Dual mode near-field scanning optical microscopy for near-field imaging of surface plasmon polariton

In this paper, we theoretically and experimentally demonstrate that metal coated apertured probes are efficient near-field probes on surfaces with high reflectivity for the scattering as well as for the collection mode near-field scanning optical microscopy (NSOM). We show that a blunt apertured metal coated tip is very effective in suppressing image dipoles which affect strongly the signals scattered from frequently used sharp metal tips or gold nanoparticle attached probes. By using a simultaneous collection and scattering mode (dual mode) NSOM we measure the near-field images of surface plasmon polariton (SPP) launched from a slit. The collection mode measures propagating SPP along lateral distance in a long scan range with high signal-to-noise ratio, and the scattering mode measures the polarization resolved near-field of SPP. Comparisons of the measured data obtained in the dual mode enable to easily characterize SPP and to separate the measured near-field into the propagating SPP and the directly transmitted light.     

Surface excitation probabilities in surface electron spectroscopies

The phenomenon of surface excitation is competitive in nature for elastic and other inelastic scattering processes in surface electron spectroscopies; the knowledge of influence of surface excitations in electron energy loss spectra is then essential for quantitative surface analysis with these spectroscopies. The inelastic scattering of an electron moving in the vicinity of a surface is considered in a self-energy formalism to estimate the contribution of surface excitation in electron-solid interactions via the total surface excitation probability. The formulation uses the optical bulk dielectric function and provides the spatial and angular dependence of the differential and total inelastic cross-sections. The kinetic energy range of probing electrons considered is 100-5000 eV and the numerical evaluation of total surface excitation probabilities are performed for several metals, Au, Ag, Cu, Ni, Fe and Ti; empirical formulae for the surface excitation probability are given for each of these materials and compared with experimental results for the surface excitation parameter. The total surface excitation probability is higher in Ag as compared to other metals under consideration, for identical conditions of electron-solid interactions.     

Exotic Behavior of Elastic Scattering Differential Cross-Sections of Weakly Bound Nucleus 17F at Small Angles

The differential cross-sections for elastic scattering of ¹⁷F and ¹⁷O on ²⁰⁸Pb have been measured at Radioactive Ion Beam Line at Lanzhou (RIBLL). The variation of the logarithms of differential cross-sections with the square of scattering angles shows clearly that there exists a turning point in the range of small scattering angles (6°—20°) for ¹⁷F having exotic structure, while no turning point was observed in the ¹⁷O elastic scattering. The experimental results have been compared with previous data. Systematical analysis on the available data seems to conclude that there is an exotic behavior of elastic scattering differential cross-sections of weakly bound nuclei with halo or skin structure as compared with that of the ordinary nuclei near stable line. Therefore the fact that the turning point of the logarithms of differential cross-sections appears at small angle for weakly bound nuclei could be used as a new probe to investigate the halo and skin phenomenon.     

Interaction between localized and propagating surface plasmons: Ag fine particles on Al surface

Samples consisting of Ag fine particles 4nm in size placed near to an Al surface were prepared by depositing Ag-SiO₂ composite films by a rf cosputtering method onto vacuum-evaporated Al films. Angle-scan attenuated total reflection (ATR) measurements were performed over a wide wavelength range (λ=350-630nm) covering the resonance region (λ-410nm) of localized surface plasmon (LSP) in the Ag particles. It was found that the existence of Ag fine particles near to the Al surface led to a deformation of the dispersion curve of the surface plasmon polariton (SPP) propagating on the Al surface, in particular, in the LSP resonance region. The interaction between LSP and SPP was found to become much stronger as the distance between the particles and the surface decreases. The theoretical calculations based on the effective medium theory, which gave an effective dielectric function of the Ag-SiO₂ composite film, reproduced the deformation of the dispersion curve of the SPP. The deformation of the dispersion observed experimentally was qualitatively explained by the behavior of the effective dielectric function of the Ag-SiO₂ composite film.     

