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In periodic systems, band degeneracies are usually protected and classified by spatial symmetries. However, the Gamma point at zero-frequency of a photonic system is an intrinsic degeneracy due to the polarization degree of freedom of electromagnetic waves. We show here that in chiral photonic crystals, such an intrinsic degeneracy node carries +(-)2 chiral topological charge and the topological characters is the same as a spin-1 Weyl point manifested as a triple degeneracy of two linear propagating bands intersecting a flat band representing the electrostatic solution. Such an intrinsic triple degeneracy point (TDP) at Gamma is usually buried in bulk band projections and the topological charge at photonic zero-frequency has never been observed. Here, by imposing space-group screw symmetry to the chiral photonic crystal, the Brillouin zone boundary is transformed into an oppositely charged nodal surface enclosing the Gamma point. The emergent Fermi-arcs on sample surface are then forced to connect the bulk band projections of these topological singularities, revealing the embedded non-trivial topology.

Nodal links are special configurations of band degeneracies in the momentum space, where nodal line branches encircle each other. In PT symmetric systems, nodal lines can be topologically characterized using the eigenvector frame rotations along an encircling loop and the linking structure can be described with non-Abelian frame charges interacting among adjacent bands. In this paper, we present a photonic multiple nodal links system, where non-adjacent band topology is proposed to characterize the hidden relation between nodal lines from non-adjacent band pairs. Through an orthogonal nodal chain, the nodal line from the lower two bands predicts the existence of nodal lines formed between the higher bands. We designed and fabricated a metamaterial, with which the multiple nodal links and non-adjacent band topology are experimentally demonstrated.

In PT symmetric systems, the notion of non-Abelian frame charges enables multiband topological characterization of the degeneracy nodes through examining the eigenvector frame rotations. Interestingly, some features of these frame charges can be viewed as an analogue of electric charges confined in conducting wires, only that they flow in momentum space along nodal lines. However, these frame charges are not integers, and non-Abelian signatures emerge when braiding between adjacent band nodal lines occurs, which flips the direction of the flow. In photonic systems, we discover that the photonic {\Gamma} point serves as the source or sink of such frame charge flow due to a hidden braiding induced by the often-ignored electrostatic mode at zero-frequency. We use biaxial photonic crystals as examples and show how complex nodal line configurations can be explained as the topological consequences of the frame charge flow from the {\Gamma} point to the Brillouin zone boundaries. We further designed and fabricated meta-crystals to experimentally observe these line nodes as manifestation of the non-Abelian frame charge flow.

In periodic systems, nodal lines are loops in the three-dimensional momentum space where two bands are degenerate with each other. Nodal lines exhibit rich topological features as they can take various configurations such as rings, links, chains and knots. These line nodes are usually protected by mirror or PT symmetry. Here we propose and demonstrate a novel type of photonic straight nodal lines in a D2d meta-crystal which are protected by roto-inversion time (roto-PT) symmetry. The nodal lines are located at the central axis and hinges of the Brillouin zone. They appear as quadrupole sources of Berry curvature flux and allow for the precise control of the quadrupole strength. Interestingly, there exist topological surface states at all three cutting surfaces, as guaranteed by the pi-quantized Zak phases along all three directions. As frequency changes, the surface state equi-frequency contours evolve from closed to open contours, and become straight lines at a critical transition frequency, at which diffraction-less surface wave propagation are demonstrated, paving way towards development of super-imaging photonic devices.

Time projection chambers (TPCs) are widely used in nuclear and particle physics. They are particularly useful when measuring reaction products from heavy ion collisions. Most nuclear experiments at low energy are performed in a fixed target configuration, in which the unreacted beam will pass through the detection volume. As the beam intensity increases, the buildup of positive ions created from the ionization of the detector gas by the beam creates the main source of space charge, distorting the nominal electric field of the TPC. This has a profound effect on the accuracy of the measured momenta of the emitted particles. In this paper we will discuss the magnitude of the effects and construct an observable more appropriate for fixed target experiments to study the effects. We also will present an algorithm for correcting the space charge and some of the implications it has on the momentum determination., Comment: 9 pages, 10 figures

