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Xunya Jiang

Publications and source records attributed to Xunya Jiang.

At least 19 recordsLinked to original sources
arXiv2025

Nontrivial topology in one- and two-dimensional asymmetric systems with chiral boundary states

Symmetry plays an important role in the topological band theory. In contrary, study on the topological properties of the asymmetric systems is rather limited, especially in higher-dimensional systems. In this work, we explore a new theory to study the topology in various one-dimensional (1D) and two-dimensional (2D) asymmetric systems with chiral boundary states. Starting from the simple SSHm model, we show the chiral topology of its edge states by redefining sublattices. Meanwhile, based on its Rice-Mele-like effective Hamiltonian, a new topological invariant $\bar{Z}$ can be defined and the bulk-edge correspondence is established. With this clear physical picture, our theory can be extended to the more complex asymmetric ladder models, or even the 2D asymmetric systems. In the 2D BBH3 model, new chiral corner states with redefined lattices are found based on our method. These corner states are independent of any spatial symmetry and exhibit the characteristics of topological bound states in the continuum (TBICs). Moreover, the topological invariant can be calculated by introducing $\bar{Z}$ into 2D. At last, we propose an acoustic experiment of the BBH3 model where chiral corner states are numerically observed. Our work exhibits a new approach to study the topological properties of asymmetric systems. By redefining sublattices, we find that the models with entirely different structures might share the same topological origins.

cond-mat.mes-hall↗
arXiv2024

Topology reconstruction for asymmetric systems by isomorphic mapping or perturbation approximation

The systems without symmetries, e.g. the spatial and chiral symmetries, are generally thought to be improper for topological study and no conventional integral topological invariant can be well defined. In this work, with multi-band asymmetric Rice-Mele-like systems as examples, for the first time we show that the topology of all gaps can be reconstructed by two general methods and topological origin of many phenomena are revealed. A new integral topological invariant, i.e. the renormalized real-space winding number, can properly characterize the topology and bulk-edge correspondence of such systems. For the first method, an isomorphic mapping relationship between a Rice-Mele-like system and its chiral counterpart is set up, which accounts for the topology reconstruction in the half-filling gaps. For the second method, the Hilbert space of asymmetric systems could be reduced into degenerate subspaces by perturbation approximation, so that the topology in subspaces accounts for the topology reconstruction in the fractional-filling gaps. Surprisingly, the topology reconstructed by perturbation approximation exhibits extraordinary robustness since the topological edge states even exist far beyond the weak perturbation limit. We also show that both methods can be widely used for other asymmetric systems, e.g. the two-dimensional (2D) Rice-Mele systems and the superconductor systems. At last, for the asymmetric photonic systems, we predict different topological edge states by our topology-reconstruction theory and experimentally observe them in the laboratory, which agrees with each other very well. Our findings open a door for investigating new topological phenomena in asymmetric systems by various topological reconstruction methods which should greatly expand the category of topology study.

cond-mat.mes-hall↗
arXiv2024

Scattering Singularity in Topological Dielectric Photonic Crystals

The exploration of topology in natural materials and metamaterials has garnered significant attention. Notably, the one-dimensional (1D) and two-dimensional (2D) Su-Schrieffer-Heeger (SSH) model, assessed through tight-binding approximations, has been extensively investigated in both quantum and classical systems, encompassing general and higher-order topology. Despite these advancements, a comprehensive examination of these models from the perspective of wave physics, particularly the scattering view, remains underexplored. In this study, we systematically unveil the origin of the 1D and 2D Zak phases stemming from the zero-scattering point, termed the scattering singularity in k-space. Employing an expanded plane wave expansion, we accurately compute the reflective spectrum of an infinite 2D photonic crystal (2D-PhC). Analyzing the reflective spectrum reveals the presence of a zero-scattering line in the 2D-PhC, considered the topological origin of the non-trivial Zak phase. Two distinct models, representing omnidirectional non-trivial cases and directional non-trivial cases, are employed to substantiate these findings. Our work introduces a novel perspective for characterizing the nature of non-trivial topological phases. The identification of the zero-scattering line not only enhances our understanding of the underlying physics but also provides valuable insights for the design of innovative devices.

physics.optics↗
arXiv2024

Enhancement of spin-orbit interaction and nearly perfect spin-conversion by 1D photonic crystal with the anisotropic defect layer

