Search

In this paper, based on an optimization problem, a sketch-and-project method for solving the linear matrix equation AXB = C is proposed. We provide a thorough convergence analysis for the new method and derive a lower bound on the convergence rate and some convergence conditions including the case that the coefficient matrix is rank deficient. By varying three parameters in the new method and convergence theorems, the new method recovers an array of well-known algorithms and their convergence results. Meanwhile, with the use of Gaussian sampling, we can obtain the Gaussian global randomized Kaczmarz (GaussGRK) method which shows some advantages in solving the matrix equation AXB = C. Finally, numerical experiments are given to illustrate the effectiveness of recovered methods., Comment: arXiv admin note: text overlap with arXiv:1506.03296, arXiv:1612.06013, arXiv:2204.13920 by other authors

In this paper, several Kaczmarz-type numerical methods for solving the matrix equation $AX=B$ and $XA=C$ are proposed, where the coefficient matrix $A$ may be full rank or rank deficient. These methods are iterative methods without matrix multiplication. Theoretically, the convergence of these methods is proved. The numerical results show that these methods are more efficient than iterative methods involving matrix multiplication for high-dimensional matrices., Comment: arXiv admin note: text overlap with arXiv:2305.16684

Fast and reliable localization of high-energy transients is crucial for characterizing the burst properties and guiding the follow-up observations. Localization based on the relative counts of different detectors has been widely used for all-sky gamma-ray monitors. There are two major methods for this counts distribution localization: $\chi^{2}$ minimization method and the Bayesian method. Here we propose a modified Bayesian method that could take advantage of both the accuracy of the Bayesian method and the simplicity of the $\chi^{2}$ method. With comprehensive simulations, we find that our Bayesian method with Poisson likelihood is generally more applicable for various bursts than $\chi^{2}$ method, especially for weak bursts. We further proposed a location-spectrum iteration approach based on the Bayesian inference, which could alleviate the problems caused by the spectral difference between the burst and location templates. Our method is very suitable for scenarios with limited computation resources or time-sensitive applications, such as in-flight localization software, and low-latency localization for rapid follow-up observations.

Recently, the gapless Dirac/Weyl nodal semimetals with linear dispersion and topologically protected modes degeneracy are rapidly growing frontiers of topological physics. Especially, type-I, type-II, and critical type-III nodal semimetals are discovered according to the tilt angles of the Dirac/Weyl cones. Here, by introducing hyperbolic metamaterials into one-dimensional photonic crystals, we design the "hyper-crystal" and study the photonic four-fold degenerate Dirac nodal line semimetals (DNLSs) with two types of perpendicularly polarized waves. Moreover, the flexibly controlled photonic DNLSs using the phase compensation effect of hyperbolic dispersion are studied. Our results not only demonstrate a new platform to realize the various photonic DNLSs, where the optical polarization plays the role of electron spin in electronic DNLSs, but also may pave a novel way to explore the abundant Dirac/Weyl physics in the simple classical wave systems., Comment: 31 pages, 14 figures

Since April 28, 2020, Insight-HXMT has implemented a dedicated observation on the magnetar SGR J1935+2154. Thanks to the wide energy band (1-250 keV) and high sensitivity of Insight-HXMT, we obtained 75 bursts from SGR J1935+2154 during a month-long activity episode after the emission of FRB 200428. Here, we report the detailed time-integrated spectral analysis of these bursts and the statistical distribution of the spectral parameters. We find that for 15%(11/75) of SGR J1935+2154 bursts, the CPL model is preferred, and most of them occurred in the latter part of this active epoch. In the cumulative fluence distribution, we find that the fluence of bursts in our sample is about an order of magnitude weaker than that of Fermi/GBM, but follows the same power law distribution. Finally, we find a burst with similar peak energy to the time-integrated spectrum of the X-ray burst associated with FRB 200428 (FRB 200428-Associated Burst), but the low energy index is harder., Comment: 35 pages, 20 figures, accepted for publication in ApJS

