  Optically trapped particles are often subject to a non-conservative
scattering force arising from radiation pressure. In this paper we present an
exact solution for the steady state statistics of an overdamped Brownian
particle subjected to a commonly used force field model for an optical trap.
The model is the simplest of its kind that takes into account non-conservative
forces. In particular, we present exact results for certain marginals of the
full three dimensional steady state probability distribution as well as results
for the toroidal probability currents which are present in the steady state, as
well as for the circulation of theses currents. Our analytical results are
confirmed by numerical solution of the steady state Fokker-Planck equation.
