Interpretation of the scattering mechanism for particles in a focused beam

Light scattering by two cases, a hemispherical solid immersion lens (HSIL) and a sphere when illuminated by a focused polarized beam, are discussed. There is a difference between the scattering coefficients of the two scatterers due to multiple reflections inside the sphere, which do not occur in the HSIL. We also derive the Debye series (DS) for the scattering coefficients of the sphere in a focused polarized beam. The DS is derived in a simple and straightforward manner in both mathematical and physical aspects. The applicability of generalized Lorenz-Mie theory (GLMT) is then discussed in terms of the definitions of the incident focused beam. We show that care must be taken when investigating the scattering phenomenon under a focusing condition. This paper aims to give deeper insight into the process of light scattering under focusing conditions.