Light scattering by Gaussian particles with internal inclusions and roughened surfaces using ray optics

We study light scattering by Gaussian-random-sphere particles that are large compared to the wavelength of the incident light using ray optics that, in addition to Fresnellian reflection and refraction, accounts for diffuse scattering. We consider two types of diffusely scattering media. One type of media constitutes a uniform medium inside the particle, i.e. a diffuse internal medium. The second type of media constitutes a layer on the surface of the particle that is thin compared to the particle dimensions and acts as a diffuse external medium mimicking the particle surface roughness. We illustrate the effects of the diffuse media on the scattering characteristics for both cases and show that incorporating diffuse scatterers allows us to explain the scattering matrices measured experimentally for Saharan sand particles large compared to the wavelength.     

Shift of the Bragg position in grazing-incidence diffraction

The intensity distribution in grazing-incidence diffraction along the grazing exit angle, a f, has been generally studied assuming the fulfilment of the Bragg condition, both experimentally and theoretically. We consider deviations of the incidence angle and detector position (θ) from the exact Bragg angle, θ _B, as well as variation of the incidence angle with respect to the surface, α _i, and lattice mismatching of layered structures. The so-called surface peak is caused by refraction and appears at the fixed angular position of the critical angle of the total external reflection, α _c. Beside it an additional peak occurs, that is explained by fulfilling the Bragg condition of the lateral wave vector components of incident and diffracted beams. This corresponds to the intersection of the truncation rod and the Ewald sphere. Therefore its angular position in the diffracted scattering fan depends on both α_i and θ ? θ _B. This additional peak is only visible if α _i is below α _C or θ > θ _B. These considerations have been verified experimentally on an InP layer.     

An angular cutoff composite model for investigation on electromagnetic scattering from two-dimensional rough sea surfaces

Based on the local configuration angle division to select the corresponding method for electromagnetic scattering calculation from rough sea surface,this paper presents an angular cutoff composite model:when the local scattered angle is in the specular region that is given by an approximately 20 degrees cone around the specular direction,the Kirchhoff approximation is applied to evaluate the specular reflection,which dominates the total scattering in this region;the small perturbation method is employed to handle the diffuse reflection which is predominant as the local scattered angle is situated out of the specular region.Numerical results are compared with those of experimental and theoretical models in several configurations as a function of incident angle,wind speed,wind direction.The comparison of numerical results of other experimental and theoretical models in several configurations shows that the new composite model is robust to give accurate numerical evaluations for the sea surface scattering.     

Analytical solution for the field in photonic structures containing cubic nonlinearity

In this work, we consider the exact solution of the stationary cubic nonlinear equation in a semi-infinite nonlinear medium in contact with a one-dimensional photonic crystal. Two kinds of analytical solutions are found for an arbitrary magnitude of the nonlinearity: a standing-wave-like one containing the inverse elliptic function Eli(?∣m), and a one-wave-type solution for transmitted TE-polarized waves. An approximate two-wave solution is proposed to describe the field propagation through the nonlinear film covering the photonic crystal. It is shown that the problem of a mixed linear-nonlinear structure may be reduced to a transcendental kernel equation determining the field inside the nonlinear part of the medium. The light reflection from a Si/SiO₂ layered structure in contact with an optically nonlinear medium is calculated. The angular-frequency photonic band diagram and power dependency are investigated. Local interface waveguide modes are considered.     

Spontaneous emission and elastic scattering of light from quantum-well excitons in a Fabry-Perot microcavity

A theory of spontaneous emission and elastic light scattering by quasi-two-dimensional excitons in a quantum well placed in a Fabry-Perot microcavity is developed. The problem is solved by means of electrodynamic Green’s functions with inclusion of fluctuations of the quantum-well width and cavity wall shape treated as a perturbation. General expressions are found in a zero approximation of perturbation theory (plane interfaces) for the radiative decay rates of quasi-two-dimensional excitons and for their energy shifts in the cavity. The boundary conditions for the electromagnetic field are taken into account through the coefficients of inward light reflection from the cavity walls. Resonance contributions to the scattering cross sections, which differ in the polarizations (p or s) of the incident and scattered waves, are derived in the lowest (Born) approximation in quantum-well width fluctuations. The spectral and angular dependences of elastic light scattering are studied numerically for Gaussian and exponential correlation functions. It is shown that the contribution from quantum-well width fluctuations to light scattering exceeds that due to single interfaces (surfaces) of a heterostructure by two orders of magnitude.     

