Nonergodic extended phase for waves in three dimensions

Wave transport in complex media is determined by the nature of quasimodes at the microscopic level. In three dimensional disordered media, waves generally undergo a phase transition from diffusion to Anderson localization, characterized by exponentially localized modes. A remarkable exception are electromagnetic waves, whose vector-like nature prevents Anderson localization to occur. Here we demonstrate that both scalar and vector (electromagnetic) waves exhibit a non-ergodic extended phase characterized by fractal quasimodes, for a broad range of disorder strengths. While electromagnetic waves remain in the non-ergodic extended phase at high disorder strength, scalar waves eventually enter a localized regime. These results pave the way for the engineering of anomalous wave transport phenomena in disordered media without spatial correlations.