Scattering from infinitely sloped surfaces by use of the Kirchhoff approximation

A simple reformulation of the double-scatter Kirchhoff approximation is presented to extend the use of this calculation method to infinitely sloped surfaces. Examples are presented for square grooves and lines on perfectly conducting surfaces. The results presented show the accuracy of the method and the errors produced by not including higher-order scattering in the calculations.     

Adjacency effects on water surfaces: primary scattering approximation and sensitivity study

The making of atmospheric corrections is a critical task in the interpretation of ocean color imagery. In coastal areas, a fraction of the light reflected by the land reaches a sensor. Modeling the reduction of image contrast when the atmospheric turbidity increases, the so-called adjacency effect, requires large amounts of computing time. To model this effect we developed a simple approach based on the primary scattering approximation for both nadir and off-nadir views. A sensitivity study indicates that the decisive criterion for measurement accuracy for aerosols is their vertical distribution. As this distribution cannot generally be determined from space, it is not possible to include a suitable correction of the adjacency effects on satellite imagery. Conversely, we propose a simple correction for molecular scattering based on the isotropic approximation. We also address the problem of reduction of the coupling between the Fresnel reflection and the atmosphere for observations of coastal water. We study the influence of the adjacency effects on determination of the abundance of chlorophyll in water by combining use of the red and the infrared bands for aerosol remote sensing and the blue/green-ratio technique for retrieval of these data.     

Kirchhoff calculations of the coherent scatter from a series of very rough surfaces

Calculations are presented for the scattering of polarized light from a series of very rough one-dimensional gold-coated surfaces, as determined by the use of the Kirchhoff approximation with geometric shadowing. These surfaces have Gaussian autocorrelation functions with a 1/e width of 3.3 μm and Gaussian probability distributions of height with standard deviation varying between 0.25 and 1.73 μm. Calculations are performed for the scattering of light of wavelength 3.392 μm, so that the validity of the geometric-shadowing approximation and the Kirchhoff approximation itself are open questions. The values of the coherent (or specular) component of the scattered light for the four nonzero elements of the Mueller matrix (which fully describe the polarization properties of the scattered light) are calculated. Comparisons between the calculated results and experimental measurements on surfaces of the same parameters [Knotts and O'Donnell, J. Opt. Soc. Am. A 11, 697 (1994)] show good agreement up to approximately 70° incidence angle.     

Light scattering from laser-damaged speckled surfaces

Scattering from an initially plane surface of a thin Plexiglas plate damaged by an impinging coherent light beam of a laser is considered. The morphology and the characteristic dimensions of the damaged speckles was studied during the evolution of the phenomenon by interferometry and the creation of diffraction patterns. The cusped interferogram created by superposition of evoluting two initial diffraction patterns, created during successive damage steps, forms caustics corresponding to hyperbolic umbilic catastrophes. An experimental study of the evolution of the damage phenomenon clarifies the mechanisms of elastic and plastic deformations of the affected zone.     

Optical scattering from rough-rolled aluminum surfaces

Bidirectional, angular resolved scatterometry was used to evaluate the feasibility of using rolled aluminum as reflectors in solar thermal collectors and solar cells. Two types of rolled aluminum with different surface roughnesses were investigated. The results show that the smoother of the two samples [rms height, (0.20 ? 0.02) mum] can be used as a nonimaging, concentrating reflector with moderate reflection losses compared with those of optically smooth aluminum reflectors. The sample with the rougher surface [rms height, (0.6 ? 0.1) mum] is not suitable as a concentrating element but can be used as planar reflectors. The orientation of the rolling grooves is then of importance for minimizing reflection losses in the system.     

Electromagnetic wave scattering from moving surfaces with high-amplitude corrugated pattern

This paper deals with the problem of electromagnetic wave scattering from rough surfaces. By means of a generalized Floquet modal representation an analytic solution can be found that is valid for any Fourier-expandable surface pattern, with no limitation on the corrugation amplitude. By means of the special relativistic frame-hopping method, the motionless solution is generalized to the case of uniform translational relative motion between the surface and the observer. Plane-wave simplification techniques are employed to minimize the algebraic complexity of the field covariance transformations. A detailed signal analysis of the electromagnetic scattered field is performed in both the frequency and the time domains.     

