Fabry-Pérot（FP） resonance, where a welldesigned PT optical resonator may operate at exceptional points with bidirectional transparency but unidirectional field localization. Overtones of such one-way localized FP resonance can be classified into a blue shifted branch and a red shifted branch. Therefore, the fundamental resonant frequency is not the lowest one. We find that the spatial field distributions of the overtones at the same absolute order are almost the same, even though their frequencies are quite different.

Parity-time symmetric acoustic system constructed by piezoelectric composite plates with active external circuits

Researches on parity-time(PT)symmetry in acoustic field can provide an efficient platform for controlling the travelling acoustic waves with balanced loss and gain.Here,we report a feasible design of PT-symmetric system constructed by piezoelectric composite plates with two different active external circuits.By judiciously adjusting the resistances and inductances in the external circuits,we obtain the exceptional point due to the spontaneous breaking of PT symmetry at the desired frequencies and can observe the unidirectional invisibility.Moreover,the system can be at PT exact phase or broken phase at the same frequency in the same structure by merely adjusting the external circuits,which represents the active control that makes the acoustic manipulation more convenient.Our study may provide a feasible way for manipulating acoustic waves and inspire the application of piezoelectric composite materials in acoustic structures.

Soliton structures in the (1+1)-dimensional Ginzburg–Landau equation with a parity-time-symmetric potential in ultrafast optics

In this paper, the （l＋l）-dimensional variable-coefficient complex Ginzburg-Landau （CGL） equation with a parity- time （PT） symmetric potential U（x） is investigated. Although the CGL equations with a PT-symmetric potential are less reported analytically, the analytic solutions for the CGL equation are obtained with the bilinear method in this paper. Via the derived solutions, some soliton structures are presented with corresponding parameters, and the influences of them are analyzed and studied. The single-soliton structure is numerically verified, and its stability is analyzed against additive and multiplicative noises. In particular, we study the soliton dynamics under the impact of the PT-symmetric potential. Results show that the PT-symmetric potential plays an important role for obtaining soliton structures in ultrafast optics, and we can design fiber lasers and all-optical switches depending on the different amplitudes of soliton-like structures.

Disorder in parity-time symmetric quantum walks

We experimentally investigate the impact of static disorder and dynamic disorder on the non-unitary dynamics of parity-time(PT)-symmetric quantum walks.Via temporally alternating photon losses in an interferometric network,we realize the passive PT-symmetric quantum dynamics for single photons.Controllable coin operations allow us to simulate different environmental influences,which result in three different behaviors of quantum walkers:a standard ballistic spread,a diffusive behavior,and a localization,respectively,in a PT-symmetric quantum walk architecture.

Defect solitons supported by parity-time symmetric defects in superlattices

The existence and stability of defect solitons supported by parity-time （PT） symmetric defects in superlattices are investigated. In the semi-infinite gap, in-phase solitons are found to exist stably for positive defects, zero defects, and negative defects. In the first gap, out-of-phase solitons are stable for positive defects or zero defects, whereas in-phase solitons are stable for negative defects. For both the in-phase and out-of-phase solitons with the positive defect and in-phase solitons with negative defect in the first gap, there exists a cutoff point of the propagation constant below which the defect solitons vanish. The value of the cutoff point depends on the depth of defect and the imaginary parts of the PT symmetric defect potentials. The influence of the imaginary part of the PT symmetric defect potentials on soliton stability is revealed.

Finding Short-Range Parity-Time Phase-Transition Points with a Neural Network

The non-Hermitian PT-symmetric system can live in either unbroken or broken PT-symmetric phase. The separation point of the unbroken and broken PT-symmetric phases is called the PT-phase-transition point.Conventionally, given an arbitrary non-Hermitian PT-symmetric Hamiltonian, one has to solve the corresponding Schrodinger equation explicitly in order to determine which phase it is actually in. Here, we propose to use artificial neural network(ANN) to determine the PT-phase-transition points for non-Hermitian PT-symmetric systems with short-range potentials. The numerical results given by ANN agree well with the literature, which shows the reliability of our new method.