There has recently been a dramatic renewal of interest in the subjects of hadron spectroscopy and charm physics. This renaissance has been driven in part by the discovery of a plethora of charmonium-like $XYZ$ states at BESIII and $B$ factories, and the observation of an intriguing proton-antiproton threshold enhancement and the possibly related $X(1835)$ meson state at BESIII, as well as the threshold measurements of charm mesons and charm baryons. We present a detailed survey of the important topics in tau-charm physics and hadron physics that can be further explored at BESIII over the remaining lifetime of BEPCII operation. This survey will help in the optimization of the data-taking plan over the coming years, and provides physics motivation for the possible upgrade of BEPCII to higher luminosity., Comment: 210 pages; Published in CPC

Many novel properties of non-Hermitian systems are found at or near the exceptional points-branch points of complex energy surfaces at which eigenvalues and eigenvectors coalesce. In particular, higher-order exceptional points can result in optical structures that are ultrasensitive to external perturbations. Here we show that an arbitrary order exceptional point can be achieved in a simple system consisting of identical resonators placed near a waveguide. Unidirectional coupling between any two chiral dipolar states of the resonators mediated by the waveguide mode leads to the exceptional point, which is protected by the transverse spin-momentum locking of the guided wave and is independent of the positions of the resonators. Various analytic response functions of the resonators at the exceptional points are experimentally manifested in the microwave regime. The enhancement of sensitivity to external perturbations near the exceptional point is also numerically and analytically demonstrated., Comment: 37 pages, 10 figures

Exceptional points (EPs) associated with a square-root singularity have been found in many non-Hermitian systems. In most of the studies, the EPs found are isotropic meaning that the same singular behavior is obtained independent of the direction from which they are approached in the parameter space. In this work, we demonstrate both theoretically and experimentally the existence of an anisotropic EP in an acoustic system that shows different singular behaviors when the anisotropic EP is approached from different directions in the parameter space. Such an anisotropic EP arises from the coalescence of two square-root EPs having the same chirality., Comment: 16 pages, 3 fiugres

It is well known that for ordinary one-dimensional (1D) disordered systems, the Anderson localization length $\xi$ diverges as $\lambda^m$ in the long wavelength limit ($\lambda\rightarrow \infty$ ) with a universal exponent $m=2$, independent of the type of disorder. Here, we show rigorously that pseudospin-1 systems exhibit non-universal critical behaviors when they are subjected to 1D random potentials. In such systems, we find that $\xi\propto \lambda^m$ with $m$ depending on the type of disorder. For binary disorder, $m=6$ and the fast divergence is due to a super-Klein-tunneling effect (SKTE). When we add additional potential fluctuations to the binary disorder, the critical exponent $m$ crosses over from 6 to 4 as the wavelength increases. Moreover, for disordered superlattices, in which the random potential layers are separated by layers of background medium, the exponent $m$ is further reduced to 2 due to the multiple reflections inside the background layer. To obtain the above results, we developed a new analytic method based on a stack recursion equation. Our analytical results are in excellent agreements with the numerical results obtained by the transfer-matrix method (TMM). For pseudospin-1/2 systems, we find both numerically and analytically that $\xi\propto\lambda^2$ for all types of disorder, same as ordinary 1D disordered systems. Our new analytical method provides a convenient way to obtain easily the critical exponent $m$ for general 1D Anderson localization problems., Comment: 36 pages, 7 figures

We use Fourier space polarimetry to study the incident angle- and polarization-dependent rotation angle and ellipticity of different diffraction orders emerging from a two-dimensional periodic Au array. The array has square lattice and circular nanoholes and thus is achiral. We find no polarization conversion occurs if the diffraction orders lie in the incident plane. However, for the orders that are diffracted away from the incident plane, their rotation angle and ellipticity vary considerably with incident angle and polarization. In particular, dramatic changes in rotation angle and ellipticity are observed when Bloch-like surface plasmon polaritons (SPPs) are excited. The experimental results are consistent with the finite-difference time-domain simulations. The transverse spin carried by the SPPs and a discrete dipole model are used complementarily to elucidate such angular and polarization dependences.

We have studied the dependence of the rotation angle and ellipticity on the sample orientation and incident polarization from metallic nanohole arrays. The arrays have four-fold symmetry and thus do not possess any intrinsic chirality. We elucidate the role of surface plasmon polaritons (SPPs) in determining the extrinsic chirality and we verify the results by using finite-difference time-domain simulation. Our results have indicated the outgoing reflection arises from the interference between the nonresonant background, which preserves the input polarization, and the SPP radiation damping, which is linearly polarized but carries a different polarization defined by the vectorial field of SPPs. More importantly, the interference manifests various polarization states ranging from linear to elliptical across the SPP resonance. We analytically formulate the outgoing waves based on temporal coupled mode theory (CMT) and the results agree well with the experiment and simulation. From CMT, we find the polarization conversion depends on the interplay between the absorption and radiative decay rates of SPPs and the sample orientation.

