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The problem of electromagnetic wave scattering on inhomogeneities of the dielectric permittivity tensor eij 3 ~i j (~) is considered. It is shown that effects caused by the coordinate dependence of .sij can be studied by means of analyzing properties of the Fourier transform of the effective dielectric permittivity tensor &k). This fact makes it possible to develop a unified approach to solving the problem of electromagnetic wave attenuation and phase and group velocity variations caused by the scattering. The scattering index y, phase velocity w, and group velocity c are calculated within the framework of the Bourret approximation in all ranges of wavelengths. Asymptotic expressions for y, 8, and c are obtained in the long (as compared to sizes of scatterers), short, and ultra-short wavelength ranges. I n the latter case the results can be obtained only when taking into account the spatial dispersion.Die Streuung elektromagnetischer Wellen an Inhomogenitaten des dielektrischen Tensors eij = = eij(v) wird untersucht. Es wird gezeigt, daD Effekte der Koordinatenabhangigkeit von qj durch Analyse der Fourier-Transformierten des effektiven dielektrischen Tensors e 5 ( k ) untersucht werden konnen. Dies ermoglicht, eine einheitliche Methode zu entwickeln fur die Losung des Problems der Schwachung elektromagnetischer Wellen und der h d e r u n g von Phasen-und Gruppen-Geschwindigkeit, die durch die Streuung verursacht werden. Streuindex y, Phasengeschwindigkeit 8 und Gruppengeschwindigkeit c werden im Rahmen der Bourret-Nitherung fur alle Bereiche der Wellenlange berechnet. Asymptotische Ausdrucke fur y, v und c werden fur Wellenliingen erhalten, die lang, kurz oder ultra-kurz (verglichen mit den Abmessungen der Streuer) sind. Im letzten Fall kann man nur ein Ergebnis erzielen, wenn man die rlumliche Dispersion berucksicht,igt.

The parameters are calculated of an electromagnetic wave propagating in a dielectric medium, which is a multiphase mixture of isotropic and anisotropic components. The dispersion equation is studied which is derived allowing for spatial dispersion giving rise to an additional branch in solving the equation and, correspondingly, to two waves, namely, a real wave and a virtual wave. The results are given of calculating numerically the scattering indices and the phase and group velocities of the two waves. In the case the calculations are made in terms of the Bourret approximation, the real wave alone must be treated.

The problem of finding the relationship between an unknown field E and the field E,, which is the solution of a similar boundary value problem for an auxiliary medium,is solved for anarbitrary (in the sense of the distribution of the nonhomogeneities and their dielectric properties) nonhomogeneous medium of volume V. The Poisson equation for the nonhomogeneous medium corresponds to the integral equation for the field E . Methods of functional analysis ere used to show that the solution of the equation can be represented in the form of the Neumann series, which in general satisfies the conditions of uniform convergence. Certain limitations on the dielectric permittivities of the auxiliary medium are derived as sufficient conditions for the convergence of the series. ,&Wi IlpOH3BOJIbHOfi (B CMbICJIe PaCnpeHeneHMR HeOnHOpOHHOCTefi M UX HM3neKTpMseCHMX CBOmCTB) HeOHHOpOAHOfi CpeHbl o6.be~a v PeUIeHa 3maW 0 HaXOmAeHMIl CBRBH MeXAy HeM3BeCTHbIM AOJIeM E M lTOJIeM E,, HBJIRIOILWMCR PeUIeHEleM MAeHTUsHOfi KpaeBOfi 3aHaqM EJIH BCnOMOraTeJIbHOfi CpeAbI. YpaBHeHMIO nyaCCOHa AJIH HeOnHOpOAHOfi CpeAbI nOCTaBJIeHO B COOTBeTCTBMe MHTeI' paJIbHOe YpaBHeHMe AJIR IIOJIR E . rIpM IIOMOLUEl anna-paTa (PyHKuHoHamHoro a~a n m a n o~a 3 a~0 , s-ro peweHne 3~0 r o ypaBHemrr npencTa-BMMO B (PopMe pRna HefiMaHa, AJIH KoToporo B 061uew cnysae BH~OJIHRIOTCR YCJIOBMR no;lysemx orpamsemfi, HaKnanbIsaeMMe Ha guanempmecme npomuaeMocm BCAO-paBHOMepHOfi CXOHMMOCTM. B Ka4eCTBe AOCTaTOsHbIX yCJIOBIlfi CXOAMMOCTM 3 T O r 0 PRna MOraTeJIbJlHOfi CpeAbI.

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