Axial optical trapping forces on two particles trapped simultaneously by optical tweezers

Optical tweezers, which utilize radiation pressure to control and manipulate microscopic particles, are used for a large number of applications in biology and colloid science. In most applications a single optical tweezers is used to control one single particle. However, two or more particles can be trapped simultaneously. Although this characteristic has been used in applications, no theoretical analysis of the trapping force or the status of the trapped particles is available to our knowledge. We present our calculation, using a ray optics model, of the axial trapping forces on two rigid particles trapped in optical tweezers. The spherical aberration that results from a mismatch of the refractive indices of oil and water is also considered. The results show that the forces exerted by the optical tweezers on the two particles will cause the two particles to touch each other, and the two particles can be stably trapped at a joint equilibrium point. We also discuss the stability of axial trapping. The calculation will be useful in applications of optical tweezers to trap multiple particles.