Splitting of a surface plasmon polariton beam by chains of nanoparticles

The operation of a micro-optical beam splitter for surface plasmon polaritons (SPP’s) formed by lined up scatterers is modeled and studied in the framework of a vectorial dipolar approach for multiple SPP scattering by equivalent non-spherical nanoparticles. It is shown that the inclusion of anisotropic polarizability of individual scatterer in the vectorial dipolar model of multiple SPP scattering allows one to obtain, in some cases, quantitative agreement between modeling and experimental results. As an example, we apply this approach to model an SPP beam-splitter formed by a chain of spheroidal particles. The dependencies of the splitting efficiency on the shape of particles, the incidence angle and the waist of an incident SPP Gaussian beam are considered. It is found that the efficiency is very sensitive to the shape of scatterers and the angle of SPP beam incidence. Comparison of numerical results with experimental data shows good agreement with respect to the particle shape and incident angular dependences. PACS 02.70.-c; 71.36.+c; 78.68.+m     

Multiphoton free-free transitions in a spatially inhomogeneous laser field

Summary The results of an investigation are presented in which it is shown how the spatial inhomogeneity of a laser field modifies the multiphoton free-free transition cross-sections compared to the case of a homogeneous field. This kind of investigation is required to make more close contact with experiments in intense fields, as in these cases the inhomogeneity is produced by the focusing of the laser beam. Furthermore, taking into account the intensity spatial distribution allows us to achieve in an effective way the asymptotic decoupling of the scattered particles from the field, which is very important for theoretical models using asymptotic initial and final states embedded in the field. Differential and total cross-sections are calculated over a wide range of parameters as functions of the scattering angle, of the incoming-particle energy and of the laser intensity and frequency. The laser spatial inhomogeneity is found to wash out most of the oscillating behaviour of multiphoton differential cross-sections, derived within the model of a homogeneous laser. Little modifications are, instead, found in the total cross-sections which are simply scaled to slightly lower values. Crosssections with zero photon exchange are increased, while those with photon exchanges are lowered. This yields the result that the sum of all the ≪inhomogeneous≫ cross-sections is equal to the sum of all the ≪homogeneous≫ ones (sum rule). The multiphoton free-free transition differential cross-sections are found to be very sensitive quantities which may be used to get information on the laser properties and on their nonlinear behaviour, when these are not precisely known. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Modeling of a surface plasmon polariton interferometer

We model the operation of a micro-optical interferometer for surface plasmon polaritons (SPPs) that comprises an SPP beam-splitter formed by equivalent scatterers lined up and equally spaced. The numerical calculations are carried out by using a relatively simple vectorial dipolar model for multiple SPP scattering [Phys. Rev. B 67 (2003) 165405]. The SPP beam-splitter is simulated elucidating the influence of system parameters, such as the angle of SPP beam incidence, scattering particle size, and inter-particle distance, on the splitting efficiency and phase difference between the transmitted and reflected beams. It is found that the splitting efficiency is very sensitive to the size of scatterers and angle of incidence. Comparing our simulations with experimental data available in the literature, we conclude that this approach can be used, with certain limitations, for modelling of SPP components assembled of individual scatterers, e.g., beam-splitters and interferometers, and suggest further improvements of the model used.     

Resonant elastic scattering of light from single quantum wells in semiconductor multilayers

A theory is developed for steady-state elastic scattering of light via quasi-2D excitons from a quantum well (QW) whose interfaces are randomly rough. The study is mainly focused on the angle dependences of radiation giving direct information about static disorder responsible for the elastic scattering. A nonlocal excitonic susceptibility is expressed in terms of random profile functions of QW interfaces. Treated is elastic scattering of light from a disordered QW in the following actual dielectric environments: (i) a uniform background, (ii) a Fabry–Perot film with rough boundaries, and (iii) a semiconductor microcavity. The cross-sections are derived analytically for scattering of linearly polarized light to the lowest (Born's) approximation with arbitrary roughness statistics. The spectral and angle dependencies of scattering intensity are analyzed numerically in the absolute-value scale with Gaussian correlation of interface roughness. The probability 10⁻² was found for the exciton-mediated scattering of a photon from a QW interface roughness whose root-mean-square height is on the level of 2×10⁻¹ nm. This probability is shown to exceed by two orders of magnitude that is typical of resonant scattering from either a single semiconductor surface or rough boundaries of a semiconductor Fabry–Perot film containing the QW. The scattering spectrum of a QW placed in a microcavity is predicted to have a doublet structure whose components are associated with the cavity exciton–polaritons.     

Enhanced optical transmission through a silver plate with a slit array

The near- and far-field properties of a large-scale silver plate with a slit array are studied by applying the FDTD method. The far region scattering properties with different incident angles are also discussed. We find out that the silver plate with a suitable placed narrow slit array can excite the enhanced optical transmission (EOT) by the excitation of the surface plasmon polarition (SPP) and the Fabry-Perot resonance, and the cutoff angle is much larger than the ordinary LEDs. These unique properties suggest possible applications to the light-transparent metal contact.     

