The far field scattering of single walled carbon nanotubes illuminated by a Gaussian beam

The common far field scattering model of rod like particles illuminated by Gaussian is not very suitable to single wall carbon nanotubes (SWCNTs). In this paper, a more favorable model of SWCNTs is derived perturbatively from Maxwell's equation. Firstly, the first-order approximation description of Gaussian beam in the two parallel Cartesian coordinates is introduced. Then, on the basis of Generalized Mie theory, the electromagnetic fields of Gaussian beam with spherical vector wave functions at any right coordinates system is deduced by adopting the relation between the spherical vector wave functions belonging to a rotating Cartesian coordinate system. Thirdly, taking advantage of the cylindrical vector wave functions given by Stratton, the relationship of the spherical vector wave functions expressed in cylindrical vector wave functions is derived as well. Finally the approximate expression of the cylinder to the far zone scattered field is solved, and the electromagnetic field of infinitely long cylinder is expanded by the cylindrical vector.