Decomposition of optical force into conservative and nonconservative components

Abstract

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.