Excitation of the radiationless anapole mode

The existence of non-radiating sources is of fundamental importance for inverse scattering problems and the design of invisible objects. However, the excitation of such radiationless sources is quite challenging. We present a method based on which the anapole mode of a high-index isotropic dielectric nanosphere can be excited but radiationless. We show that this radiationless anapole is attributed to the destructive interference of the Cartesian dipole and toroidal moment of the induced current by our proposed focused radially polarized beam illumination. Further, with a standing-wave illumination formed by two counter-propagating focused radially polarized beams under 4π configuration, the ideal radiationless anapole can be excited. This result illustrates a case where the reciprocity condition is not violated, and yet, a radiationless mode can be excited by external illumination.