Localization without recurrence and pseudo-Bloch oscillations in optics

Dynamical localization, i.e., the absence of secular spreading of a quantum or classical wave packet, is usually associated with Hamiltonians by the pure point spectrum, i.e., with a normalizable and complete set of eigenstates. Such systems always show quasi-periodic dynamics (recurrence). Here, we show, rather counter-intuitively, that dynamical localization can be observed in Hamiltonians with an absolutely continuous spectrum, where recurrence effects are forbidden. An optical realization of such a Hamiltonian is proposed based on beam propagation in a self-imaging optical resonator with a phase grating. Localization without recurrence in this system is explained in terms of pseudo-Bloch optical oscillations.