Physics of optical tweezers.

We outline the basic principles of optical tweezers as well as the fundamental theory underlying optical tweezers. The optical forces responsible for trapping result from the transfer of momentum from the trapping beam to the particle and are explained in terms of the momenta of incoming and reflected or refracted rays. We also consider the angular momentum flux of the beam in order to understand and explain optical torques. In order to provide a qualitative picture of the trapping, we treat the particle as a weak positive lens and the forces on the lens are shown. However, this representation does not provide quantitative results for the force. We, therefore, present results of applying exact electromagnetic theory to optical trapping. First, we consider a tightly focused laser beam. We give results for trapping of spherical particles and examine the limits of trappability in terms of type and size of the particles. We also study the effect of a particle on the beam. This exact solution reproduces the same qualitative effect as when treating the particle as a lens where changes in the convergence or divergence and in the direction of the trapping beam result in restoring forces acting on the particle. Finally, we review the fundamental theory of optical tweezers.