Critical properties of lattices of diffusively coupled quadratic maps

We study the critical properties of lattices of coupled logistic maps in the regime where the individual maps are closely above the onset of chaos. We discuss both spatial and temporal characteristics and especially the link between them. We show that the mutual information function between two points on the lattice decays exponentially with distance. In this way we find support for the relation xi approximately lambda(-1/2) between the coherence length xi and the largest Lyapunov exponent lambda which is further corroborated by a detailed study of the spreading of small perturbations. Finally we study the structure function of the lattice field variable. It shows that at the onset of chaos the lattice remains smooth.     

Resonance and absorption band in the classical magnetoactive semiconductor-insulator superlattice

Electromagnetic wave propagation in the classical semiconductor-dielectric superlattice is investigated in the limit of wavelengths, exceeding the lattice spatial period. The resonance and absorption band have been experimentally discovered in a frequency range below the semiconductor plasma frequency in the presence of the dc magnetic field normal to the wave vector and the lattice periodicity direction.     

Oscillatory energy exchange between waves coupled by a dynamic artificial crystal

We describe a general mechanism of controllable energy exchange between waves propagating in a dynamic artificial crystal. We show that if a spatial periodicity is temporarily imposed on the transmission properties of a wave-carrying medium while a wave is inside, this wave is coupled to a secondary counterpropagating wave and energy oscillates between the two. The oscillation frequency is determined by the width of the spectral band gap created by the periodicity and the frequency difference between the coupled waves. The effect is demonstrated with spin waves in a dynamic magnonic crystal.     

Transport and Conductance in Fibonacci Graphene Superlattices with Electric and Magnetic Potentials

We investigate the electron transport and conductance properties in Fibonacci quasi-periodic graphene superlattices with electrostatic barriers and magnetic vector potentials.It is found that a new Dirac point appears in the band structure of graphene superlattice and the position of the Dirac point is exactly located at the energy corresponding to the zero-averaged wave number.The magnetic and electric potentials modify the energy band structure and transmission spectrum in entirely diverse ways.In addition,the angular-dependent transmission is blocked by the potential barriers at certain incident angles due to the appearance of the evanescent states.The effects of lattice constants and different potentials on angular-averaged conductance are also discussed.     

Simplified design of low-loss and flat dispersion photonic crystal waveguide on SOI

A low-loss and flat dispersion line-defect photonic crystal waveguide is proposed with a simplified waveguide-design on silicon-on-insulator (SOI) based on hexagonal lattice of 2D photonic crystals. A propagation loss of 3.6 dB/mm and flat dispersion over a large wavelength band is reported with an easy-to-implement design without disturbing the periodicity (keeping lattice constant and hole diameter fixed) in the line-defect photonic crystals. The combined effect of photonic crystals (in-plane periodicity) and the vertical layers on SOI results in efficient waveguiding and dispersion characteristics.     

Electronic and hole minibands in quantum wire arrays of different crystallographic structure

We consider semiconductor heterostructures consisting of GaAs rods embedded in Al_xGa_1 − xAs and disposed in sites of a square or triangular lattice. The electronic and hole spectra around the conduction band bottom and the valence band top are examined for electrons and holes propagating in plane of periodicity, versus geometry of the lattice formed by the rods, concentration of Al in the matrix material, and structural parameters including the filling fraction and the lattice constant. Our calculations use the envelope function and are based on the effective-mass approximation. We show that the electronic and hole spectra resulting from the periodicity of the heterostructure, depend on the factors considered and that the effect of lattice geometry varies substantially with lattice constant. For low lattice constant values the minigaps are significantly wider in the case of triangular lattice, while for high lattice constant values only slightly thiner minigaps occur in the square lattice-based arrays. We discuss the consequences of our findings for the efficiency of solar cells.     

Discrete embedded modes in the continuum in 2D lattices

We study the problem of constructing bulk and surface embedded modes (EMs) inside the quasi-continuum band of a square lattice, using a potential engineering approach à la Wigner and von Neumann. Building on previous results for the one-dimensional (1D) lattice, and making use of separability, we produce examples of two-dimensional envelope functions and the two-dimensional (2D) potentials that produce them. The 2D embedded mode decays like a stretched exponential, with a supporting potential that decays as a power law. The separability process can cause that a 1D impurity state (outside the 1D band) can give rise to a 2D embedded mode (inside the band). The embedded mode survives the addition of random perturbations of the potential; however, this process introduces other localized modes inside the band, and causes a general tendency towards localization of the perturbed modes.     

