Ab initio derivation of multipolar expansion of optical force

Like many other physical quantities, the optical force can be expanded using multipole expansion, which has been done in [Nat. Photon. 5, 531], up to electric octupole order. However, in that study, the existence of radiation multipoles were pre-assumed, and the role of the fundamental building units, charges, are not evident. Here, we derive the same multipolar expression of optical force by treating the particles as a collection of point charges or point dipoles, which results in more transparent physics and mathematics.