Highly Efficient Excitation of Surface Plasmons Using a Si Gable Tip

A compact and highly efficient technique to excite SPP mode at an Au/SiO₂ interface by using an engineered high index (silicon) gabled tip at the 1550 nm wavelength has been proposed. The optimized geometry of the Si tip enables a highly efficient excitation of the single interface SPP mode through near field interaction in an ultra‐compact setup. An experimental demonstration of the proposed scheme is also presented in the paper which converts 25.5% of the total input power to an SPP mode. With an improved fabrication, this efficiency can reach as high as 52%. The device is compact, facilitates on‐chip excitation of the SPP, its fabrication is compatible with the standard Si fabrication processes, and, as such it is expected to be very useful in the design of future integrated photonic circuits as well as integrated sensors. Also, this scheme can find applications in studying nonlinear characteristics of materials.     

Scattering of elastic waves by multiple elastic circular cylinders with imperfect interface

In the current paper a general method is presented for the rigorous solution for the scattering of elastic waves by a cluster of elastic circular cylinders of infinite length. The interface separating the cylinder from the surrounding media is considered to be homogeneous imperfect. Specifically, the tractions are continuous but the displacements are discontinuous and proportional in terms of interface stiffness parameters to their respective traction components. Using the exact theory of multipole expansion, analytic solutions for the scattered and internal fields excited by an incident plane P-wave, an incident cylindrical P-wave and an incident plane SV-wave are derived.

Numerical results for directivity patterns and scattering cross-sections are presented for a finite hexagonal array of elastic circular inclusions with imperfect interface. The results show that the sequence of maxima and minima in the curves of scattered cross-sections becomes more undistinguishable as the interface becomes more imperfect. Also, the results reveal that large low-frequency peaks of the scattered cross-sections, which correspond to resonance scattering, can be observed for both the low-velocity and high-velocity elastic cylinders with extremely imperfect interface while the small high-frequency peaks of the scattered cross-sections can appear for low-velocity elastic cylinders with relatively perfect interface. Furthermore, the results clearly show that the interaction effects between cylinders cannot be ignored for an incident plane SV-wave as compared to an incident plane P-wave. More importantly is the fact that the reciprocity relations, which hold for elastic wave scattering by a single cylinder, no longer apply for elastic wave scattering by multiple cylinders.     

Differential and integral cross-sections of e-O<Subscript>2</Subscript>, O<Subscript>3</Subscript>, NO,CO scattering at energies 100–1000 eV

A modified additivity rule is formulated to calculate the differential cross-sections for elastic scattering of electrons from molecules. It improves the results at small angles and at relatively lower incident energies (<1000 eV). Integral cross-sections calculated presently are combined with the known total ionization cross-sections to obtain total (complete) cross-sections. An extension of the present approximation to larger molecules is also suggested.     

能量在10Bev以下的π-N,p-N和p-N相互作用

本文试把到写稿时为止(1961年3月底)的一切关于π-N,p-N和p-p的作用和入射粒子能量在几百Mev.至10Bev.范围以内的实验工作予以报导和总论。举凡关于这些作用的总截面、弹性散射截面和非弹性散射截面,都经收集整理,并加以分析。这些截面随能量的增减而变化的情况,都以曲线表达,并且与理论结果作出比较。曲线中有几个重要和有趣之点,也予以指出。在π-N作用中的几个共振峯和关于他们的理论解释,也经较详细的叙述。在弹性散射方面,我们将微分截面的角分布和理论作了比较。在非弹性散射方面,我们把多重产生、动量分布、角分布、横动量和它们与入射粒子能量的关系,都加以分析和讨论。我们特别注意和讨论了下列二种情况:在π-p作用时,质子总是向后散射;而在p-p作用时,两个质子总是不各向均匀地但向前后对称地散射。这种现象被称为质子的“边缘”碰撞。我们认为,这些和其他事实都可能表明了在质子内的确有“核心”的存在,而且这个“核心”非常的小,它的直径比0.4×10^-13厘米要小得多。     

Scattering of elastic waves by multiple elastic circular cylinders with imperfect interface

In the current paper a general method is presented for the rigorous solution for the scattering of elastic waves by a cluster of elastic circular cylinders of infinite length. The interface separating the cylinder from the surrounding media is considered to be homogeneous imperfect. Specifically, the tractions are continuous but the displacements are discontinuous and proportional in terms of interface stiffness parameters to their respective traction components. Using the exact theory of multipole expansion, analytic solutions for the scattered and internal fields excited by an incident plane P-wave, an incident cylindrical P-wave and an incident plane SV-wave are derived.

