Validity of rough surface backscattering models

A study of the regions of validity for rough surface scattering models is conducted for surfaces with Gaussian and power law power spectra. Models included in the study are physical optics (PO), geometrical optics, small perturbation method and small slope approximation. The range of validity of the PO model is commonly described by a bound on the radius curvature of the surface relative to the electromagnetic wavelength. We show empirically that for backscattering the region of accuracy is more accurately described by a bound on surface slope. For surfaces with a Gaussian power spectrum, the PO model is accurate to within 2 dB for RMS surface slope values less than 0.59 cos³θ. For surfaces with a power law power spectral density, the PO model is accurate for significant slope values (RMS surface height/wavelength of the dominant spectral peak) less than 0.037 cos³θ. These conditions are valid up to approximately 30°. The regions of validity of other models in the study are also shown to be well approximated by bounds on surface slope.     

Multiple scattering in the high-frequency limit with second-order shadowing function from 2D anisotropic rough dielectric surfaces: II. comparison with numerical results

Abstract

This second part presents illustrative examples of the model developed in the companion paper, which is based on the first- and second-order optics approximation. The surface is assumed to be Gaussian and the correlation height is chosen as anisotropic Gaussian. The incoherent scattering coefficient is computed for a height rms range from 0.5λ 1λwhere λ is the electromagnetic wavelength), for a slope rms range from 0.5 to 1 and for an incidence angle range from 0 to 70°. In addition, simulations are presented for an anisotropic Gaussian surface and when the receiver is not located in the plane of incidence. For a metallic and dielectric isotropic Gaussian surfaces, the cross- and co-polarizations are also compared with a numerical approach obtained from the forward.backward method with a novel spectral acceleration algorithm developed by Torrungrueng and Johnson (2001, JOSA A 18). (Some figures in this article are in colour only in the electronic version)     

Numerical,analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement

Abstract

This paper Presents numerical simulations, theoretical analysis, and millimeter wave experiments for scattering from one-dimensional very rough surfaces. First, numerical simulations are used to investigate the effects of roughness spectrum, height variation, interface medium, polarization, and incident angle on the backscattering enhancement. The enhanced backscattering due to rough surface scattering is divided into two cases; the RMS height close to a wavelength and RMS slope close to unity, and RMS height much smaller than a wavelength with surface wave contributions. Results also show that the enhancement is sensitive to the roughness spectrum. Next, a theory based on the first- and second-order Kirchhoff approximation modified with angular and propagation shadowing is developed. The theoretical solutions provide a physical explanation of backscattering enhancement and agree well with the numerical results. In addition to the scattering of a monochromatic wave, the analytical results of the broadening and lateral spreading of a pulsed beam wave scattering from rough surfaces are also discussed. Finally, the existence of backscattering enhancement from one-dimensional very rough conducting surfaces with exact Gaussian statistics and Gaussian roughness spectrum is verified by a millimeter-wave experiment. Experimental results which show enhanced backscattering for both TE and TM polarizations for different angles of incidence are presented.     

Multiple scattering in the high-frequency limit with second-order shadowing function from 2D anisotropic rough dielectric surfaces: II. comparison with numerical results

This second part presents illustrative examples of the model developed in the companion paper, which is based on the first- and second-order optics approximation. The surface is assumed to be Gaussian and the correlation height is chosen as anisotropic Gaussian. The incoherent scattering coefficient is computed for a height rms range from 0.5λ 1λwhere λ is the electromagnetic wavelength), for a slope rms range from 0.5 to 1 and for an incidence angle range from 0 to 70°. In addition, simulations are presented for an anisotropic Gaussian surface and when the receiver is not located in the plane of incidence. For a metallic and dielectric isotropic Gaussian surfaces, the cross- and co-polarizations are also compared with a numerical approach obtained from the forward.backward method with a novel spectral acceleration algorithm developed by Torrungrueng and Johnson (2001, JOSA A 18). (Some figures in this article are in colour only in the electronic version)     

The sticking coefficient of H2 on Ni(111) as a function of particle energy and angle of incidence: A test of detailed balancing

The sticking coefficient of H₂/Ni(111) changes proportionally to the beam energy. The angular distribution of the probability of adsorption varies with cos^3.5θ; the angular distribution of desorption is found to change as cos^4.5θ at 300 K. Assuming validity of detailed balancing, the adsorption data suggest an energy distribution for desorption which agrees with existing time-of-flight measurements.     

Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement

This paper Presents numerical simulations, theoretical analysis, and millimeter wave experiments for scattering from one-dimensional very rough surfaces. First, numerical simulations are used to investigate the effects of roughness spectrum, height variation, interface medium, polarization, and incident angle on the backscattering enhancement. The enhanced backscattering due to rough surface scattering is divided into two cases; the RMS height close to a wavelength and RMS slope close to unity, and RMS height much smaller than a wavelength with surface wave contributions. Results also show that the enhancement is sensitive to the roughness spectrum. Next, a theory based on the first- and second-order Kirchhoff approximation modified with angular and propagation shadowing is developed. The theoretical solutions provide a physical explanation of backscattering enhancement and agree well with the numerical results. In addition to the scattering of a monochromatic wave, the analytical results of the broadening and lateral spreading of a pulsed beam wave scattering from rough surfaces are also discussed. Finally, the existence of backscattering enhancement from one-dimensional very rough conducting surfaces with exact Gaussian statistics and Gaussian roughness spectrum is verified by a millimeter-wave experiment. Experimental results which show enhanced backscattering for both TE and TM polarizations for different angles of incidence are presented.     

The wettability of polytetrafluoroethylene and polymethylmethacrylate by aqueous solutions of Triton X-100 and propanol mixtures

Measurements of advancing contact angles (θ) were carried out for aqueous solutions of Triton X-100 (TX-100) and propanol mixtures at constant TX-100 concentration equal to 1 × 10⁻⁷, 1 × 10⁻⁶, 1 × 10⁻⁵, 1 × 10⁻⁴, 6 × 10⁻⁴ and 1 × 10⁻³ M, respectively, on polytetrafluoroethylene (PTFE) and polymethyhmethacrylate (PMMA). Using obtained results the changes of cosθ and adhesional tension against surface tension of all series of aqueous solutions of TX-100 and propanol mixtures (γ_LV) for PTFE and PMMA surfaces were shown. On the basis of these changes it was deduced that adsorption of TX-100 and propanol mixtures at PTFE-solution and solution-air interfaces is the same but the adsorption of TX-100 and propanol mixtures at solution-air interface is considerably higher than at PMMA-solution one. In the case of PTFE this conclusion was confirmed by relationship between cosθ and the reciprocal of the surface tension of solution. Extrapolation of the relationships between cosθ and/or adhesional tension and the surface tension of solutions to the points corresponding to the cosθ = 1 and adhsional tension equal to the surface tension of solution, the critical surface tension of PTFE and PMMA wetting was determined. The average values of critical surface tension of wetting determined from these relationships for PTFE are lying in the range of its surface tension values determined from contact angles of different kinds of liquids, which can be find in the literature, but for PMMA are considerably lower than the surface tension. The double value of the critical surface tension of PTFE wetting is equal to adhesion work of the solution to its surface and for PMMA there is not any correlation between these magnitudes.Using the measured values of the contact angles and Young equation the PTFE(PMMA)-aqueous solution interfacial tension was determined. The interfacial tension values of PTFE-aqueous solution were also calculated from the Fainerman and Miller equation in which the correcting parameter of nonideality of the surface monolayer was introduced and compared to those obtained from Young equation. From this comparison it results that the changes of PTFE-solution interface tension as a function of propanol concentration can be described by the Fainerman and Miller equation.     

Angular distribution of the reaction np → dπ0

Differential cross sections of the reaction np → dπ⁰ have been measured for incident neutron energies between 470 MeV and 590 MeV. The angular distributions are fitted by a power series. A significant cos⁴θ contribution is found.     

Classical trajectory calculations of the dissociation of hydrogen on copper: III. The effect of surface roughness

Further calculations have been performed for the dissociation of H₂ on copper in which the empirical potential surface has been increased in roughness as suggested by our previous studies. This change is effected through an increase in the barriers to adatom surface diffusion, keeping the minimum energy requirements for dissociation about the same. The result is to bring the calculation into satisfactory agreement with molecular beam experiments. We examine the effect of changing the internal energy (vibration and rotation), mass, (D₂), the adatom binding site, and evaluate the validity of the correlating parameter E⊥ = Ecos²θ.     

