Wave and defect dynamics in nonlinear photonic quasicrystals

Abstract

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.

Qualitative and quantitative analysis of stability and instability dynamics of positive lattice solitons

“…This shows that initially, the perturbed soliton undergoes a drift instability with little self-focusing, but that once the collapse accelerates, it is so fast so that the drift dynamics becomes negligible. (24). Here Ωx ≈ 3 in (a2) and Ωx ≈ 1.09i in (b).…”

“…Such lattices appear naturally in certain molecules [70,71], have been investigated in optics [16,23,24,25,26] and in BEC [72], and can be formed optically by the far-field diffraction pattern of a mask with point-apertures that are located on the N vertices of a regular polygon, or equivalently, by the sum of N plane waves (cf. [16,73]) with wavevectors (k x , k y ) whose directions are equally distributed over the unit circle.…”

“…In recent years there has been a considerable interest in the study of solitons in lattice-type systems. Such solitons have been observed in optics using waveguide arrays, photo-refractive materials, photonic crystal fibers, etc., in both one-dimensional and multidimensional lattices, mostly periodic sinusoidal square lattices [1,2,3,4,5,6,7,8] or single waveguide potentials [9,10,11], but also in discontinuous lattices (surface solitons) [12], radially-symmetric Bessel lattices [13], lattices with triangular or hexagonal symmetry [14,15], lattices with defects [16,17,18,19,20,21,22], with quasicrystal structures [16,23,24,25,26,27,28] or with random potentials [29,30]. Solitons have also been observed in the context of Bose-Einstein Condensates (BEC) [31,32], where lattices have been induced using a variety of techniques.…”

Geometric stabilization of extendedS=2vortices in two-dimensional photonic lattices: Theoretical analysis, numerical computation, and experimental results

“…Indeed, the theoretical proposal [5] of such lattice solitons was followed quickly by their experimental realization in 2D induced lattices [9,10], subsequently leading to the observation of a host of novel solitons in this setting, including dipole [11], multipole [12], necklace [13], and rotary [14] solitons as well as discrete [15,16] and gap [17] vortices. In addition to lattice solitons, photonic lattices have enabled observations of other intriguing phenomena such as higher order Bloch modes [18], Zener tunneling [19], and localized modes in honeycomb [20], hexagonal [21] and quasi-crystalline [22] lattices, and Anderson localization [23] (see, e.g., the recent review [24] for additional examples). In parallel, experimental development in the area of BECs closely follows, with prominent recent results including the observation of bright, dark and gap solitons in quasi-onedimensional settings [25], with the generation of similar structures in higher dimensions being experimentally feasible for BECs trapped in optical lattices [26,27].…”

Existence and stability of multisite breathers in honeycomb and hexagonal lattices

“…More recently, the dynamics of non-square lattices have become a focal point of interest, both in the context of periodic photonic structures [17,18,19,20], and in that of quasi-crystalline [21] or completely disordered lattices [22]. While most of the above works had a view towards applications based on photorefractive crystals, there exist many other applications where such non-square lattices may be relevant.…”