  We propose a rigorous theory for the optical trapping by optical vortices,
which is emerging as an important tool to trap mesoscopic particles. The common
perception is that the trapping is solely due to the gradient force, and may be
characterized by three real force constants. However, we show that the optical
vortex trap can exhibit complex force constants, implying that the trapping
must be stabilized by ambient damping. At different damping levels, particle
shows remarkably different dynamics, such as stable trapping, periodic and
aperiodic orbital motions.
