arXiv subjects

Pi-Gang Luan

Publications and source records attributed to Pi-Gang Luan.

At least 19 recordsLinked to original sources

arXiv2022

Hybrid topological photonic crystals

Photonic topological phases offering unprecedented manipulation of electromagnetic waves have attracted much research interest which, however, have been mostly restricted to a single band gap. Here, we report on the experimental discovery of hybrid topological photonic crystals which host simultaneously quantum anomalous Hall and valley Hall phases in different photonic band gaps. The underlying hybrid topological phase manifests itself in the edge responses as the coexistence of the chiral edge states and valley Hall edge states in different frequency ranges. We experimentally verify such an emergent phenomenon and show that such a feature enables novel multiplexing of photon transport in the edge channels. Our study reveals a situation with coexisting topology of distinct nature in a single photonic system that may enable frequency-dependent filtering and manipulation of topological edge photons.

cond-mat.mes-hall↗

arXiv2022

Electromagnetic Energy Density in Hyperbolic Metamaterials

We derive the energy density associated with an electromagnetic wave passing through a hyperbolic metamaterial (HMM). Both types of HMMs are studied. By considering a dispersive and absorbing HMM as an effective uniaxial crystal, we find that under the influence of an electromagnetic wave, the response of type I (type II) HMM in the directions perpendicular to and parallel to the optical axis are similar to those of Lorentz (Drude) and Drude (Lorentz) media, respectively. Numerical examples are presented to reveal the general characteristics of the direction-dependent energy storage capacity of both types of HMMs.

physics.optics↗

arXiv2017

Lagrangian description and Hamiltonian density for the electrodynamics of dispersive metamaterials

The Lagrangians and dissipation functions are proposed for use in the electrodynamics of the double-negative and chiral metamaterials with finite loss. The double-negative metamaterial considered here is the wires and split rings periodic structure, while the chiral metamaterial is the single-resonance helical resonators array. For either system, application of Legendre transformation leads to a Hamiltonian density identical to the energy density obtained in our previous work based on the Poynting theorem and the mechanism of the power loss. This coincidence implies the correctness of the energy density formulas obtained before. The Lagrangian description and Hamiltonian formulation can be further developed for exploring the properties of the elementary excitations or quasiparticles in dispersive metamaterials due to light-matter interactions.

physics.class-ph↗

arXiv2017

On the possibility of superluminal energy propagation in a hyperbolic metamaterial of metal-dielectric layers

The energy propagation of electromagnetic fields in the effective medium of a one-dimensional photonic crystal consisting of dielectric and metallic layers is investigated. We show that the medium behaves like Drude and Lorentz medium, respectively, when the electric field is parallel and perpendicular to the layers. For arbitrary time-varying electromagnetic fields in this medium, the energy density formula is derived. We prove rigorously that the group velocity of any propagating mode obeying the hyperbolic dispersion must be slower than the speed of light in vacuum, taking into account the frequency dependence of the permittivity tensor. That is, it is not possible to have superluminal propagation in this dispersive hyperbolic medium consisting of real dielectric and metallic material layers. The propagation velocity of a wave packet is also studied numerically. This packet velocity is very close to the velocity of the propagating mode having the central frequency and central wave vector of the wave packet. When the frequency spread of the wave packet is not narrow enough, small discrepancy between these two velocities manifests, which is caused by the non-penetration effect of the evanescent modes. This work reveals that no superluminal phenomenon can happen in a dispersive anisotropic metamaterial medium made of real materials.

physics.optics↗

arXiv2014

Coriolis Force Induced Quantum Hall Effect for Phonons

A two-dimensional mass-spring system with Honeycomb lattice for mimicking phononic quantum Hall effect is proposed. Its band structure shows the existence of Dirac cones and unconventional edge states that is similar to the vibrational modes in graphene. Interestingly, as the system is placed on a constantly rotational coordinate system, the Coriolis force resulted from the non-inertial reference frame provides a possibility to break the time-reversal symmetry. Thus, caused from topologically non-trivial band gaps, phononic edge states are present between bands, which are verified by the calculation of Chern numbers for corresponding bands.

cond-mat.mes-hall↗

arXiv2010

Influences of source displacement on the features of subwavelength imaging of a photonic crystal slab

In this paper we study the characteristics of subwavelength imaging of a photonic crystal (PhC) superlens under the influence of source displacement. For square- and triangular-lattice photonic crystal lenses, we investigate the influence of changing the lateral position of a single point source on the imaging uniformity and stability. We also study the effect of changing the geometrical center of a pair of sources on the resolution of the double-image. Both properties are found to be sensitive to the displacement, which implies that a PhC slab cannot be treated seriously as a flat lens. We also show that by introducing material absorption into the dielectric cylinders of the PhC slab and widening the lateral width of the slab, the imaging uniformity and stability can be substantially improved. This study helps us to clarify the underlying mechanisms of some recently found phenomena concerning imaging instability.