Multipeaked Solitons in Parity-Time Complex Superlattice with Dual Periods

The existence and stability of multipeaked solitons are investigated in a parity-time symmetric superlattice with dual periods under both self-focusing and self-defocusing nonlinearity. For self-defocusing nonlinearity, dipole solitons with low power and all the odd-peak solitons can exist stably in the first gap, while dipole solitons with high power and even-peak （except two） solitons are unstable. For self-focusing nonlinearity, even-peak out-of-phase solitons can propagate stably in the infinite gap, while odd-peak in-phase solitons are unstable.

基于Parity-Time对称结构极点效应构建光学三极管模型

为了构建光学三极管模型,设计了一个基于半导体磁性材料InSb的PT(parity-time)对称耦合微腔的结构模型。通过结构参数优化,产生了PT对称结构磁场强耦合的极点效应。在极点频率附近,通过改变输入电流信号改变施加在磁性材料上的磁感应强度,实现极点状态下信号的放大输出。这种放大可以是同相,也可以是反相,该设计实现了特殊光学三极管模型。

Optical resonance in inhomogeneous parity-time symmetric systems

We show that inhomogeneous waveguides of slowly varied parity-time(PT) symmetry support localized optical resonances.The resonance is closely related to the formation of exceptional points separating exact and broken PT phases.Salient features of this kind of non-Hermitian resonance, including the formation of half-vortex flux and the discrete nature,are discussed.This investigation highlights the unprecedented uniqueness of field dynamics in non-Hermitian systems with many potential adaptive applications.

Dual-Coupled Robust Wireless Power Transfer Based on Parity-Time-symmetric Model

The characteristics of the wireless power transfer(WPT)system vary under different transfer distances.As distance increases,efficiency drops off sharply,limiting the wider use of WPT technology.In order to mitigate this problem,this paper proposes a novel dual-coupled WPT system,where both electric-coupled mechanism and magnetic-coupled mechanism are utilized to enhance the transfer efficiency.Furthermore,a Parity-Time(PT)-symmetric circuit is utilized to realize robustness of the system.The coupled-mode model of the system is established and the expressions of operating frequency,transfer efficiency and output power are deduced.Analysis results indicate that in the unbroken PT-symmetric state,compared with single-coupled systems,the proposed system can keep constant performance within a longer distance;in broken PT-symmetric state,the proposed system has higher transfer efficiency.Simulated results and comparative results are in accordance with the theoretical analysis.Within 1.4m,this scheme can transfer power with constant efficiency of 77%and constant output power of 70W.

Tunable optical second-order sideband effects in a parity-time symmetric optomechanical system

We theoretically investigate the optical second-order sideband generation(OSSG)in an optical parity-time(PT)symmetric system,which consists of a passive cavity trapping the atomic ensemble and an active cavity.Compared with the double-passive system,it is found that near the exceptional point(EP),the efficiency of the OSSG increases sharply not only for the blue probepump detuning resonant case but also for the red one.Using experimentally achievable parameters,we study the effect of the atomic ensemble on the efficiency of the OSSG in the PT-symmetric system.The numerical results show that the efficiency of the OSSG is 30%higher than that of the first-order sideband,which is realized easily by simultaneously modulating the atom-cavity coupling strength and detuning.Moreover,the efficiency of the OSSG can also be tuned effectively by the pump power,and the efficiency is robust when the pump power is strong enough.This study may have some guidance for modulating the nonlinear optical properties and controlling light propagation,which may stimulate further applications in optical communications.

Enhanced absorption and electrical modulation of graphene based on the parity-time symmetry optical structure

In order to realize the ultrastrong absorption of graphene with electrical modulation properties, we designed a composite structure of graphene and parity-time(PT) symmetry photonic crystal, which is achieved by placing the graphene layer on the top layer of the PT symmetry photonic crystal. In this paper, the absorption properties of graphene and the electrical modulating properties of the structure were theoretically analyzed based on the transfer matrix method. The result shows that the proposed structure can achieve the absorption of 31.5 d B for the communication wavelength of 1550 nm;meanwhile,by setting the electric field intensity to ±0.02 V/nm, the absorption of graphene can be largely modulated to realize an electrically switchable effect, the modulation depth of graphene absorption can reach nearly 100%, and the operation speed is also close to 8.171 GHz. This investigation provides a novel approach to design graphene-based optoelectronic devices and optical communication devices.

