Disordered Potential Landscapes for Anomalous Delocalization and Superdiffusion of Light

The prominent distinction between order and disorder in optics has been understood in terms of the spatial spreading of waves. In the Anderson picture of optical disorder, light localization has been elucidated by the interference of multiple scatterings from disorders, thus implying a natural correspondence between the localization and disordered potentials. Here, we focus on the disorder of a wave itself to achieve a new class of disordered optical potentials with continuous landscapes, distinguished from conventional Anderson disorder or abnormal disorders in discrete systems. Starting from the disordered but extended ground state for the Schrödinger-like wave equation, we inversely develop the landscape of an optical potential, the disorder pattern of which is similar to Brownian random-walk motion. We then demonstrate that the modes in such a structure can extend over an anomalously large region of space, and also exhibit superdiffusive wave transport. Such behaviors are in contrast to the wavelength-scale localization commonly referred to as Anderson localization in conventional disordered potentials. Our results enable wave delocalization and signal transport in generalized disordered potentials with anomalous modal properties, without the aid of interactions between on-site and hopping energies.