Wave-momentum shaping for moving objects in heterogeneous and dynamic media

Non-contact manipulation of objects using waves, pioneered by optical tweezers, has broad applications. Acoustic waves offer advantages due to biocompatibility, penetration of heterogeneous media, and wide frequency range enabling manipulation of various sized objects. While existing techniques, such as those using standing waves, acoustic vortices, or holograms, achieve object manipulation, they require highly controlled and static environments, limiting real-world applicability. This research addresses this limitation by introducing a wave-momentum shaping approach that enables object manipulation in disordered and dynamic environments. The core innovation is the continuous optimization of the mode mixture of sound waves to transfer optimal momentum to the object, updating in real-time as the scattering changes due to object movement. This approach eliminates the need for precise environmental control and proximity to the target, significantly expanding the potential applications of wave-based object manipulation.

Various strategies for manipulating objects and particles using acoustic waves have been developed. These include methods for collective or selective manipulation, often relying on controlled, static environments. Techniques such as using standing waves to trap particles at pressure nodes or antinodes, employing acoustic vortices for selectivity, and incorporating lenses, metasurfaces, or holograms for advanced control have been explored. Acoustofluidic and acoustophoretic devices, and wave-controlled microrobots, have been developed for lab-on-a-chip and biomedical applications. However, a common limitation is the need for a precisely controlled and static environment, which restricts applicability to real-world scenarios involving disordered or dynamic environments where manipulation needs to occur at a distance.

The proposed wave-momentum shaping approach uses an iterative algorithm based on far-field measurements and a guide-star for object position. The experimental setup consists of a two-dimensional acoustic waveguide with a movable object and scatterers. Two arrays of speakers control incident acoustic mode mixtures, and microphones measure outgoing mixtures to determine the scattering matrix S(t), which evolves as the object moves. The momentum transferred to the object (Δpa) is related to the variation of S with object coordinate a through the generalized Wigner-Smith (GWS) operator Q = −iS⁻¹ dS/da. The eigenstate of Q with the highest eigenvalue provides the optimal input mode mixture for maximal momentum transfer. An iterative algorithm is used: (1) Initial random wave fields are sent, and S matrices are measured at three nearby points. (2) The gradient of S with respect to coordinates is estimated. (3) Q is constructed and diagonalized to obtain mode mixtures and momentum expectations. (4) A superposition of eigenvectors is sent to move the object, and S is measured again. (5) Steps 2-4 are repeated until the object reaches the target. The method was tested for both linear and angular momentum transfer, and in a dynamic scenario with moving scatterers. Acoustic pressure field maps were also measured to visualize the created pressure fields around the object during manipulation.

The experiments demonstrate successful manipulation of objects in both static and dynamic disordered media. For linear momentum transfer, an object was successfully guided along an S-shaped path in a static scattering medium. The agreement between theoretical momentum prediction and measured velocity confirms the effectiveness of the approach. For angular momentum transfer, an object was rotated both clockwise and anticlockwise by switching the input states with positive and negative eigenvalues, respectively. In a dynamic scenario with randomly moving scatterers, the target object followed a predefined sinusoidal path with minimal deviation from the intended trajectory despite the unpredictable motion of the surrounding scatterers. Acoustic pressure field measurements showed the creation of pressure hot spots that propel the object in the desired direction, highlighting the mechanism of wave-momentum shaping. The method's ability to operate without needing prior knowledge of the object or the environment and its robustness to environmental changes are significant advancements.

The results demonstrate a robust and adaptable method for wave-based object manipulation in complex environments, overcoming limitations of previous techniques. The success in both static and dynamic scenarios underscores the method's robustness and potential for real-world applications. The reliance solely on far-field measurements and a guide-star measurement reduces complexity and eliminates the need for precise environmental control. This approach has implications for diverse fields, including biomedical applications (e.g., targeted drug delivery, cell manipulation), sensing, and micro-manufacturing, where precise object control in complex environments is crucial. The adaptability of the method to various wave types and scales is also noteworthy, paving the way for potential extensions to other domains like optical manipulation.

This paper presents an experimental demonstration of controlling object translation and rotation in complex, dynamic scattering media using wave-momentum shaping. The iterative protocol, requiring only far-field scattering matrix information and a positional guide-star, allows optimal linear and angular momentum transfer for manipulation in both static and dynamic environments. The method's robustness, independence from object properties and interaction force modeling, and adaptability suggest broad applicability across various fields. Future work could explore manipulation of objects with different sizes and shapes, and extensions to other wave types.

While the method demonstrated excellent control in the experimental setup, scalability to significantly more complex environments and a larger number of objects requires further investigation. The accuracy of the gradient approximation in the GWS operator calculation could be improved by incorporating more sophisticated methods for estimating the scattering matrix gradient. The current experimental setup uses audible sound; extending this to higher frequencies (e.g., ultrasound) for manipulating smaller objects would be beneficial. The influence of absorption losses on the overall effectiveness of momentum transfer could also be studied in more detail.