Surface defect gap solitons in two-dimensional optical lattices

We investigate the existence and stability of surface defect gap solitons at an interface between a defect in a two-dimensional optical lattice and a uniform saturable Kerr nonlinear medium. The surface defect embedded in the two-dimensional optical lattice gives rise to some unique properties. It is interestingly found that for the negative defect, stable surface defect gap solitons can exist both in the semi-infinite gap and in the first gap. The deeper the negative defect, the narrower the stable region in the semi-infinite gap will be. For a positive defect, the surface defect gap solitons exist only in the semi-infinite gap and the stable region localizes in a low power region.     

Surface defect kink solitons

We reveal the existence of dynamically stable nonlinear defect kink modes at an interface separating a defocusing Kerr medium and an imprinted semi-infinite lattice with a positive or negative defect covering single or several lattice sites. Increasing the number of defect sites equivalently results in a band-gap shift of lattice which in return alters the existence domains and stability properties of defect solitons. Comparing with the uniform semi-infinite lattice, the instability of kink soliton in lattice with a negative defect is significantly suppressed, especially for in-phase soliton. Our results provide an effective way for the realization of stable in-phase kink solitons.     

Band-gap guidance in optically induced photonic lattices with a negative defect

We report the first experimental demonstration of band-gap guidance of light in an optically induced two-dimensional photonic lattice with a single-site negative defect (akin to a low-index core in photonic-crystal fibers). We discuss the difference between spatial guidance at a regular and a defect site, and show that the guided beam through the defect displays fine structures such as vortex cells that arise from defect modes excited at higher band gaps. Defect modes at different wavelengths are also observed.     

Quantum dynamics of a driven correlated system coupled to phonons

Nonequilibrium interplay between charge, spin, and lattice degrees of freedom on a square lattice is studied for a single charge carrier doped in the t-J-Holstein model. In the presence of a static electric field we calculate the quasistationary state. With increasing electron-phonon (e-ph) coupling the carrier mobility decreases; however, we find increased steady state current due to e-ph coupling in the regime of negative differential resistance. We explore the distribution of absorbed energy between the spin and the phonon subsystem. For model parameters as relevant for cuprates, the majority of the gained energy flows into the spin subsystem.     

Surface defect gap solitons in one-dimensional dual-frequency lattices

We study the surface defect gap solitons in an interface between a defect of one-dimensional dual-frequency lattices and the uniform media. Some unique properties are revealed that such lattices can broaden the region of semi-finite gap, and the semi-finite gap exists not only in the positive and zero defects but also in the negative defect; unlike in the regular lattices, the semi-finite gap exists in the positive and zero defects but does not exist in the negative defect. In particular, stable solitons exist almost in the whole semi-finite gap for the positive and zero defects. These properties are different from other lattices with defects. In addition, it is found that the existence of surface dual-frequency lattice solitons does not need a threshold power.     

Bloch-wave packet control in truncated modulated optical lattices

We study the reflection of Bloch wave packets at the interface of an optical lattice possessing a shallow longitudinal out-of-phase refractive index modulation in the adjacent waveguides. We show that the relation between the transmitted and reflected energy flows can be efficiently controlled by tuning the frequency and depth of the modulation. Thus, complete beam reflection may be achieved for a set of resonant modulation frequencies at which light tunneling between adjacent guides of modulated lattice is inhibited.     

3-d Model for strain ordering in steel: I Static effects

We present a spring-defect model in 3-dimensions to describe the connection between elastic distortion and interstitial carbon ordering associated with phase transition from a body centred cubic (BCC) to body centered tetragonal (BCT) structure in BCC metals such as α-iron. The presence or the absence of the carbon is modelled in terms of a pseudo spinŝ=+1or -l.An Ising interaction between carbon atoms is recovered after eliminating the lattice degrees of freedom, which is longranged. The coupling between the spin and lattice degrees of freedom allows for a systematic study of ferroelasticity and the variation of the lattice parameter with carbon concentration. The mean field results for the paraelastic to ferroelastic transition, lattice parameter and static compliance are presented. The significant feature of this calculation is not only a derivation of the defect-defect interaction, but also an explicit calculation of the strain dipole tensor associated with each defect, from a microscopic model.     

Defect modes supported by optical lattices in photovoltaic-photorefractive crystals

We study defect modes in optically induced one-dimensional lattices in photovoltaic-photorefractive crystals. These defect modes exist in different bandgaps due to the change of defect intensity. For a positive defect, defect mode branches exist not only in the semi-infinite bandgap, but also in the first and second bandgaps. When the defect mode branch is fixed, the confinement of defect modes increases with the defect strength parameter. For a negative defect, defect mode branches exist only in the first and second bandgaps. For a given defect mode branch, the strongest confinement of the defect modes appears when the lattice intensity at the defect site is not the smallest in its branch. On the other hand, when the defect strength parameter is fixed, the most localized defect modes arise in the semi-infinite bandgap for the positive defect and in the first bandgap for the negative defect.     

