  Optical forces have been fruitfully applied in a broad variety of areas that
not only span the traditional scientific fields such as physics, chemistry, and
biology, but also in more applied fields. It is customary and useful to split
the optical force into the (conservative) gradient force and the
(non-conservative) scattering and absorption force. These forces are different
in attributes. The ability to tailor them will open great potential in
fundamental optics and practical applications. Here, we present an analytical
and a numerical approach to calculate these forces, and, with these tools, we
create a fairly general class of 2D conservative optical force field. In
general, particles immersed in an optical force do not obey equilibrium
statistical mechanics, making the analysis complicated. With conservative
forces, these issues are resolved.
