Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack

A theoretical method is described for calculating the bidirectional scattering characteristic for any given thin-film multilayer geometry in which the surfaces and interfaces are assumed to be rough, and where statistical inhomogeneities in the optical permittivities may also exist in each layer. The light energy scattered in any direction depends on geometrical thickness, the permittivities of the ideal layer stack and also on the corresponding auto- and cross-correlation functions. The expressions that are obtained for the scattered field are completely general in the sense of the Born approximation of first order in the imperfections and the exciting fields. The contributions of interface and volume scattering can be assumed arbitrarily because both are derived in a unique way. The main new result consists in the occurrence of four different possibilities of coupling between the scattered and exciting waves due to the standing wave character of both light waves. It is easy to show that the case of a columnar structure reduces the theoretical effort and leads to a similarity of this volume case to that of normal interface scattering. The matrix formalism used in analogy to the normal calculations of reflection and transmission coefficients allows a simple physical interpretation of the light propagation through the layer system and straightforward numerical calculations.     

Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack

Abstract

A theoretical method is described for calculating the bidirectional scattering characteristic for any given thin-film multilayer geometry in which the surfaces and interfaces are assumed to be rough, and where statistical inhomogeneities in the optical permittivities may also exist in each layer. The light energy scattered in any direction depends on geometrical thickness, the permittivities of the ideal layer stack and also on the corresponding auto- and cross-correlation functions. The expressions that are obtained for the scattered field are completely general in the sense of the Born approximation of first order in the imperfections and the exciting fields. The contributions of interface and volume scattering can be assumed arbitrarily because both are derived in a unique way. The main new result consists in the occurrence of four different possibilities of coupling between the scattered and exciting waves due to the standing wave character of both light waves. It is easy to show that the case of a columnar structure reduces the theoretical effort and leads to a similarity of this volume case to that of normal interface scattering. The matrix formalism used in analogy to the normal calculations of reflection and transmission coefficients allows a simple physical interpretation of the light propagation through the layer system and straightforward numerical calculations.     

Scattering of sound waves by a turbulent wake

In this investigation, the Doppler shifted power spectrum of the scattering cross-section is obtained for plane acoustic waves scattered by fluid flow fluctuations appropriate to a turbulent wake. The wake considered in this paper is assumed almost homogeneous and isotropic and of low Reynolds number.It is shown that the evaluation of the Doppler scattering cross-section essentially reduces to the calculation of the wave number converted and frequency shifted energy spectrum function of the turbulent flow fluctuations. In prescribing the low Reynolds number turbulence spectrum, inertial forces are assumed negligible. Convective effects of the macro-eddies, which cause a Doppler shift in the scattered waves, are considered using a Lagrangian-type of space-time velocity correlation.After finding the spectrum of turbulent fluctuations, the Doppler shifted power spectrum of the scattering cross-section, which characterizes the scattered waves, is obtained explicitly for the far field approximation.     

Surface wave scattering by a nano-object situated on a surface

The scattering of the surface electromagnetic waves by a nano-defect (object) on a surface was calculated. The scattered field has been considered as a field caused by the current generated by the self-consistent local field inside the defect. In turn, the self-consistent local field has been determined as a result of solution of the integral Lippmann-Schwinger equation. The effective susceptibility of the object has been calculated using a self-consistent procedure. The corrections of self-energy part due to direct and indirect electromagnetic interactions, as well as due to interaction with surface wave field are taken into account. The self-energy part is calculated analytically within the framework of the near-field approximation. The scattering indicatrisses in reciprocal space have been computed for different shapes of the scatterer. Strong dependence of the scattered field on geometry of the scatterer has been found and explained.     

Temperaturabhängigkeit des Streuuntergrundes im Elektroneninterferenzdiagramm polykristalliner Silberschichten

The filtered and unfiltered intensities of electrons (30 to 50 kev) scattered in thin polycrystalline silver foils (300 to 1400 Å) were measured by means of a retarding field apparatus in the temperature range from 170 to 380 °K. Further the absorption coefficients due to the inelastic and the different elastic scattering processes were determined. It is shown, that the diffuse elastic scattering intensity increases with temperature for all values of thickness and electron energy. From the measured absorption coefficients the contributions of the different elastic scattering processes to the total background intensity are calculated. It turns out, that the main contribution is due to multiple scattering processes including both Bragg reflections and thermal diffuse scattering. Furthermore it is shown, that in contrary to the filtered diagram the background intensity of the unfiltered diagram increases with temperature only for larger scattering angles. In the small angle region a reversed temperature behaviour is observed. This effect is caused by that part of inelastically scattered electrons at low angles coming directly from the primary beam and from the low order diffraction rings.     

