Separation of surface and volume effects in scattering from heterogeneous rough surfaces: derivation of a splitting rule

We give theoretical support to the splitting rule, which was recently observed numerically for the scattering from heterogeneous rough surfaces. Under certain general conditions, the incoherent intensity of a composite medium with a rough interface is the sum of the incoherent intensity of the rough homogeneous surface with an effective permittivity and the incoherent intensity of the same composite medium below a flat interface. The coherent intensity is merely that of the rough effective homogeneous surface. The effective permittivity is given accurately by the Bruggemann mixing rule, provided that the scale of fluctuations in the volume is small with respect to the electromagnetic wavelength.     

Scattering of the electromagnetic waves from a rough surface

The electromagnetic field scattered by a rough surface of a semi-infinite body is computed up to the second order of a perturbation scheme with the surface roughness as a perturbation parameter. The calculations are based on the equation of motion of the polarization within the Lorentz–Drude (plasma) model of polarizable, non-magnetic, homogeneous matter. The surface roughness contributes both to the main (specularly) reflected and refracted fields and diffuse scattering, or gives rise to secondary (second-order) diffraction peaks for a regular grating. The calculations are performed both for the s- and p-waves. Two-dimensional modes, resonant at certain frequencies, are identified, confined to and propagating only on the surface, as a consequence of the surface roughness.     

Effect of spatial coherence on scattering from optically inhomogeneous media

The properties of light scattered from material systems depend on the characteristics of input optical fields. We study numerically the effect of the state of spatial coherence on the properties of scattered fields. Using a customized coupled dipole technique, we demonstrate that this influence manifests in changes of the statistics of intensities scattered at different angles.     

Scattering from rough thin films: discrete-dipole-approximation simulations

We investigate the wave-optical light scattering properties of deformed thin circular films of constant thickness using the discrete-dipole approximation. Effects on the intensity distribution of the scattered light due to different statistical roughness models, model dependent roughness parameters, and uncorrelated, random, small-scale porosity of the inhomogeneous medium are studied. The suitability of the discrete-dipole approximation for rough-surface scattering problems is evaluated by considering thin films as computationally feasible rough-surface analogs. The effects due to small-scale inhomogeneity of the scattering medium are compared with the analytic approximation by Maxwell Garnett, and the results are found to agree with the approximation.     

Scattering from anisotropic plasma-coated PEMC cylinder buried beneath a slightly rough surface

A general theoretical formulation is done to calculate the field scattered by perfect electromagnetic conductor (PEMC) cylinder coated with anisotropic plasma material. It is buried below a slightly rough surface. Spectral plane wave representation of fields and small perturbation method are used to calculate multiple reflections between coated cylinder and rough surface. To validate the present formulation, scattered field from a PEMC cylinder coated with double negative (DNG) material is obtained from the present formulation. Scattering pattern of non coated PEC/PEMC cylinder or coated with isotropic material can also be obtained by the proper selection of physical parameters such as anisotropy, admittance of PEMC cylinder and permittivity of hosting medium. Analytical expressions of scattered field for a sinusoidal rough surface are given along with their physical interpretation to get a good insight. Effect of geometrical and physical parameters on scattering pattern is observed.     

Scattering from a topological insulator cylinder buried below a slightly rough surface

Electromagnetic scattering from a topological insulator (TI) cylinder buried beneath a rough surface is considered. To account for the interactions of the scattered field and the rough surface, spectral plane wave representation of fields is used along with small perturbation method. Both time-reversal symmetry TI cylinder and time-reversal symmetry broken TI cylinder are considered to evaluate the scattered-transmitted field above the rough surface for different values of the periods of the rough surface and the size of the object. It is observed that co- and cross-polarized field components show a maximum before the time-reversal symmetry is broken. The co-polarized component remains almost constant while the cross-polarized component decreases for time-reversal symmetry broken case.     

