Multiple Kerker conditions in arbitrary dielectric spheres

High refractive index dielectric particles present unique light scattering properties in the spectral range dominated by electric and magnetic dipolar resonances. These properties are absent in non-resonant low-index particles due to the strong overlap between dipolar and higher order multipolar contributions. Here we propose to induce duality and zero optical backscattering (first Kerker conditions) at multiple size parameter values on arbitrary dielectric spheres by illuminating with a tightly focused dipolar beam. As an illustrative example, we show that duality signatures, including topological optical vortices and enhanced spin orbit optical mirages, can be induced on arbitrary sized spheres of Polystyrene immersed in water.