On the structures of some light scattering theories depending on whether or not the Bromwich formulation may be used, e.g. spherical versus spheroidal coordinates

The generalized Lorenz-Mie theories for a homogeneous sphere (interaction between an electromagnetic arbitrary shaped beam and a sphere defined by its diameter and its complex refractive index), and for other particles as well (such as cylindrical particles, with circular or elliptical cross-sections) have been developed by using the Bromwich method. Conversely, this method cannot be used for spheroidal particles. Whether it is possible or not to use the Bromwich method implies a certain number of consequences concerning (i) the definition of TM- and TE-waves, (ii) the definition of genuine beam shape coefficients to describe the beam, (iii) the possibility of developing a localized beam model to describe the illuminating beam. These three issues may be enlightened by referring to the properties of the Bromwich method.