Scattering mechanism in doped semiconductors with a smooth random field

The scattering mechanism of charge carriers in doped compensated semiconductors with a smooth random field is considered in the interval of temperatures 4–100°K and of impurity concentrations 10¹⁴–10¹⁸ cm^–3. It is shown that in the conditions mentioned above at the lowest temperatures scattering in the Coulomb field associated with charged impurity dominates, while at elevated temperatures scattering in the smooth random field is important. Scattering by phonons and by resonant and virtual levels associated with the random potential is insignificant in the present conditions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 23–27, February, 1984.     

Scattering of an electromagnetic wave from a slightly random cylindrical surface: horizontal polarization

Abstract

The scattering of an electromagnetic wave from a random cylindrical surface ir studied for a plane-wave incidence with S-(TE) polarization, by means ofthe stochastic scattering theory developed by Nakayama, Ogura. Sakati et al. The theory is based on the Wiener-Ito stochastic functional calculus combined with the group-theoretic consideration concerning the homogeneity of the random surface. The random surface is assumed to be a homogeneous Gaussian random field on the cylinder C, homogeneous with respect to the group of motiolrs on C: translations along the axis and rotations around the axis. An operator D operating on a random field on C is introduced in such a way that D keeps the homogeneous random surface invariant This gives a reprerentation of the cylbdrical group and commutes with the boundary condition and the Maxwell equation. Thus, for an injection of the mth cylindrical TE or TM wave, which is a vector eigenfunction of the D operator, the scattered random wave field is an eigenfunctiou with the same eigenvalue: it satisfies the Maxwell equation and is a stoch-tic Iunctional of the Gaussian random surface, BO that it can be expressed in a vector form of the Wiener-Ito expansion in t e m of TE and TM waves and orthogonal functional. of the Gaussian random measures associated with the random cylindrical surface. In the analysis the random surface is modelled by an approximate boundaiy condition representing a perfectly conducting cylindrical surface with a slight roughness. The boundary condition on the random cylinder is transformed into a hierarchy of equations for the Wiener kernels which can be solved approximately. The random wave field for a plane-wave injection is obtained by summing these fields over m. From the stochastic representation of the electromagnetic field so obtained, various statistical characteristics can be calculated the coherent scattering amplitude. total coherent power flow, incoherent power flow, differential sections for coherent rcatlerhig and incoherent scattering, etc. The power conservation law is cast into a stochastic electromagnetic version of the optical theorem stating that the total scatteiing cross section is given by the imaginary part of the forward coherent scattering amplitude. Numerical calculations are made for a planewave injection with S-(TE) polarization. The case of p-(TM) polarization can be treated in a similar manner.     

A scale model investigation of sound reflection from building façades

A simple model for predicting the sound reflected from a building façade is developed based upon the assumption that the scattering coefficient is small. This model is then used as the basis of an experimental attempt to measure the scattering properties of scale model façades featuring a similar degree of surface irregularity to that found on real buildings. A series of measurements made on a simple scale model are described and the effect of a non-uniform distribution of façade scattering is examined. The measured value of the scattering coefficient is found to be small and not very sensitive to the degree of surface irregularity. A progression of energy from a specular reflection field to a diffuse reflection field for successive orders of reflections is observed. It is suggested that the dominant mechanism of sound propagation for higher order reflections is via random scattering and that the development of propagation models based upon purely random scattering is a valid approach.     

Scattering of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces – study with the curvilinear coordinate method

We present a method giving the bi-static scattering coefficient of two-dimensional (2-D) perfectly conducting random rough surface illuminated by a plane wave. The theory is based on Maxwell's equations written in a nonorthogonal coordinate system. This method leads to an eigenvalue system. The scattered field is expanded as a linear combination of eigensolutions satisfying the outgoing wave condition. The boundary conditions allow the scattering amplitudes to be determined. The Monte Carlo technique is applied and the bi-static scattering coefficient is estimated by averaging the scattering amplitudes over several realizations. The random surface is represented by a Gaussian stochastic process. Results are compared to published numerical and experimental data. Comparisons are conclusive.     

