  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.
