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

TL;DR

This paper investigates optical forces on toroidal nanostructures, revealing how toroidal and electric dipole resonances contribute to force enhancement and proposing a framework to distinguish their effects.

Contribution

It introduces a conceptual framework to differentiate toroidal and electric dipole contributions to optical forces using source and field representations.

Findings

Optical force enhancement is linked to toroidal dipole resonance.

The same force can be attributed to electric dipole resonance in an alternative representation.

Optical force effectively identifies toroidal responses even with weak scattering.

Abstract

We study the optical forces acting on toroidal nanostructures. A great enhancement of optical force is unambiguously identified as originating from the toroidal dipole resonance based on the source-representation, where the distribution of the induced charges and currents is characterized by the three families of electric, magnetic, and toroidal multipoles. On the other hand, the resonant optical force can also be completely attributed to an electric dipole resonance in the alternative field-representation, where the electromagnetic fields in the source-free region are expressed by two sets of electric and magnetic multipole fields based on symmetry. The confusion is resolved by conceptually introducing the irreducible electric dipole, toroidal dipole, and renormalized electric dipole. We demonstrate that the optical force is a powerful tool to identify toroidal response even when its scattering intensity is dwarfed by the conventional electric and magnetic multipoles.