Largest eigenvalue statistics of wavefront shaping in complex media

In wavefront shaping, waves are focused through complex media onto one or more target points, and the resulting intensity enhancement is quantified by the enhancement factor. While reproducible enhancement is crucial in experiments, the fluctuations of the enhancement factor remain largely unexplored. Here, we combine experiments, simulations, and exact analytical results using random matrix theory to determine its full distribution in multi-point focusing. Our theoretical framework goes beyond the Marčenko-Pastur law-valid only in the limit of a large number of channels-by accurately predicting the mean enhancement in finite-channel experiments and its fluctuations whenever long-range mesoscopic correlations are negligible (e.g., in weakly scattering media or under limited wavefront control). Notably, in the strongly scattering regime, experiments and simulations reveal giant fluctuations in the enhancement factor, which we attribute directly to long-range mesoscopic correlations. From a fundamental perspective, our results provide a direct method for quantifying long-range correlations in wavefront-shaping-based focusing, even with a limited number of input control channels. On the applied side, they enable the accurate prediction of the enhancement factor and a lower bound on its fluctuations, which are crucial for biomedical imaging, optical metrology, optical trapping, and communication through scattering media.