Nonlinear scatterers in nonlinear media: Born approximation and local perturbation method

Abstract

Wave scattering by inhomogeneous nonlinear particles placed in a nonlinear host medium is studied. In the case of weak scattering the scattering indicatrix is calculated in the first Born approximation. Scattering from small nonlinear particles loaded in a medium with saturation of permittivity is studied by the local perturbation method. A small perturbation method is developed for nonlinear equations of rather general type with a random, intensity-dependent, scattering potential.     

Study on optical wave scattering from slightly Gaussian rough surface of layered medium

The optical wave scattering from the slightly rough surface of three-layer medium is studied. The formulaes of the scattering coefficients for different polarizations are derived using the small perturbation method.     

Localization of a small change in a multiple scattering environment without modeling of the actual medium

A method to actively localize a small perturbation in a multiple scattering medium using a collection of remote acoustic sensors is presented. The approach requires only minimal modeling and no knowledge of the scatterer distribution and properties of the scattering medium and the perturbation. The medium is ensonified before and after a perturbation is introduced. The coherent difference between the measured signals then reveals all field components that have interacted with the perturbation. A simple single scatter filter (that ignores the presence of the medium scatterers) is matched to the earliest change of the coherent difference to localize the perturbation. Using a multi-source/receiver laboratory setup in air, the technique has been successfully tested with experimental data at frequencies varying from 30 to 60 kHz (wavelength ranging from 0.5 to 1 cm) for cm-scale scatterers in a scattering medium with a size two to five times bigger than its transport mean free path.     

Optical solitons in resonant and nonresonant nonlinear media in the presence of perturbations

We studied the optical solitons in nonlinear resonant and nonresonant media in the presence of perturbations, assuming that the transient effects are stimulated by the light scanning beam. We treated a slight deviation from the exact necessary condition for the soliton existence (2betanu=1), as a small perturbation for the integrable system, studying its influence upon the soliton propagation conditions. The approximation is constructed by the help of an algebraic version of the soliton perturbation theory using a Riemann boundary problem in connection with the inverse scattering method. We have obtained the soliton equation and we have solved it in the presence of a small perturbation in the adiabatic approximation. In this case we have demonstrated that for a Lorentz profile line the amplitude of the soliton remains unchanged, the only effect of the perturbation results in a phase shift.     

Theory of scanning near-field magnetooptical microscopy

An analytical theory of scanning near-field magnetooptical microscopy is developed. The theory is based on the elastic scattering of light by small, resonantly polarizable particles, which are used to scan the plane surface of a nonuniformly magnetized medium. The effective polarizability of the particles is calculated with the effect of dynamic “image forces” taken into account in all orders of perturbation theory with respect to the interaction of the particle with a demagnetized ferromagnet, and the magnetooptical perturbation is calculated to first order in the magnetization. The major contributions to the magnetooptical light scattering for a ferromagnetic structure magnetized perpendicular to the surface are found, including a quasistatic approximation for the near-field particle-magnet interaction. The optical size resolution of a magnetic (dielectric) inhomogeneity is estimated. Zh. Tekh. Fiz. 68, 86–91 (July 1998)     

Nonlinear acoustic waves in a collisional self-gravitating dusty plasma

Using the reductive perturbation method,we investigate the small amplitude nonlinear acoustic wave in a collisional self-gravitating dusty plasma.The result shows that the small amplitude dust acoustic wave can be expressed by a modified Korteweg-de Vries equation,and the nonlinear wave is instable because of the collisions between the neutral gas molecules and the charged particles.     

Effective response in nonlinear spherical coated composites under external AC and DC electric fields

By using the perturbation method,effective nonlinear direct current(DC) and alternating current(AC) responses of nonlinear composites with spherical coated inclusions randomly embedded in a host medium are studied under the action of an external electric field E a = E 0 + E 1 sin ωt + E 3 sin 3ωt with different amplitudes and frequencies.The local potentials of composites at all harmonics are given in the inclusion particles and the host regions.All effective nonlinear responses to composites and the relationship between the effective nonlinear responses at all harmonics are also deduced for the spherical coated inclusions in a dilute limit.     

Scattering and absorption of particles by a black hole involving a global monopole

Under the conditions that the wavelength of a particle is much larger than its radius of central mass, and the Schwarzschild field is weak, the scattering of a particle has been studied by many researchers. They obtained that scalar and vector particles abide by Rutherford’s angle distribution by using the low level perturbation method and the scattered field’s approximation in a weak field. The scattering cross section of a photon coincides with the section in Newton’s field of point mass. We can obtain the photon’s polarization effect by calculating the second-order perturbation in the linear Schwarzschild field. This article discusses the scattering and absorption of a particle by a black hole involving a global monopole by using the aforesaid method.     

Investigation on electromagnetic scattering from rough soil surface of layered medium using the small perturbation method

Electromagnetic scattering from a rough surface of layered medium is investigated, and the formulae of the scattering coefficients for different polarizations are derived using the small perturbation method. A rough surface with exponential correlation function is presented for describing a rough soil surface of layered medium, the formula of its scattering coefficient is derived by considering the spectrum of the rough surface with exponential correlation function; the curves of the bistatic scattering coefficient of HH polarization with variation of the scattering angle are obtained by numerical calculation. The influence of the permittivity of layered medium, the mean layer thickness of intermediate medium, the roughness surface parameters and the frequency of the incident wave on the blstatic scattering coefficient is discussed. Numerical results show that the influence of the permittivity of layered medium, the mean layer thickness of intermediate medium, the rms and the correlation length of the rough surface, and the frequency of the incident wave on the bistatic scattering coefficient is very complex.     

