The Sh-matrices method applied to light scattering by small lenses

The introduction of the Sh-matrices in the T-matrix method allows the shape-dependent parameters to be separated from size- and refractive-index-dependent parameters. This separation also allows for the surface integrals to be solved and for analytic solutions to the light-scattering from particles of some shapes to be found. In this manuscript we derive and analyze the analytical solution for small concave lenses bounded with different spherical surfaces.