Although photon spin-orbit interaction (SOI) has been extensively studied, the vortex-conversion efficiency and the enhancement of spin Hall effect in abnormal modes in SOI remain to be investigated. Using an one-dimensional (1D) photonic crystal (PhC) system with the anisotropic defect layer(ADL), we firstly find that the generation efficiency of the vortex beam is close to 50\% when the number of periodic layers of the PhC reaches 5. Secondly, We also discussed the case where linearly polarized light is obliquely incident on a defect state system, and find that the destructive interference between the normal mode and the abnormal mode reaches the maximum, resulting in the enhancement of the spin hall displacement, and the effect can be enhanced at any angle of incidence in this system. Finally, we found that in the defect mode, the mutual conversion of normal and abnormal mode spins can be regulated, and the conversion efficiency can be close to 100\%.

physics.optics↗
arXiv2024

Dual-polarization huge photonic spin Hall shift and deep-subwavelength sensing based on topological singularities in one-dimensional photonic crystals

Although several efforts have been taken to enhance the photonic spin Hall shift in deep-subwavelength region, according to effective medium theory, the fundamental confliction between near-zero reflection coefficient and near-zero incident angle still hinders the further application. Here, we reveal a fundamental breakdown of effective medium theory due to the existing of topological singularity in deep-subwavelength region in one-dimensional photonic crystals. We find that near the topological singularity, huge photonic spin Hall shift can be achieved for s-polarization and p-polarization. At the topological singularity, the reflected filed is split as dipole-like distribution with zero photonic spin Hall shift for both-polarizations, which is resulted from the interfere of the spin-maintained normal light and spin-flipped abnormal light. Based on the theoretical research, dual-polarizations thickness and dielectric constant sensing devices can be designed in deep-subwavelength region. Further more, by applying more complicated layered structure, multi-channels dual-polarizations detection and broadband dual-polarizations huge spin Hall shift platform can be designed. This work paves the way to exploring the topological properties and polarization control of photonic crystals and provides a prospective method for the design of multi-channels sensitive detection spin optical devices.

physics.optics↗
arXiv2022

Higher-order topological states in photonic Thue-Morse quasicrystals: quadrupole insulator and a new origin of corner states

Corner states (CSs) in higher-order topological insulators (HOTIs) have recently been of great interest in both crystals and quasicrystals. In contrast to electronic systems, HOTIs have not been found in photonic quasicrystals (PQCs). Here, we systemically study the higher-order topology in the two-dimensional Thue-Morse photonic quasicrystals (TM-PQCs). Not only the topological phase transition and the non-trivial CSs with fractional charge induced by multipole moments, but also a new type of CSs are found due to the complex structure of TM-PQCs near corners. The different origins of these CSs are also analyzed based on the tight-binding model. Our work opens the door to explore richer HOT physics beyond photonic crystals and the robustness of CSs in PQC shows the potential for applications.

physics.optics↗
arXiv2022

Topological properties of two-dimensional photonic square lattice without $C_4$ and $M_{x(y)}$ symmetries

Rich topological phenomena, edge states and two types of corner states, are unveiled in a two-dimensional square-lattice dielectric photonic crystal without both $C_4$ and $M_{x(y)}$ symmetries. Specifically, non-trivial type-I corner states, which do not exist in systems with $C_4$ and $M_{x(y)}$ since the degeneracy, are protected by non-zero quadrupole moment, no longer quantized to but less than $0.5$. Excellent properties, e.g. sub-wavelength localization and air-concentrated field distribution, are presented. Type-II corner states, induced by long-range interactions, are easier realized due to asymmetry. This work broadens the topological physics for the symmetries-broken systems and provides potential applications.

physics.optics↗
arXiv2019

A re-formulization of the transfer matrix method for calculating wave-functions in higher dimensional disordered open systems

We present a numerically stable re-formulization of the transfer matrix method (TMM). The iteration form of the traditional TMM is transformed into solving a set of linear equations. Our method gains the new ability of calculating accurate wave-functions of higher dimensional disordered systems. It also shows higher efficiency than the traditional TMM when treating finite systems. In contrast to the diagonalization method, our method not only provides a new route for calculating the wave-function corresponding to the boundary conditions of open systems in realistic transport experiments, but also has advantages that the calculating wave energy/frequency can be tuned continuously and the efficiency is much higher. Our new method is further used to identify the necklace state in the two dimensional disordered Anderson model, where it shows advantage in cooperating the wave-functions with the continuous transmission spectrum of open systems. The new formulization is very simple to implement and can be readily generalized to various systems such as spin-orbit coupling systems or optical systems.

physics.comp-ph↗
arXiv2019

A Study Of a Wide-Angle Scanning Phased Array Based On a High-Impedance Surface Ground Plane