Comparative analysis of multi-wave mixing and measurements of the higher-order nonlinearities in resonant media

The features of degenerate multi-wave mixing in resonant media (dye solutions) have been studied theoretically and experimentally. It has been demonstrated that thermal nonlinearity due to the induced absorption from the excited level contributes significantly to the efficiency of four-wave mixing, but results in lower efficiency of higher-order interactions. The measurement results obtained for the energy efficiency of four-, six- and eight-wave mixing enable calculations of the third-, fifth- and seventh-order nonlinear optical susceptibilities, respectively. Experimentally, the method proposed for measurements of the higher-order nonlinearities has been realized with the use of the multi-wave mixing at second harmonic λ = 532 nm of monopulse YAG:Nd³⁺ laser radiation in a Rhodamine 6G dye solution. The ratios ∣χ⁽⁵⁾∣/∣χ⁽³⁾∣ and ∣χ⁽⁷⁾∣/∣χ⁽⁵⁾∣ are determined to be of the order of 10⁻⁵ cm³/erg.     

Multiple small-angle neutron scattering for an arbitrary value of the born parameter

Computer calculations are made of the intensity of multiple small-angle neutron scattering using the general Moliére formula [8] over a wide range of variation of the Born parameter, embracing the diffraction and refraction regimes, and a transition region between diffraction and reflection. A comparison is made with approximate formulas obtained earlier by Maleev et al. [9, 10] in the limiting cases of the Born parameter α ? 1 and α ? 1 for the diffraction and refraction regimes, respectively. It is shown that over a wide range of values of α the results of the calculations using the approximate and general formulas are the same. The theoretical conclusions were checked experimentally using data from measurements of small-angle neutron scattering for the domain structure of ferromagnets. Measurements were made of the neutron beam broadening for samples of different thickness and these were used to determine the effective domain sizes in pure iron and nickel exposed to thermal treatment and plastic deformation, and also in the Invar alloys Fe⁶⁵Ni³⁵and Fe³Pt. An analysis is made of the angular dependence of magnetic small-angle neutron scattering at the asymptote.     

Planar quarter wave stacks prepared from chalcogenide Ge-Se and polymer polystyrene thin films

Planar quarter wave stacks based on amorphous chalcogenide Ge-Se alternating with polymer polystyrene (PS) thin films are reported as Bragg reflectors for near-infrared region. Chalcogenide films were prepared using a thermal evaporation (TE) while polymer films were deposited using a spin-coating technique. The film thicknesses, d∼165 nm for Ge₂₅Se₇₅ (n=2.35) and d∼250 nm for polymer film (n=1.53), were calculated to center the reflection band round 1550 nm, whose wavelengths are used in telecommunication. Optical properties of prepared multilayer stacks were determined in the range 400-2200 nm using spectral ellipsometry, optical transmission and reflection measurements. Total reflection for normal incidence of unpolarized light was observed from 1530 to 1740 nm for 8 Ge-Se+7 PS thin film stacks prepared on silicon wafer. In addition to total reflection of light with normal incidence, the omnidirectional total reflection of TE-polarized light from 8 Ge-Se+7 PS thin film stacks was observed. Reflection band maxima shifted with varying incident angles, i.e., 1420-1680 nm for 45° deflection from the normal and 1300-1630 nm for 70° deflection from the normal.     

The reflection of light swift particles from heavy solid targets

The reflection of light particles bombarding heavy targets has been investigated with the single-collision model, which assumes straight line trajectories between the surface and the large angle scattering event upon incidence and exit of the swift particle. This model allows analytical integration, under some approximations, to yield energy and angular distributions of reflected particles as well as particle and energy reflection coefficients in terms of analytical formulae. The results are compared with data from the Monte Carlo computer program TRIM for H and He incident on Au. This comparison shows that the model can be applied for reduced energies larger thanε=5, and that it is well suited for any higher energy up to relativistic energies, in contrast to previous theoretical or empirical formulae.     

High-resolution H atom scattering from NaCl(001)

The NaCl(001) surface is studied using an H atom beam at energies of 76.3 and 86.3 meV. Elastic diffractive scattering is investigated under different incident angles and crystal orientations. Selective adsorption resonances are measured, determining experimentally the energy levels of the H atom bound to the surface. The energy spectrum is reproduced reasonably by a Morse potential with a well depth D = 29.2 meV and a range parameter k = 0.04 nm^?1.     

