Second-harmonic generation from magnetic metamaterials

We observe second-harmonic generation from metamaterials composed of split-ring resonators excited at 1.5-micrometer wavelength. Much larger signals are detected when magnetic-dipole resonances are excited, as compared with purely electric-dipole resonances. The experiments are consistent with calculations based on the magnetic component of the Lorentz force exerted on metal electrons-an intrinsic second-harmonic generation mechanism that plays no role in natural materials. This unusual mechanism becomes relevant in our work as a result of the enhancement and the orientation of the local magnetic fields associated with the magnetic-dipole resonances of the split-ring resonators.     

Optical negative refraction in bulk metamaterials of nanowires

Negative refraction in metamaterials has generated great excitement in the scientific community. Although negative refraction has been realized in microwave and infrared by using metamaterials and by using two-dimensional waveguide structures, creation of a bulk metamaterial showing negative refraction at visible frequency has not been successful, mainly because of the significant resonance losses and fabrication difficulties. We report bulk metamaterials made of nanowires that show such negative refraction for all incident angles in the visible region. Moreover, the negative refraction occurs far from any resonance, resulting in a low-loss and a broad-band propagation at visible frequencies. These remarkable properties can substantially affect applications such as imaging, three-dimensional light manipulation, and optical communication.     

Magnetic response of metamaterials at 100 terahertz

An array of single nonmagnetic metallic split rings can be used to implement a magnetic resonance, which arises from an inductor-capacitor circuit (LC) resonance, at 100-terahertz frequency. The excitation of the LC resonance in the normal-incidence geometry used in our experiments occurs through the coupling of the electric field of the incident light to the capacitance. The measured optical spectra of the nanofabricated gold structures come very close to the theoretical expectations. Additional numerical simulations show that our structures exhibit a frequency range with negative permeability for a beam configuration in which the magnetic field couples to the LC resonance. Together with an electric response that has negative permittivity, this can lead to materials with a negative index of refraction.     

实数集R的不同拓扑结构和拓扑性质

 针对实数空间R中不同的拓扑结构，讨论实数空间R若干拓扑结构之间的关系，并讨论在不同的拓扑结构中，聚点、极限点等有关性质。     

Water-induced fabric transitions in olivine

The interpretation of seismic anisotropy in Earth's upper mantle has traditionally been based on the fabrics (lattice-preferred orientation) of relatively water-poor olivine. Here we show that when a large amount of water is added to olivine, the relation between flow geometry and seismic anisotropy undergoes marked changes. Some of the puzzling observations of seismic anisotropy in the upper mantle, including the anomalous anisotropy in the central Pacific and the complicated anisotropy in subduction zones, can be attributed to the enrichment of water in these regions.     

Gate-variable optical transitions in graphene

Two-dimensional graphene monolayers and bilayers exhibit fascinating electrical transport behaviors. Using infrared spectroscopy, we find that they also have strong interband transitions and that their optical transitions can be substantially modified through electrical gating, much like electrical transport in field-effect transistors. This gate dependence of interband transitions adds a valuable dimension for optically probing graphene band structure. For a graphene monolayer, it yields directly the linear band dispersion of Dirac fermions, whereas in a bilayer, it reveals a dominating van Hove singularity arising from interlayer coupling. The strong and layer-dependent optical transitions of graphene and the tunability by simple electrical gating hold promise for new applications in infrared optics and optoelectronics.     

模糊拓扑空间的m-紧(I)

在模糊拓扑空间中利用强开覆盖的概念引进一个称作 m-紧的紧性定义 ,并研究了它与模糊网的 m-收敛之间的关系 .证明了 Tychonoff乘积定理对 m-紧性成立 .     

Dynamics of conformational transitions in polymers

Conformational transitions in polymers involve large angle rotations about bonds. The process must proceed in a way that does not require gross movements of the macromolecules. The dynamics have been investigated by computer simulation and kinetic theory. The rate-determining step in the transition is found to occur in a mode which is kept local by distortion of nearby parts of the molecule. One especially important type of cooperativity, crank-like counterrotation of second-neighbor bonds, is identified. Experiments which provide evidence about the dynamics of conformational transitions are discussed.     

