  We present a multipole expansion theory for optical force exerting on a
particle immersed in generic monochromatic free-space optical field. Based on
the theory, we have, for the first time, successfully decomposed the optical
force on a spherical particle of arbitrary size into a conservative and a
nonconservative parts, which are, respectively, written as a gradient of a
scalar function and curl of a vector function in an explicit and analytical
form. As a result, a scalar potential and a vector potential can be defined, up
to gauge freedoms, for the optical force. The decomposition shed light on the
understanding of the optical force and pave a new way to engineer optical force
for various purposes such as equilibrium statistical mechanics as well as
optical micromanipulation.