Robust topological edge modes may evolve into complex-frequency modes when a physical system becomes non-Hermitian. We show that, while having negligible forward optical extinction cross section, a conjugate pair of such complex topological edge modes in a non-Hermitian $\mathcal{PT}$-symmetric system can give rise to an anomalous sideway scattering when they are simultaneously excited by a plane wave. We propose a realization of such scattering state in a linear array of subwavelength resonators coated with gain media. The prediction is based on an analytical two-band model and verified by rigorous numerical simulation using multiple-multipole scattering theory. The result suggests an extreme situation where leakage of classical information is unnoticeable to the transmitter and the receiver when such a $\mathcal{PT}$-symmetric unit is inserted into the communication channel., Comment: 16 pages, 8 figures

It is well known that a closed loop of magnetic dipoles can give rise to the rather elusive toroidal moment. However, artificial structures required to generate the necessary magnetic moments are typically optically large, complex to make and easily compromised by the kinetic inductance at high frequencies. Instead of using magnetic dipoles, we propose a minimal model based on just three aligned discrete electric dipoles in which the occurrence of resonant toroidal modes is guaranteed by symmetry. The advantage of this model is its simplicity and the same model supports toroidal moments from the microwave regime up to optical frequencies as exemplified by a three-antenna array and a system consisting of three nano-sized plasmonic particles. Both the microwave and high-frequency configurations exhibit non-radiating "anapoles". Experiments in the microwave regime confirm the theoretical predictions., Comment: 21 pages, 6 figures

Non-Hermitian systems with parity-time (PT) symmetric complex potentials can exhibit a phase transition when the degree of non-Hermiticity is increased. Two eigenstates coalesce at a transition point, which is known as the exceptional point (EP) for a discrete spectrum and spectral singularity for a continuous spectrum. The existence of an EP is known to give rise to a great variety of novel behaviors in various fields of physics. In this work, we study the complex band structures of one-dimensional photonic crystals with PT symmetric complex potentials by setting up a Hamiltonian using the Bloch states of the photonic crystal without loss or gain as a basis. As a function of the degree of non-Hermiticity, two types of PT symmetry transitions are found. One is that a PT-broken phase can re-enter into a PT-exact phase at a higher degree of non-Hermiticity. The other is that two spectral singularities, one originating from the Brillouin zone center and the other from the Brillouin zone boundary, can coalesce at some k-point in the interior of the Brillouin zone and create a singularity of higher order. Furthermore, we can induce a band inversion by tuning the filling ratio of the photonic crystal, and we find that the geometric phases of the bands before and after the inversion are independent of the amount of non-Hermiticity as long as the PT-exact phase is not broken. The standard concept of topological transition can hence be extended to non-Hermitian systems., Comment: 19 pages, 6 figures

Non-Hermitian systems distinguish themselves from Hermitian systems by exhibiting a phase transition point called an exceptional point (EP), which is the point at which two eigenstates coalesce under a system parameter variation. Many interesting EP phenomena such as level crossings/repulsions in nuclear/molecular and condensed matter physics, and unusual phenomena in optics such as loss-induced lasing and unidirectional transmission can be understood by considering a simple 2x2 non-Hermitian matrix. At a higher dimension, more complex EP physics not found in two-state systems arises. We consider the emergence and interaction of multiple EPs in a four-state system theoretically and realize the system experimentally using four coupled acoustic cavities with asymmetric losses. We find that multiple EPs can emerge and as the system parameters vary, these EPs can collide and merge, leading to higher order singularities and topological characteristics much richer than those seen in two-state systems.