Physical optics theory for the scattering of waves by an impedance strip

The physical optics integral of the scattered waves by an impedance strip is derived by using the modified theory of physical optics. The surface currents of the physical optics integral, which was introduced for the scattered waves by an impedance half-plane, are taken into account. The uniform diffracted fields of the impedance strip are evaluated asymptotically. The second order diffraction terms are also obtained. The total scattered field and its subcomponents are plotted and the effect of the second order diffraction and strip width to the scattering is investigated numerically.     

Numerical and theoretical evaluations of AC losses for single and infinite numbers of superconductor strips with direct and alternating transport currents in external AC magnetic field

AC losses in a superconductor strip are numerically evaluated by means of a finite element method formulated with a current vector potential. The expressions of AC losses in an infinite slab that corresponds to a simple model of infinitely stacked strips are also derived theoretically. It is assumed that the voltage-current characteristics of the superconductors are represented by Bean’s critical state model. The typical operation pattern of a Superconducting Magnetic Energy Storage (SMES) coil with direct and alternating transport currents in an external AC magnetic field is taken into account as the electromagnetic environment for both the single strip and the infinite slab. By using the obtained results of AC losses, the influences of the transport currents on the total losses are discussed quantitatively.     

Interaction of electromagnetic waves with a magnetized nonuniform plasma slab

The absorption, reflection, and transmission of electromagnetic waves by a nonuniform plasma slab immersed in an ambient uniform magnetic field of various strengths are studied in this paper. The effects of the plasma parameters and magnetic field strength on the absorbed, reflected, and transmitted power are discussed. The magnetized nonuniform plasma slab is modeled by a series of magnetized uniform plasma subslabs. The calculation results show that the effects of the magnetic field strength and density gradient on the absorbed power, as well as the frequency band of resonant absorption, are significant. A complete analysis utilizing the scattering matrix method is also used to compare the above calculation results which neglect multiple reflections between subslab interfaces. Broadband absorption of electromagnetic waves can be achieved by changing the magnetic field strength and plasma density. More than 90% of the electromagnetic wave power can be absorbed in a magnetized nonuniform plasma slab with width of 12 cm and the absorption bandwidth can range from 1 to 20 GHz with different plasma parameters and external magnetic field strengths.     

Radiation modes of a five-layer symmetric slab waveguide

The radiation modes of a five-layered symmetric slab waveguide are treated in detail. Since the slab is assumed to be infinitely extended in the yz plane, all field quantities are considered to be independent of y. The analysis is based on modal expansion formulation and the modes can be classified as TE and TM as well as even and odd ones. Applying the boundary conditions at interfaces, the expansion coefficients of the field components are easily calculated. In addition, the normalization factors and the orthogonality properties are determined by deriving appropriate integrals over the cross section of the waveguide. Finally, the validity of the orthogonality relations between the radiation modes and the guided ones, which propagate in such a waveguide, is proved explicitly.     

Wave diffraction by a concave statistically rough surface

We consider a statistically rough impedance surface that is concave on average in contrast to a plane. Backscattering from such a surface is considered based on the small perturbation theory method. The diffraction problem is divided into two parts which are considered separately: the problem of scattering by small roughness (assumed to be local) and the propagation of incident and scattered fields over a smooth large-scale concave surface. In contrast to the 'two-scale' scattering model, the zero-order unperturbed wavefield is not assumed to be specularly reflected from the local tangent plane to the smooth surface, but it is a solution of a corresponding diffraction problem. Two particular cases of smooth surfaces are considered: first, the inner surface of a concave cylinder with a constant radius and finite angular pattern, and second, a compound surface that consists of a coupled half-plane and the cylindrical surface mentioned above. In a geometrical optics limit and with propagation at low grazing angles, the analytical results for a zero-order (unperturbed) field are obtained for these two cases in the form of a series over multiple specular reflected fields. It is shown that these non-local processes lead to the essential increase in the backscattering cross section in comparison with the two-scale model and tangent-plane approach.     