Large-angle in-plane light scattering from rough surfaces

An in-plane light scattering setup that is capable of measuring large azimuthal scattering angles is presented. This type of measurement makes it easier to probe large k(parallel) at a fixed k(perpendicular) value (k(parallel) and k(perpendicular) are momentum transfer vectors parallel and perpendicular to the surface, respectively). Therefore the system allows us to explore small lateral scale and large vertical roughness (approximately lambda, the wavelength of the probe beam) of a rough surface. In-plane intensity measurements from a rough backside Si wafer and a Cu thin-film surface are reported. The structure factor that is related to surface roughness parameters is obtained from the measured in-plane intensity profiles. Both scalar (Beckmann-Kirchhoff) and vector (Rayleigh-Rice) theories have been applied to interpret the experimental data. The roughness parameters obtained from the scattering measurements are compared with those measured by atomic-force microscopy.     

Scattering of electromagnetic waves from two-dimensional rough surfaces with an impedance approximation

The sparse-matrix-flat-surface iterative approach has been implemented for perfectly conducting surfaces and modified to enhance convergence stability and speed for very rough surfaces. Monte Carlo simulations of backscattering enhancement using a beam decomposition technique are compared with millimeter-wave laboratory experimental data. Strong but finite conductivity for metals or thin skin depth for dielectrics is simulated by an impedance approximation. This gives rise to a nonhypersingular integral equation derived from the magnetic field integral equation. The effect of finite conductivity for a metal at visible wavelengths is shown.     

Extending the size-parameter range for plane-wave light scattering from infinite homogeneous circular cylinders

An algorithm that extends the possible size-parameter range for the calculation of plane-wave light scattering from infinite homogeneous circular cylinders by use of Mie-type analysis has been developed. This algorithm is based on the calculation of the ratios of Bessel functions instead of the Bessel functions or their logarithmic derivatives directly. This algorithm agrees with existing methods (when those methods converge). It also converges for large size parameters when other algorithms often do not.     

Fast analysis of electrically large electromagnetic scattering/radiation problems using the adaptive cross approximation with FFT

This paper presents a multilevel method for solving electromagnetic scattering/radiation problems. The original domain is decomposed using the octree technique. At the octree levels, the adaptive cross approximation (ACA) is employed to calculate the dominant sources and responses, and the long-distance interactions are computed using the fast Fourier transform (FFT). The algorithm leads to a great reduction in memory requirement and computing time. Numerical examples demonstrate that the proposed method has a good accuracy and a high computational efficiency.     

小斜率近似方法分析粗糙界面声散射问题

利用小斜率近似方法计算了起伏海面的声散射特性,得到了具有高斯分布粗糙海面的平均反射系数（即镜反射系数）计算公式,并与微扰法和Kirchhoff近似做了比较,结果表明小斜率近似是一种非常有效的分析起伏表面散射特性的近似方法。最后讨论了海面镜反射系数随海面的不平整度（波浪的均方根高度）、声波频率和声波入射方向的变化关系,得出了只有在声波波长和起伏波浪高度可比拟时,才有明显的镜反射的结论。这为分析浅海目标声散射特性时,选择是否需要考虑海面（海底）所引起的多途效应提供了理论依据。     

Radiation of an infinite isothermal cylinder with account of scattering

The radiation problem of a cylinder filled by a radiating, absorbing, and scattering medium is treated. The transport equation is solved analytically within the P₁ approximation for an arbitrary scattering indicatrix by the spherical harmonic method.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 35, No. 1, pp. 141–144, July, 1978.     

Second-order perturbation theory for scattering from heterogeneous rough surfaces

We propose a model to calculate scattering from inhomogeneous three-dimensional, rough surfaces on top of a stratified medium. The roughness is made up of an ensemble of deposits with various shapes and permittivities whose heights remain small with respect to the wavelength of the incident light. This geometry is encountered in the remote sensing of soil surfaces, or in optics wherever there are contaminated planar components. Starting from a volume-integral equation involving the Green's tensor of the stratified medium, we derive a height-perturbative expansion up to second-order. Our formulation, which depends explicitly on the profiles of each deposit and on the Fresnel coefficients of the layered substrate, accounts for double-scattering events and permits an evaluation of depolarization in the plane of incidence. Comparisons with rigorous calculations in the simplified case of two-dimensional geometries are presented. It is shown that the second-order scattering term can be much more important for heterogeneous surfaces than for their homogeneous counterparts.     

