Mie Resonances and Kerker Effects in Parametric Time-Modulated Spheres

We provide a theoretical description of light scattering by a spherical particle whose permittivity is modulated with twice the frequency of the incident light. Such a sphere acts as a finite-size photonic time crystal and permits optical parametric amplification. We show that the control of the temporal modulation strength provides a qualitatively new route to spectrally overlap different parametric Mie resonances in the sphere for controlling its far-field pattern and satisfying the Kerker scattering conditions.