Magnetars are neutron stars with extreme magnetic field and sometimes manifest as soft gamma-ray repeaters (SGRs). SGR J1935+2154 is one of the most prolific bursters and the first confirmed source of fast radio burst (i.e. FRB 200428). Encouraged by the discovery of the first X-ray counterpart of FRB, Insight-Hard X-ray Modulation Telescope (Insight-HXMT) implemented a dedicated 33-day long ToO observation of SGR J1935+2154 since April 28, 2020. With the HE, ME, and LE telescopes, Insight-HXMT provides a thorough monitoring of burst activity evolution of SGR J1935+2154, in a very broad energy range (1-250 keV) with high temporal resolution and high sensitivity, resulting in a unique valuable data set for detailed studies of SGR J1935+2154. In this work, we conduct a comprehensive analysis of this observation including detailed burst search, identification and temporal analyses. After carefully removing false triggers, we find a total of 75 bursts from SGR J1935+2154, out of which 70 are single-pulsed. The maximum burst rate is about 56 bursts/day. Both the burst duration and the waiting time between two successive bursts follow log-normal distributions, consistent with previous studies. We also find that bursts with longer duration (some are multi-pulsed) tend to occur during the period with relatively high burst rate. There is no correlation between the waiting time and the fluence or duration of either the former or latter burst. It also seems that there is no correlation between burst duration and hardness ratio, in contrast to some previous reports. In addition, we do not find any X-ray burst associated with any reported radio bursts except for FRB 200428., Comment: 31 pages, 10 figures, accepted for publication in ApJS

The growth model of black hole is still a controversial topic. In the stationary metric, all in-falling matter must be accumulated outside the event horizon of the black hole, as clocked by a distant external observer. In the time-dependent metric, all in-falling matter can fall into the event horizon of the final black hole within very short time. We test these two growth models by joining LIGO and Insight-HXMT observations. We find the stationary model is inconsistent with LIGO and Insight-HXMT observations., Comment: 6 pages

Photonic bandgap design is one of the most basic ways to effectively control the interaction between light and matter. However, the traditional photonic bandgap is always dispersive (blueshift with the increase of the incident angle), which is disadvantageous to the construction of wide-angle optical devices. Hypercrystal, that the photonic crystal with layered hyperbolic metamaterials (HMMs), can strongly modify the bandgap properties based on the anomalous wavevector dispersion of the HMM. Here, based on phase variation compensation between HMM and isotropic dielectric layers, we propose for the first time to design nonreciprocal and flexible photonic bandgaps using magneto-optical HMMs in one-dimensional photonic crystals. Especially for the forward and backward incident light, the blueshift and dispersionless of the forward and backward cavity modes are designed respectively to realize the interesting omnidirectional nonreciprocal absorber. Our results show high (low) absorption about 0.99 (0.25) in an angle range of 20-75 degrees for the forward (backward) incident light at the wavelength of 367 nm. The nonreciprocal omnidirectional cavity mode not only facilitates the design of perfect unidirectional optical absorbers working in a wide-angle range, but also possesses significant applications for all-angle reflectors and filters.

As a basic building block, optical resonant cavities (ORCs) are widely used in light manipulation; they can confine electromagnetic waves and improve the interaction between light and matter, which also plays an important role in cavity quantum electrodynamics, nonlinear optics and quantum optics. Especially in recent years, the rise of metamaterials, artificial materials composed of subwavelength unit cells, greatly enriches the design and function of ORCs. Here, we review zero-index and hyperbolic metamaterials for constructing the novel ORCs. Firstly, this paper introduces the classification and implementation of zero-index and hyperbolic metamaterials. Secondly, the distinctive properties of zero-index and hyperbolic cavities are summarized, including the geometry-invariance, homogeneous/inhomogeneous field distribution, and the topological protection (anomalous scaling law, size independence, continuum of high-order modes, and dispersionless modes) for the zero-index (hyperbolic) metacavities. Finally, the paper introduces some typical applications of zero-index and hyperbolic metacavities, and prospects the research of metacavities., Comment: 82 pages, 29 figures