SCATTERING AND RADIATION CHARACTERISTICS OF STEP DISCONTINUITY IN LEFT-HANDED SLAB WAVEGUIDE OPERATING IN EVANESCENT SURFACE MODE

The scattering and radiation characteristics of a step discontinuity in left-handed (LH) slab waveguide operating in evanescent surface mode of TE and TM polarization are analyzed by a method, which combines the rigorous mode-matching method with the multi-mode network theory. In the analysis the radiation problem is transformed into a propagation problem so as to tremendously simplify the calculation procedure. The dispersion properties of the grounded planar LH slab waveguide for both ordinary and evanescent surface modes are examined, from which the left-hand property of the operating mode is testified. The relative scattered power and radiation pattern of the step are given for the first time, from which the backward radiation of the stepped LH guide is clearly demonstrated. The frequency scanning characteristics of the step under consideration in this paper are just opposite to that of the ordinary antenna, which makes the considered structure promising candidate for new type of planar antennas. Supported by the National Natural Science Foundation of China (No.60371010, No.60471037, No. 63531020)     

A pseudopotential based theory of the driving forces for electromigration in metals

We present a pseudopotential calculation of the driving forces for atomic migration in metals in the presence of electron currents. When electrons are scattered by impurities in a metal, we find that a force is generally exerted on each atom in the vicinity of the scattering center. Because the scattering is predominantly elastic, it is possible to express this force field as the classical electrostatic force arising from the total electronic charge, as has been assumed by Friedel and Bosvieux. The electron charge density is determined from a pseudopotential calculation, and the resulting force is expressed as a sum of effective interactions between the diffusing atom and all crystal defects.The forces on an atom arising from the electron scattering and from the applied electric field together comprise the driving force which causes a net current of atoms. The driving forces are calculated for intestitial and vacancy migration in several metals, and the results are found to compare favorably with most experimental data.     

二维随机粗糙面上导体目标复合瞬态散射的混合算法

提出用时域积分方程法(TDIE)与时域基尔霍夫近似法(TDKA)的混合算法来求解二维导体随机粗糙面及其上方二维导体目标的复合瞬态散射,推导出了在TM波入射情形下显式及隐式格式的时间步进方程.将粗糙面与目标分别进行TDKA和TDIE计算,并考虑目标与粗糙面之间的耦合,对TDKA和TDIE进行混合迭代,既大大降低了粗糙面求解的复杂度,又保证了计算精度.数值算例中,考虑了角反射器(开放体)和圆柱(封闭体)两种目标,分别计算了目标表面电流响应和电场远场响应.计算结果表明,和单纯TDIE法相比,本文混合方法计算效率 关键词： 随机粗糙面 复合瞬态散射 时域积分方程法和时域基尔霍夫近似法 混合算法     

多层光学薄膜矢量散射的理论与实验研究

本文提出一种用以计算多层光学薄膜的矢量散射波场分布的新方法。并应用统计学原理,详细讨论了不同膜层界面的互相关模型及相应的光学薄膜散射特性。推导中应用了薄膜光学的惯用概念,所得公式亦比较简洁。还实验测量了光学薄膜的散射波场分布,并根据所建立的模型确定了所测光学薄膜的界面互相关特性。 关键词：     

Laser removal of mold growth from paper

Femtosecond laser nano-processing by enhanced light scattered from nanospheres has received much attention. Enhanced scattered near field enables us to ablate nanoholes at nanometer scales below the diffraction limit. In addition, the interference between the scattered far field and the irradiated laser enables us to fabricate spatially controlled periodic surface structures. In this paper, we simulated the time evolution of scattered near field and far field during the free electron excitation in silicon (Si) by femtosecond laser irradiation. The optical property of Si changes from dielectric to metal-like Si due to the increase of the free electron number density excited by femtosecond laser pulse. It is elucidated that the scattered field of Si shifts from Mie scattering to plasmonic scattering during laser irradiation. We achieved the optimal free electron density and laser intensity for precisely controlled periodic surface structures fabrication. We explained the temporal behavior of the scattering near field and far field from the standpoint of dielectric function of the materials.     

