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The manipulation of small objects with light has become an indispensable toolin many areas of research ranging from physics to biology and medicine. Here wedemonstrate how to implement micro-manipulation at the optimal level ofefficiency for targets of arbitrary shape and inside complex environments suchas disordered media. Our approach is to design wave-fronts in the far-fieldthat have optimal properties in the near-field of the target such as to applyto it the strongest possible force, pressure or torque as well as to achievethe most efficient focus at the target position. Free of any iterativeoptimization, our approach only relies on a simple eigenvalue problemestablished from the scattering matrix of the system and its dependence on thetarget parameters. To illustrate this theoretical concept, we perform aproof-of-principle experiment in the microwave regime, which fully confirms ourpredictions.

Optimal Wave Fields for Micro-manipulation in Complex Scattering Environments