Light scattering by a finite cylinder containing a spherical cavity using Sh-matrices

We use the Sh-matrix formalism that contains the shape-dependent parameters of the T-matrix to derive an analytical solution for the light scattering from a finite cylinder containing a spherical cavity. The integral expressions for the Sh-matrix elements are simpler than those of the T-matrix elements and the case of a sphere embedded in a finite cylinder these integrals can be solved analytically.