Elastic and inelastic scattering of protons from Li between 25 and 45 MeV

The elastic and inelastic scattering of protons from ⁶Li has been studied at incident energies of 25.9, 29.9, 35.0, 40.1 and 45.4 MeV. The 2.18 MeV (3⁺, T = 0) first excited state of ⁶Li was found to be strongly excited, but the 3.56 MeV (0⁺, T = 1) second excited state was quite weakly excited. Angular distributions for excitation of the 2.18 MeV level were measured at all five energies, while angular distributions for excitation of the 3.56 MeV level were extracted only at 25.9 and 45.4 MeV. To test the applicability of the optical model for the scattering of protons from such a light nucleus the elastic scattering angular distributions have been analyzed using the eleven-parameter search code SEEK. Available polarization angular distributions were included in the analysis. Reasonable fits to the data have been obtained with an average geometry potential. Theoretical estimates of the real part of the optical potential and the inelastic scattering differential cross sections have been made using the microscopic model for proton-nucleus scattering. Both phenomenological and realistic forces have been considered and the necessary nuclear transition densities have been extracted from experimental elastic and inelastic electron scattering data. An estimate of a possible spin-spin term in the optical potential has also been made.     

Exact finite-range DWBA description of the60Ni(160,12C)64Zn reaction at 60 MeV incident energy

Cross section angular distributions of⁶⁰Ni(¹⁶O,¹²C)⁶⁴Zn reactions leading to three strongly excited states at 60 MeV incident energy and the¹⁶O+⁶⁰Ni and¹²C+⁶⁴Zn elastic scattering at 60 MeV respectively 45 MeV and 54 MeV have been measured using aQ3D magnetic spectrograph. EFR-DWBA calculations assuming the transfer of anα-cluster in its 0s ground state are able to describe the general features of the strongly oscillating experimental angular distributions using a surface transparent optical model potential. The optical model parameters used in the DWBA calculations are obtained from fits of the elastic scattering data of incident and exit channels. The importance of “correct” optical model parameters in the exit channels for relative spectroscopic factors will be discussed and the extracted relative spectroscopic factors will be compared to previous (⁶Li,d) results.     

Large angle scattering of α-particles from 32S

The elastic scattering of α-particles from ³²S was studied in the incident energy range between 4 and 8.9 MeV. In order to ascertain whether quasi-molecular states exist, as predicted in the α-³²S system, excitation functions were measured, and angular distribution measurements were carried out using targets with different thicknesses in the angular range from θ_lab = 30° to 175° at each extreme in the excitation functions. The analysis of the angular distribution data at back angles was performed using the Regge-pole method. A resonance with J = 3 was observed at 7.7 MeV in the α-³²S system. Evidence was also found for both a broad resonance which can be characterized by an angular momentum J = 1, and for a narrow J = 2 resonance.     

A study of the odd isotopes of copper using the 58, 60, 62, 64Ni(τ, d) 59, 61, 63, 65Cu and 48Ca(τ, d)49Sc reactions

Experimental measurements are reported for the ^{58, 60, 62, 64}Ni(τ, d) ^{59, 61, 63, 65}Cu and ⁴⁸Ca(τ, d)⁴⁹Sc reactions and for the elastic scattering of ³He particles from ^{58, 60, 62, 64}Ni and ⁴⁸Ca targets at an incident energy of 18 MeV. The (τ, d) angular distributions cover the angular range from approximately θ_c.m. = 5° to 90° and the elastic scattering angular distributions range from θ_c.m. = 12° to 172°. In the (τ, d) reactions several weakly excited states, not previously seen in stripping reactions, have been identified and assignments of the transferred angular momentum made. The ⁴⁸Ca(τ, d)⁴⁹Sc reaction data are used in conjunction with the theoretical sum rules of MacFarlane and French to determine the normalization factors to be used with DWBA calculations for different sets of optical potentials. These normalization factors are used to extract spectroscopic strengths and centroid energies from the Ni(τ, d)Cu data which are compared with published model calculations for the odd copper isotopes. It is concluded that these calculations invariably fail to give a consistent picture of the odd copper isotopes mainly due to the use of centroid energies as variable parameters in the model calculations.     

Polarization modulation spectroscopy of surface plasmon resonance

The features of surface plasmon resonance in gold nanofilms deposited on the surface of a total-internal-reflection prism have been investigated theoretically, using the Fresnel equation, and experimentally, with application of the polarization modulation technique. The angular characteristics of the polarization difference of the reflection coefficients for s-and p-polarized light, Δρ = R _s ² ? R _p ² , were measured in the wave-length range λ = 0.4–2.0 μm. It is shown that the characteristics of Δρ, in contrast to the results of standard measurements by the surface plasmon resonance method, have a resonance peak. Due to this, the characteristics of the polarization difference contain nonresonant components whose magnitudes are determined by the internal reflection coefficients for the metal and insulator; these parameters depend on the film thickness. The calculated and experimental data coincide when the model assumes exponential dependence of the refractive indices and extinction coefficients on the thickness of the metal film. It is established that the characteristic parameter of the exponential is a metal film thickness of 11.0 ± 0.5 nm, at which the film optical parameters correspond to the bulk characteristics.     