Scattering of an electromagnetic wave from a slightly random cylindrical surface: horizontal polarization

The scattering of an electromagnetic wave from a random cylindrical surface ir studied for a plane-wave incidence with S-(TE) polarization, by means ofthe stochastic scattering theory developed by Nakayama, Ogura. Sakati et al. The theory is based on the Wiener-Ito stochastic functional calculus combined with the group-theoretic consideration concerning the homogeneity of the random surface. The random surface is assumed to be a homogeneous Gaussian random field on the cylinder C, homogeneous with respect to the group of motiolrs on C: translations along the axis and rotations around the axis. An operator D operating on a random field on C is introduced in such a way that D keeps the homogeneous random surface invariant This gives a reprerentation of the cylbdrical group and commutes with the boundary condition and the Maxwell equation. Thus, for an injection of the mth cylindrical TE or TM wave, which is a vector eigenfunction of the D operator, the scattered random wave field is an eigenfunctiou with the same eigenvalue: it satisfies the Maxwell equation and is a stoch-tic Iunctional of the Gaussian random surface, BO that it can be expressed in a vector form of the Wiener-Ito expansion in t e m of TE and TM waves and orthogonal functional. of the Gaussian random measures associated with the random cylindrical surface. In the analysis the random surface is modelled by an approximate boundaiy condition representing a perfectly conducting cylindrical surface with a slight roughness. The boundary condition on the random cylinder is transformed into a hierarchy of equations for the Wiener kernels which can be solved approximately. The random wave field for a plane-wave injection is obtained by summing these fields over m. From the stochastic representation of the electromagnetic field so obtained, various statistical characteristics can be calculated the coherent scattering amplitude. total coherent power flow, incoherent power flow, differential sections for coherent rcatlerhig and incoherent scattering, etc. The power conservation law is cast into a stochastic electromagnetic version of the optical theorem stating that the total scatteiing cross section is given by the imaginary part of the forward coherent scattering amplitude. Numerical calculations are made for a planewave injection with S-(TE) polarization. The case of p-(TM) polarization can be treated in a similar manner.     

Electromagnetic wave scattering from a random medium layer with a random interface

Abstract

The problem of electromagnetic wave scattering from a random medium layer with a random interface is considered. The layer has planar boundaries on average. Assuming that both the random perturbations of the interface and the random fluctuations of permittivity of the medium are small, a first-order perturbation solution to the scattered field is obtained. Using this solution, the bistatic scattering coefficients γ_αβ are calculated and expressed in a compact and meaningful form. The various terms that constitute γ_αβ are identified with distinct scattering processes. Since it is often of particular interest, the special case of backscattering is considered. Finally, the results are compared with those of others.     

Non-circular gaussian speckle contrast in the exact theory of multiple scattering of waves from random rough surfaces

In this paper the expression for the speckle contrast, under the assumption of non-circular gaussian statistics of the scattered field, is derived by using the exact scattering theory of waves by random rough surfaces previously established by the authors. This implies to find the second order moment 〈A²〈 of the scattering amplitude. It is shown that this zero outside the specular direction for large correlation distances of the random heights of the surface. as such, it coincides with the value obtained from the Kirchhoff approximation of Beckmann's theory and contributes to support the use of Beckmann's theory for measurements of speckle contrast in the specular direction, even when multiple scattering takes place.     

Scalar plane wave scattering from a thin film with two-dimensional fluctuation

This paper deals with a scalar plane wave scattering from a thin film with two-dimensional fluctuation by means of the stochastic functional approach. The refractive index of the thin film is written as a Gaussian random field in the transverse directions with infinite extent, and is invariant in the longitudinal direction with finite thickness. An explicit form of the random wavefield involving effects of multiple scattering is obtained in terms of a Wiener-Hermite expansion under small fluctuation. The first- and second-order incoherent scattering cross-sections are calculated numerically and illustrated in figures. In the incoherent scattering, scattering ring, quasi-anomalous scattering, enhanced scattering and gentle enhanced scattering may occur.     