This paper presents a two-dimensional infinite dipole array system with a mushroom-like high-impedance surface (HIS) ground plane with wide-angle scanning capability in the E-plane. The unit cell of the proposed antenna array consists of a dipole antenna and a four-by-four HIS ground. The simulation results show that the proposed antenna array can achieve a wide scanning angle of up to 65$^{\circ}$ in the E-plane with an excellent impedance match and a small $S11$. Floquet mode analysis is utilized to analyze the active impedance and the reflection coefficient. Good agreement is obtained between the theoretical results and the simulations. Using numerical and theoretical analyses, we reveal the mechanism of such excellent wide scanning properties. For the range of small scanning angles, these excellent properties result mainly from the special reflection phase of the HIS ground, which can cause the mutual coupling between the elements of the real array to be compensated by the mutual coupling effect between the real array and the mirror array. For the range of large scanning angles, since the surface wave (SW) mode could be resonantly excited by a high-order Floquet mode $\textrm{TM}_{-1,0}$ from the array and since the SW mode could be converted into a leaky wave (LW) mode by the scattering of the array, the radiation field from the LW mode is nearly in phase with the direct radiating field from the array. Therefore, with help from the special reflection phase of the HIS and the designed LW mode of the HIS ground, the antenna array with an HIS ground can achieve wide-angle scanning performance.

physics.app-ph↗
arXiv2018

Two Classes of Singularities and Novel Topology in a Specially Designed Synthetic Photonic Crystals

Zak phase and topological protected edge state are usually studied in one-dimensional(1D) photonic systems with spatial inversion symmetry(SIS). Interestingly in this work, we find specific classes of 1D structure without SIS can be mapped to system with SIS and also exhibit novel topology, which manifest as phase cut lines(PCLs) in our specially designed synthetic photonic crystals(SPCs). Zak phase defined in SIS is extended to depict the topology of PCLs after redefinition and topological protected edge state is also achieved in our 1D structure without SIS. In our SPCs, the relationship between Chern numbers in two-dimension(2D) and the extended Zak phases of 1D PCLs is given, which are bound by the first type singularities. Higher Chern numbers and multi chiral edge states are achieved utilizing the concept of synthetic dimensions. The effective Hamiltonian is given, based on which we find that the band edges of each PCLs play a role analogous to the valley pseudospin and our SPC is actually a new type of valley photonic crystal which is usually studied in graphene-like honeycomb lattice. The chiral valley edge transport is also demonstrated. In higher dimension, the shift of the first type singularity in expanded parameter space will lead to the Weyl point topological transition which we proposed in our previous work. In this paper, we find a second type of singularities which manifests as a singular surface in our expanded parameter space. The shift of the singular surface will lead to the nodal line topological transition. Astonishingly, we find the states on the singular surface possess extremely high robust against certain randomness, based on which a topological wave filter is constructed.

physics.optics↗
arXiv2018

The Connection of Topology between Systems with Different Dimensions: 1D Zak Phases to 2D Chern Number, Weyl Point as the Jumping Channel for One Singularity and Nodal Line to Merge All Singularities

The topology in different dimensions has attracted enormous interests, e.g. the Zak phase in 1D systems, the Chern number in 2D systems and the Weyl points or nodal lines in the systems with higher dimensions. It would be fantastic to find the connection of different topology in different dimensions from one simple model and reveal the deep physical picture behind them. In this work, we propose a new model which starts from a binary-layered 1D photonic crystal, and by introducing synthetic dimensions the topology of higher dimension systems could appear. From this model, we find that the topology of band gap and the Chern number of the 2D systems can be predicted by the parity-switching types and the Zak phases of the 1D systems with spatial inversion symmetry(SIS), respectively. The chiral edge state is confirmed by the winding number of the reflection phase in the topological nontrivial gap. Different types of the topological transition in higher dimensions are found, where two bands degenerated as Weyl point or nodal line. Surprisingly, we find that the topological connection between different dimensions and the topological transition types in this model can be explained by the evolving of two singularities which give rise to nonzero Zak phase of the 1D systems with SIS. When transporting one singularity between adjacent bands, the Weyl point takes the role as the instantaneous jumping channel of the singularity in the parameter space, and then both the Zak phases of 1D systems with SIS and the Chern number of 2D systems are changed. While both singularities moves to band-gap edges from two adjacent bands, they will merge into the nodal line. The theory for such model is also constructed. We propose that such topology connection between different dimensions could be quite universal for other systems.

