Parametric Mie Resonances and Directional Amplification in Time-Modulated Scatterers

We provide a theoretical description of light scattering by spherical particle the permittivity which is modulated in time at twice frequency incident light. Such acts as finite-sized photonic crystal and, despite its subwavelength spatial extent, can host optical parametric amplification. Conditions Mie resonances sphere are derived. show that time-modulated materials route to tailor directional amplification, qualitatively different from scatterers made gain media. design two characteristic spheres simultaneously exhibit amplification and desired radiation patterns, including those with zero backward and/or vanishing forward scattering. The latter provides an opportunity for creating shadow-free detectors