Defect modes in one-dimensional photonic lattices

Linear defect modes in one-dimensional photonic lattices are studied theoretically. For negative (repulsive) defects, various localized defect modes are found. The strongest confinement of the defect modes appears when the lattice intensity at the defect site is nonzero rather than zero. When launched at small angles into such a defect site of the lattice, a Gaussian beam can be trapped and undergo snake oscillations under appropriate conditions.     

Improved photonic crystal directional coupler with short length

We investigate a photonic crystal (PC) waveguide coupler which is formed by two closely spaced linear waveguides in a two-dimensional triangular lattice of air holes. Our study shows that shifting one row of the air holes between the waveguides affects the dispersion curves of the guided modes and if the triangular lattice of air holes between the waveguides is replaced by a rectangular lattice, this modification results in an ultra-short coupling structure with coupling length less than 3a, where a is the lattice constant. Also, we investigate the effect of changing the radii of air holes that are adjacent to or between the waveguides on the coupling length and show that increasing the radius of air holes between the waveguides decreases the coupling length. We analyze the output spectrum of an ultra-short channel drop filter designed based on this structure.     

Charge injection in molecular wires grafted on metallic surfaces: electron-lattice interaction

We study the injection of single charge carrier in one-dimensional molecular wires in the presence of coherent electron-lattice coupling. We show that charge injection at the molecule/metal interface induces lattice distortions in the molecule itself reflecting the formation of polaron-like defect. The behaviour of the charge density of the injected carrier and the mean position of the carrier depend strongly on the value of the injection energy relative to the band edges of the molecular wires.     

Hydrogen incorporation in diamond: the vacancy-hydrogen complex

We report the identification of the vacancy-hydrogen complex in single crystal diamond synthesized by chemical vapor deposition. The S=1 defect is observed by electron paramagnetic resonance in the negative charge state. The hydrogen atom is bonded to one of the carbon atoms neighboring the vacancy. Unlike the analogous defect in silicon, no symmetry lowering reconstruction occurs between the three remaining carbon dangling orbitals. The very small measured hydrogen hyperfine interaction is explained by dipolar coupling between the hydrogen and the unpaired electron probability density delocalized on the three equivalent carbon neighbors.     

Kerr nonlinear switch based on ultra-compact photonic crystal directional coupler

In this paper, an all optical switch based on nonlinear photonic crystal directional coupler has been simulated and analyzed by the finite difference time domain (FDTD) method. The lunched pump signal increases the refractive indices of the central row of the coupler, due to nonlinear Kerr effect, hence the coupler works in the nonlinear conditions and lightwave guides to the other output port. We have tried to increase the coupling efficiency and reduce the required power in the nonlinear status by optimizing the bends structure and increasing the interaction between dielectric and lightwave signal. Therefore, the input signal beam can be controlled to be exchanged between two output ports to earn the highest output power ratio and the smallest amount of power required for nonlinear performance, the physical length of the coupler is determined to be 20a, where a is the structure lattice constant.     

Reentrant and whirling hexagons in non-Boussinesq convection

We review recent computational results for hexagon patterns in non-Boussinesq convection. For sufficiently strong dependence of the fluid parameters on the temperature we find reentrance of steady hexagons, i.e. while near onset the hexagon patterns become unstable to rolls as usually, they become again stable in the strongly nonlinear regime. If the convection apparatus is rotated about a vertical axis the transition from hexagons to rolls is replaced by a Hopf bifurcation to whirling hexagons. For weak non-Boussinesq effects they display defect chaos of the type described by the two-dimensional (2D) complex Ginzburg–Landau equation. For stronger non-Boussinesq effects the Hopf bifurcation becomes subcritical and localized bursting of the whirling amplitude is found. In this regime the coupling of the whirling amplitude to (small) deformations of the hexagon lattice becomes important. For yet stronger non-Boussinesq effects this coupling breaks up the hexagon lattice and strongly disordered states characterized by whirling and lattice defects are obtained.     