Estimation of scattering from a moist rough surface with spheroidal dust particles

The scattering from moisture rough surface with spheroidal dust particles having surface with spheroidal dust particles has recently received much attention. In part due to the recent prediction and observation of the spheroidal dust particles in rough surfaces under elastic wave by the Kirchhoff scattering model and scalar approximation with slope. Our analysis shows that the scattering depends on the moisture (2–4·5%) with spheroidal dust particles. At slightly moisture rough surface the dielectric properties increase with change in field amplitude in a rough surface with spheroidal dust particles.     

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。     

High-order perturbation theory for light scattering from a rough metal surface.

The angular distribution of the mean diffuse intensity scattered from a metal surface with one-dimensional roughness is studied with perturbation theory. From an approach based on the reduced Rayleigh equations in p polarization, exact perturbation terms up to eighth order in the height parameter are developed for surface roughness consistent with a stationary Gaussian process. The theory is evaluated for a number of cases in which surface plasmon polariton excitation is significant and produces effects such as backscattering enhancement. For surface roughness having a wide Gaussian power spectrum, it is found that the high-order terms lead to roughness-induced broadening of the backscattering peak. For rectangular spectra, two cases are studied in which backscattering effects are due to sixth- and eighth-order terms; both cases provide good comparisons with previously unexplained experimental results. Further, because of an eighth-order term, the diffuse intensity is shown to contain a specular peak that also relies on polariton excitation. This new effect is studied in detail and is found to arise from the constructive interference of contributions produced by multiple-scattering processes, although the time-reversed paths that produce backscattering enhancement are not essential to the specular effect.     

Wave scattering from inhomogeneous anisotropic layers

Summary An analytic method is outlined to solve the problem of the scattering of harmonic waves from an inhomogenous anisotropic layer which admits a plane of material symmetry. Horizontally and vertically polarized waves are represented by couples of backward and forward modes. The amplitude and the polarization of each couple are obtained via a first-order Riccati differential equation while continuity requirements, imposed on each couple at the edge of the layer, yield the necessary boundary conditions. Reflection coefficients are derived at the outset and within the layer as a function of the depth, and transmission of the energy flux is evaluated. A wave-splitting is introduced in a natural way, and comparison with previous investigations is performed.     

Polarization of specular reflection and near-specular scattering by a rough surface

Polarization of specular reflection and near-specular scattering (NSS) by a randomly rough surface is investigated by the use of a Mueller matrix formulation. The collective effect by a rough surface on the average specular field results in reflectance loss and polarization, which can be explained by an effective medium theory. Effects of random NSS can be represented by a scattering matrix that is partially coherent and polarized. The incoherent and unpolarized part of scattering causes depolarization, and the coherent and polarized parts of scattering change the apparent polarization properties of specular reflection. Results of a simulation and least-squares fit of ellipsometric data to the models including the NSS effect, for a black anodized aluminum sample, are presented. Simultaneous least-squares fits for both ellipsometric data and reflectance data at multiple angles of incidence at three different wavelengths gave approximately the same rms roughness, which agrees with the profilometric values reported previously.     

随机起伏界面声散射的实验与理论研究

进行了二维粗糙海面声波散射特性的水池实验,测量了不同入射角、散射角以及方位角条件下所对应的散射强度。实验通过不同位置风扇对水面的吹拂获得粗糙水面,分别对水平面上互相垂直的两个方向上的水面波高变化进行了测量,利用周期图法估计出这两个方向上的空间功率谱,验证了实验中的粗糙水面是各向同性的。利用改进的空间域处理技术去除了总声波信号中的直达波和其他固定位置散射体的散射信号,获得了粗糙水面的声波散射信号。利用小斜率近似方法计算了二维粗糙海面的声散射特性。实验与模拟计算结果比较,证实了计算二维粗糙海面声波散射特性的小斜率近似方法的有效性与准确性,相互印证了实验与理论。     

