Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems: I. General formulation

The generalized Lorenz–Mie theory in the strict sense describes the interaction between an illuminating arbitrary shaped beam and a homogeneous sphere characterized by its diameter d and its complex refractive index m. It relies on the method of separation of variables expressed in spherical coordinates. Other generalized Lorenz–Mie theories (for other kinds of scatterers) expressed in spherical coordinates are available too. In these theories, the illuminating beam is expressed by using expansions with expansion coefficients depending on some fundamental coefficients named beam shape coefficients, more specifically spherical beam shape coefficients. In this paper we present a general formulation for the transformation of spherical beam shape coefficients through rotations of coordinate systems.