text: Optical tweezers are capable of manipulating nanometer and micron-sized dielectric particles, and even individual atoms, by exerting extremely small forces via a highly focused laser beam. The beam is typically focused by sending it through a microscope objective. Near the narrowest point of the focused beam, known as the beam waist, the amplitude of the oscillating electric field varies rapidly in space. Dielectric particles are attracted along the gradient to the region of strongest electric field, which is the center of the beam. The laser light also tends to apply a force on particles in the beam along the direction of beam propagation. This is due to conservation of momentum: photons that are absorbed or scattered by the tiny dielectric particle impart momentum to the dielectric particle. This is known as the scattering force and results in the particle being displaced slightly downstream from the exact position of the beam waist, as seen in the figure.
  Optical traps are very sensitive instruments and are capable of the manipulation and detection of sub-nanometer displacements for sub-micron dielectric particles. For this reason, they are often used to manipulate and study single molecules by interacting with a bead that has been attached to that molecule. DNA and the proteins and enzymes that interact with it are commonly studied in this way.
  For quantitative scientific measurements, most optical traps are operated in such a way that the dielectric particle rarely moves far from the trap center. The reason for this is that the force applied to the particle is linear with respect to its displacement from the center of the trap as long as the displacement is small. In this way, an optical trap can be compared to a simple spring, which follows Hooke's law.