physics.optics↗
arXiv2014

Far-field super-resolution imaging with a planar hyperbolic metamaterial lens beyond the Fabry-Perot resonance condition

We demonstrate achieving the far-field super-resolution imaging can be realized by using a planar hyperbolic metamaterial lens (PHML), beyond the Fabry-Perot resonance condition. Although the thickness of the PHML is much larger than wavelength, the PHML not only can transmit radiative waves and evanescent waves with high transmission, but also can collect all the waves in the image region with the amplitudes of them being the same order of magnitude. We present a design for a PHML to realize the far-field super-resolution imaging, with the distance between the sources and the images 10 times larger than wavelength. We show the superresolution of our PHML is robust against losses, and the PHML can be fabricated by periodic stacking of metal and dielectric layers.

physics.optics↗
arXiv2012

Impurity-induced bound states in superconductors with topological order

The study of classical spins in topological insulators [Phys. Rev. B {\bf 80}, 115216 (2009)] is generalized to topological superconductors. Based on the characteristic features of the so-called $F$-function, Bogoliubov-de Gennes Hamiltonian for superconductors is classified to positive, negative, and zero "gap" categories for topologically trivial and nontrivial phases of a topological superconductor as well as a BCS superconductor respectively. It is found that the $F$-function determines directly the presence or absence of localized excited states, induced by bulk classical spins and nonmagnetic impurities, in superconducting gap and their persistence with respect to impurity strength. Our results provide an alternative way to identify topologically insulating and superconducting phases in experiments while without resorting to the surface properties.

cond-mat.supr-con↗
arXiv2012

Characterizing Short Necklace States in Logarithmic Transmission Spectrum of Strongly Localized Systems

High transmission plateaus exist widely in the logarithmic transmission spectra of localized systems. Their physical origins are short chains of coupled-localized-states embedded inside the localized system, which are dubbed as "short necklace states". In this work, we define the essential quantities and then, based on these quantities, we investigate the short necklace states' properties statistically and quantitatively. Two different approaches are utilized and the results from them agree with each other very well. In the first approach, the typical plateau-width and the typical order of short necklace states are obtained from the correlation function of logarithmic transmission. In the second approach, we investigate statistical distributions of the peak/plateau-width measured in logarithmic transmission spectra. A novel distribution is found, which can be exactly fitted by the summation of two Gaussian distributions. These two distributions are the results of sharp peaks of localized states and the high plateaus of short necklace states. The center of the second distribution also tells us the typical plateau-width of short necklace states. With increasing the system length, the scaling property of typical plateau-width is very special since it almost does not decrease. The methods and the quantities defined in this work can be widely used on Anderson localization studies.

cond-mat.dis-nn↗
arXiv2012

Switchable Hyperbolic Metamaterials With Magnetic Control

A switchable hyperbolic material (SHM) is investigated, with which one can turn on or off the hyperbolic dispersion of the material via magnetic control. The SHM has simple structure, with a one-dimensional periodic stacking of dielectric layer and gyromagnetic layer. The hyperbolic dispersion of SHM is due to the negative effective permeability of gyromagnetic layers, and it can be transformed into a regular circular dispersion when the d.c. magnetic field is switched off. This switchable dispersion transition is reversible, which may have great potential applications in many fields.

physics.optics↗
arXiv2012

Controlling spontaneous emission of a two-level atom by hyperbolic metamaterials

Within the frame of quantum optics we analyze the properties of spontaneous emission of two-level atom in media with indefinite permittivity tensor where the geometry of the dispersion relation is characterized by an ellipsoid or a hyperboloid(hyperbolic medium). The decay rate is explicitly given with the orientation of the dipole transition matrix element taken into account. It indicates that for the ellipsoid case the intensity of the photons coupled into different modes can be tuned by changing the direction of the matrix element and for the hyperboloid case it is found that spontaneous emission in hyperbolic medium can be dramatically enhanced compared to the dielectric background. Moreover, spontaneous emission exhibit the strong directivity and get the maximum in the asymptote direction.

physics.optics↗
arXiv2012

Short Necklace States, Logarithm Transmission Fluctuation and Localization Length

We investigate the widely-existing short necklace states in random systems. It is found that their peak width and relative height in lnT spectra keep almost constant when the system length increases, which is explained by the coupled-resonator theory with intrinsic parameters. This property makes them special in contribution of lnT fluctuation. Further, short necklace states can help us to deeply understand the physical meaning of localization length and the delocalized effectin localized regime.

cond-mat.dis-nn↗