Wave diffraction by a concave statistically rough surface

Abstract

We consider a statistically rough impedance surface that is concave on average in contrast to a plane. Backscattering from such a surface is considered based on the small perturbation theory method. The diffraction problem is divided into two parts which are considered separately: the problem of scattering by small roughness (assumed to be local) and the propagation of incident and scattered fields over a smooth large-scale concave surface. In contrast to the ‘two-scale’ scattering model, the zero-order unperturbed wavefield is not assumed to be specularly reflected from the local tangent plane to the smooth surface, but it is a solution of a corresponding diffraction problem. Two particular cases of smooth surfaces are considered: first, the inner surface of a concave cylinder with a constant radius and finite angular pattern, and second, a compound surface that consists of a coupled half-plane and the cylindrical surface mentioned above. In a geometrical optics limit and with propagation at low grazing angles, the analytical results for a zero-order (unperturbed) field are obtained for these two cases in the form of a series over multiple specular reflected fields. It is shown that these non-local processes lead to the essential increase in the backscattering cross section in comparison with the two-scale model and tangent-plane approach.     

Extremely asymmetrical scattering of slab modes in periodic Bragg arrays

The steady-state extremely asymmetrical scattering of electromagnetic modes in a slab with a periodically corrugated boundary is analyzed theoretically. A new approach, based on allowance for the diffractional divergence of a scattered wave, is used with the approximation of slowly varying amplitudes and a Fourier analysis. The structure of the incident and scattered waves inside and outside the array is determined. The amplitudes of the scattered waves are found to be much larger than the amplitude of the incident wave. The typical time of relaxation to steady-state scattering is found to depend on the distance from the array boundary through which the incident wave enters the array. Conditions of applicability of the results obtained are also presented.     

Phonon scattering at siliconcrystal surfaces

Our observations of the reflection or backscattering of high-frequency phonons (v =280 GHz to 1 THz) at silicon-solid interfaces disagree significantly with predictions from the acoustic mismatch model. Interfaces composed of materials theoretically wellmatched, show high scattering experimentally. In contrast, interfaces theoretically poorly matched, show less phonon scattering than expected. Generally, this is best expressed by the fact that the interface scattering ranges from roughly 30–60% for different phonon modes with little dependence on the material covering the silicon crystal and different techniques of interface preparations. Thus, our experiments indicate that the well-known Kapitza anomaly of the phonon scattering at solid-liquid helium interfaces is not a special case; the same anomaly appears to be present at all tested interfaces. Our experiments are compared with detailed calculations which either assume pure specular or pure diffusive scattering. In these calculations the influence of the crystal anisotropy for the phonon propagation (phonon focussing) is included. This comparison shows, especially for the free silicon surface, that phonons are completely diffuse scattered. Hence, the acoustic mismatched model relying on specular reflection cannot be applied to the real silicon interface. The frequency dependence of phonon scattering at a free silicon interface indicates the existence of at least two different diffusive scattering mechanisms. Within our experimental limits in these two scattering processes the phonons are elastically scattered.     

Electromagnetic scattering from a two dimensional perfect electromagnetic conductor (PEMC) strip and PEMC strip grating simulated by circular cylinders

Electromagnetic scattering of an incident plane wave from a rectangular strip and strip grating, are presented semi-analytically. The strip and strip grating are simulated by joining parallel perfect electromagnetic conductor (PEMC) circular cylinders and are illuminated by a TM_z incident plane wave. The PEMC medium does not allow electromagnetic energy to enter. An interface of this medium serves as an ideal boundary to the electromagnetic field. The solution is based on the application of the boundary conditions on the surface of each cylinder in terms of its local coordinate system. The technique is used to predict the scattered field pattern of PEMC strip and PEMC strip grating.     

Evaluation of light scattering in attenuated total reflection configuration

A theoretical investigation of light scattering in first-order Born approximation in order to analyse the different scattering sources is presented for the case of the so-called Kretschmann attenuated total reflection (ATR) configuration. This three-layer system consists of a high permittivity superstrate acting as a prism, a thin metallic layer and air as substrate. The interesting aspect of this system is the occurrence of a resonance for both the exciting and the scattered light caused by surface plasmon polaritons (SPPs) at the metal-air interface. The scattered light will be calculated under the assumption of different illumination and detection conditions. The scattering contributions are assumed to be caused by the roughness of both interfaces and the volume inhomogeneities in the metallic layer. The calculated curves show the principal possibility of analysing the different scattering sources by an appropriate experimental strategy.