Tutorial on the analytical calculation of optical forces on spherical particles in optical tweezers

Arthur Ashkin was awarded the 2018 Nobel prize in physics for the invention of optical tweezers. Since the first publication in 1986 Optical Tweezers have been used as a tool to measure forces and rheological properties of microscopic systems. For the calibration of these measurements, the knowledge of the forces is fundamental. However, it is still common to deduce the optical forces from assumptions based on the particle size with respect to the trapping laser wavelength. This show the necessity to develop a complete and accurate electromagnetic model that does not depend on early approximations of the force model. Furthermore, the model we developed has several advantages, such as morphology--dependent resonances, size dependence for large spheres, and multipole effects from smaller particles, just to name a few. In this tutorial, we review and discuss the physical modeling of optical forces in optical tweezers, which are the resultant forces exerted by a trapping beam on a sphere of any size and composition.