Reprint of : Absorbing/Emitting Phonons with one dimensional MOSFETs

We consider nanowires in the field effect transistor device configuration. Modeling each nanowire as a one dimensional lattice with random site potentials, we study the heat exchanges between the nanowire electrons and the substrate phonons, when electron transport is due to phonon-assisted hops between localized states. Shifting the nanowire conduction band with a metallic gate induces different behaviors. When the Fermi potential is located near the band center, a bias voltage gives rise to small local heat exchanges which fluctuate randomly along the nanowire. When it is located near one of the band edges, the bias voltage yields heat currents which flow mainly from the substrate towards the nanowire near one boundary of the nanowire, and in the opposite direction near the other boundary. This opens interesting perspectives for heat management at submicron scales: arrays of parallel gated nanowires could be used for a field control of phonon emission/absorption.     

Absorbing/emitting phonons with one dimensional MOSFETs

We consider nanowires in the field effect transistor device configuration. Modeling each nanowire as a one dimensional lattice with random site potentials, we study the heat exchanges between the nanowire electrons and the substrate phonons, when electron transport is due to phonon-assisted hops between localized states. Shifting the nanowire conduction band with a metallic gate induces different behaviors. When the Fermi potential is located near the band center, a bias voltage gives rise to small local heat exchanges which fluctuate randomly along the nanowire. When it is located near one of the band edges, the bias voltage yields heat currents which flow mainly from the substrate towards the nanowire near one boundary of the nanowire, and in the opposite direction near the other boundary. This opens interesting perspectives for heat management at submicron scales: arrays of parallel gated nanowires could be used for a field control of phonon emission/absorption.     

The inverse scattering transformation in the angular momentum plane

The inverse scattering transformation (IST) with the angular momentum () as a spectral variable turned out to be a useful method to deal with rotationally invariant problems in field theory at higher spatial dimensions [Refs. (1) and (2)]. We derive the direct and inverse scattering problems for thev-dimensional radial Schrödinger equation for variable and fixed energy (negative or positive). We determine the scattering data (SD) in one to one correspondence with the potential and derive the corresponding Gelfand-Levitan equation. A family of exactly solvable potentials for any and fixed energy is obtained. The trace identities associated to this IST are derived for both signs of the energy. They relate integrals of local polynomials in the potential and its derivatives timesr ^2n–1(n1) with the SD. The presence of this power ofr makes these relations useful in higher dimensions.Laboratoire associé au CNRS     

Approximations to wave propagation through a lattice of Dirichlet scatterers

A scheme of matched asymptotic expansions is used to obtain approximations to the dispersion relation when waves, governed by the Helmholtz equation, propagate through a two-dimensional lattice of scatterers on each of which a homogeneous Dirichlet boundary condition is imposed. The scatterers must be identical, but can be of any shape as long as each is small relative to the wavelength and the lattice periodicity. The results differ from those obtained using homogenisation in that there is no requirement that the wavelength be much longer than the lattice periodicity, and hence it is possible to describe band gaps.     

Laser cooling of atoms in optical lattices including quantum statistics and dipole–dipole interactions

We develop a mean-field approach to include dipole-dipole interactions and quantum statistics in the atomic dynamics in bright and dark optical lattices including the proper spatial potentials instead of a simple δ-approximation. For classical distinguishable particles the results are even quantitatively similar to the properly scaled δ-function model. As the dominant effect bright and dark lattices exhibit opposite shifts in the lattice band energies and differ in their localisation properties as a function of density. The spatial-dependent potential allows strong modifications also in dark lattices, but the main conclusions obtained in the δ-approximation turn out to be still valid. Interestingly, important quantitative differences from the δ-model can occur as far as the effect of statistics in concerned, especially for fermions. We study the quantum statistical effects as a function of detuning and lattice well depths and identify the case of lattices with deep wells and large detunings as the preferred parameter region to observe them. Received 24 November 1999 / revised version: 24 June 1999 / Published online: 8 September 1999     

Indium square root 7 x square root 3 on Si(111): a nearly free electron metal in two dimensions

We present measurements of the Fermi surface and underlying band structure of a single layer of indium on Si(111) with square root 7 x square root 3 periodicity. Electrons from both indium valence electrons and silicon dangling bonds contribute to a nearly free, two-dimensional metal on a pseudo-4-fold lattice, which is almost completely decoupled at the Fermi level from the underlying hexagonal silicon lattice. The mean free path inferred from our data is quite long, suggesting the system might be a suitable model for studying the ground state of two-dimensional metals.     