Real structure influence on the electron–phonon coupling properties of niobium

We performed density functional theory calculations using niobium (Nb) as a model system of a conventional superconductor, to correlate the distortion of twin defects with the electron–phonon coupling properties. Calculations using different settings of the Nb elementary cell (relaxed, distorted, super cell with zig‐zag twin defect) showed that only by including real structure elements into the setting, the Eliashberg spectral function representing the electron–phonon coupling properties was derived convincingly. Based on these density functional theory calculations of the electron–phonon cou‐ pling properties of Nb, we suggest a model for a combined superconducting/charge density wave ground state which uses a lattice distortion induced into the crystal by two‐dimensional defects as modulated background potential of the charge density wave phase. The coexistence of both phases is hereby necessary for a fine‐tuning of the Fermi surface within the small local domain of the defect to match the wavelength of the lattice distortion and the Fermi wavelength by pairing fermions to bosons. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Broadband waveguide intersections with low cross talk in photonic crystal circuits

We propose a new mechanism for constructing waveguide intersections with broad bandwidth and low cross talk in photonic crystal (PC) circuits. The intersections are created by combination of coupled-cavity wave-guides (CCWs) with conventional line-defect waveguides. This mechanism utilizes the strong dependence of the defect coupling on the field pattern in the defects and the alignment of the defects (i.e., the coupling angle) in CCWs. By properly designing the defect mode, we demonstrate through numerical simulation the establishment of such a waveguide intersection in one of the most useful PCs, which is based on a two-dimensional triangular lattice of air holes made in a dielectric material. The transmission of a 500-fs pulse at ~1.3 microm is simulated by use of the finite-difference time-domain method, showing negligible distortion and low cross talk.     

Type-I Weyl points induced by negative coupling in photonic crystal

Weyl points, which are the degenerate points in three-dimensional momentum space, have been widely studied in the photonic system, and show some intriguing phenomena such as topologically protected surface states and chiral anomalies. Type-I Weyl systems possess a complete bandgap, and topologically protected surface states can be excited without disturbing the bulk states.In this work, we investigate the influence of the sign of coupling coefficient on the topological property of the system and find that type-I Weyl points can be realized by introducing a negative coupling between the stacking layers of the designed photonic crystal. We propose a new strategy to construct a type-I Weyl system by stacking the hexagonal photonic lattice. Different from the topological nontrivial photonic system with a positive coefficient, the negative couplings in the photonic system are realized by adding another resonating site between stacking layers. We theoretically demonstrate that the effective coupling between the resonating sites in adjacent layers sign-flips through the judicious design of the nearest coupling strength and eigenfrequency of the additional sites. The surface states at opposite boundaries of the proposed system have opposite group velocities, which is the feature of type-I Weyl points. Our study provides a new method of exploring topologically protected photonic systems and developing possible topological devices.     

Fermionic atoms in a three dimensional optical lattice: observing Fermi surfaces, dynamics, and interactions

We have studied interacting and noninteracting quantum degenerate Fermi gases in a three-dimensional optical lattice. We directly image the Fermi surface of the atoms in the lattice by turning off the optical lattice adiabatically. Because of the confining potential, gradual filling of the lattice transforms the system from a normal state into a band insulator. The dynamics of the transition from a band insulator to a normal state is studied, and the time scale is measured to be an order of magnitude larger than the tunneling time in the lattice. Using a Feshbach resonance, we increase the interaction between atoms in two different spin states and dynamically induce a coupling between the lowest energy bands. We observe a shift of this coupling with respect to the Feshbach resonance in free space which is anticipated for strongly confined atoms.     

Three-dimensional quasi-Tonks gas in a harmonic trap

We analyze the macroscopic dynamics of a Bose gas in a harmonic trap with a superimposed two-dimensional optical lattice, assuming a weak coupling between different lattice sites. We consider the situation in which the local chemical potential at each lattice site can be considered as that provided by the Lieb-Liniger solution. Because of the weak coupling between sites and the form of the chemical potential, the three-dimensional ground-state density profile and the excitation spectrum acquire remarkable properties different from both 1D and 3D gases. We call this system a quasi-Tonks gas. We discuss the range of applicability of this regime, as well as realistic experimental situations where it can be observed.     

Vibrational entropy of dislocations in Al

The region nearest to a lattice defect must be described by an atomistic model, while a continuum model suffices further away from the defect. We study such a separation into two regions for an edge dislocation. In particular we focus on the excess defect energy and vibrational entropy, when the dislocation core is described by a cluster of about 500–100?atoms, embedded in a large discrete and relaxed, but static, lattice. The interaction between the atoms is given by a potential of the embedded-atom model type referring to Al. The dynamic matrix of the vibrations in the cluster is fully diagonalized. The excess entropy ΔS near the core has positive and negative contributions, depending on the sign of the local strain. Typically, ΔS/k _B ≈ 2 per atomic repeat length along the dislocation core in fcc Al. In the elastic continuum region far from the dislocation core the excess entropy shows the same logarithmic divergence as the elastic energy. Although the work refers to a specific material and defect type, the results are of a generic nature.