The emergence of Artificial Intelligence of Things (AIoT) has provided novel insights for many social computing applications such as group recommender systems. As distance among people has been greatly shortened, it has been a more general demand to provide personalized services to groups instead of individuals. In order to capture group-level preference features from individuals, existing methods were mostly established via aggregation and face two aspects of challenges: secure data management workflow is absent, and implicit preference feedbacks is ignored. To tackle current difficulties, this paper proposes secure Artificial Intelligence of Things for implicit Group Recommendations (SAIoT-GR). As for hardware module, a secure IoT structure is developed as the bottom support platform. As for software module, collaborative Bayesian network model and non-cooperative game are can be introduced as algorithms. Such a secure AIoT architecture is able to maximize the advantages of the two modules. In addition, a large number of experiments are carried out to evaluate the performance of the SAIoT-GR in terms of efficiency and robustness.

With the prevalence of Internet of Things (IoT)-based social media applications, the distance among people has been greatly shortened. As a result, recommender systems in IoT-based social media need to be developed oriented to groups of users rather than individual users. However, existing methods were highly dependent on explicit preference feedbacks, ignoring scenarios of implicit feedback. To remedy such gap, this paper proposes an implicit feedback-based group recommender system using probabilistic inference and non-cooperative game(GREPING) for IoT-based social media. Particularly, unknown process variables can be estimated from observable implicit feedbacks via Bayesian posterior probability inference. In addition, the globally optimal recommendation results can be calculated with the aid of non-cooperative game. Two groups of experiments are conducted to assess the GREPING from two aspects: efficiency and robustness. Experimental results show obvious promotion and considerable stability of the GREPING compared to baseline methods., Comment: I don't want to share this paper

The magnetic shield plays an important role in magnetic near-field control. However, the requirements of efficient, ultrathin, lightweight and cheap are still the challenges. Here, we firstly propose a composite metamaterial in which the mu-near-zero media is covered with a ferrite slab. We verify that this structure can enhance the shielding effectiveness in a small area. Furthermore, we optimize the magnetic path by changing the bulk ferrite slab into a patterned slab. In this way, significant shielding effectiveness enhancement can be achieved in a large area. Experimental results show that the maximum shielding effectiveness (SE) of the composite metamaterial with a patterned ferrite is 20.56 dB, which is nearly 19 dB higher than that of a single ferrite slab with the same thickness of the composite metamaterial. The results on the composite metamaterial would be very useful in the applications involving magnetic shielding., Comment: 5 pages, 5 figures

Planar waveguides can limit the transmission of electromagnetic waves in a specific direction and have a wide range of applications in filters, sensors, and energy-transfer devices. However, given the increasing demand for planar integrated photonics, new waveguides are required with excellent characteristics such as more functionality, greater efficiency, and smaller size. In this work, we report the experimental results for a subwavelength planar microwave-regime waveguide fabricated from circuit-based magnetic hyperbolic metamaterial (HMM) and develop the associated theory. HMM is a special type of anisotropic metamaterial whose isofrequency contour (IFC) takes the form of an open hyperboloid. Because of the open-dispersion IFCs, HMMs support propagating high-k modes with large effective refractive indices, which allows planar hyperbolic waveguides to be miniaturized. In particular, as opposed to the traditional dielectric slab waveguide, the group velocity of the hyperbolic guided modes is negative-a characteristic that can be exploited to realize the backward propagation of electromagnetic waves. Furthermore, we study the abnormal photonic spin Hall effect and experimentally demonstrate an ultracompact backward coupler based on hyperbolic waveguides. The experimental results are consistent with numerical simulations. This work not only reveals the significant potential of circuit-based platforms for the experimental study of the propagation and coupling of guided modes but also promotes the use of HMMs in the microwave regime for numerous integrated functional devices.

