Table 1 Optical conditions of the incident light to achieve different signs of Fee and Fem.

The shaded boxes highlight the optical conditions for the OPFs. Here, ed, md, and eq are the complex amplitudes of the electric dipole, magnetic dipole, and electric quadrupole modes of the incoming light to the NP, respectively; See (or Sem) is the scattering coefficient consisting of electric dipole and electric quadrupole (or electric dipole and magnetic dipole) of the Lorenz-Mie scattering coefficient of the NP.

Electric dipole-electric quadrupole interactions
Scattering coefficients of NPOptical force
Re(See) < 0Im(See) > 0
Amplitudes of multipole terms of incoming light to NP
ed: electric dipole, eq: electric quadrupole
Fee < 0
Im(edeq*) > 0Re(edeq*) < 0
Im(edeq*) < 0Re(edeq*) < 0
whenRe(See)Im(edeq*)<Im(See)Re(edeq*)|
Im(edeq*) > 0Re(edeq*) > 0
whenRe(See)Im(edeq*)>Im(See)Re(edeq*)|
Im(edeq*) < 0Re(edeq*) > 0Fee > 0
Electric dipole-magnetic dipole interactions
Scattering coefficients of NPOptical force
Re(Sem) > 0Im(Sem) > 0
Amplitudes of multipole terms of incoming light to NP
ed: electric dipole, md: magnetic dipole
Fem < 0
Im(edmd*) < 0Re(edmd*) < 0
Im(edmd*) > 0Re(edmd*) < 0
whenRe(Sem)Im(edmd*)<Im(Sem)Re(edmd*)|
Im(edmd*) < 0Re(edmd*) > 0
whenRe(Sem)Im(edmd*)>Im(Sem)Re(edmd*)|
Im(edmd*) > 0Re(edmd*) > 0Fem > 0