Optical forces on small particles from partially coherent light

We put forward a theory on the optical force exerted upon a dipolar particle by a stationary and ergodic partially coherent light field. We show through a rigorous analysis that the ensemble averaged electromagnetic force is given in terms of a partial gradient of the space variable diagonal elements of the coherence tensor. Further, by following this result we characterize the conservative and non-conservative components of this force. In addition, we establish the propagation law for the optical force in terms of the coherence function of light at a diffraction plane. This permits us to evaluate the effect of the degree of coherence on the force components by using the archetypical configuration of Young's two apertures diffraction pattern, so often employed to characterize coherence of waves.