The exploration of non-Hermitian systems with parity-time (PT) symmetry has witnessed immense research interest both fundamentally and technologically in a wide range of subject areas in physics and engineering. One significant example of the principal emerging fields in this context is the PT symmetric wireless applications using multiple coils that are spatially separated but mutually coupled with position-dependent coupling strength. Such a spatial PT configuration limits the flexibility and miniaturization of the PT symmetric designs. As far as this is concerned, inspired by scattering induced two opposite whispering-gallery (WG) modes in an optical resonator, analogously here we experimentally demonstrate a specially constructed second-order (2-nd order) PT symmetry in a single coil resonator, whose currents with two different directions are excited by internal bypass capacitor. Our proposed structure has the following peculiar feature: First, the bypass capacitor induces coupling in spectral resonances allow us to observe a 2-nd order phase transition between symmetry regimes, without the need of a second coil in the spatial PT case. Under this circumstance, this specially constructed PT symmetry can be regarded as synthetic PT symmetry, which is enabled by coupling modes with different directions. Second, by introducing two or more internal bypass capacitors, the synthetic high-order PT symmetric system bearing such as third-order exceptional point in a single coil resonator can be realized. These results will provide a new paradigm to realize higher-order PT symmetry towards the investigation of non-Hermitian physics in a synthetic perspective, which can be extended to other physical platforms such as optics and acoustics.

As an important class of systems with unique topological effects beyond the periodic lattices, quasiperiodic topological structures have attracted much attention in recent years. Due to the quasiperiodic modulation, the topological states in the quasiperiodic topological structures have the characteristics of self-similarity, which can be used to observe the charming Hofstadter butterfly. In addition, because of the asymmetric distribution, the edge states in quasiperiodic chain can be used to realize the adiabatic pumping. When the topological parameters in quasiperiodic topological lattices are considered as synthetic dimensions, they can also be used to study the topological properties with higher dimensions. Here, by using ultra-subwavelength resonators, we design and fabricate a type of one-dimensional quasiperiodic Harper chain with asymmetric topological edge states for the directional wireless power transfer (WPT). By further introducing a power source into the system, we selectively light up two Chinese characters which is composed of LED lamps at both ends of the chain. Moreover, the directional WPT implemented by the topological quasiperiodic chain has the property of topological protection, which is immune to the internal disorder perturbation of the structure. Not only do we apply the asymmetric edge state for directional WPT, but also may further actively control the directional WPT by using the external voltage. In addition, this work provides a flexible platform for designing new WPT devices, such as using the corner states in high-order topological structures or the skin effect in the non-Hermitian topological lattices., Comment: 19 pages, 5 figures

The topological characteristics, including invariant topological orders, band inversion, and the topological edge mode (TEM) in the photonic insulators, have been widely studied. Whether people can take advantage of intriguing topological modes in simple one-dimensional systems to implement some practical applications is an issue which people are increasingly concerned about. In this work, based on a photonic dimer chain composed of ultra-subwavelength resonators, we verify experimentally that the TEM in the effective second-order parity-time (PT) system is immune to the inner disorder perturbation, and can be used to realize the long-range wireless power transfer (WPT) with high transmission efficiency. To intuitively show the TEM can be used for WPT, a power signal source is used to excite the TEM. It can be clearly seen that two LED lamps with 0.5-W at both ends of the structure are lighted up with the aid of TEMs. In addition, in order to solve the special technical problems of standby power loss and frequency tracking, we further propose that a WPT system with effective third-order PT symmetry can be constructed by using one topological interface mode and two TEMs. Inspired by the long-range WPT with TEMs in this work, it is expected to use more complex topological structures to achieve energy transmission with more functions, such as the WPT devices whose direction can be selected flexibly in the quasiperiodic or trimer topological chains., Comment: 31 pages, 10 figures

In this work, we treat the rotation of the optical axis as a new degree of freedom and theoretically propose a tilted linear-crossing metamaterials (TLCMM). Specifically, the conical dispersions of the NLCMM and TLCMM have the same shapes as type-I and type-II Dirac cones, respectively, in condensed matter physics. Upon rotating the optical axis angle such that it is equal to the cone angle, we find that this special TLCMM has the shape of a type-III Dirac cone. This critical TLCMM can have many unique properties and is of a fundamentally different nature than neighboring phases. When EM waves with large wave vectors are incident to a metamaterial with an open IFC to free space, the incident EM wave is strongly reflected due to wave-vector mismatch. Here, we use boundary conditions and the causality law to reveal that TLCMM high-k modes can achieve abnormal refraction without reflection and filtering. Moreover, these phenomenon are observed experimentally in a planar circuit-based system. The circuit-based TLCMM not only provides a versatile platform for the study of robust negative refraction phenomena in metamaterials, but also has a planar structure that is easier to integrate. Our results regarding the manipulation of EM waves may enable their use in planar-integrated photonics including for directional propagation, cloaking, and switching., Comment: 29 pages, 7 figures