Dynamics of solitons in periodic systems with different nonlinear media

To analyze pulse dynamics in an optical system consisting of a periodic sequence of nonlinear media, a composite model is used. It includes a model of the resonance interaction of an ultrashort light pulse with the energy transition of the medium with allowance made for an upper level pump and an almost integrable model that describes the propagation of the light field in the other medium with a cubic nonlinearity and dispersion. Additional allowance is made for losses and other kinds of interaction by introducing perturbation terms. On the bases of the inverse scattering transform and perturbation theory, a simple method for analyzing specific features of soliton evolution in periodic systems of this kind is developed. It is used to describe various modes of soliton evolution in such a system, including chaotic dynamics.     

Effective AC response of nonlinear spherical coated composite

An effective nonlinear response of a nonlinear composite with spherical coated inclusions randomly embedded in a host medium under the action of an external AC electric field, {{\bm E}}_a = {{\bm E}}_1 \sin (\omega t) + {{\bm E}}_3 \sin (3\omega t), is investigated using a perturbation method. The local potentials of the composite at higher harmonics are given both in the region of local inclusion particles and in the local host region under the external AC electric field. All effective nonlinear responses of the composite and the relationship between the effective nonlinear responses at the fundamental frequency and third harmonics are also studied for spherical coated inclusion in a dilute limit.     

Multiple scattering and the structure of a finite thickness of scatterer

The transport equation is solved for a scattering medium of finite thickness. A method is given for approximate derivation of the size distribution for the particles on the basis of multiple scattering. An appendix deals with the particular case of particles that are small in relation to the wavelength.     

Sound scattering by random fractal inhomogeneities in the ocean

Sound scattering by random volume inhomogeneities (fluctuations of the refraction index in a medium) with an arbitrary anisotropy is considered using the small perturbation method (Born’s approximation). Surfaces (boundaries) of the inhomogeneities are deemed to be fractal ones: the energy spectra of the refraction index fluctuations follow the power law with a nonintegral exponent. Formulas are obtained for the volume scattering coefficient. Frequency and angular dependences of the scattering coefficient and their relations to the fractal dimension of inhomogeneities with different kinds of anisotropy and different sizes (on the sound wavelength scale) are presented. The fractal dimension of the inhomogeneities is estimated.     

Light absorption and scattering by a photolayer with closely packed particles

Light absorption and scattering by weakly absorbing layers of close-packed fine-grained silver halide particles was studied. Absorption characteristics of an elementary volume and a photolayer were found to have a nonlinear and nonmonotonic dependence on the concentration. Qualitative specific features of this dependence in the range of medium values of volume concentrations from 0.4 to 0.8 were expressed by an empirical formula. The average cosine of the depth brightness diagram and the probability of photon survival Λ in a concentrated photolayer were calculated. The analysis of changes in Λ in a close-packed medium in a more general case, irrespective of the size and the degree of absorption of particles, was carried out. A conclusion was made concerning the character of changes in the scattering indicatrix of a photolayer caused by an increase of its density.     

具有二维fBm特征的分层介质粗糙面电磁散射的特性研究

运用微扰法研究了平面波入射分层介质粗糙面的电磁散射,推出了不同极化状态下的双站散射系数公式.采用二维fBm分形粗糙面来模拟实际的分层介质粗糙面,结合二维fBm分形粗糙面的功率谱导出了平面波入射二维fBm分形分层介质粗糙面的散射系数计算公式.通过数值计算得到了HH极化下双站散射系数随散射角的变化曲线,讨论了分维、底层介质介电常数、中间介质介电常数和厚度及入射波频率对双站散射系数的影响,得到了二维fBm分形分层介质粗糙面散射系数的分维特征、基本特征、分区特征和随频率变化的特征. 关键词： 电磁散射 二维fBm分形粗糙面 分层介质 微扰法     

Wave processes in microinhomogeneous elastic media with hysteretic nonlinearity and relaxation

The nonlinear propagation of an initially harmonic acoustic wave in a microinhomogeneous medium containing defects with quadratic hysteretic nonlinearity and relaxation is studied by the perturbation method. The frequency dependences of the effective nonlinearity parameters are determined for the self-action of the quasi-harmonic acoustic wave and the higher harmonic generation processes.     

Interaction between ultra short pulses and a dense scattering medium by Monte Carlo simulation: consideration of particle size effect

With an enough short-pulse incident to an individual particle, elementary scattering modes can be observed: internal or external reflection, refraction and diffraction. Simulation of pulse propagation in dense scattering medium is usually computed for large observation time, so that time delays of pulse interaction with the particles are negligible compared to propagation times between particle. A Monte Carlo method is proposed to compute the propagation of an incident 100 fs laser pulse in dense medium taking into account time-dependent scattering characteristics of particle: observation time of scattered light is less than 5000 fs. Two extreme cases are exemplified: predominance of direct and single-scattered photons appears in a thin time window for small particles (1 μm). On the contrary multiple scattering is always predominant and scrambles the transmitted signal for large particles (100 μm).