Light reflection from finite conductors with a Gaussian random roughness using Kirchhoff and geometric optics approximations

A comparison between exact solutions and two approximate models, Kirchhoff approximation (KA) and geometric optics approximation (GOA), for reflection from random Gaussian rough conductive metallic surfaces for three regimes of correlation length in both cases of polarization TM and TE has been reported. The phenomenon of excitation of surface plasmons (SPs) has been shown only at TM polarization for KA. The domains of validity of both approximate models have been quantified. It is shown that accuracy and efficiency of any approximate method depended of various parameters: surface roughness, polarization, SPs effects, wavelength, and surface materials. KA is efficient for weakly rough surfaces with correlation length greater than wavelength, but when rms height increases GOA is more suitable than KA. Excitation of SPs is observed only at TM-polarized light, only for weakly rough surfaces with correlation length less than wavelength using KA and not GOA.     

Polarization fluctuations of Gaussian Schell-model type photon beams in a slant channel with non-Kolmogorov turbulence

Polarization properties of Gaussian Schell-mode type photon beams propagating through the non-Kolmogorov turbulence in a slant channel are studied which are based on the model of quantum field and the effective photon annihilation/creation operator. Our numerical results show that the degree of polarization increases with the increasing of the transverse coherent width of source ρ_s0, the source's transverse size ω₀ and the power law of the turbulent spectrum, but the degree of polarization P decreases as the zenith angle θ increases. The effect of the wavelength of light beam on the degree of polarization of Gaussian Schell-model beams is small.     

4He+在Al和Si单晶晶面沟道中的半波长及阻止本领

采用高分辨探测系统,在不同的入射角θ_in和出射角θ_out的条件下,测量了1—2MeV⁴He⁺入射在Al(100)面和Si(110),(100)面中的背散射能谱。得到了背散射能谱振荡峰的间距ΔE与cosθ_in/cosθ_out的直线关系,从而获得了1—2MeV⁴He⁺在这三个晶面中的振荡半波长及阻止本领。实验得到的半波长与理论计算值在误差范围内一致,晶面沟道方向的阻止本领略大于随机方向的阻止本领。 关键词：     

fcc金属表面能的各向异性分析及表面偏析的预测

本文将元素变量(φ^*和n_WS)和MAEAM相结合,从原子尺度上对10种fcc金属Cu,Ag,Au,Ni,Pd,Pt,Rh,Al,Ir和Pb的38个不同晶面的表面能进行模拟计算及各向异性分析. 结果表明,fcc金属的密排面(111)的表面能最小,则该晶粒取向优先生长,与实验结果和第一原理的LMTO-ASA计算结果一致;各个晶面的表面能均随着其他晶面与(111)晶面的夹角cosθ_(hkl)的增长而呈线性 关键词： FCC金属 MAEAM 表面能 表面偏析     

Scattering from very rough metallic and dielectric surfaces: a theory based on the modified Kirchhoff approximation

This paper presents a theory of scattering from very rough metallic and dielectric surfaces using the first- and second-order Kirchhoff approximations (KA) modified with the angular and propagation shadowing. The shadowing functions limit the single and double scattered waves which are illuminated and not shadowed by the surface. The theoretical results are compared with the Monte Carlo simulations showing the range of validity of the theory. The theory is applicable to the range where the RMS height is close to a wavelength and the RMS slope is close to unity, and the second medium is lossy. The second-order scattering includes two waves travelling in opposite directions on the surface, giving a physical explanation of the enhanced backscattering.     