Polarized angular dependence of out-of-plane light-scattering measurements for nanoparticles on wafer

Bidirectional ellipsometry has been developed as a technique for distinguishing among various scattering features near surfaces. The polarized angular dependence of out-of-plane light-scattering by the nanoparticles on wafer is calculated and measured according to Rayleigh limit. These calculations and measurements yield angular dependence of bidirectional ellipsometric parameters for out-of-plane scattering. The experimental data show good agreement with theoretical predictions for different diameter of nanoparticles. The results suggest that improvements for accuracy are possible to perform measurements of scattering features from nanoparticles. The angular dependence and the polarization of light scattered by nanoparticles can be used to determine the size of nanoparticulate contaminants on silicon wafers.     

Room-temperature electrosynthesized ZnO thin film with strong (0 0 2) orientation and its optical properties

ZnO thin film with strong orientation (0 0 2) and smooth surface morphology was electrosynthesized on ITO-coated glass substrate at room temperature under pulsed voltage. Photoluminescence (PL) shows two obvious peaks: violet band and strong green band. The former is due to the free-excitonic transition and the latter is believed to arise from the single ionized oxygen vacancy (V_O⁺). Raman scattering reveals that the 580 cm⁻¹ mode and the shoulder peak mode at 550 cm⁻¹ originate from the N-related local vibration mode (LVM) and E₁ (LO) mode, respectively.     

Carbon sputtering yield measurements at grazing incidence

In this investigation, carbon sputtering yields were measured experimentally at varying angles of incidence under Xe⁺ bombardment. The measurements were obtained by etching a coated quartz crystal microbalance (QCM) with a low energy ion beam. The material properties of the carbon targets were characterized with a scanning electron microscope (SEM) and Raman spectroscopy. C sputtering yields measured under Ar⁺ and Xe⁺ bombardment at normal incidence displayed satisfactory agreement with previously published data over an energy range of 200 eV-1 keV. For Xe⁺ ions, the dependence of the yields on angle of incidence θ was determined for 0° ≤ θ ≤ 80°. Over this range, an increase in C sputtering yield by a factor of 4.8 was observed, with the peak in yield occurring at 70°. This is a much higher variation compared to Xe⁺ → Mo yields under similar conditions, a difference that may be attributed to higher scattering of the incident particles transverse to the beam direction than in the case of Xe⁺ → C. In addition, the variation of the yields with θ was not strongly energy dependent. Trapping of Xe in the surface was observed, in contrast to observations using the QCM technique with metallic target materials. Finally, target surface roughness was characterized using atomic force microscope measurements to distinguish between the effects of local and overall angle of incidence of the target.     

Surface channeling of swift light ions

A fast computer code is developed to provide information about the trajectories of swift light particles incident on crystalline targets under surface channeling conditions. The approximations used in the model are tested by comparison of trajectory calculations with the MARLOWE simulation program. The simulation of experimental energy distributions allows discussing various inelastic energy loss models for the interaction of 150 keV protons with a nickel surface. The results suggest that plasmon excitations are not sufficient to account for the measured energy losses. It is found that the Oen-Robinson formula, including inelastic energy losses by single electron excitations in dense materials reasonably well applies to the reflection of light ions from metallic surfaces in channeling conditions. The measured light intensity emitted from 200 keV He⁺ reflected ions in various directions close to compact atomic surface rows is compared with the calculated reflection coefficient. The results suggest that most of the particles reflected in ionic state do not penetrate the target surface. Detailed comparison between light emission measurements and calculated reflection intensities, however, requires accurate modelling of the surface topography as well as of the deexcitation mechanisms involved in the surface reflection of light ions.     

Comparison of the amplification coefficients of conjugate and non-conjugate waves in stimulated light scattering

The energies of conjugate and non-conjugate waves in stimulated light scattering were experimentally measured simultaneously. The level of spontaneous scattered light was measured with the same setup. These data allow to compare amplification coefficients of conjugate and non-conjugate waves. The coefficient for the conjugate wave proved to be two times greater then for the non-conjugate wave, assuming that ～√N_m modes are excited inside the light guide with carbondisulfide, which was used as scattering medium. N_m is the maximal number of light guide modes which can propogate within a solid angle occupied by scattering light.