Electromagnetic wave scattering by large-scale inhomogeneities in a bragg cavity

We study the single scattering of a plane electromagnetic wave by random inhomogeneities in a plane periodically nonuniform layer with a reflecting rear boundary. It is shown that when the incident wave satisfies the condition of excitation of the fundamental Bragg cavity mode and its field is large in the layer depth, the average angular spectrum of the backscattered wave field at the cavity output has a narrow maximum proportional to the exponent of the quadruple optical thickness of the periodic structure. This maximum corresponds to the condition of excitation of the fundamental Bragg cavity mode by the scattered field. The other spectral maxima have small amplitudes and intensities. Such scattering takes place if the characteristic size of random inhomogeneities in the direction perpendicular to the layer boundary exceeds the scale of multiple scattering on a periodic structure. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 11, pp. 1342–1354, November, 1997.     

Scalar plane wave scattering from a thin film with two-dimensional fluctuation∗∗

This paper deals with a scalar plane wave scattering from a thin film with two-dimensional fluctuation by means of the stochastic functional approach. The refractive index of the thin film is written as a Gaussian random field in the transverse directions with infinite extent, and is invariant in the longitudinal direction with finite thickness. An explicit form of the random wavefield involving effects of multiple scattering is obtained in terms of a Wiener–Hermite expansion under small fluctuation. The first- and second-order incoherent scattering cross-sections are calculated numerically and illustrated in figures. In the incoherent scattering, scattering ring, quasi-anomalous scattering, enhanced scattering and gentle enhanced scattering may occur.     

Spectral Changes of Light Produced by Multiple Scattering from Space-Time Fluctuating Random Media under the Born Approximation

Changes in the spectrum of light scattered by space-time fluctuating random media are investigated theoretically within the accuracy of the second-order Born approximation, as a continuation of the previous paper [Opt. Commun. 123 (1996) 234]. Effects of multiple scattering on the resultant field are manifested by a number of illustrative examples. It is shown, in particular, that the spectrum of the scattered light to be observed under practical circumstances is distorted by the process of multiple scattering. Comparison between spectra of both single and multiple scattering lights is also presented in the framework of the dynamic scattering.     

Polarization characteristics of an electromagnetic wave scattered from a slightly random surface: +45° polarized incidence

Abstract

The present paper deals with the scattering of an obliquely polarized electromagnetic (EM) wave from a slightly rough surface, which is assumed to be a two-dimensional (2D), homogeneous and isotropic Gaussian random field. In contrast to the cases of TE(s) and TM(p) polarized incidence, the scattering profile for an obliquely polarized incidence is not symmetric with respect to the incident plane, despite the fact that the random surface is statistically isotropic.     

Wave scattering from a random rough surface: reciprocal theorem and backscattering enhancement

The present paper gives a more complete treatment of the scattering from a two-dimensional random surface than previous works. Reciprocal theorems for the stochastic wave field and the incoherent scattering distribution (bistatic cross section) are derived and the presence of backscattering enhancement in the case of a slightly random Neumann surface is demonstrated. A physical interpretation of the backscattering enhancement associated with the presence of anomalous scattering on a slightly random Neumann surface is given. Some numerical calculations are performed to show the incoherent scattering distribution and the backscattering enhancement.     

Scattering of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces - study with the curvilinear coordinate method

We present a method giving the bi-static scattering coefficient of two-dimensional (2-D) perfectly conducting random rough surface illuminated by a plane wave. The theory is based on Maxwell's equations written in a nonorthogonal coordinate system. This method leads to an eigenvalue system. The scattered field is expanded as a linear combination of eigensolutions satisfying the outgoing wave condition. The boundary conditions allow the scattering amplitudes to be determined. The Monte Carlo technique is applied and the bi-static scattering coefficient is estimated by averaging the scattering amplitudes over several realizations. The random surface is represented by a Gaussian stochastic process. Results are compared to published numerical and experimental data. Comparisons are conclusive.     