Longitudinal wave scattering from rough crack-like defects

The roughness of crack-like defects affects ultrasonic wave scattering and this, in turn, affects defect detection and characterization. The first part of this paper is concerned with the efficient numerical modeling of scattering from rough cracks, i.e., a finite element local scattering (FELS) model. The scattered field is presented in the form of a scattering matrix, which describes the far-field scattering coefficient for all possible combinations of incident and scattering directions. The scattering matrices for many different realizations of rough cracks are simulated using both a FELS model and a model based on the Kirchhoff approximation. It is shown that the difference between scattering matrices extracted from the Kirchhoff model and the FELS model is less than 8%, for rough cracks with a standard deviation less than 0.3 wavelengths and a correlation length longer than 0.5 wavelengths, at incident and scattering angles ranging from -80° to 80° relative to the normal direction of the mean surface. Because the Kirchhoff model is significantly more efficient than the FELS model, it is used for subsequent simulations in which many realizations of rough cracks are studied to gain insight into the statistical nature of the scattering process. In line with previous work, a distinction is made between the coherent and diffuse contributions to the overall scattered field, in which the former represents the ensemble average over multiple surface realizations. The coherent and diffuse contributions of scattered field from various types of rough cracks are simulated. It is shown that surface roughness directly affects the coherent contribution to scattering behavior, whereas the diffuse contribution is affected by both surface roughness and correlation length, especially for rougher cracks.     

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.     

Slope distribution of a rough surface measured by transmission scattering and polarization

Transmission scattering from medium to air was used to measure the slope distribution of the rough plane surface of a transparent glass hemisphere. A facet model successfully explained the measured results of refraction, scattering, and polarization: Transmission scattering existed for incident angles greater than the critical angle, all measured curves for the normalized scattered intensity versus the facet slope angle for different detection directions overlapped, and the measured polarization of scattering was approximately constant for >99% of the facets. The slope distribution obtained by transmission scattering agrees with those of the surface profiles in the valid range of the profiler and can represent the slope distribution of the rough surface.     

Electromagnetic scattering by refractive index variations over a rough conducting surface

Abstract

This paper presents a numerical method for calculating the scattered field when a vertically polarized Gaussian beam is incident on a flat or slightly rough conducting surface at a grazing angle and the refractive index of the propagation medium has a profile which is not constant. The method is a solution to the parabolic approximation of the full wave equation. The results presented are taken for a linear and log-linear refractive index profile.     

Radiative transfer in inhomogeneous stratified scattering media with use of the auxiliary function method

The auxiliary function method consists of taking full advantage of the expansion of the phase function on spherical harmonics in order to deduce an integral equation from the radiative transfer equation. In contrast to the discrete-ordinate method, it is free of the channel concept, the unknowns being a function only of the optical depth. After presenting the method, we show that it is very accurate and particularly well fitted when the scattering medium is continuously inhomogeneous in albedo and phase function and also for sublayers with different refractive index.     

Scattering from very rough layers under the geometric optics approximation: further investigation

Scattering from very rough homogeneous layers is studied in the high-frequency limit (under the geometric optics approximation) by taking the shadowing effect into account. To do so, the iterated Kirchhoff approximation, recently developed by Pinel et al. [Waves Random Complex Media17, 283 (2007)] and reduced to the geometric optics approximation, is used and investigated in more detail. The contributions from the higher orders of scattering inside the rough layer are calculated under the iterated Kirchhoff approximation. The method can be applied to rough layers of either very rough or perfectly flat lower interfaces, separating either lossless or lossy media. The results are compared with the PILE (propagation-inside-layer expansion) method, recently developed by Déchamps et al. [J. Opt. Soc. Am. A23, 359 (2006)], and accelerated by the forward-backward method with spectral acceleration. They highlight that there is very good agreement between the developed method and the reference numerical method for all scattering orders and that the method can be applied to root-mean-square (RMS) heights at least down to 0.25lambda.