Moulding Optical Tweezers for 3D Enhanced Trapping

Across the many applications of optical tweezers, from microbiology to quantum physics, the most commonly applied optical trap is a tightly focused Gaussian beam. In this work we explore to what extent beam shaping can be used to improve the trapping of microparticles in all three dimensions simultaneously. A common measure of how well an optical trap constrains the motion of particles is the trap stiffness $k$ , relating how quickly the optical restoring force on a particle grows as the particle is displaced. Assuming the optical restoring forces in different dimensions do not couple, we can independently define a trapping stiffness for each dimension (i.e. $k_{x},k_{y},k_{z}$ . Previous work has shown how to improve trap stiffness in one dimension [1–4]. Unfortunately this typically results in a reduction of the trap stiffness in the other dimensions, or even complete instability of the trap. Here we explore how to increase the stiffness of all three dimensions while retaining a stable optical trap. We mould the spatial profile of the laser beam in the far-field using a spatial light modulator (SLM) which is driven by an iterative optimisation algorithm. We restrict the search space by limiting the modes shaped by the SLM to a set of concentric annuli. We adjust the relative phase of the annuli to suppress the motion of a trapped particle.