Unpolarized emissivity with shadow and multiple reflections from random rough surfaces with the geometric optics approximation: application to Gaussian sea surfaces in the infrared band

The emissivity from a stationary random rough surface is derived by taking into account the multiple reflections and the shadowing effect. The model is applied to the ocean surface. The geometric optics approximation is assumed to be valid, which means that the rough surface is modeled as a collection of facets reflecting locally the light in the specular direction. In particular, the emissivity with zero, single, and double reflections are analytically calculated, and each contribution is studied numerically by considering a 1D sea surface observed in the near infrared band. The model is also compared with results computed from a Monte Carlo ray-tracing method.     

Frequency dependence of the specular and diffuse phonon scattering from silicon surfaces

Phonon backscattering experiments with polished silicon surfaces show that there is no Kapitza anomaly at frequencies corresponding to the aluminum junction detector threshold (80 GHz), whereas at higher frequencies the anomalous transmission into liquid helium or solid nitrogen increases (reduced backscattering by the coverage), closely related to the increase of the diffuse scattering at the uncovered surface.     

Potential-dependent surface-enhanced Raman scattering from adsorbed thiocyanate for characterizing silver surfaces with improved reproducibility

Surface-enhanced Raman scattering (SERS) spectroelectrochemistry is used to characterize electrochemically roughened and highly polished polycrystalline silver SERS-active substrates. Changes in the nitrile stretching vibrational mode of adsorbed thiocyanate are used as an in situ spectroscopic probe: the potential dependence of band position (Stark tuning), shape, and scattering intensity of this mode are measured in order to investigate differences between SERS-active sites found on smooth and roughened electrode surfaces. Results obtained from thiocyanate adsorbed onto two different types of highly polished Ag surfaces (alumina and diamond polishing) show discrete populations of SERS-active adsorption sites that remain stable over a wide potential range. This behavior stands in contrast to that observed on electrochemically roughened surfaces, where very strong Stark tuning, large vibrational bandwidths, and irreversible loss of SERS enhancement upon negative potential excursions can be attributed to a diverse population of labile SERSactive sites that exhibit strong charge-transfer interactions with the adsorbate and large chemical SERS enhancement.     

Cross sections for surface plasmon polariton scattering from a nanoparticle in the dipole approximation

The differential and total cross sections for the scattering of surface electromagnetic waves in the optical frequency range (surface plasmon polaritons, SPPs) from a small particle into waves in the near-field zone (SPPs) and into waves propagating from the surface to the far-field zone have been calculated within the framework of the dipole approximation. The efficiencies of these scattering channels are compared as dependent on the main parameters of the system. An increase in the wavelength of the radiation exciting SPPs at a plane dielectric-metal interface (air-gold) may lead to a change in the most effective scattering channel.     

Numerical approximation of light scattering from tenuous cylindrical membranes at normal incidence

A numerical method has been developed to calculate the scattered field from a complex matrix of cylindrical membranes that are thin relative to wavelength with a refractive index close to that of the medium. The membranes are broken into a collection of adjacent parallel thin fibers, each fiber is assigned an internal field, and vector summation of the fields scattered by each fiber is used to calculate the total scattered field. For an incident wave in the TM mode the internal field of each membrane fiber is chosen to be equal to the incident field (the Born approximation). For the TE mode the internal field is determined by the local membrane orientation (φ) and relative refractive index (m) according to A sin 2φ for the component in the direction of incidence and 1 - A(1 - cos 2φ)for the transverse component, where A = (m(2) - 1)/2m(2). The method has application to light scattering by cell membranes in bundles of nerve axons.     

Fourth- and higher-order small-perturbation solution for scattering from dielectric rough surfaces

A recursive solution of the small-perturbation method for rough surface scattering is presented. These results permit fourth- and higher-order corrections to rough surface scattering coefficients to be determined in a form that explicitly separates surface and electromagnetic properties. Sample results are presented for the fourth-order correction to the specular reflection coefficient of a rough surface and the sixth-order correction to incoherent scattering cross sections.