Localization and delocalization of light in photonic moire lattices (2009.08131v1)

Abstract: 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.

• The paper reports the first experimental observation of 2D light localization-delocalization transitions in photonic moiré lattices to control wave dynamics.
• It employs a Schrödinger-like paraxial model and numerical simulations to predict mode behavior and density of states variations.
• These findings offer novel insights for optical data processing and waveguide design, expanding applications in synthetic material engineering.

Localization and Delocalization of Light in Photonic Moiré Lattices

The paper under review explores the dynamics of wave propagation in photonic moiré lattices and demonstrates experimental realization of light localization and delocalization transitions (LDT) in two-dimensional optical systems. Photonic moiré lattices are constructed by overlaying two periodic sublattices with a relative rotation, enabling control over parameters like symmetry and periodicity. This research addresses key questions about wave localization in engineered photonic structures, extending the understanding previously confined largely to crystalline and disordered media.

Key Contributions

1. Photonic Moiré Lattice Construction: The authors successfully create two-dimensional photonic moiré lattices with controllable parameters and symmetry by overlaying square or hexagonal sublattices. Unlike traditional crystalline structures, these lattices can transition smoothly between periodic, aperiodic, and quasicrystalline configurations based on the rotation angle and amplitude of sublattices.
2. Localization-Delocalization Transition: The paper reports the first experimental evidence of two-dimensional LDT in deterministic optical settings. The localization process observed here diverges from traditional Anderson localization, which requires disorder. Instead, it leverages flat-band physics. Experimental observations confirm that altering sublattice depths or twist angles can result in distinct localization or delocalization behavior of wave packets.
3. Theoretical Framework and Numerical Simulations: The propagation dynamics of light beams in moiré lattices are governed by a Schrödinger-like equation under the paraxial approximation. The paper illustrates how form-factor calculations and variations in the density of states (DOS) can predict modes' localization, validated with numerical simulations.

Results

• Localization in Incommensurable Lattices: A localized mode emerges when the second sublattice's amplitude exceeds a threshold value, denoted by $p_2^{\rm LDT}$. The transition occurs independently of periodicity, enabled by the flattening of higher energy bands.
• Role of Pythagorean Lattices: The paper analyzes scenarios using commensurable moiré lattices, tied to Pythagorean rotation angles, where lattice periodicity is restored, and modes remain delocalized irrespective of other parameters.
• Hexagonal Moiré Lattices: By rotating hexagonal sublattices, the authors extend observations to hexagonal symmetry, offering a broader validation of LDT across varying geometrical configurations.

Implications and Future Directions

These findings broaden the scope of light manipulation using photonic structures, suggesting potential applications in optical data processing and waveguide design. The research opens avenues for studying other phenomena, such as conductivity in quasiperiodic lattices owing to the tunable nature of moiré patterns. Moreover, the methodology can be extended to other physical settings, including atomic systems and material science, particularly in exploring two-dimensional physics beyond traditional lattice arrangements.

The paper contributes significantly to the understanding of wave propagation and localization in engineered photonic structures, offering insights applicable to condensed matter physics and potentially influencing future developments in synthetic material design.