Photonic topological edge states in one-dimensional dimer chains have long been thought to be robust to structural perturbations by mapping the topological Su-Schrieffer-Heeger model of a solid-state system. However, the edge states at the two ends of a finite topological dimer chain will interact as a result of near-field coupling. This leads to deviation from topological protection by the chiral symmetry from the exact zero energy, weakening the robustness of the topological edge state. With the aid of non-Hermitian physics, the splitting frequencies of edge states can be degenerated again and topological protection recovered by altering the gain or loss strength of the structure. This point of coalescence is known as the exceptional point (EP). The intriguing physical properties of EPs in topological structures give rise to many fascinating and counterintuitive phenomena. In this work, based on a finite non-Hermitian dimer chain composed of ultra-subwavelength resonators, we propose theoretically and verify experimentally that the sensitivity of topological edge states is greatly affected when the system passes through the EP. Using the EP of a non-Hermitian dimer chain, we realize a new sensor that is sensitive to perturbation at the end of the structure and yet topologically protected from internal perturbation. Our demonstration of a non-Hermitian topological structure with an EP paves the way for the development of novel sensors that are not sensitive to internal manufacturing errors but are highly sensitive to changes in the external environment., Comment: 21 pages, 5 figures

Photonic and acoustic topological insulators exhibiting one-way transportation that is robust against defects and impurities are typically realized in coupled arrays of two-dimensional ring resonators. These systems have produced a series of applications, including optical isolators, delay lines, and lasers. However, the structures are complicated because an additional coupler ring between neighboring rings is needed to construct photonic pseudo-spin. In this work, a photonic analogue of the quantum spin Hall effect is proposed and experimentally demonstrated in an anomalous Floquet topological insulator in the microwave regime. This improved design takes advantage of the efficient and backward coupling of negative-index media. The results contribute to the understanding of topological structures in metamaterials and point toward a new direction for constructing useful topological photonic devices., Comment: 8 pages, 13 figures

The spatially confined evanescent microwave photonics have been proved to be highly desirable in broad practical scenarios ranging from robust information communications to efficient quantum interactions. However, the feasible applications of these photonics modes are limited due to the lack of fundamental understandings and feasible directional coupling approaches at sub-wavelengths. Here, we experimentally demonstrate the efficient near-field photonic routing achieved in waveguides composed of two kinds of single-negative metamaterials. Without mimicking the polarization features, we propose all-electric near-field metasource in subwavelength scale and exemplify its near-field functions like Janus, Huygens and spin sources, corresponding to time-reversal, parity-time and parity symmetries of its inner degree of freedom. Our work furthers the understandings about optical near-field symmetry and feasible engineering approaches of directional couplings, which would pave the way for promising integrated mircrowave photonics devices., Comment: 6 pages, 4 figures

Manipulating the property of iso-frequency contour (IFC) will provide a powerful control for the interaction between light and matter. Importantly, hyperbolic metamaterials (HMMs), a class of artificial anisotropic materials with hyperbolic IFC have been intensively investigated. Because of the open dispersion curves, HMMs support propagating high-k modes and possess enhanced photonic density of states. As a result, HMMs can be utilized to realize hyper-lens breaking the diffraction limit, meta-cavity laser with subwavelength scale, high sensitivity sensor, long-range energy transfer and so on. In order to make it easier for people who are about to enter this burgeoning and rapidly developing research field, this tutorial article not only introduces the basic physical properties of HMMs, but also discusses the dispersion manipulation of HMMs and HMM-based structures such as hypercrystals. The theoretical methods and experimental platforms are given in this tutorial. Finally, some potential applications associated with hyperbolic dispersion are also introduced