Addition theorem for the spherical vector wave functions and its application to the beam shape coefficients

Abstract

The translational addition theorem for the spherical vector wave functions (SVWFs) of the first kind is derived in an integral form by the use of the relations between the SVWFs and cylindrical vector wave functions. The integral representation provides a theoretical procedure for the calculation of the beam shape coefficients in the generalized Lorenz-Mie theory. The beam shape coefficients in the cylindrical or spheroidal coordinates, which correspond to an arbitrarily oriented infinite cylinder or spheroid, can be obtained conveniently by using the addition theorem for the SVWF under coordinate rotations and the expansions of the SVWF in terms of the cylindrical or spheroidal vector wave functions.