Numerical results for directivity patterns and scattering cross-sections are presented for a finite hexagonal array of elastic circular inclusions with imperfect interface. The results show that the sequence of maxima and minima in the curves of scattered cross-sections becomes more undistinguishable as the interface becomes more imperfect. Also, the results reveal that large low-frequency peaks of the scattered cross-sections, which correspond to resonance scattering, can be observed for both the low-velocity and high-velocity elastic cylinders with extremely imperfect interface while the small high-frequency peaks of the scattered cross-sections can appear for low-velocity elastic cylinders with relatively perfect interface. Furthermore, the results clearly show that the interaction effects between cylinders cannot be ignored for an incident plane SV-wave as compared to an incident plane P-wave. More importantly is the fact that the reciprocity relations, which hold for elastic wave scattering by a single cylinder, no longer apply for elastic wave scattering by multiple cylinders.     

Scattering of a surface plasmon polariton beam by chains of dipole nanoparticles

Scattering and splitting of surface plasmon polaritons (SPPs) by a chain of strongly interacting nanoparticles located near a metal surface are numerically studied. The applied numerical model is based on the Green’s function formalism and point–dipole approximation for scattering by nanoparticles. Dependencies of the splitting efficiency on the inter-particle distance in the chain and on the angle of incidence of the SPP Gaussian beam are considered. It is found that the splitting efficiency depends on the inter-particle distances especially when the angle between the SPP beam and the chain is relatively small. The role of multiple scattering in the SPP splitting by the chains of nanoparticles is also discussed.     

Elastic and rotational excitation cross-sections for electron-water collisions in the low- and intermediate-energy ranges

We present a theoretical study on electron-H2O collisions in the low- and intermediate-energy ranges. More specifically, we report calculated elastic differential, integral and momentum transfer cross-sections as well as rotational excitation cross-sections in the (2–500)-eV range. In our calculations, an optical potential is used to represent the electron-molecule interaction. The Schwinger variational method combined with the distorted-wave approximation is used to solve the scattering equations. The comparison of our calculated results with other theoretical and/or experimental data available in the literature is very encouraging.     

A shell-model calculation in the continuum for the reaction N15(n,n′) N15

Using the shell-model approach to nuclear reactions, the Lippmann-Schwinger equation for elastic and inelastic nucléon scattering is solved numerically. The procedure is based upon an adaptation of a method due toWeinberg. The differential and total elastic and inelastic cross-sections and the asymmetry of the scattering of a transversally polarised beam of neutrons are calculated. The positions (energies and total widths) and residues (partial widths) of the scattering matrix in the complex plane are determined. The results are discussed and compared with previous treatments.     

Elastic neutron-deuteron scattering with local potentials

Neutron-deuteron scattering is studied within the Faddeev formalism using local two-body S-wave potentials. The equations are solved by applying Padé technique to the multiple scattering series. The rate of convergence is found to be rapid enough for practical purposes. With this method the differential and total cross sections are calculated up to 50 MeV neutron laboratory energy and the results are compared with those of the separable potential model. In particular large differences are found in the forward direction of the differential cross-sections. Up to 22 MeV there is good agreement with experimental data. The differential cross-sections for local potentials up to about 14 MeV depend very little on the existence of a soft core in the two-body spin-triplet potential, but its effect becomes more important at higher energies.     

Elastic and total cross-sections for electron scattering by acetylene in the intermediate energy range

We present a joint theoretical-experimental study on electron scattering by C₂H₂ in the intermediate energy range. We report calculated elastic differential, integral, and momentum-transfer as well as total (elastic + inelastic) and absorption cross-sections at impact energies ranging from 10 to 500 eV. Also, experimental absolute elastic cross-sections are reported in the (50-500)-eV energy range. A complex optical potential is used to represent the electron-molecule interaction dynamics. The iterative Schwinger variational method, combined with the distorted-wave approximation, is used to solve the scattering equations. Experimentally, the angular distributions of the scattered electrons are converted to absolute cross-sections using the relative flow technique. The comparison of our calculated with our measured results, as well as with other experimental and theoretical data available in the literature, is encouraging.Received: 26 August 2004, Published online: 5 October 2004PACS: 34.80.Bm Elastic scattering of electrons by atoms and molecules