Optimal Blind Focusing on Perturbation‐Inducing Targets in Sub‐Unitary Complex Media

Abstract The scattering of waves in a complex medium is perturbed by polarizability changes or displacements of embedded targets. These perturbations can serve as perfectly non‐invasive guidestars for focusing on the targets. Here, a fundamental but to‐date overlooked difference between these two perturbation types is theoretically derived: the change of the scattering matrix is of rank one [two] for a polarizability change [displacement] of a point‐like target; optimal strategies to perfectly focus on the target in both cases are identified accordingly. In particular, in the latter case, optimal focusing requires at least two target displacements. Furthermore, for the case of dynamic complex media additionally featuring parasitic perturbers, a non‐invasive scheme to achieve optimal time‐averaged power delivery to a perturbation‐inducing target is established. In all cases, no assumptions about the unitarity of the system's scattering matrix or the perturbation strength are necessary. All results are experimentally demonstrated in the microwave regime using a strongly sub‐unitary lossy chaotic cavity as a complex medium. The experiments highlight that the target's “structural scattering” is irrelevant [must be negligible] in the case of target polarizability changes [displacements]. The presented results are expected to find applications in communications, cybersecurity, wireless bioelectronics, flow‐cytometry, and self‐propelled nano‐swimmers.