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In classical mechanics, a particle cannot escape from an unbounded potentialwell. Naively, one would expect a similar result to hold in wave mechanics,since high barriers make tunneling difficult. However, this is not always thecase and it is known that wave delocalization can arise in certain models withincommensurate unbounded potentials sustaining critical states, i.e. statesneither fully extended nor fully localized. Here we introduce a different andbroader class of unbounded potentials, which are not quasi-periodic and do notrequire any specially-tailored shape, where wave delocalization is observed.The results are illustrated by considering light dynamics in synthetic photoniclattices, which should provide a feasible platform for the experimentalobservation of wave delocalization in unbounded potentials.

Delocalization of light in photonic lattices with unbounded potentials