We study wave dynamics in honeycomb photonic lattices, and demonstrate the unique phenomenon of conical diffraction around the singular diabolical (zero-effective-mass) points connecting the first and second bands. This constitutes the prediction and first experimental observation of conical diffraction arising solely from a periodic potential. It is also the first study on k space singularities in photonic lattices. In addition, we demonstrate "honeycomb gap solitons" residing in the gap between the second and the third bands, reflecting the special properties of these lattices.
The recent proposal of optical induction for producing nonlinear photonic lattices has revolutionized the study of nonlinear waves in waveguide arrays. In particular, it enabled the first observation of (2+1) dimensional lattice solitons, which were the first 2D solitons observed in any nonlinear periodic system in nature. Since then, progress has been rapid, with many fundamental discoveries made within the past two years. Here, we review our theoretical and experimental contributions to this effort.
Quasicrystals are unique structures with long-range order but no periodicity. Their properties have intrigued scientists ever since their discovery and initial theoretical analysis. The lack of periodicity excludes the possibility of describing quasicrystal structures with well-established analytical tools, including common notions like Brillouin zones and Bloch's theorem. New and unique features such as fractal-like band structures and 'phason' degrees of freedom are introduced. In general, it is very difficult to directly observe the evolution of electronic waves in solid-state atomic quasicrystals, or the dynamics of the structure itself. Here we use optical induction to create two-dimensional photonic quasicrystals, whose macroscopic nature allows us to explore wave transport phenomena. We demonstrate that light launched at different quasicrystal sites travels through the lattice in a way equivalent to quantum tunnelling of electrons in a quasiperiodic potential. At high intensity, lattice solitons are formed. Finally, we directly observe dislocation dynamics when crystal sites are allowed to interact with each other. Our experimental results apply not only to photonics, but also to other quasiperiodic systems such as matter waves in quasiperiodic traps, generic pattern-forming systems as in parametrically excited surface waves, liquid quasicrystals, and the more familiar atomic quasicrystals.
Quasicrystals are aperiodic structures with rotational symmetries forbidden to conventional periodic crystals; examples of quasicrystals can be found in aluminum alloys, polymers, and even ancient Islamic art. Here, we present direct experimental observation of disorder-enhanced wave transport in quasicrystals, which contrasts directly with the characteristic suppression of transport by disorder. Our experiments are carried out in photonic quasicrystals, where we find that increasing disorder leads to enhanced expansion of the beam propagating through the medium. By further increasing the disorder, we observe that the beam progresses through a regime of diffusive-like transport until it finally transitions to Anderson localization and the suppression of transport. We study this fundamental phenomenon and elucidate its origins by relating it to the basic properties of quasicrystalline media in the presence of disorder.
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