Inspired by the discovery of quantum hall effect and topological insulator, topological properties of classical waves start to draw worldwide attention. Topological non-trivial bands characterized by non-zero Chern numbers are realized with external magnetic field induced time reversal symmetry breaking or dynamic modulation. Due to the absence of Faraday-like effect, the breaking of time reversal symmetry in an acoustic system is commonly realized with moving background fluids, and hence drastically increases the engineering complexity. Here we show that we can realize effective inversion symmetry breaking and effective gauge field in a reduced two-dimensional system by structurally engineering interlayer couplings, achieving an acoustic analog of the topological Haldane model. We then find and demonstrate unidirectional backscattering immune edge states. We show that the synthetic gauge field is closely related to the Weyl points in the three-dimensional band structure., Comment: 21 pages, 9 figures

Pseudospin plays a central role in many novel physical properties of graphene and other artificial systems which have pseudospins of 1/2. Here we show that in certain photonic crystals (PCs) exhibiting conical dispersions at k = 0, the eigenmodes near the "Dirac-like point" can be described by an effective spin-orbit Hamiltonian with a pseudospin of 1, treating wave propagations in the upper cone, the lower cone and a flat band (corresponding to zero refractive index) within a unified framework. The 3-component spinor gives rise to boundary conditions distinct from those of pseudospin-1/2, leading to new wave transport behaviors as manifested in Klein tunneling and supercollimation. For example, collimation can be realized more easily with pseudospin-1 than pseudospin-1/2. The special wave scattering properties of pseudospin-1 photons, coupled with the discovery that the effective photonic "potential" can be varied by a simple change of length scale, may offer new ways to control photon transport., Comment: 34 pages, 6 figures

Surface impedance is an important concept in classical wave systems such as photonic crystals (PCs). For example, the condition of an interface state formation in the interfacial region of two different one-dimensional PCs is simply Z_SL +Z_SR=0, where Z_SL (Z_SR)is the surface impedance of the semi-infinite PC on the left- (right-) hand side of the interface. Here, we also show a rigorous relation between the surface impedance of a one-dimensional PC and its bulk properties through the geometrical (Zak) phases of the bulk bands, which can be used to determine the existence or non-existence of interface states at the interface of the two PCs in a particular band gap. Our results hold for any PCs with inversion symmetry, independent of the frequency of the gap and the symmetry point where the gap lies in the Brillouin Zone. Our results provide new insights on the relationship between surface scattering properties, the bulk band properties and the formation of interface states, which in turn can enable the design of systems with interface states in a rational manner.

We present a systematic analysis of two-pion interferometry for the central Au+Au collisions at $\sqrt{S_{NN}}$ = 3, 5, 7, 11, 17, 27, 39, 62, 130 and 200 GeV/c with the help of a multiphase transport (AMPT) model. Emission source-size radius parameters $R_{long}$, $R_{out}$, $R_{side}$ and the chaotic parameter $\lambda$ are extracted and compared with the experimental data. Transverse momentum and azimuthal angle dependencies of the HBT radii are also discussed for central Au+Au collisions at 200 GeV/c. The results show that the HBT radii in central collisions do not change much above 7 GeV/c. For central collisions at 200GeV/c, the radii decrease with the increasing of transverse momentum $p_{T}$ but not sensitive to the azimuthal angle. These results provide a theoretical reference for the energy scan program of the RHIC-STAR experiment., Comment: 4 pages, 4 figures; submitted to Chinese Physics C

We follow the temporal evolution of mesoscopic intensity fluctuations and correlation in strongly localized samples. We find an initial burst in relative transmission fluctuations in random one dimensional (1D) samples due to fluctuations in the arrival time of ballistic transmission. Relative fluctuations subsequently rise, then drop to a minimum at a time t_m, after which they increase rapidly in 1D simulations and quasi-1D (Q1D) measurements. For t > 3t_m, results in 1D and Q1D samples converge towards predictions of a dynamic single parameter scaling model. These results reflect the changing number of modes participating appreciably in transmission as the impact of longer lived modes grows with time delay.

We argue from both technical and physical points of view that the main result shown in the Comment [arXiv:0709.2619] by Cherrolet et al. [Phys. Rev. B 80, 037101 (2009)] as well as the authors' interpretations of the result are not sufficient to draw the conclusion that the scaling law at the mobility edge takes the form T \propto 1/L^2. On the other hand, we believe that the result shows some evidence of T \propto ln L/L^2 behavior found in S. K. Cheung and Z. Q. Zhang, Phys. Rev. B 72, 235102 (2005) [arXiv:cond-mat/0509381]. More calculations with even larger L's are necessary to give a more definitive answer to this question., Comment: 7 pages, 1 figure

