Freespace twistronics for optical supertopologies

TL;DR

The paper introduces freespace twistronics, a framework that elevates moiré physics to freely propagating light by twisting two volumes of topological optical lattices. Using $N$-wave interference and Gaussian beamlet approximations, it demonstrates a spectrum of high-dimensional optical supertopologies, including skyrmionium bags, skyrmion bags, skyrmion clusters, nested superlattices, and topological quasicrystals, protected by nondiffracting propagation and robustness to perturbations. The experimental results, achieved with an SLM, show long-range, propagation-invariant textures and self-healing behavior when obstructed, validating the approach and its potential for robust information transfer and encryption. By enabling controllable topology in free space, this work unlocks new directions in moiré photonics, higher-dimensional topologies, and interactions with matter, with implications across communications and photonic topology research.

Abstract

Twistronics, the study of moiré superlattices of twisted bilayer 2D materials creating nontrivial physical effects, has recently revolutionized diverse subjects from materials to optoelectronics, nanophotonics, and beyond. Here, breaking the reliance on materials, we present twistronics in higher-dimensional free space, where the twisted lattice is not a layer of 2D material but a 3D propagating light field with topological textures. Moiré structured light with a twist angle can generate a rich set of high-dimensional topologies, including skyrmionium bags, skyrmion bag superlattices, skyrmion clusters, and optical quasicrystals, with controllable symmetry. Many of these textures have not been reported before. Importantly, in contrast to prior moiré superlattices, our freespace optical moiré textures maintain their topologies over a long propagation distances, showing nondiffractive behavior and robustness against perturbations and obstacles. Our work unlocks higher dimensions to manipulate moiré photonics with high-capacity topologies to address modern challenges of robust information transfer and encryption.

Figures (13)

• Figure 1: Concept of freespace twistronics and supertopologies. (a) A basic freespace topological optical lattice field, which hosts C$_6$ symmetric skyrmionium lattices at each $x$-$y$ plane and propagate along $z$-axis with nondiffraction. The inset highlights the skyrmionium texture as an unit cell at a transverse plane, where the inner skyrmion with unit topology is marked by dashed line. (b) Schematic of the morié pattern formed by superimposing two topological optical lattice fields (blue and black, where the dots represent centers of unit cells) with a twisted angle $\theta$ to $z$-axis. The inset shows a schematic morié superlattice pattern at a transverse plane. (c) The resultant morié structured light shows skyrmionium bag superlattices when $\theta=13.2^{\circ}$. The inset shows a skyrmionium bag, where multiple elementary skyrmioniums are surrounded by a bag skyrmioniums. (d) Nested superlattices with target-skyrmion-skyrmionium mixed topology obtained when $\theta=27.8^{\circ}$. The inset highlights a target skyrmion composed by multiple radially nested skyrmions with number of $n>2$. (e) Skyrmion cluster superlattices in twisted bi-volume C$_4$ skyrmion lattices when $\theta=16.26^{\circ}$. The inset shows a skyrmion cluster texture composed by $n$ skyrmions with total skyrmion number of $|N_\text{sk}|=n$. (f) Skyrmion bag superlattices in twisted bi-volume C$_6$ skyrmion lattices, when $\theta=13.2^{\circ}$. The insert shows a skyrmion bag with $n$ elementary skyrmions surrounded by a bag skyrmion with total skyrmion number of $|N_\text{sk}|=n-1$.
• Figure 2: Experimental results of optical supertopologies. Long-range distributions of $S_z$, spin textures of featured topological structures (in red-dashed line boxes of long-range patterns correspondingly), and corresponding skyrmion density distributions for twisted C$_6$ skyrmionium lattices obtaining (a1-a3) skyrmionium bag superlattices at $\theta=13.2^{\circ}$ (blue arrows mark the long-range periodic unit vectors of supercell), (b1-b3) isolated skyrmionium bag at $\theta=16.4^{\circ}$, (c1-c3) skyrmion cluster superlattices at $\theta=21.8^{\circ}$, (d1-d3) nested superlattice at $\theta=27.8^{\circ}$; and for twisted C$_4$ skyrmion lattices obtaining skyrmion cluster superlattices for different baby skyrmion numbers in supercell of (e1-e3) $n=25$ at $\theta=10.35^{\circ}$, (f1-f3) $n=13$ at $\theta=12.66^{\circ}$, (g1-g3) $n=13$ at $\theta=16.26^{\circ}$, (h1-h3) $n=5$ at $\theta=22.61^{\circ}$. The experimental skyrmion numbers $N_\text{sk}$ of featured supertopologies, marked by big dashed lines in (a2-h2), are shown in (a3-h3), respectively. The experimental $N_\text{sk}$ values of selected protected baby skyrmions ("$\alpha$","$\beta$","$\gamma$",) marked by black dashed lines are shown in (a3-d3), correspondingly.
• Figure 3: Hierarchical supertopology decomposition. (a1) Theoretical spatial Fourier spectrum of stokes vector of a skyrmionium bag superlattice at $\theta=16.4^{\circ}$, where the distribution is located at a set of concentric circles in wavenumber-space, and (a2-a8) the corresponding hierarchical real-space textures as skyrmion lattices and skyrmion bag superlattices. The white arrows in (a1) mark the three circles of wavenumber radii $k_1$, $k_2$, and $k_3$ for the cases of skyrmion bag generation. (b1-b3) Experimental results of skyrmion bag, skyrmion cluster superlattices, and topological quasicrystal, with measured textures and skyrmion density distributions, at twisted angles of $16.4^{\circ}$, $21.8^{\circ}$, and $27.8^{\circ}$, respectively, measured skyrmion numbers of selected topological featured in dashed lines are marked. Unit of coordinates: mm.
• Figure 4: Nondiffracting topologically stable propagation. (a1-d1) Experimental results of the propagation-dependent supertopological textures for two skyrmionium bags at $\theta=13.2^{\circ}$ and $16.4^{\circ}$ and two skyrmion clusters at $\theta=10.35^{\circ}$ and $12.7^{\circ}$, respectively, form $z=0$ to 50 cm. The featured side is marked correspondingly in each texture pattern. (a2,b2) The simulated and experimental skyrmion numbers for the skyrmionium bags ($n=7$) and the protected baby skyrmions in which (the error bars evaluate the numerical difference for the 7 baby skyrmions), corresponding to (a1,b1). (c2,d2) The simulated and experimental skyrmion numbers for the skyrmion clusters ($n=25$ and $n=13$), corresponding to (c1,d1).
• Figure 5: Self-healing topologies against obstacles. Experimental results of skyrmionium bag propagation passing through obstacles for (a1) a disk, marked in gray, blocking the center skyrmionium and (a2) two disks blocking two skyrmioniums in bag, at $z=0$. (c-e) The simulated and experimental skyrmion number versus propagation for the baby skyrmion protected in the blocked skyrmionium in (a1) and that two in the two blocked skyrmioniums ("$\alpha$" and "$\beta$") in (b1), respectively.