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Register a new userLocalization and delocalization of light in photonic moire lattices
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Moire lattices consist of two identical periodic structures overlaid with a relative rotation angle. Present even in everyday life, moire lattices have been also produced, e.g., with coupled graphene-hexagonal boron nitride monolayers, graphene-graphene layers, and layers on a silicon carbide surface.A fundamental question that remains unexplored is the evolution of waves in the potentials defined by the moire lattices. Here we experimentally create two-dimensional photonic moire lattices, which, unlike their material predecessors, have readily controllable parameters and symmetry allowing to explore transitions between structures with fundamentally different geometries: periodic, general aperiodic and quasi-crystal ones. Equipped with such realization, we observe localization of light in deterministic linear lattices. Such localization is based on at band physics, in contrast to previous schemes based on light difusion in optical quasicrystals,where disorder is required for the onset of Anderson localization. Using commensurable and incommensurable moire patterns, we report the first experimental demonstration of two-dimensional localization-delocalization-transition (LDT) of light. Moire lattices may feature almost arbitrary geometry that is consistent with the crystallographic symmetry groups of the sublattices, and therefore afford a powerful tool to control the properties of light patterns, to explore the physics of transitions between periodic and aperiodic phases, and two-dimensional wavepacket phenomena relevant to several areas of science.
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Exploration of the impact of synthetic material landscapes featuring tunable geometrical properties on physical processes is a research direction that is currently of great interest because of the outstanding phenomena that are continually being uncovered. Twistronics and the properties of wave excitations in moire lattices are salient examples. Moire patterns bridge the gap between aperiodic structures and perfect crystals, thus opening the door to the exploration of effects accompanying the transition from commensurate to incommensurate phases. Moire patterns have revealed profound effects in graphene-based systems1,2,3,4,5, they are used to manipulate ultracold atoms6,7 and to create gauge potentials8, and are observed in colloidal clusters9. Recently, it was shown that photonic moire lattices enable observation of the two-dimensional localization-to-delocalization transition of light in purely linear systems10,11. Here, we employ moire lattices optically induced in photorefractive nonlinear media12,13,14 to elucidate the formation of optical solitons under different geometrical conditions controlled by the twisting angle between the constitutive sublattices. We observe the formation of solitons in lattices that smoothly transition from fully periodic geometries to aperiodic ones, with threshold properties that are a pristine direct manifestation of flat-band physics11.
We report on the experimental observation of reduced light energy transport and disorder-induced localization close to a boundary of a truncated one-dimensional (1D) disordered photonic lattice. Our observations uncover that near the boundary a higher level of disorder is required to obtain similar localization than in the bulk.
We investigate numerically the effect of long-range interaction on the transverse localization of light. To this end, nonlinear zigzag optical waveguide lattices are applied, which allows precise tuning of the second-order coupling. We find that localization is hindered by coupling between next-nearest lattice sites. Additionally, (focusing) nonlinearity facilitates localization with increasing disorder, as long as the nonlinearity is sufficiently weak. However, for strong nonlinearities, increasing disorder results in weaker localization. The threshold nonlinearity, above which this anomalous result is observed grows with increasing second-order coupling.
We investigate the optical properties of a photonic crystal composed of a quasi-one-dimensional flat-band lattice array through finite-difference time-domain simulations. The photonic bands contain flat bands (FBs) at specific frequencies, which correspond to compact localized states as a consequence of destructive interference. The FBs are shown to be nondispersive along the $Gammarightarrow X$ line, but dispersive along the $Gammarightarrow Y$ line. The FB localization of light in a single direction only results in a self-collimation of light propagation throughout the photonic crystal at the FB frequency.
It is proposed that the propagation of light in disordered photonic lattices can be harnessed as a random projection that preserves distances between a set of projected vectors. This mapping is enabled by the complex evolution matrix of a photonic lattice with diagonal disorder, which turns out to be a random complex Gaussian matrix. Thus, by collecting the output light from a subset of the waveguide channels, one can perform an embedding from a higher-dimension to a lower-dimension space that respects the Johnson-Lindenstrauss lemma and nearly preserves the Euclidean distances. It is discussed that distance-preserving random projection through photonic lattices requires intermediate disorder levels that allow diffusive spreading of light from a single channel excitation, as opposed to strong disorder which initiates the localization regime. The proposed scheme can be utilized as a simple and powerful integrated dimension reduction stage that can greatly reduce the burden of a subsequent neural computing stage.
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