The eigenvibrations and time-dependent layer displacement-layer displacement correlation functions are analyzed in a free-standing thin smectic-A films with the help of a discrete layer model. The film motions are described using the Chebyshev polynomials of second kind, U(n)(x). The eigenfrequencies problem is essentially simplified within the framework of this approach since the numerical solution of the high degree algebraic characteristic equation is replaced by the analytical solution of a rather simple trigonometrical equation. The dependences of eigenmodes on wave number q(perpendicular) were analyzed. For small q(perpendicular) one mode is a low frequency acoustic wave and other modes are high frequency optical oscillations. As the wave number q(perpendicular) increases all modes successively turn into relaxation when starting with the acoustic mode. The rather simple expression for susceptibility matrix and for spectral densities of layer displacement correlation functions were obtained using the Chebyshev polynomials. It was shown that the frequency dependences of spectral densities are sensitive to wave number q(perpendicular). For small q(perpendicular) the spectral densities of displacement-displacement correlation functions have a sharp peak and for large q(perpendicular) they turn into a contours of Lorentzian type.
The intensity of coherent backscattering from pointlike anisotropic scatterers is calculated. The polarized component has a peak in the backward direction, whereas the depolarized component does not exhibit a backscattering enhancement unlike the depolarized component for the isotropic scatterer case. These results agree with the measurement data on a disordered nematic liquid crystal. ͓S1063-651X͑96͒02208-8͔ PACS number͑s͒: 42.25.Ϫp Coherent backscattering ͓1-10͔ manifests itself as a sharp enhancement of light scattered backward in a narrow angular interval ϳ/l ext where is the wavelength and l ext is the extinction length. The effect is observed in highly opalescing systems in which the extinction length is significantly less than the linear size of the system. It has been studied in latex suspensions ͓1-3,5,11,12͔, ceramics ͓4͔, porous glasses ͓13͔, etc.The physical mechanism underlying coherent backscattering is quite simple. The coherent plane waves incident upon a turbid system become generally incoherent due to the multiple scattering from randomized inhomogeneities except for the waves which pass some sequence of scatterers in opposite directions. These waves can be coherent. However their interference is important only for backward direction. Such an interference is quite general for any wave process and it was first anticipated and discovered in the multiple scattering of conductance electrons in disordered metals ͓14,15͔.The backscattering problem was solved analytically for pointlike scatterers in Refs. ͓6,7,9,16͔ for a scalar field and in Refs. ͓7,8,17,18͔ for an electromagnetic field. Stephen and Cwilich ͓7͔ took into consideration the polarization effects. They showed that the backscattering peak occurs in both polarized and depolarized components. The magnitude of the peak of the polarized component is five to seven times higher than that of the depolarized component, and its form is close to triangular while the form of the peak of the depolarized component is close to Lorentzian. These results are confirmed in numerous light scattering experiments in latex suspensions ͓1-3,5,11,12͔.The coherent backscattering problem may be important not only for scalar scatterers but also for tensor ones since this effect is studied for various systems such as ceramics ͓4͔, porous glasses ͓13͔, polycrystals and liquid crystals ͓4,11͔, etc. In these systems the permittivity anisotropy may be significant. The coherent backscattering from anisotropic pointlike scatterers was briefly considered in ͓7͔. However one cannot test experimentally results obtained there because an expression for the scattered light intensity, obligatorily real, contains an imaginary part for the case of totally anisotropic fluctuations.This paper presents the study of coherent backscattering from the pointlike anisotropic scatterers. We find that the depolarized component does not practically exhibit the backscattering enhancement unlike the depolarized component for the isotropic scatterer case. The backscattering measurements performed...
We consider the multiple scattering of light by fluctuations of the director in a nematic liquid crystal. Using methods of numerical simulation the peak of the coherent backscattering and the coefficients of anisotropic diffusion are calculated. The calculations were carried out without simplifying assumptions on the properties of the liquid crystal. The process of multiple scattering was simulated as a random walk of photons in the medium. We investigated in detail the transition to the diffusion regime. The dependence of the diffusion coefficients on the applied magnetic field and the wavelength of light were studied. The results of simulation showed a non-monotonic dependence of the diffusion coefficients on the external magnetic field. A qualitative explanation of this behavior was suggested using a simple scalar model. For calculation of the peak of the coherent backscattering we used the semianalytical approach as long as in nematic liquid crystals this peak is extremely narrow. The parameters of backscattering peak and of diffusion coefficients which were found in numerical simulations were compared with the experimental data and the results of analytical calculation.
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