Optical Pulling Force and Tractor Beams

Light-matter interaction has been an interesting subject of intense analytical and experimental research since the formulation of Maxwell's electromagnetic wave theory. Optical forces exerted on particles excited by incident light waves have been studied for the last few decades. The interaction of light with materials gives rise to light scattering from the particle in the form of energy. The divergence of the Maxwell stress tensor provides a good approximation of the total optical forces on a particle. The divergence of the stress tensor is mathematically equal to the time average Lorentz force since [special characters omitted]. Others have claimed that the stress tensor is "fraught with danger," but it is a matter of application. The stress tensor approach is computationally simpler since application of the divergence theorem allows for a reduction of dimension in the integration. For example, you can either integrate the force density over the volume of an object (3-D), or integrate the divergence of the stress tensor on a surface (2-D) enclosing the volume. It gives a straightforward prediction of the total optical forces on a particle, but may be challenging in the case of multiple particles or for larger particles. The Rayleigh approximation estimates the radiation pressure on small particles in the propagation direction of light, but may be inappropriate for larger particles in comparison to the wavelength of the incident light waves.;Light waves exert radiation pressure on a particle and pushes it away from the light source toward the direction of propagation. It is shown that plane waves propagating in a rectangular waveguide not only push a passive particle toward the propagation direction, but also pull it toward the light source. The particle remains trapped in the transverse direction of the rectangular waveguide. The Lorentz force and the Rayleigh approximation are applied to calculate the total force on the particle. The push-pull phenomenon depends on the frequency of the incident light wave. Optical pulling of a spherical Rayleigh particle along the surface of a dielectric slab waveguide is also shown. The particle is trapped in the transverse direction near the surface of the slab and can be pushed or pulled in the longitudinal direction along the surface of the slab. The pushing and pulling forces switch near the switching frequency of the slab.;The manipulation of a small particle on the surface of a material due to the control of standing waves generated on the surface is presented. Evanescent waves pull the particle toward the surface of the material and the particle is trapped by the standing waves. Two mirrors are used and the adjustments of the mirrors allows precise and arbitrary manipulation of the trapped particle on the surface of the material. The magnitude of the pulling force on the particle depends on the angle of incident of light waves.