X-ray scattering from a randomly rough surface

Abstract

On the basis of the method of reduced Rayleigh equations we present a simple and reciprocal theory of the coherent and incoherent scattering of x-rays from one- and two-dimensional randomly rough surfaces, that appears to be free from the limitations of earlier theories of such scattering based on the Born and distorted-wave Born approximations. In our approach, the reduced Rayleigh equation for the scattering amplitude(s) is solved perturbatively, with the small parameter of the theory η(ω) = 1 - ε(ω), where ε(ω) is the dielectric function of the scattering medium. The magnitude of η(ω) for x-rays is in the range from 10^?6 to 10^?3, depending on the wavelength of the x-rays. The contributions to the mean differential reflection coefficient from the coherent and incoherent components of the scattered x-rays are calculated through terms of second order in η(ω). The resulting expressions are valid to all orders in the surface profile function. The results for the incoherent scattering display a Yoneda peak when the scattering angle equals the critical angle for total internal reflection from the vacuum-scattering medium interface for a fixed angle of incidence, and when the angle of incidence equals the critical angle for total internal reflection for a fixed scattering angle. The approach used here may also be useful in theoretical studies of the scattering of electromagnetic waves from randomly rough dielectric-dielectric interfaces, when the difference between the dielectric constants on the two sides of the interface is small.     

Multiple light scattering from metal and dielectric rough surfaces

Abstract

A numerical study is done on light scattering from one-dimensional random rough surfaces supporting both dielectrics and metals. The influence of the corrugation on the Brewster angle as well as on the angular distribution of transmitted intensity into the dielectric is investigated. The authors also obtain enhanced backscattering in the light reflected from metallic surfaces. Finally they discuss the influence of roughness on the drop of reflectance due to polariton absorption.     

Brewster angle for anisotropic materials from the extinction theorem

We explore the physical origin of the Brewster angle in the external and internal reflections associated with an anisotropic material. We obtain the expressions of the reflected fields and the existence condition of the Brewster angle by using the extinction theorem. It is found that the Brewster angle will occur if the total contribution of the material’s electric and magnetic dipoles to the reflected field becomes zero. In internal reflection, the requirements on the material parameters ε and μ for the Brewster angle are the same as those in external reflection, and the Brewster angle is just the refraction angle in external reflection at the incidence of the external Brewster angle. The results of the present paper are applicable to dielectric and magnetic materials, including metamaterials. PACS 73.20.Mf; 78.20.Ci; 41.20.Jb; 42.25.Fx     

Directional hemispherical radiative properties of random dielectric rough surfaces

In this paper the directional hemispherical reflectivity and transmissivity of one-dimensional, randomly rough, dielectric surfaces are determined by the use of the integral method. This method is derived from electromagnetic theory without any restrictive hypotheses. Since this exact approach is computationally very intensive, a geometric optics approximation method is also developed. Curves displaying radiative properties versus the correlation length for a constant mean square deviation of the surface from flatness are presented. In this respect, the influence on the validity of the approximate method of multiple scattering, the shadowing effect and the real index of refraction of the dielectric have been investigated. Transverse electric and transverse magnetic polarized incident plane waves are considered. For the latter, our interest is focused on the influence of roughness on the reflected and transmitted intensities for an angle of incidence close to the Brewster angle.     

On a Mathematical Framework for the Constitutive Equations of Anisotropic Dielectric Relaxation

Three classes of time-domain non-relativistic anisotropic dielectric constitutive equations of increasing generality are discussed. In each class dissipativity is ensured by the choice of a class of convolution kernels in the D-to-E constitutive equation expressing the electric field E in terms of the electric displacement field D. Defining properties of the inverse (E-to-D) kernels and their Fourier-Laplace transforms (complex dielectric functions) are determined by inversion of the D-to-E constitutive equation. By this procedure it is shown that dielectric functions of the dipolar dielectrics are tensor-valued Bernstein functions while the dielectric functions of the Drude-Lorentz type are tensor-valued negative definite functions. The properties of the complex dielectric permittivities are also determined for either class. The theory is applied to an exhaustive review of empirical response functions of real dielectric materials encountered in the literature. Each class of convolution kernels is consistent with existence of a conserved energy, but in one case a strictly dissipative energy can be constructed.     

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)     

Dielectric linear response of magnetized electrons: Drag force on ions

The drag force on ions moving in a magnetized electron plasma is calculated in dielectric linear response. Various representations of the dielectric function ε(k, ω) are investigated for their suitability to display the limits for an infinite and a vanishing magnetic field. While the influence of the magnetic field is negligible in certain regions of k-space, it introduces in other regions a strong oscillatory structure in the dielectric function. This requires a careful treatment of the multidimensional integrations necessary for the drag force. The contributions from oscillatory integrands are treated by the saddle point method. Explicit results are obtained for the dependence of the drag force on the magnetic field, the direction of motion of the ion relative to the magnetic field, the shielding in the electron plasma, its density and the anisotropy of the electron temperature. The importance of the collective response of the electrons is investigated for limiting cases of the magnetic field. The validity of the linearization of the dielectric theory is checked by comparison with results obtained by numerical simulation of the nonlinear Vlasov-Poisson equation. For strong magnetic fields and low ion velocities, the simulations rather agree with the complementary binary collision model than with linear response.     

