Raman scattering of nanocrystalline silicon embedded in SiO2

Raman scattering of nanocrystalline silicon embedded in SiO₂ matrix is systematically investigated. It is found that the Raman spectra can be well fitted by 5 Lorentzian lines in the Raman shift range of 100–600 cm⁻¹. The two-phonon scattering is also observed in the range of 600–1100 cm⁻¹. The experimental results indicate that the silicon crystallites in the films consist of nanocrystalline phase and amorphous phase; both can contribute to the Raman scattering. Besides the red-shift of the first order optical phonon modes with the decreasing size of silicon nanocrystallites, we have also found an enhancement effect on the second order Raman scattering, and the size effect on their Raman shift     

Optical properties of nanocrystalline silicon embedded in SiO2

Nanocrystalline silicon embedded SiO₂ matrix has been formed by annealing the a-SiO_x films fabricated by plasma enhanced chemical vapor deposition technique. Absorption and photoluminescence spectra of the films have been studied in conjunction with micro-Raman scattering spectra. It is found that absorption presents an exponential dependence of absorption coefficient to photon energy in the range of 1.5–3.0 eV, and a sub-band appears in the range of 1.0–1.5 eV. The exponential absorption is due to the indirect band-to-band transition of electrons in silicon nanocrys-tallites, while the sub-band absorption is ascribed to transitions between surfaces and/or defect states of the silicon nanocrystallites. The existence of Stokes shift between absorption and photoluminescence suggests that the phonon-assisted luminescence would be enhanced due to the quantum confinement effects.     

Growth mechanism and quantum confinement effect of silicon nanowires

The methods for synthesizing one-dimensional Si nanowires with controlled diameter are introduced. The mechanism for the growth of Si nanowires and the growth model for different morphologies of Si nanowires are described, and the quantum confinement effect of the Si nanowires is presented. Project supported by the National Natural Science Foundation of China (Grant No. 19834080) and Zhou Peiyuan Special Foundation of Mathematics and Physics.     

Preparation and optical properties of GaSb nanoparticles embedded in SiO2 composite films

The composite films of GaSb nanoparticles embedded in SiO₂ matrices were fabricated by radio-frequency magnetron co-sputtering. Transmission electron microscope and X-ray diffraction pattern indicate that the GaSb nanoparticles were uniformly dispersed in SiO₂ matrices. Room temperature transmission spectra exhibit a blue shift of about 2.73 eV. The blue shift increases with decreasing size of GaSb nanoparticles, suggesting the existence of quantum size effects. Room temperature Raman spectra show that there is a larger Raman peak red shift and broadening of the composite films than that of bulk GaSb. This phenomenon is explained by photon confinement effect and tensile stress effect     

Preparation and optical properties of GaSb nanoparticles embedded in SiO2 composite films

The composite films of GaSb nanoparticles embedded in SiO₂ matrices were fabricated by radio-frequency magnetron co-sputtering. Transmission electron microscope and X-ray diffraction pattern indicate that the GaSb nanoparticles were uniformly dispersed in SiO₂ matrices. Room temperature transmission spectra exhibit a blue shift of about 2.73 eV. The blue shift increases with decreasing size of GaSb nanoparticles, suggesting the existence of quantum size effects. Room temperature Raman spectra show that there is a larger Raman peak red shift and broadening of the composite films than that of bulk GaSb. This phenomenon is explained by photon confinement effect and tensile stress effect     

Resonance free regions in magnetic scattering by two solenoidal fields at large separation

We consider the problem of quantum resonances in magnetic scattering by two solenoidal fields at large separation in two dimensions. This system has trapped trajectories oscillating between two centers of the fields. We give a sharp lower bound on resonance widths when the distance between the two centers goes to infinity. The bound is described in terms of backward amplitudes calculated explicitly for scattering by each solenoidal field. The study is based on a new type of complex scaling method. As an application, we also discuss the relation to semiclassical resonances in scattering by two solenoidal fields.     