Quantumlike dynamics of classical particles in ponderomotive potentials

The average dynamics of a classical particle under the action of a high-frequency radiation resembles quantum particle motion in a conservative field with an effective de Broglie wavelength lambda equal to the particle average displacement on the oscillation period. In a quasiclassical field, with a spatial scale large compared to lambda, the guiding-center motion is adiabatic. Otherwise, a particle exhibits quantized eigenstates in ponderomotive potential wells, tunnels through "classically forbidden" regions, and experiences stochastic reflection from attractive potentials.     

Two-dimensional photonic crystals with pure germanium-on-insulator

We have investigated pure germanium two-dimensional photonic crystals. The photonic crystals which exhibit resonances in the near infrared spectral range were fabricated on germanium-on-insulator substrates using standard silicon-based processing. The germanium-on-insulator substrate consists of a thin layer of pure germanium-on-oxide deposited on a silicon substrate. The optical properties are probed by the direct band gap optical recombination of pure germanium at room temperature. Resonant optical modes are evidenced between 1.68 and 1.53 μm in different type of hexagonal cavities (H1-H5). The spectral position of the modes is controlled by the lattice periodicity and air filling factor of the photonic crystals. Close to the Ge band edge, the quality factors are limited by the bulk material absorption.     

Band structure and oscillatory electron-phonon coupling of Pb thin films determined by atomic-layer-resolved quantum-well states

Using a low temperature growth method, we have prepared atomically flat Pb thin films over a wide range of film thickness on a Si-(111)-7 x 7 surface. The Pb film morphology and electronic structure are investigated in situ by scanning tunneling microscopy and angle-resolved photoemission spectroscopy. Well-defined and atomic-layer-resolved quantum-well states of the Pb films are used to determine the band structure and the electron-phonon coupling constant (lambda) of the films. We found an oscillatory behavior of lambda with an oscillation periodicity of two atomic layers. Almost all essential features in the Pb/Si(111) system, such as the growth mode, the oscillatory film stability, and the 9 monolayer envelope beating pattern, can be explained by our results in terms of the electron confinement in Pb films.     

Acoustic beam splitting in a sonic crystal around a directional band gap

Beam splitting upon refraction in a triangular sonic crystal composed of aluminum cylinders in air is experimentally and numerically demonstrated to occur due to finite source size,which facilitates circumvention of a directional band gap.Experiments reveal that two distinct beams emerge at crystal output,in agreement with the numerical results obtained through the finite-element method.Beam splitting occurs at sufficiently-small source sizes comparable to lattice periodicity determined by the spatial gap width in reciprocal space.Split beams propagate in equal amplitude,whereas beam splitting is destructed for oblique incidence above a critical incidence angle.     

Discrete lattice systems and the equivalence of microcanonical,canonical and grand canonical Gibbs states

It is proven that a microcanonical Gibbs measure on a classical discrete lattice system is a mixture of canonical Gibbs measures, provided the potential is approximately periodic, has finite range and possesses a commensurability property. No periodicity is imposed on the measure. When the potential is not approximately periodic or does not have the commensurability property, the inclusion does not hold.As a by-product, a new proof is given of the fact that for a large class of potentials, a canonical Gibbs measure is a mixture of grand canonical measures. Thus the equivalence of ensembles is obtained in the sense of identical correlation functions.     

Optimized interactions for targeted self-assembly: application to a honeycomb lattice

We devise an inverse statistical-mechanical methodology to find optimized interaction potentials that lead spontaneously to a target many-particle configuration. Target structures can possess varying degrees of disorder, thus extending the traditional idea of self-assembly to incorporate both amorphous and crystalline structures as well as quasicrystals. For illustration purposes, our computational technique is applied to yield an optimized isotropic (nondirectional) pair potential that spontaneously yields the three-coordinated honeycomb lattice as the ground state structure in two dimensions. This target choice is motivated by its three-dimensional analog, the diamond lattice, which is known to possess desirable photonic band gap properties.