Largest eigenvalue statistics of wavefront shaping in complex scattering media

In wavefront shaping, light, sound, and other waves are focused through complex scattering media onto one or more target positions, 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, numerical simulations, and exact random-matrix theory to determine its full distribution for multi-target focusing. Exact finite-size random-matrix predictions accurately describe both the mean enhancement factor and its fluctuations beyond the asymptotic Marčenko-Pastur regime, whenever long-range mesoscopic correlations are negligible (e.g., in weakly scattering media or when only a limited number of input channels is controlled). In contrast, strongly scattering media exhibit giant enhancement-factor fluctuations that increasingly exceed these parameter-free predictions as the number of controlled input channels increases. These findings establish the enhancement factor not only as a measure of focusing performance, but also as a sensitive statistical observable that provides a simple and experimentally accessible probe of long-range mesoscopic correlations.