physics.optics↗

arXiv2010

Note on the positiveness of magnetic energy stored in the Wire-SRR metamaterial

Recently, a new energy density formula for electromagnetic waves in the metamaterial consisting of arrays of conducting wires and split-ring-resonators (SRR) has been derived [Phys. Rev. E 80, 046601 (2009), arXiv:0909.1043]. According to that formula, the positiveness is obvious for the electric part of the energy density but not clear for the magnetic part. In this paper, I show that the magnetic energy density is also positively definite.

physics.optics↗

arXiv2010

Imaging an off-plane shear wave source with two-dimensional phononic-crystal lens

A two dimensional flat phononic crystal (PC) lens for focusing off-plane shear waves is proposed. The lens consists of a triangular lattice hole-array, embedded in solid matrix. Self-collimation effect is employed to guide the shear waves propagating through the lens along specific directions. Dirichlet-to-Neumann Maps (DtN) method is employed to calculate the band structure of the PC, which can avoid the problems of bad convergence and fake bands automatically in the void-solid PC structure. When the lens is illuminated by the off-plane shear waves emanating from a point source, a subwavelength image appears in the far-field zone. The imaging characteristics are investigated by calculating the displacement fields explicitly using the multiple-scattering method, and the results are in good agreement with the ray-trace predictions. Our results may provide insights for designing new phononic devices.

cond-mat.other↗

arXiv2009

Power loss and electromagnetic energy density in a dispersive metamaterial medium

The power loss and electromagnetic energy density of a metamaterial consisting of arrays of wires and split-ring resonators (SRRs) are investigated. We show that a field energy density formula can be derived consistently from both the electrodynamic (ED) approach and the equivalent circuit (EC) approach. The derivations are based on the knowledge of the dynamical equations of the electric and magnetic dipoles in the medium and the correct form of the power loss. We discuss the role of power loss in determining the form of energy density and explain why the power loss should be identified first in the ED derivation. When the power loss is negligible and the field is harmonic, our energy density formula reduces to the result of Landau's classical formula. For the general case with finite power loss, our investigation resolves the apparent contradiction between the previous results derived by the EC and ED approaches.

cond-mat.mes-hall↗

arXiv2007

Charged particle motion in a time-dependent flux-driven ring: an exactly solvable model

We consider a charged particle driven by a time-dependent flux threading a quantum ring. The dynamics of the charged particle is investigated using classical treatment, Fourier expansion technique, time-evolution method, and Lewis-Riesenfeld approach. We have shown that, by properly managing the boundary conditions, a time-dependent wave function can be obtained using a general non-Hermitian time-dependent invariant, which is a specific linear combination of initial angular-momentum and azimuthal-angle operators. It is shown that the linear invariant eigenfunction can be realized as a Gaussian-type wave packet with a peak moving along the classical angular trajectory, while the distribution of the wave packet is determined by the ratio of the coefficient of the initial angle to that of the initial canonical angular momentum. From the topologically nontrivial nature as well as the classical trajectory and angular momentum, one can determine the dynamical motion of the wave packet. It should be noted that the peak position is no longer an expectation value of the angle operator, and hence the Ehrenfest theorem is not directly applicable in such a topologically nontrivial system.

cond-mat.mes-hall↗

arXiv2005

Exact approaches to charged particle motion in a time-dependent flux-driven ring

We consider a charged particle which is driven by a time-dependent flux threading a circular ring system. Various approaches including classical treatment, Fourier expansion method, time-evolution method, and Lewis-Riesenfeld method are used and compared to solve the time-dependent problem. By properly managing the boundary condition of the system, a time-dependent wave function of the charged particle can be obtained by using a non-Hermitian time-dependent invariant, which is a specific linear combination of initial angular-momentum and azimuthal-angle operators. The eigenfunction of the linear invariant can be realized as a Gaussian-type wave packet with a peak moving along the classical angular trajectory, while the distribution of the wave packet is determined by the ratio of the coefficient of the initial angle to that of the initial canonical angular momentum. In this topologically nontrivial system, we find that although the classical trajectory and angular momentum can determine the motion of the wave packet; however, the peak position is no longer an expectation value of the angle operator. Therefore, in such a system, the Ehrenfest theorem is not directly applicable.

cond-mat.mes-hall↗

arXiv2004

Lewis-Riesenfeld approach to the solutions of Schrodinger equation in the presence of the presence of a time-dependent linear potential

