Reexamination of Kerker's conditions by means of the phase diagram

For passive electromagnetic scatterers, we explore a variety of extreme limits on directional scattering patterns in a phase diagram, regardless of the details on the geometric configurations and material properties. By demonstrating the extinction cross sections with the power conservation intrinsically embedded in the phase diagram, we give an alternative interpretation for Kerker's first and second conditions, associated with zero backward scattering (ZBS) and nearly zero forward scattering (NZFS). Physical boundaries and limitations for these directional radiations are illustrated along with a generalized Kerker's condition with implicit parameters. By taking the dispersion relations of gold silicon core-shell nanoparticles into account, we reveal the realistic parameters to experimentally implement ZBS and NZFS at optical frequencies by means of a phase diagram.