Localization-delocalization wavepacket transition in Pythagorean aperiodic potentials

Abstract

We introduce a composite optical lattice created by two mutually rotated square patterns and allowing observation of continuous transformation between incommensurate and completely periodic structures upon variation of the rotation angle θ. Such lattices acquire periodicity only for rotation angles cos θ = a/c, sin θ = b/c, set by Pythagorean triples of natural numbers (a, b, c). While linear eigenmodes supported by lattices associated with Pythagorean triples are always extended, composite patterns generated for intermediate rotation angles allow observation of the localization-delocalization transition of eigenmodes upon modification of the relative strength of two sublattices forming the composite pattern. Sharp delocalization of supported modes for certain θ values can be used for visualization of Pythagorean triples. The effects predicted here are general and also take place in composite structures generated by two rotated hexagonal lattices.

Localization and delocalization of light in photonic moiré lattices

“…Here we report on the first experimental realization of reconfigurable photonic moiré lattices with controllable parameters and symmetry. The lattices are induced by two super-imposed periodic patterns [29,30] (sublattices) with either square or hexagonal primitive cells [31]. The sublattices of each moiré pattern have tunable amplitudes and twist angle.…”

Observation of Magic Angle and Wall State in Twisted Bilayer Photonic Graphene

“…With the structurally designable of waveguide system, we may able to achieve the direct observation of other magic angles [25] in twisted bilayer graphene in near future. Besides, the newly found wall state may also exist in other lattice structure [41],…”

Photonic Band Gaps and Resonance Modes in 2D Twisted Moiré Photonic Crystal

“…The twisted bilayer photonic crystal consists of two layers of identical photonic crystal stacked into moiré patterns [19,[22][23][24] that also revealed magic-angle photonic flat bands with a non-Anderson-type localization [23]. Several research groups have generated twisted photonic crystals in photorefractive crystals with a shallow refractive index modulation and have observed the localization and delocalization of light waves [25][26][27][28][29][30][31].…”