We have measured pulsed microwave transmission through quasi-1D samples with lengths up to three localization lengths. For times approaching four times the diffusion time \tau_D, transmission is diffusive in accord with the self-consistent theory of localization for the renormalized diffusion coefficient in space and frequency, D(z,\Omega). For longer times, the transmission decay rate first agrees with and later falls increasingly below the self-consistent theory. Beyond the Heisenberg time, the decay rate approaches the predictions of a dynamic single parameter scaling model which reflects the decay of long-lived localized modes and converges to the results of 1D simulations., Comment: 5 RevTex pages, 3 figures; submitted to PRL

The propagation of classical wave in disordered media at the Anderson localization transition is studied. Our results show that the classical waves may follow a different scaling behavior from that for electrons. For electrons, the effect of weak localization due to interference of recurrent scattering paths is limited within a spherical volume because of electron-electron or electron-phonon scattering, while for classical waves, it is the sample geometry that determine the amount of recurrent scattering paths that contribute. It is found that the weak localization effect is weaker in both cubic and slab geometry than in spherical geometry. As a result, the averaged static diffusion constant D(L) scales like ln(L)/L in cubic or slab geometry and the corresponding transmission follows ~ln L/L^2. This is in contrast to the behavior of D(L)~1/L and ~1/L^2 obtained previously for electrons or spherical samples. For wave dynamics, we solve the Bethe-Salpeter equation in a disordered slab with the recurrent scattering incorporated in a self-consistent manner. All of the static and dynamic transport quantities studied are found to follow the scaling behavior of D(L). We have also considered position-dependent weak localization effects by using a plausible form of position-dependent diffusion constant D(z). The same scaling behavior is found, i.e., ~ln L/L^2., Comment: 11 pages, 12 figures. Submitted to Phys. Rev. B on 3 May 2005

The photonic band structures in certain two- and three-dimensional periodic networks made of one-dimensional waveguides are studied by using the Floquet-Bloch theorem. We find that photonic band gaps exist only in those structures where the fundamental loop exhibits anti-resonant transmission. This is also true for quasi-periodic networks in two and three dimensions, where the photonic band structures are calculated from the spectra of total transmission arising from a source inside the samples. In all the cases we have studied, it is also found that the gap positions in a network are dictated by the frequencies at which the anti-resonance occurs., Comment: 7 pages, 10 figures and 1 table. Published in Phys. Rev. B, 70, 125104 (2004)

We study the dynamics of wave propagation in nominally diffusive samples by solving the Bethe-Salpeter equation with recurrent scattering included in a frequency-dependent vertex function, which renormalizes the mean free path of the system. We calculate the renormalized time-dependent diffusion coefficient, D(t), following pulsed excitation of the system. For cylindrical samples with reflecting side walls and open ends, we observe a crossover in dynamics in the transformation from a quasi-1D to a slab geometry implemented by varying the ratio of the radius, R, to the length, L. Immediately after the peak of the transmitted pulse, D(t) falls linearly with a nonuniversal slope that approaches an asymptotic value for R/L>>1. The value of D(t) extrapolated to t=0, depends only upon the dimensionless conductance g for R/L<<1 and upon kl and L for R/L>>1, where k is the wave vector and l is the bare mean free path., Comment: 9 pages, 5 figures, published in Methods and Applications of Analysis, Vol. 11, No. 3, pp. 001-010 (International Press, MA, Sep 2004)

We find a renormalized "time-dependent diffusion coefficient", D(t), for pulsed excitation of a nominally diffusive sample by solving the Bethe-Salpeter equation with recurrent scattering. We observe a crossover in dynamics in the transformation from a quasi-1D to a slab geometry implemented by varying the ratio of the radius, R, of the cylindrical sample with reflecting walls and the sample length, L. Immediately after the peak of the transmitted pulse, D(t) falls linearly with a nonuniversal slope that approaches an asymptotic value for R/L >> 1. The value of D(t) extrapolated to t = 0 depends only upon the dimensionless conductance, g, for R/L << l 1 and only upon kl for R/L >> 1, where k is the wave vector and l is the bare mean free path., Comment: 4 pages, 5 figures

We report the observation of nonexponential decay of pulsed microwave transmission through quasi-one-dimensional random dielectric media that signals the breakdown of the diffusion model of transport for temporally coherent extended waves. The decay rate of transmission falls nearly linearly in time due to a nearly gaussian distribution of the coupling strengths of quasi-normal electromagnetic modes to free space at the sample surfaces. The peak and width of this distribution scale as L^{-2.05} and L^{-1.81}, respectively., Comment: Revised paper: new figures and references, and comparison to theory predictions are added