Observation of Parity-Time Symmetry Breaking in Single-Photon Interferometer

We experimentally simulate a parity-time(PT)-symmetric quantum dynamics in a non-Hermitian system using a single-photon interferometer.We measure quantum final state using quantum state tomography.We observe the quantum state evolutions ranging from regions of unbroken to broken PT-symmetry using the single-photon interferometer.We experimentally prove that the eigenvalue of energy changes from real to imaginary corresponding to the non-Hermitian system from the PT-symmetry unbroken region to the PT-symmetry broken region.To the best of our knowledge,this is the first work to intuitively show the exceptional points of PT-symmetry non-unitary quantum dynamics in a single-photon interferometer from the energy perspective.

Topology in parity-time-symmetric quantum walks

The study of non-Hermitian systems with parity-time(PT)symmetry is a rapidly developing frontier in recent years?Experimentally,PT-symmetric systems have been realized in classical optics by balancing gain and loss,which holds great promise for novel optical devices and networks?Here we report experimental realization of passive PT-symmetric quantum dynamics for single photons by temporally alternating photon losses in the quantum walk(QW)interferometers.The ability to impose PT symmetry allows us to realize and investigate Floquet topological phases driven by PT-symmetric QWs.We observe topological edge states between regions with different topological invariants?Topological invariants can be defined by winding numbers,Zak phases,general geometry phases and can be calculated?Can they be detected directly?We give an answer by reporting the experimental detection of bulk topological invariants in non-unitary QWs?The topological invariant of the non-unitary quantum walk is manifested in the quantized average displacement of the walker,which is probed by monitoring the photon loss.Furthermore,we report the experimental study of dynamic quantum phase transitions(DQPTs)and photonic skyrmions using discrete-time QWs?We simulate quench dynamics between distinct Floquet topological phases using quantum-walk dynamics,and experimentally characterize DQPTs and emergent skyrmion structures.Our results pave the way for realizing quantum mechanical PT-synthetic devices and augurs exciting possibilities for exploring topological properties of non-Hermitian systems using discretetime QWs.

Kármán vortex street in a spin–orbit-coupled Bose–Einstein condensate with PT symmetry

The dynamics of spin–orbit-coupled Bose–Einstein condensate with parity-time symmetry through a moving obstacle potential is simulated numerically. In the miscible two-component condensate, the formation of the Kármán vortex street is observed in one component, while ‘the half-quantum vortex street' is observed in the other component. Other patterns of vortex shedding, such as oblique vortex dipoles, V-shaped vortex pairs, irregular turbulence, and combined modes of various wakes, can also be found. The ratio of inter-vortex spacing in one row to the distance between vortex rows is approximately0.18, which is less than the stability condition 0.28 of classical fluid. The drag force acting on the obstacle potential is simulated. The parametric regions of Kármán vortex street and other vortex patterns are calculated. The range of Kármán vortex street is surrounded by the region of combined modes. In addition, spin–orbit coupling disrupts the symmetry of the system and the gain-loss affects the local particle distribution of the system, which leads to the local symmetry breaking of the system, and finally influences the stability of the Kármán vortex street. Finally, we propose an experimental protocol to realize the Kármán vortex street in a system.

Exceptional-point-enhanced sensing in an all-fiber bending sensor

An exceptional-point(EP)enhanced fiber-optic bending sensor is reported.The sensor is implemented based on paritytime(PT)-symmetry using two coupled Fabry-Perot(FP)resonators consisting of three cascaded fiber Bragg gratings(FBGs)inscribed in an erbium-ytterbium co-doped fiber(EYDF).The EP is achieved by controlling the pumping power to manipulate the gain and loss of the gain and loss FP resonators.Once a bending force is applied to the gain FP resonator to make the operation of the system away from its EP,frequency splitting occurs,and the frequency spacing is a nonlinear function of the bending curvature,with an increased slope near the EP.Thus,by measuring the frequency spacing,the bending information is measured with increased sensitivity.To achieve high-speed and high-resolution interrogation,the optical spectral response of the sensor is converted to the microwave domain by implementing a dual-passband microwave-photonic filter(MPF),with the spacing between the two passbands equal to that of the frequency splitting.The proposed sensor is evaluated experimentally.A curvature sensing range from 0.28 to 2.74 m^(−1) is achieved with an accuracy of 7.56×10^(−4 )m^(−1 )and a sensitivity of 1.32 GHz/m^(−1),which is more than 4 times higher than those reported previously.