Investigation of surface topology of printed nanoparticle layers using wide‐angle low‐Q scattering

A new small‐angle scattering technique in reflection geometry is described which enables a topological study of rough surfaces. This is achieved by using long‐wavelength soft X‐rays which are scattered at wide angles but in the low‐Q range normally associated with small‐angle scattering. The use of nanometre‐wavelength radiation restricts the penetration to a thin surface layer which follows the topology of the surface, while moving the scattered beam to wider angles preventing shadowing by the surface features. The technique is, however, only applicable to rough surfaces for which there is no specular reflection, so that only the scattered beam was detected by the detector. As an example, a study of the surfaces of rough layers of silicon produced by the deposition of nanoparticles by blade‐coating is presented. The surfaces of the blade‐coated layers have rough features of the order of several micrometers. Using 2 nm and 13 nm X‐rays scattered at angular ranges of 5°≤θ≤ 51° and 5°≤θ≤ 45°, respectively, a combined range of scattering vector of 0.00842 Å^?1≤Q≤ 0.4883 Å^?1 was obtained. Comparison with previous transmission SAXS and USAXS studies of the same materials indicates that the new method does probe the surface topology rather than the internal microstructure.     

Angular distributions of auger electron emission: Clean and gas-adsorbed polycrystalline Ni surfaces

The excitation angle (β) and emission angle (θ) dependences of the Ni M₂,₃VV (61 eV) and Ni L₃VV (850 eV) Auger emissions from clean polycrystalline Ni surfaces, and the S L₂, ₃ M₂, ₃M₂, ₃ (150 eV) Auger emission from S-adsorbed poly-Ni surfaces have been investigated. In the case of Ni (61 eV) and S Auger emissions, the β-dependence shows the $\text{1}\text{cos β}$ distribution, while a significant deviation from $\text{1}\text{cos β}$ is observed for Ni (850 eV) Auger emission. The cosθ distribution and the intermediate between isotropic and cosθ distributions are observed for Ni (61 eV), and for Ni (850 eV) and S Auger emissions, respectively. Those results have been found to be in fairly good agreement with the calculations based on the simple continuum model without consideration of the diffraction effect and the inherent anisotropic emission.     

Contribution of coloured Higgs bosons to e+e− annihilation into two jets

We examine the effect of the coloured Higgs bosons (of the integer-charge quark model) on electron-positron annihilation into two jets. The overall angular distribution of the quark + gluon + Higgs jets in the scaling limit is found to be 1+0.57 cos²θ.     

Angular distribution for the np → dπ0 reaction

The relative differential cross section for the reaction np → dπ⁰ has been measured at incident neutron energies of 459, 648 and 802 MeV. The c.m. angular distributions are fitted by the functional form A + cos²θ + B cos⁴θ. The values obtained for the parameters A and B are in agreement with those obtained from pp → dπ⁺ analyses, consistent with isospin invariance in these reactions.     

Polarized SERS study of an individual Ag nanowire with bulb humps

Polarization-dependent surface enhanced Raman scattering (SERS) of an individual Ag nanowire (NW) with bulb humps (including nm-scaled bulb humps on the body part and a bulb NW-tip) was investigated. Strong SERS effect was observed from the bulb NW-tip, which exhibited cos²θ dependence relative to the polarization angle θ of the incident laser. Such dependence is similar to that of the NW-body with bulb humps, but different from that of the other NW-tip with crown shape. Their different polarized SERS behaviors along with the bulb hump effect on SERS were discussed.     

The angular dependence of flux,mean energy and speed ratio for D2 molecules desorbing from a Ni(111) surface

Experimental data are presented for the angular dependence of the relative flux, the mean energy and the speed ratio of deuterium molecules desorbing from a Ni(111) crystal surface at a surface temperature of T_s = 1143 K and at sulphur coverages ranging between 30% and less than 2% of a monolayer.The angular flux distribution is sharply peaked in the forward direction (cos^dθwith 3 ? d ? 5) and the mean energy 〈E〉 of the desorbate depends strongly on the desorption angle θ. For normal desorption $\text{(θ = 0°)}\text{〈E〉}\text{2k}$ is about 700 K higher than T_s and for glancing angles (θ = 80°) it decreases to about 400 K below T_s The results obtained on sulphur free and sulphur covered Ni(111) surfaces are compared with our former data on polycrystalline nickel. The main differences in the kinetic features can be ascribed to the surface roughness. Accordingly, the angular distributions of flux, mean energy, and speed ratio, which deviate strongly from the Knudson and Maxwellian law, do not seem to depend considerably on sulphur coverage and surface structure. A qualitative explanation for these deviations is presented using the principle of detailed balancing.