Confinement-induced phase transitions in simple liquids

The liquid-to-solid transition of a simple model liquid confined between two surfaces was studied as a function of surface separation. From large surface separations (more than 1000 angstroms) down to a separation corresponding to seven molecular layers, the confined films displayed a liquid-like shear viscosity. When the surface separation was further decreased by a single molecular spacing, the films underwent an abrupt, reversible transition to a solid. At the transition, the rigidity of the confined films (quantified in terms of an "effective viscosity") increased reversibly by at least seven orders of magnitude.     

Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials

A form of optical circuitry is overviewed in which a tapestry of subwavelength nanometer-scale metamaterial structures and nanoparticles may provide a mechanism for tailoring, patterning, and manipulating local optical electric fields and electric displacement vectors in a subwavelength domain, leading to the possibility of optical information processing at the nanometer scale. By exploiting the optical properties of metamaterials, these nanoparticles may play the role of "lumped" nanocircuit elements such as nanoinductors, nanocapacitors, and nanoresistors, analogous to microelectronics. I show that this concept of metamaterial-inspired nanoelectronics ("metactronics") can bring the tools and mathematical machinery of the circuit theory into optics, may link the fields of optics, electronics, plasmonics, and metamaterials, and may provide road maps to future innovations in nanoscale optical devices, components, and more intricate nanoscale metamaterials.     

关于Fuzzy拓扑空间的可数性

在以往研究提出的Ｆｕｚｚｙ的点概念和邻近构造思想的基础上，构造了Ｆｕｚｚｙ拓人间的禽近性质，并有效地将拓扑空间的基的概念推广到Ｆｕｚｚｙ拓扑空间，给出了Ｆｕｚｚｙ拓人间的（广义）第一可数性公理Ｆ－Ｃ１及（广义）第二可数性公理Ｆ－Ｃ１；讨论了它们之间的与性质。     

浅议一般拓扑空间中集合之间的关系

在一般拓扑空间中讨论了抽象集合的概念,研究了其性质,得出如下结论,即：所有的δ-开集都是开集,所有开集又都是α-开集,α-开集是半开集且预开集,半开集或预开集是β-开集,反之则不成立。     

Phase transitions of Dirac electrons in bismuth

The Dirac Hamiltonian, which successfully describes relativistic fermions, applies equally well to electrons in solids with linear energy dispersion, for example, in bismuth and graphene. A characteristic of these materials is that a magnetic field less than 10 tesla suffices to force the Dirac electrons into the lowest Landau level, with resultant strong enhancement of the Coulomb interaction energy. Moreover, the Dirac electrons usually come with multiple flavors or valley degeneracy. These ingredients favor transitions to a collective state with novel quantum properties in large field. By using torque magnetometry, we have investigated the magnetization of bismuth to fields of 31 tesla. We report the observation of sharp field-induced phase transitions into a state with striking magnetic anisotropy, consistent with the breaking of the threefold valley degeneracy.     

Folding and unbinding transitions in tethered membranes

Molecular dynamics simulations of tethered membranes indicate that an attraction between the monomers leads to a well-defined sequence of folding transitions with decreasing temperature. With insights gained from Landau theory and simulations of bimembranes, the folding transitions are found to be intimately linked to the unbinding of membranes. Finite-size effects, mainly due to the loss of entropy from edge fluctuations, play an important role in hindering folding transitions.     

Phase transitions and heterogeneity in lipid bilayers

The optical reflectivity of several well-characterized lipid bilayer systems has been correlated with calorimetric studies of the membrane components. There is a large increase in mean membrane thickness when a bilayer is cooled below the transition temperature of the membrane lipid. Similar studies on membranes generated from a mixture of two lipids possessing different degrees of unsaturation suggest that between the characteristic transition temperatures of the two lipids, the bilayer contains clusters of gel and liquid crystalline lipid which coexist within the plane of the membrane.