Investigation of Raman spectrum for nano-SnO2

The dependence of the microstructural change and lattice space symmetry of nano-SnO₂ on the annealing temperature has been studied systematically using Raman spectroscopy and X-ray diffraction. Comparing the results of nano-SnO₂ with the results of amorphous film and single crystal of SnO₂, it is found that the new Raman peaks N₁ and N₂ are in accordance with Matossi’s force constant model completely. When the annealing temperature is near 673K, the local lattice disorders and the density of vacant lattice decrease rapidly in the nano-SnO₂ grains. The lattice distortion and the new Raman peaks disappear almost at the same time. The possible mechanisms of the microstructural change and the new Raman peaks N₁ and N₂ are discussed. Project supported by the Foundation of State Science and Technology Commission and the Natural Science Foundation of Anhui Province.     

Vibrational excitation differential cross sections of low-energy electron scattering from N2 molecule

The vibrational excitation differential cross sections (DCS) of low-energy electron-N₂ scattering are studied using vibrational close-coupling (VCC) scattering method and quantum scattering potentials which include static, exchange, and polarization contributions based onab initio calculations. By including the contributions of 11 partial waves (up tol = 21), 15 vibrational states, and 16 molecular symmetries (up to ∧ = 7), the converged vibrational excitation (0→2, 0→3, 0→4) DCSs, the scattering resonance, and the vibrational multi-peak structure agree well with experimental results. Project supported by the National Natural Science Foundation of China (Grant No. 19674038) and the Science Foundation of Chinese Education Ministry.     

Electron in the Aharonov-Bohm potential and in the Coulomb field in 2+1 dimensions

We obtain exact solutions of the Dirac equation in 2+1 dimensions and the electron energy spectrum in the superposition of the Aharonov-Bohm and Coulomb potentials, which are used to study the Aharonov-Bohm effect for states with continuous and discrete energy spectra. We represent the total scattering amplitude as the sum of amplitudes of scattering by the Aharonov-Bohm and Coulomb potentials. We show that the gauge-invariant phase of the wave function or the energy of the electron bound state can be observed. We obtain a formula for the scattering cross section of spin-polarized electrons scattered by the Aharonov-Bohm potential. We discuss the problem of the appearance of a bound state if the interaction between the electron spin and the magnetic field is taken into account in the form of the two-dimensional Dirac delta function. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 149, No. 3, pp. 502–517, December, 2006. An erratum to this article is available at .     

The scattering theory of C. Wilcox in elasticity

We extend the abstract time‐dependent scattering theory of C.H. Wilcox to the case of elastic waves. Most of the results are proved with the minimal assumption that the obstacle satisfies the energy local compactness condition (ELC). This holds especially for the existence and unitarity of the wave operators. Copyright © 2002 John Wiley & Sons, Ltd.     

Windowed Green function method for wave scattering by periodic arrays of 2D obstacles

This paper introduces a novel boundary integral equation (BIE) method for the numerical solution of problems of planewave scattering by periodic line arrays of two-dimensional penetrable obstacles. Our approach is built upon a direct BIE formulation that leverages the simplicity of the free-space Green function but in turn entails evaluation of integrals over the unit-cell boundaries. Such integrals are here treated via the window Green function method. The windowing approximation together with a finite-rank operator correction—used to properly impose the Rayleigh radiation condition—yield a robust second-kind BIE that produces superalgebraically convergent solutions throughout the spectrum, including at the challenging Rayleigh–Wood anomalies. The corrected windowed BIE can be discretized by means of off-the-shelf Nyström and boundary element methods, and it leads to linear systems suitable for iterative linear algebra solvers as well as standard fast matrix–vector product algorithms. A variety of numerical examples demonstrate the accuracy and robustness of the proposed methodology.     

Asymptotic profiles and asymptotic distributions of energy in elastic waves scattering

We compute the asymptotic wave profiles for the exterior problemin elasticity with homogeneous Neumann condition. We give preciseresults on the asymptotic distribution of the elastic energyin various subsets of space. These results are obtained viathe use of a recently developed extension of the scatteringtheory of C. Wilcox (Mabrouk & Helali, 2002).     

New characterizations of solutions in inverse scattering theory

This paper introduces a new approach to characterize the shape ω of a scattering medium (either an acoustically soft obstacle or an inhomogeneous medium) by the far field data. In contrast to the Linear Sampling Method normality of the far field operator is not needed. Therefore, also scattering by limited far field data and absorbing media can be treated. While in the Linear Sampling Method the points in the interior of ω are characterized by the solution of an integral equation of the first kind, for our new method a constrained optimization problem has to be solved. Although this new approach is more time consuming some numerical experiments at the end of this paper show the practicability of the method.     

