Designing Coherent Optical Environment for Dynamic Optical Manipulation with a Simple Control Beam

We propose a framework for designing coherent optical environments that enable versatile and dynamic optical manipulation. In contrast to conventional material-based near-field platforms, our approach employs a structured coherent light field -- optimized via a back-propagation-based inverse design algorithm -- as the manipulation environment. This light-based platform allows a simple control beam, such as a single plane wave or a low-numerical-aperture Gaussian beam, to steer micro-objects effectively. By establishing a one-to-one correspondence between control beam parameters (e.g., phase/polarization of a plane wave) and particle trapping positions, our method enables real-time and versatile control of particles. A wide range of two- and three-dimensional trajectories -- including circles, squares, tree-like paths, and epicycle-deferent curves -- can be achieved solely by modulating the phase of the control beam. This design strategy for the structured-light environments offers a dynamically reconfigurable, all-optical, and contact-free platform for advanced optical manipulation in free space, with promising applications in nanorobotics, biological probing, and beyond.