Optimal wave fields for micromanipulation in complex scattering environments
In this work we show how to implement the manipulation of small objects with light at the optimal level of efficiency for arbitrarily shaped targets and inside disordered media. Our starting point is the Wigner-Smith time-delay operator, which involves the derivative of the scattering matrix with respect to frequency. The eigenstates of this time-delay operator have a well-defined time-delay between entering and exiting a given system. This concept can be generalized in the sense that the derivative of the scattering matrix is taken with respect to an arbitrary parameter alpha. The eigenstates of the resulting generalized Wigner-Smith (GWS) operator then represent the conjugate quantity to alpha (e.g., if alpha is the position of the target, the eigenvalues of the GWS operator correspond to momenta). That allows us to realize the highest possible transfer of linear momentum, pressure, or angular momentum onto the target as well as to achieve the most efficient focus inside the target without needing any near field information but only the system’s scattering matrix and its dependence on small shifts in specific target parameters.