Energy Approach for Microscopic Particles Manipulation using Optical Tweezers

In this article we use Lyapunov Second Theorem as well as LaSalle Theorem in order to determine the attraction region of an optical trap and to design an steering strategy to move a microscopic particle by means of optical tweezers. A variational approach based on Lagrangian formulation is used to obtain the equations of motion of a particle in the optical trap[1]. System is proved to be locally asymptotically stable under the assumption that Stoke’s drag force acts on the particle. Then, a stable control strategy to move the particle from an initial rest position to a desired final position is derived from Lyapunov second theorem and LaSalle invariance theorem. Key-Words: Optical tweezers, Lyapunov theorem, LaSalle invariance theorem, Stability, Microparticles, Lagrangian, Particle steering