Analytical and numerical programing in laser scattering phenomena and experimetal technics

Abstract

The problem of laser scattering is very complex. It includes analysis of specific cross section depending on the size and shape of scattering center, summation and the inclusion of correlation between the scattering centers. In the theory are many tasks including: mathematical problems, selecting respective apparatus, as well as physical interpretations and modelling of supposed effects. Between them are of special interest practical problems of distributions of the scatterers and manipulations with them. The definitions of generalized functions could be of interest for other type of scatterers (not only spherical case). Our investigations concern the generalized function versus size. In this paper the problems of summation and scattering on cylindrical objects of different sizes will be analyzed and calculated. To solve these problems, we use analytical and numerical methods. The intensity of scattered electromagnetic radiation by the object of cylindrical symmetry is analyzed. The case of linearly polarized laser irradiation with polarization normal to the axis of homogeneous cylinder is considered. Starting from the standard expression for scattered intensity, a new relation with introduced special functions is developed. As the principal problem, a mathematical summability of the obtained expression (trigonometric series with Bessel functions as coefficients) and the convergency of the series in classical and general sense are pointed out.