We present a simple, yet effective, approach for optical induction of Lieb photonic lattices, which typically rely on the femtosecond laser writing technique. Such lattices are established by judiciously overlapping two sublattices (an "egg-crate" lattice and a square lattice) with different periodicities through a self-defocusing photorefractive medium. Furthermore, taking advantage of the superposition of localized flat-band states inherent in the Lieb lattices, we demonstrate distortion-free image transmission in such two-dimensional perovskite-like photonic structures. Our experimental observations find good agreement with numerical simulations.

We report the first experimental demonstration of localized flat-band states in optically induced Kagome photonic lattices. Such lattices exhibit a unique band structure with the lowest band being completely flat (diffractionless) in the tight-binding approximation. By taking the advantage of linear superposition of the flat-band eigenmodes of the Kagome lattices, we demonstrate a high-fidelity transmission of complex patterns in such two-dimensional pyrochlore-like photonic structures. Our numerical simulations find good agreement with experimental observations, upholding the belief that flat-band lattices can support distortion-free image transmission.

We demonstrate self-trapping and rotation of higher-band dipole and quadruple-like gap solitons by single-site excitation in a two-dimensional square photonic lattice under self-focusing nonlinearity. Experimental results show that the second-band dipole gap solitons reside in the first photonic (Bragg reflection) gap, whereas the quadruple-like gap solitons are formed in an even higher photonic gap, resulting from modes of the third-band. Moreover, both dipole and quadruple-like gap solitons exhibit dynamical rotation around the lattice principle axes and the direction of rotation is changing periodically during propagation, provided that they are excited under appropriate initial conditions. In the latter case, the nonlinear rotation is accompanied by periodic transitions between quadruple and doubly-charged vortex states. Our numerical simulations find good agreement with the experimental observations.

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