The scattering of electromagnetic waves in fractal media

The scattering of electromagnetic waves in fractal media is studied. The fractal dimension is naturally involved in the formulation of two physical problems studied in this paper. The general theory of multiple scattering of electromagnetic wave in fractal media is developed by modifying Twersky's theory. Statistical quantities, such as the average field and average intensity of the multiple scattered wave, are studied for a wave propagating in a fractal medium. The scattering cross section of the medium is deduced. The backscattering of electromagnetic waves is also studied. The results showing the range of dependence of the backscattered signals are in agreement with numerical simulations by Rastogi and Scheucher (1990). It also suggests a method of measuring the fractal dimension of the fractal embedded media using radar sounding. The theory developed in this paper can also be used for problems related to multiple scattering of other kinds of waves, such as acoustic waves, elastic waves etc, in fractal media.     

Localization of electromagnetic waves in three-dimensional fractal cavities

Three-dimensional fractals called the Menger sponge, with a fractal dimension D=log(20/log(3, were fabricated from epoxy resin by stereolithography. Clear attenuation of both reflection and transmission intensity was observed at 12.8 GHz for a cubic specimen with an edge size of 27 mm that was constructed up to the third stage of the self-similar patterns. The electromagnetic field was found to be confined in the central part of the specimen at this frequency. The localization is not caused by the presence of a photonic band gap as in photonic crystals but should be attributed to a singular photon density of states realized in the fractal structure. This is the first report on such localization of electromagnetic waves in three-dimensional fractal cavities.     

Interaction of electromagnetic waves with fractal structures

A review and analysis is presented of the state of theoretical and experimental investigations of the problem of the interaction of electromagnetic waves with different inhomogeneous media possessing fractal properties. Such problems are classified and the approaches to solving them are discussed, including those implemented by the present authors.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 76–87, October, 1993.     

On the theory of scattering of electromagnetic waves in media with space-time velocity fluctuations

We express the effective permittivity tensor for a medium that is, on the average, motionless and nonstationary. It is shown that fast time pulsations of velocity lead to an increase in the average wave field and in the propagation velocity of an electromagnetic wave. Using a computer, we compare the surfaces of the frequency spectra of the strength of the scattered field for the Gaussian and diffusion components of the solenoidal velocity field. Dips are shown to emerge in the frequency spectrum that corresponds to the diffusion correlation function as the velocity pulsation increases.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 9, pp. 1091–1095, September, 1996.     

电磁波在旋波介质中的传播特性研究

介绍了旋波介质的结构特征，讨论了旋波材料的电磁性质和物质方程，结合麦克斯韦方程和边界条件。给出了电磁波入射介质的反射系数和透射系数。，     

On electromagnetic waves in chiral media

We analyze the propagation of electromagnetic waves through chiral media, i.e., through composite media consisting of macroscopic chiral objects randomly embedded in a dielectric. The peculiar effects that such media have on the polarization properties of the waves are placed in evidence. To demonstrate the physical basis of these effects, a specific example, chosen for its analytical simplicity, is worked out from first principles.     

Surface electromagnetic waves in Faraday media

The effect of unidirectional propagation of surface electromagnetic waves on the interface between an isotropic Faraday medium and isotropic optically inactive medium is predicted. Such waves can be excited when the intensity of an external magnetic field exceeds a certain threshold. Solutions to the dispersion relation are analyzed, and existence conditions for the surface waves are established.     

The fractal interpretation of the weak scattering of elastic waves

Nondestructive methods, in particular the measurement of elastic waves, have become increasingly important in determining the microstructure of many materials in recent years. One of these methods is observing the attenuation of ultrasonic waves of known amplitude and direction, e.g., in granular metals. The waves are exponentially attenuated with distance with a frequency-dependent attenuation fractor. The attenuation factor can be decomposed into two parts: absorption and scattering. Experimentally, the absorption part varies linearly with frequency, while the scattering part has a noninteger power law behavior, the exponent of which is related to the strength of the material. Theoretically, at long wavelengths the exponent is 4 (Rayleigh scattering) while for grain-sized wavelengths it is 2 (diffusive scattering). We relate the attenuation factor to the forward scattering amplitude which is related to the frequency dependence of the scatterers and their cross sections. We attribute the noninteger attenuation exponent to a fractal distribution of grain shapes and sizes.Supported by the Defense Advanced Research Projects Agency.     

