Optical wave propagation in double-periodic, quasi-periodic and disturbed optical lattices

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The investigation of wave propagation in superlattices and distorted single-period lattices has been so far merely theoretical, although this is - due to universal properties - of fundamental interest and related to many physical systems. The main reasons for this situation are the still challenging technologies for model sample fabrication, a difficult but necessary almost full control of the wave and lattice properties, and a non-desired nonlinear interaction of waves with the lattice itself in most systems investigated so far.In this proposal, we plan to investigate experimentally optical wave propagation in one-dimensional optical superlattices and distorted single-period lattices. Fabrication of optical lattices will be performed using lithium niobate crystals, where one can achieve a full control of (super-) lattice periods, coupling constants, and magnitude of an optional nonlinearity. For the case of superlattices within this project, these may be either commensurate or incommensurate. By adequate sample fabrication different types of distortions in single-period lattices can be obtained externally by holographic recording in photorefractive lithium niobate. Furthermore, wave propagation can be easily controlled to be either linear or nonlinear. With the experimental techniques developed recently in our group, we are able to directly measure full 1D band structures including gaps and propagation constants of solitary states within a gap, and to directly observe excited states (either extended Floquet-Bloch modes, nonlinear extended modes, and localized states). Taking these prerequisites into account, by using this model system of wave propagation in periodic potentials, we will investigate physical situations in between the two limiting cases of purely periodic lattices where all states are extended, and completely random lattices where any state is localized.