Gaussian beam scattering from arbitrarily shaped objects with rough surfaces

Abstract

The scattered field of Gaussian beam scattering from arbitrarily shaped dielectric objects with rough surfaces is investigated for optical and infrared frequencies by using the plane wave spectrum method and the Kirchhoff approximation, and the formulae for the coherent and incoherent scattering cross sections are obtained theoretically based on geometrical optics and tangent plane approximations. The infrared laser scattering cross sections of a rough sphere are calculated at 1.06 μm, and the influence of the beam size is analysed numerically. It is shown that when the beam size is much larger than the size of the object, the results in this paper will be close to those of an incident plane wave.     

Current density distribution along conducting sheath helix encapsulated silver metal cylinder coated with dielectric material under L-nihility and upon oblique incidence

Abstract

This communication is aimed at investigating the electromagnetic (EM) characteristics of silver metal cylinder coated with homogeneous dielectric material, which is loaded with tightly wound perfectly electrical conducting sheath helix (outside of the dielectric layer) structure of different angles of orientation. Considering the L-nihility kind of behavior of silver metal at a particular frequency, the current density distributions are discussed corresponding to the parallel polarization (transverse magnetic) of the incident EM wave. The investigations are made taking into account the different values of oblique incidence, and also, the orientation angle of sheath helix structure. It is found that the current density, and hence the scattering of radiation, greatly depends on these parameters, and its magnitude increases with the increase in helix pitch as well as the angle of incidence.     

Capillary oscillations and stability of a charged, viscous drop in a viscous dielectric medium

The scalarization method is used to obtain a dispersion relation for capillary oscillations of a charged, conducting drop in a viscous, dielectric medium. It is found that the instability growth rate of the charged interface depends substantially on the viscosity and density of the surrounding medium, dropping rapidly as they are increased. In the subcritical regime the influence of the viscosity and density of both media leads to a nonmonotonic dependence of the damping rate of the capillary motions of the liquid on the viscosity or density of the external medium for a fixed value of the viscosity or density of the internal medium. The falloff of the frequencies of the capillary motions with growth of the viscosity or density of the external medium is monotonic in this case. Zh. Tekh. Fiz. 68, 1–8 (September 1998)     

SO-FDTD Analysis on Magnetized Plasma

In this paper, a novel finite-difference time-domain (FDTD) method with recursive relationships among operators is developed for magnetized dispersive medium, named as the shift operator FDTD(SO-FDTD). The dielectric property of magnetized dispersive medium is written as rational polynomial function, the relationship between D and E is deduced in time-domain. And its high accuracy and efficiency are verified by calculating the reflection and transmission coefficients of electromagnetic waves through a collision plasma slab.     

Scattering of waves from nonlinear media with rough surfaces

Abstract

Reflection and scattering of waves from plane and statistically rough interfaces between nonlinear media are studied theoretically. New hysteresis-type dependences of the reflection and transmission coefficients on the amplitude of the incident wave and on the angle of incidence are predicted. Scattering diagrams for diffusely reflected and transmitted fields are calculated. It is found that when the dielectric constant is a steep function of the incident amplitude, nonlinearity suppresses the Bragg resonant scattering mechanism. Smooth roughness of the boundary is shown to enhance the penetration of evanescent waves into nonlinear media.     

Theory of absorption of electromagnetic radiation by highly inhomogeneous two-component systems

Calculations are made of the permittivity of a composite formed by a mixture of a dielectric matrix and macroscopic magnetic inclusions. It is shown that the dielectric loss tangent in this material is a complex function of their concentration x, and this function is determined. The dependence of the absorption maximum on x is determined and it is shown that the maximum is only observed in the presence of foreign inclusions. Conditions for the existence of an absorption maximum are obtained for the two most interesting physical cases. A method of calculating the components of the depolarization tensor is proposed for a thin-film composite. Zh. Tekh. Fiz. 69, 89–94 (July 1999)     

FDTD analysis on the effect of plasma parameters on the reflection coefficient of the electromagnetic wave

In this paper, the dielectric constant of dispersive medium is written as rational polynomial function, and the relationship between D and E is derived in time-domain. It is named shift operator FDTD (SO-FDTD) method. Compared to the analytical solution, the high accuracy and efficiency of this method is verified by calculating the reflection coefficient of the electromagnetic wave through a cold plasma slab. The effect on reflection coefficient is calculated by using the SO-FDTD method. The result shows that some factors effect on reflection coefficient. They are as follows: plasma thickness, electron density, electron distribution and incident frequency. And on most conditions, parabola distribution helps reduce reflection coefficient more effectively than homogeneous distribution.     