Instability of electromagnetic waves in bistable media

It is shown that boundary-condition peculiarities can give rise to a situation in which stable of weak and strong absorption are not realized in an optically bistable medium. Then, a wave entering the medium is in an unstable state, as a result of which the radiation is modulated.Scientific-Industrial Organization Laser Technology, Erevan University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 35, Nos. 3, 4, pp. 226–233, March–April, 1992.     

Remarks on the radiative transfer approach to scattering of electromagnetic waves in layered random media

The radiative transfer (RT) approach is widely used in applications involving scattering from layered random media with rough interfaces. Although it has been successful in several applications in various disciplines it is well known that this approach involves certain approximations. In this paper these assumptions and approximations are reexamined. To enable this a statistical wave approach is employed to this problem and the governing equations for the first and second moments of the wave functions are derived. A transition is hence made to arrive at a system of equations corresponding to that of the RT approach. It is hence found that more conditions are implicitly involved in the RT approach than generally believed to be sufficient.     

Surface electromagnetic waves on magnetic media

We assume complex magnetic and dielectric properties of two adjacent, isotropic, semi-infinite media and examine surface electromagnetic waves (SEW) at their plane interface. The dispersion curves and non-radiative conditions are derived and compared with other results. Comments are made about which materials will allow surface electromagnetic waves. The importances of the dielectric constants of the sample and the overlayer materials are emphasized with an example, Si and NiO.     

Monte-Carlo simulation of light scattering in fractal porous media

Monte-Carlo simulation of light propagation in a porous medium with a mass fractal morphology was carried out. It was shown that the simulation results can be used to analyze experimental data on light scattering and to study the porous medium structure. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 2, pp. 193–196, March–April, 2008.     

分形海面的微波电磁散射计算模型

利用2维Weierstrass带限函数建立了模拟粗糙海面形状的模型,讨论了分形维数、频率幅度尺度因子等分形参数对海面形状的影响。以粗糙海面形状模型为基础,针对模拟的分形海面形状,从亥姆霍兹积分出发,利用基尔霍夫近似推导出2维分形海面的电磁散射系数,并进行了数值模拟。对微波电磁散射特性随分形维数、频率幅度尺度因子、入射波入射角变化的规律做了进一步讨论分析。在低掠射角时电波会受海面的遮挡,用遮挡函数对散射系数进行修正。研究表明：随着分形维数的增大,散射峰分布变均匀。频率幅度尺度因子越大,散射也越分散。随着入射角的增大,后向散射也逐渐增强,而前向散射逐渐减弱。     

分形海面的微波电磁散射计算模型

利用2维Weierstrass带限函数建立了模拟粗糙海面形状的模型,讨论了分形维数、频率幅度尺度因子等分形参数对海面形状的影响。以粗糙海面形状模型为基础,针对模拟的分形海面形状,从亥姆霍兹积分出发,利用基尔霍夫近似推导出2维分形海面的电磁散射系数,并进行了数值模拟。对微波电磁散射特性随分形维数、频率幅度尺度因子、入射波入射角变化的规律做了进一步讨论分析。在低掠射角时电波会受海面的遮挡,用遮挡函数对散射系数进行修正。研究表明:随着分形维数的增大,散射峰分布变均匀。频率幅度尺度因子越大,散射也越分散。随着入射角的增大,后向散射也逐渐增强,而前向散射逐渐减弱。     

The scattering of flexural waves by random fractal inhomogeneities in a thin plate

The scattering of flexural waves by small statistical fractal inhomogeneities in a thin plate is considered. An expression for the average intensity of the fluctuations of the scattered wave field is obtained. A relation of the intensity to the plate parameters and to the fractal dimension of the inhomogeneities is determined. An expected frequency dependence of the attenuation of flexural waves in a plate due to the scattering by fractal inhomogeneities is discussed.