Exciton optics of a disordered semiconductor

Interband light absorption in a disordered semiconductor is considered with due allowance for exciton effects. Allowance is made for the scattering of the electron and hole in a weak static random field and also for collisions of the second kind experienced by the exciton on interaction with a random field. It is shown that the contribution of these latter to the half width of the absorption line of the exciton spectrum (even at temperatures of the order of the exciton ionization energy) is considerably smaller than the contribution arising from the scattering of the particles forming the exciton.     

Scattering from Alpha-Stable Non-Gaussian Distributed Surfaces

The scattering problem of alpha-stable non-Gaussian distributed rough surfaces is studied. The alpha-stable non-Gaussian distribution is used to describe the surfaces that exhibit sharp and sparse peaks, not usually seen in Gaussian distributed surfaces. Then a magnetic field integral equation is formulated to calculate the scattered field and the scattering coefficient. Numerical simulations show that the magnitude distribution of the scattered field is affected significantly by the probability distribution of the surface when the height of the surface changes in a random way. In addition, simulation results are presented as bistatic scattering coefficient for alpha-stable distributed surfaces.     

Diffusion of charged particles in strong large-scale random and regular magnetic fields

The nonlinear collision integral for the Green’s function averaged over a random magnetic field is transformed using an iteration procedure taking account of the strong random scattering of particles on the correlation length of the random magnetic field. Under this transformation the regular magnetic field is assumed to be uniform at distances of the order of the correlation length. The single-particle Green’s functions of the scattered particles in the presence of a regular magnetic field are investigated. The transport coefficients are calculated taking account of the broadening of the cyclotron and Cherenkov resonances as a result of strong random scattering. The mean-free path lengths parallel and perpendicular to the regular magnetic field are found for a power-law spectrum of the random field. The analytical results obtained are compared with the experimental data on the transport ranges of solar and galactic cosmic rays in the interplanetary magnetic field. As a result, the conditions for the propagation of cosmic rays in the interplanetary space and a more accurate idea of the structure of the interplanetary magnetic field are determined.     

Metal-insulator transitions between quantum Hall plateaus

Metal-insulator transitions between quantum Hall (QHE) plateaus due to inelastic scattering are discussed in a smooth random potential within the framework of semiclassical approximation. Inelastic scattering rates due to both electron-phonon and electron-electron interactions are calculated. The electron-phonon scattering rate is dramatically influenced by a strong magnetic field and is found to be linear in temperature for a wide range of temperatures, corresponding to an effective reduction of the Debye temperature. The electron-electron scattering rate is still proportional to the temperature squared. Applying these results to the temperature scaling exponent κ for the width of the transition region between QHE plateaus, we argue that is dictated by the inelastic scattering rate and the percolation length, instead of the localization length.     

同材质颗粒不同填充密度的随机介质中光场的空间分布

用时域有限差分法研究了同一材质的颗粒在不同填充密度下的随机介质中光局域化问题. 依据随机介质激光的实验参数,模拟了颗粒填充密度不同的随机介质中光场的空间分布. 结果表明：当散射颗粒的散射平均自由程与波长相当时,随机介质中的光场分布呈现局域化的特征,而且随着颗粒填充密度增大,光场的局域化程度增强. 因此,在同样的抽运激励下,颗粒填充密度越大的随机增益介质越容易产生激光辐射. 数值模拟结果与实验定性符合. 关键词： 随机激光 时域有限差分法 颗粒填充密度 局域化     

Scattering of a plane wave by one-dimensional dielectric random rough surfaces—study with the curvilinear coordinate method

We present a method giving the bi-static scattering coefficient of a one-dimensional dielectric random rough surface illuminated by a plane wave. The theory is based on Maxwell's equations written in a nonorthogonal coordinate system. For each medium, this method leads to an eigenvalue system. The scattered field is expanded as a linear combination of eigensolutions satisfying the outgoing wave condition. The boundary conditions allow the diffraction amplitudes to be determined. The Monte Carlo technique is applied and the bi-static scattering coefficient is estimated by averaging the scattering amplitudes over several realizations. The results of a Gaussian random process with a Gaussian roughness spectrum are compared to published experimental and numerical data. Comparisons are conclusive.