Delocalization of light in photonic lattices with unbounded potentials

In classical mechanics, a particle cannot escape from an unbounded potential well. Naively, one would expect a similar result to hold in wave mechanics, since high barriers make tunneling difficult. However, this is not always the case and it is known that wave delocalization can arise in certain models with incommensurate unbounded potentials sustaining critical states, i.e. states neither fully extended nor fully localized. Here we introduce a different and broader class of unbounded potentials, which are not quasi-periodic and do not require any specially-tailored shape, where wave delocalization is observed. The results are illustrated by considering light dynamics in synthetic photonic lattices, which should provide a feasible platform for the experimental observation of wave delocalization in unbounded potentials.