The scattering of electromagnetic wave at oblique incidence in a homogeneous chiral medium

We consider the scattering of a time-harmonic electromagnetic wave by a perfectly and imperfectly conducting infinite cylinder at oblique incidence respectively. We assume that the cylinder is embedded in a homogeneous chiral medium and the cylinder is parallel to the z axis. Since the x components and y components of electric field and magnetic field can be expressed in terms of their z components, we can derive from Maxwell's equations and corresponding boundary conditions that the scattering problem is modeled as a boundary value problem for the z components of electric field and magnetic field. By using Rellich's lemma and variational approach, the uniqueness and the existence of solutions are justified.     

Diagonal forms of the translation operators in the fast multipole algorithm for scattering problems

The integral equations of acoustic and electromagnetic scattering generate large dense systems of linear equations. These systems are efficiently solved with iterative methods where the matrix-vector multiplication is computed using a special fast method, such as the fast Fourier transform or the fast multipole method (FMM). In this paper, the so called diagonal forms of the translation operators for the fast multipole method are derived starting from integral representations of certain special functions. Error analysis of the FMM is given, considering both the truncation error of potential expansions and the errors from the use of numerical integration in the diagonal translation theorem. The implications of the error bounds on the FMM algorithm are discussed.This work has been financially supported by the Jenny and Antti Wihuri Foundation and by the Cultural Foundation of Finland.     

Error analysis of the DtN-FEM for the scattering problem in acoustics via Fourier analysis

In this paper, we are concerned with the error analysis for the finite element solution of the two-dimensional exterior Neumann boundary value problem in acoustics. In particular, we establish explicit priori error estimates in H¹ and L²- norms including both the effect of the truncation of the DtN mapping and that of the numerical discretization. To apply the finite element method (FEM) to the exterior problem, the original boundary value problem is reduced to an equivalent nonlocal boundary value problem via a Dirichlet-to-Neumann (DtN) mapping represented in terms of the Fourier expansion series. We discuss essential features of the corresponding variational equation and its modification due to the truncation of the DtN mapping in appropriate function spaces. Numerical tests are presented to validate our theoretical results.     

Shape derivative of the volume integral operator in electromagnetic scattering by homogeneous bodies

We study the shape derivative of the strongly singular volume integral operator that describes time‐harmonic electromagnetic scattering from homogeneous medium. We show the existence and a representation of the derivative, and we deduce a characterization of the shape derivative of the solution to the diffraction problem as a solution to a volume integral equation of the second kind.     

TEM and Raman scattering investigation of carbon in annealed Co/C soft X-ray multilayers

The structures of the carbon sublayers in the annealed Co/C soft X-ray multilayers fabricated by using a dual-facing-target sputtering system have been characterized by transmission electron microscopy (TEM) and Raman spectroscopy (RS). The results suggest that the structural variations in the carbon layers can be roughly divided into three stages, i.e. ordering, crystalline and grain growth stages. At the ordering stage with annealing temperatures below 400°C, the amorphous carbon layers change from ones of bond-angle disorder and fourfold-bonding only to ones of threefold-bonding. At the crystalline stage, the amorphous carbon layers in the as-deposited multilayers crystallize to graphite crystallites in the annealing temperature range of 500–600°C. At the grain growth stage, the specimens are annealed at temperatures higher than 700°C. A growth in the graphite crystallite dimensions is observed, which is consistent with the TEM results. Project supported by the National Natural Science Foundation of China and Beijing Zhongguancun Associated Center of Analysis and Measurement.     

Bifurcations and Exact Solutions of the Raman Soliton Model in Nanoscale Optical Waveguides with Metamaterials

In this paper, we study Raman soliton model in nanoscale optical waveguides with metamaterials, having polynomial law non-linearity. By using the bifurcation theory method of dynamical systems to the equations of $\phi(\xi)$, under 24 different parameter conditions, we obtain bifurcations of phase portraits and different traveling wave solutions including periodic solutions, homoclinic and heteroclinic solutions for planar dynamical system of the Raman soliton model. Under different parameter conditions, 24 exact explicit parametric representations of the traveling wave solutions are derived. The dynamic behavior of these traveling wave solutions are meaningful and helpful for us to understand the physical structures of the model.