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We study the optical forces acting on toroidal nanostructures. A greatenhancement of optical force is unambiguously identified as originating fromthe toroidal dipole resonance based on the source-representation, where thedistribution of the induced charges and currents is characterized by the threefamilies of electric, magnetic, and toroidal multipoles. On the other hand, theresonant optical force can also be completely attributed to an electric dipoleresonance in the alternative field-representation, where the electromagneticfields in the source-free region are expressed by two sets of electric andmagnetic multipole fields based on symmetry. The confusion is resolved byconceptually introducing the irreducible electric dipole, toroidal dipole, andrenormalized electric dipole. We demonstrate that the optical force is apowerful tool to identify toroidal response even when its scattering intensityis dwarfed by the conventional electric and magnetic multipoles.

Optical force on toroidal nanostructures: toroidal dipole versus renormalized electric dipole