Gain-controlled directional scattering in core-shell nanoparticles mediated by magnetic toroidal dipoles

Toroidal dipole moments arise from poloidal current distributions and form a distinct class of electromagnetic excitations with unique near-field characteristics. Using Lorenz-Mie theory, we show that interference between conventional magnetic and magnetic toroidal dipoles in core-shell nanoparticles produces Fano resonances and pronounced forward-backward scattering asymmetry. By introducing optical gain in the dielectric core, we demonstrate that the toroidal mode can be selectively enhanced, enabling control of near-field confinement and far-field scattering directionality. As the gain varies, we find that the system undergoes a continuous transition from suppressed backscattering to suppressed forward scattering through an intermediate regime of dominant magnetic-dipole radiation. This dipolar scattering pattern is associated with a phase resonance of the magnetic toroidal dipole and a reversal of the poloidal current handedness. These results identify gain-controlled toroidal excitations as a tunable mechanism for directional scattering in nanoscale systems.