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Optimal wave fields for micromanipulation in complex scattering environments


The manipulation of small objects with light has become an indispensable tool in many areas of research, ranging from physics to biology and medicine1,2,3,4,5,6,7. Here, we demonstrate how to implement micromanipulation at the optimal level of efficiency for arbitrarily shaped targets and inside complex environments such as disordered media. Our approach is to design wavefronts in the far field8,9,10,11,12,13,14,15 with optimal properties in the near field of the target to apply the strongest possible force, pressure or torque as well as to achieve the most efficient focus inside the target. This non-iterative technique only relies on a simple eigenvalue problem established from the system’s scattering matrix and its dependence on small shifts in specific target parameters (access to the near field of the target is not required). To illustrate this concept, we perform a proof-of-principle experiment in the microwave regime, fully confirming our predictions.

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Fig. 1: Experimental set-up.
Fig. 2: Optimal transfer of angular momentum.
Fig. 3: Focusing with the GWS operator.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors on reasonable request.


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We thank P. Ambichl, N. Bachelard, H. Cao, S. Gigan, J. Hüpfl, F. Libisch, O. D. Miller and D. B. Phillips for stimulating discussions, and L. Kogler for helpful advice on NGSolve. The simulations were carried out in part on the Vienna Scientific Cluster (VSC). M.K., A.B., K.P. and S.R. were partly supported by the European Commission under project NHQWAVE No. MSCA-RISE 691209 and by the Austrian Science Fund (FWF) under project number P32300 (WAVELAND). A.B. is the recipient of a DOC fellowship of the Austrian Academy of Sciences at the Institute for Theoretical Physics of the Vienna University of Technology (TU Wien). The experiments were carried out in Nice during a long-term visit of K.P. and were supported by the European Commission’s H2020 programme through the Open Future Emerging Technology Project ‘NEMF21’ (664828).

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The theoretical and numerical analysis was carried out by M.H., M.K. and A.B. under the supervision of S.R., whereas Y.V.F. contributed to the derivation of equation (2). Measurements and data evaluation were carried out by K.P. under the supervision of U.K. M.H. and S.R. wrote the manuscript with input from all authors.

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Correspondence to Ulrich Kuhl or Stefan Rotter.

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Supplementary Figs. 1–6 and discussion.

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Horodynski, M., Kühmayer, M., Brandstötter, A. et al. Optimal wave fields for micromanipulation in complex scattering environments. Nat. Photonics 14, 149–153 (2020).

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