Hybrid topological photonic crystals.

Topologically protected photonic edge states offer unprecedented robust propagation of photons that are promising for waveguiding, lasing, and quantum information processing. Here, we report on the discovery of a class of hybrid topological photonic crystals that host simultaneously quantum anomalous Hall and valley Hall phases in different photonic band gaps. The underlying hybrid topology manifests itself in the edge channels as the coexistence of the dual-band chiral edge states and unbalanced valley Hall edge states. We experimentally realize the hybrid topological photonic crystal, unveil its unique topological transitions, and verify its unconventional dual-band gap topological edge states using pump-probe techniques. Furthermore, we demonstrate that the dual-band photonic topological edge channels can serve as frequency-multiplexing devices that function as both beam splitters and combiners. Our study unveils hybrid topological insulators as an exotic topological state of photons as well as a promising route toward future applications in topological photonics.

Electromagnetic energy density in hyperbolic metamaterials.

We present the theory of electromagnetic energy propagation through a dispersive and absorbing hyperbolic metamaterial (HMM). In this way, the permittivity tensor components of HMM (especially, nanowire HMM) may appear to be hopeless, but as a non-trivial step, we find that they can be cast into more transparent forms. We find under the influence of an electromagnetic wave, the responses of nanowire HMM (multilayer HMM) in the directions perpendicular to and parallel to the optical axis are similar to those of Lorentz (Drude) and Drude (Lorentz) media, respectively. We obtain simple expressions for the electromagnetic energy density formula of both typical structures of HMMs, i.e., nanowire and multilayer HMMs. Numerical examples reveal the general characteristics of the direction-dependent energy storage capacity of both nanowire and multilayer HMMs. The results of this study may shed more physical insight into the optical characteristics of HMMs.

Gain-assisted hybrid-superlens hyperlens for nano imaging.

We propose an innovative active imaging device named gain-assisted hybrid-superlens hyperlens and examine its resolving power theoretically. This semi-cylindrical device consists of a core of semi-cylindrical super-lens and a half cylindrical outer shell of hyperlens. Both the superlens and hyperlens parts of the device are appropriately designed multi-layered metal-dielectric structures having indefinite eigenvalues of dielectric tensors. The dielectric layers of the hyperlens are doped with Coumarin, which play the role of gain medium. The gain medium is analyzed thoroughly using a generic four-level system model, and the permittivity of the gain medium is extracted from this analysis for simulating the imaging characteristics of the device. According to our simulation at wavelength of 365 nm, an excellent resolution power much better than the diffraction limit value can be achieved.

Electromagnetic energy density in a single-resonance chiral metamaterial.

We derive the electromagnetic energy density in a chiral metamaterial consisting of uncoupled single-resonance helical resonators. Both the lossless and absorptive cases are studied, and the energy density is shown to be positively definite. The key relation making the derivation successful is the proportionality between the magnetization and the rate of change of the electric polarization of the medium. The same time-domain formulation of energy density also applies to the bianisotropic medium proposed by Zhang et al. [Phys. Rev. Lett.102, 023901 (2009)PRLTAO0031-900710.1103/PhysRevLett.102.023901]. This work may provide insights for studying time-dependent phenomena in metamaterials.

Influence 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 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.

Imaging off-plane shear waves with a 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 a solid matrix. The self-collimation effect is employed to guide the shear waves propagating through the lens along specific directions. The 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.

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 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.

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 a classical treatment, a Fourier expansion technique, a time-evolution method, and the Lewis-Riesenfeld approach. We have shown that, by properly managing the boundary conditions, a time-dependent wavefunction 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 wavepacket with a peak moving along the classical angular trajectory, while the distribution of the wavepacket 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 wavepacket. 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.

Periodic dielectric waveguide beam splitter based on co-directional coupling.

A compact beam splitter consisting of three branches of periodic dielectric waveguides (PDW) is designed and analyzed theoretically. Both the symmetrical and asymmetrical configurations of the beam splitter are studied. The band structure for the guided modes is calculated by using finite-difference time-domain (FDTD) method with Bloch-type boundary conditions applying in an appropriate supercell. The field patterns for the whole structure and the transmissions for the output ports are calculated using the multiple scattering method. By utilizing the co-directional coupling mechanism, the light injected into the input branch can be efficiently transferred into the two output branches if the phase matching conditions are satisfied. The coupling length is short and the broad-band requirement can be achieved. Bending loss is small and high transmission (above 95%) can be preserved for arbitrarily bent PDW if the bend radius of each bend exceeds five wavelengths. This feature indicates that the periodic dielectric waveguide beam splitter (PDWBS) is a high efficiency device for power redistribution while avoiding the lattice orientation restriction of the photonic crystal waveguides (PCW).

Transmission characteristics of finite periodic dielectric waveguides.

Transmission properties of the periodic dielectric waveguide (PDWG) formed by aligning a sequence of dielectric cylinders in air are investigated theoretically. Unlike photonic crystal waveguides (PCWs), light confinement in a PDWG is due to total internal reflection. Besides, the dispersion relation of the guided modes is strongly influenced by the dielectric periodicity along the waveguide. The band structure for the guided modes is calculated using a finite-difference time-domain (FDTD) method. The first band is used for guiding light, which makes PDWG single mode. Transmission is calculated using the multiple scattering method for various S shaped PDWGs, each containing two opposite bends. When PDWG operates in appropriate frequency ranges, high transmission (above 90%) is observed, even if the radius of curvature of the bends is reduced to three wavelengths. This feature indicates that the guiding ability of PDWG can be made better than the conventional waveguide when used in an optical circuit. In addition, PDWG has the advantage that it can be bent to any arbitrary shape while still preserves the high transmission, avoiding the geometric restriction that PCWs are subject to.

Photonic crystal beam splitters.

This work studies two-dimensional photonic crystal beam splitters with two input ports and two output ports. The beam splitter structure consists of two orthogonally crossed line defects and one point defect in square-lattice photonic crystals. The point defect is positioned at the intersection of the line defects to divide the input power into output ports. If the position and the size of the point defect are varied, the power of two output ports can be identical. The beam splitters can be used in photonic crystal Mach-Zehnder interferometers or switches. The simulation results show that a large bandwidth of the extinction ratio larger than 20 dB can be obtained while two beams are interfered in the beam splitters. This enables photonic crystal beam splitters to be used in fiber optic communication systems.

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 Schrödinger equation of some quantum mechanical problems.

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 indicates that the fundamental assumption of statistical mechanics holds in this system.

Effect of dielectric responses on localization in one-dimensional random periodic-on-average layered systems.

Dielectric response effects on wave localization in random periodic-on-average layered systems are studied. Based on Monte Carlo simulations and products of random matrices, statistics of the Lyapunov exponent are determined efficiently for very long systems. An oscillatory behavior for 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 omega(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.