Metadisorder for designer light in random-walk systems

Disorder plays a critical role in signal transport, by controlling the correlation of systems. In wave physics, disordered potentials suppress wave transport due to their localized eigenstates from random-walk scattering. Although the variation of localization with tunable disorder has been intensively studied as a bridge between ordered and disordered media, the general trend of disorder-enhanced localization has remained unchanged, failing in envisaging the existence of delocalization in highly-disordered potentials. Here, we propose the concept of 'metadisorder': tunable random-walk systems having a designed eigenstate with unnatural localization. We demonstrate that one of the eigenstates in a randomly-coupled system can always be arbitrarily molded, regardless of the degree of disorder, by adjusting the self-energy of each element. Ordered waves are then achieved in highly-disordered systems, including planewaves and globally- collective resonances. We also devise counterintuitive functionalities in disordered systems, such as 'small-world-like' transport from non-Anderson-type localization, phase-conserving disorder, and phase-controlled beam steering.