We reexamine the general solution of a Schrödinger equation in the presence of a time-dependent linear potential in configuration space based on the Lewis-Riesenfeld framework. For comparison, we also solve the problem in momentum space and then Fourier transform the solution to get the general wave function. Appropriately choosing the weight function in the latter method, we can obtain the same wave function as the former method. It is found that non-Hermitian time-dependent linear invariant can be used to obtain Gaussian-type wave-packet (GTWP) solutions of the time-dependent system. This operator is a specific linear combination of the initial momentum and initial position operators. This fact indicates that the constants of integration such as the initial position and initial momentum that determine the classical motion play important roles in the time-dependent quantum system. The eigenfunction of the linear invariant is interpreted as a wave packet with a "center of mass" moving along the classical trajectory, while the ratio between the coefficients of the initial position and initial momentum determines the width of the wave packet.

quant-ph↗

arXiv2004

Unified treatment for classical waves in two-dimensional media

A unified treatment for the propagation of classical waves in inhhomogeneous media is proposed. We deal with four kinds of waves, they are the acoustic wave in fluid, the elastic shear wave in two diemnsional solid, and the E- and H-polarized electromagnetic waves in two diemnsional lossless medium. We first show that a universal wave equation governing the wave motion of all these four kinds of waves can be derived. We then introduce an auxiliary field, and give the universal expressions for the energy densities and energy flows of these waves. This unified treatment provides intuitive insights, which may be helpful in understanding the essential physics of various wave phenomena, or useful for designing new photonic and sonic devices.

cond-mat.mtrl-sci↗

arXiv2004

Analysis on the imaging properties of a left-handed material slab

We investigate in this paper the imaging properties of an absorptive left-handed material (LHM) slab. For a line source, a geometric explanation to the reason of the thickness limitation on an ideal slab is given. For a lossy slab, the imaging properties are determined by the wavelength, the slab thickness, the distance from the source to the nearer boundary of the slab, and the absorption effect. Varying the ratios between these quantities, the image width can be changed from wavelength to subwavelength scale. In the former situation, the energy density is mainly concentrated at the two image spots. In the later case, though image of subwavelength width appears on the focal plane, however, most energy is located at about the two boundaries of the slab, and beyond the boundaries the wave amplitude decays exponentially. The relations between the subwavelength imaging and uncertainty principle is also discussed.

physics.optics↗

arXiv2003

Drifting diffusion on a circle as continuous limit of a multiurn Ehrenfest model

We study the continuous limit of a multibox Erhenfest urn model proposed before by the authors. The evolution of the resulting continuous system is governed by a differential equation, which describes a diffusion process on a circle with a nonzero drifting velocity. The short time behavior of this diffusion process is obtained directly by solving the equation, while the long time behavior is derived using the Poisson summation formula. They reproduce the previous results in the large $M$ (number of boxes) limit. We also discuss the connection between this diffusion equation and the Schr$\ddot{\rm o}$dinger equation of some quantum mechanical problems.

physics.atom-ph↗

arXiv2002

Poincaré cycle of a multibox Ehrenfest urn model with directed transport

We propose a generalized Ehrenfest urn model of many urns arranged periodically along a circle. The evolution of the urn model system is governed by a directed stochastic operation. Method for solving an $N$-ball, $M$-urn problem of this model is presented. The evolution of the system is studied in detail. We find that the average number of balls in a certain urn oscillates several times before it reaches a stationary value. This behavior seems to be a peculiar feature of this directed urn model. We also calculate the Poincaré cycle, i.e., the average time interval required for the system to return to its initial configuration. The result can be easily understood by counting the total number of all possible microstates of the system.

cond-mat.stat-mech↗

arXiv2002

Effect of dielectric responses on localization in 1D random periodic-on-average systems

Dielectric response effects on wave localization in random periodic-on-average layered systems (POAS) are studied. Based on Monte Carlo simulations and products of Random Matrices, statistics of the Lyapunovmexponent are determined efficiently for very long systems. A novel oscillatory behavior for the Lyapunov exponent is found and explained for mildly strong scattering conditions. We also show the emergence of strongly localized states in metallic layered systems with intermediate disorder for frequencies above the plasma frequency $ω_{p}$ of metals, as is not shown in dielectrics. Furthermore, the violation of universal single parameter scaling behaviors in different regimes of multiple scattering is discussed.

cond-mat.dis-nn↗

arXiv2002

Reflection of matter waves by a moving wall

Reflection of a normal incident matter wave by a perfectly reflecting wall moving with a constant velocity is investigated. A surprising phenomenon is found-that if the the wall moves faster than the phase velocity of the incident wave, both the reflected and incident waves propagate in the same direction. This counter-intuitive result is an example which shows that common sense is not always credible when one deals with quantum problems.

quant-ph↗