Studies on the Dielectric Behavior of Silica-Filled Butyl Rubber Vulcanizates After Cyclic Deformation

Abstract

The broadband dielectric spectroscopy (10^?3–10⁶ Hz) is used to study the effect of stress-strain cycles on the dielectric properties of butyl rubber vulcanizates filled with silica. The influence of chemical modification of the surface of the silica by silane coupling agent (Si69) also was investigated. In addition Transmission Electron Microscopy (TEM) and Differential Scanning Calorimetry (DSC) were carried out. Dielectric investigations of the samples were done after stress-strain cycles with maximum elongation 26%, 40%, 60%, and 80% from elongation at break, respectively. It was found that the dielectric properties recovered after storage at room temperature for about one year.     

Dielectric properties of a wide-temperature ferroelectric phase in a fluorinated compound

ABSTRACT

A broad-frequency dielectric spectroscopy (100 Hz to 10 MHz) was used to investigate newly synthesized fluorinated compound. This compound exhibits a wide-temperature ferroelectric phase. Due to the fact that the compound does not crystallize at temperatures available in our DSC equipment, additional measurements were done at the very low temperatures (down to ?100 °C) to find the crystallization temperature. Finally, we did not manage to crystallize the investigated compound. Compound under studies seems to be overcooled. Observed dielectric modes are described and their parameters are shown in this paper. Additionally, DC field influence on dielectric response is shown and analyzed here. Both modes observed at the low temperature are recognized as the molecular ones.     

A numerical evaluation of Rayleigh's theory applied to scattering by randomly rough dielectric surfaces

Abstract

We present a numerical simulation of scattering by one-dimensional randomly rough surfaces. It is based on the use of plane-wave expansions to describe the Melds on the surface (i.e. Rayleigh hypothesis). Accuracy and convergence properties of two different numerical implementations are studied. Some examples of results for a dielectric and a metallic Gaussian rough surface are shown to be in good agreement with calculations by a rigorous numerical method. The Rayleigh method appears to be a fast computation tool for dielectric surfaces with slopes of less than 0.2.     

Scattering of an electromagnetic wave from a slightly random dielectric surface: Yoneda peak and Brewster angle in incoherent scattering

Abstract

The scattering of an electromagnetic wave from a two-dimensional, slightly rough dielectric surface is studied based on the stochastic functional approach. It is shown that in the case of TM(p)-polarized incidence there exists a zero in the incoherent scattering at the angle we call the ‘Brewster scattering angle’, which depends on the incident angle in contrast to the Brewster angle of coherent reflection which is independent of the incident angle, that a ‘quasi-anomalous scattering’ can generally occur in the optically denser medium at the critical angle of total reflection in both TE(s)- and TM(p)-polarized incidence, regardless of which side of the random surface is illuminated, and that the Yoneda peak in the x-ray scattering can be interpreted as a special case of the quasi-anomalous scattering which becomes sharper when the relative refractive index becomes closer to unity as in the x-ray region. Cross-polarized scattering and enhanced backscattering due to the second-order effect are also calculated.     

Investigating low-frequency dielectric properties of a composite using the distribution of relaxation times technique

The distribution of relaxation times approach, a less frequently employed dielectric data analysis technique, is utilized to better understand the relaxation characteristics of composites consisting of metal-coated, hollow glass spheres dispersed in a paraffin wax matrix. The dielectric properties of the composite samples are measured by means of impedance spectroscopy in the frequency range 0.1?mHz to 10?MHz. The application of a mixture law is not appropriate for the analysis of the frequency-dependent properties of the considered system on this broad frequency range. However, utilization of the distribution of relaxation times procedure to study the dielectric behaviour shows clear trends in the mixtures’ relaxation spectra. Relaxation processes of the paraffin wax and those specific to the composites are found from the extracted distribution of relaxation times spectra. The influence of the filler concentration, q, on the dielectric properties is examined; a relaxation with a narrow distribution at intermediate frequencies becomes broad with the addition of the filler. This relaxation, in the form of the low-frequency-dispersions (also known as constant phase angle) phenomenon, dominates the dielectric properties of the composites with high bead concentration, q>0.15. The variation in dielectric properties of individual samples whose bead concentrations q are nominally the same is discussed in terms of possible microstructural variations.     

A comparative study of the effective dielectric constant of a medium containing randomly distributed dielectric spheres embedded in a homogeneous background medium

Abstract

The effective dielectric constant ∈_eff of a medium containing randomly distributed dielectric particles has been analysed by conventional methods: Foldy's approximation, the quasi-crystalline approximation (QCA) and the QCA with coherent potential. These conventional methods, however, have been indicated to become invalid for particles with a high dielectric constant; we have thus presented a new method that is valid for them. This paper compares ∈_eff of our method with those of the conventional methods by changing the volume fraction and the dielectric constant of spheres. As a result, our method is shown to be more powerful for the analysis of ∈_eff than the conventional methods.