Integrate vortex and corner states in fractals

Topological corner states lock light at lattice corners and resist signal damage from manufacturing flaws or structural deformation. Vortex beams carry orbital angular momentum, making them ideal for packing more data into light signals. Bringing these two together could create next-generation optical chips with stable, high-volume data transmission. However, corner states in standard higher-order topological insulators are tightly confined zero-dimensional single modes and their compact spatial structure cannot accommodate the wide, multi-site phase patterns that define vortex light. All previously observed corner solitons only carried trivial flat phase distributions, with no measurable vortex features.

To solve this issue, the research team built a photonic lattice based on Sierpiński gasket fractal geometry, fabricated in fused silica via femtosecond laser direct writing. Unlike regular periodic lattices, fractal higher-order topological insulators host pairs of degenerate corner modes. By superimposing these paired linear modes, the team constructed stable linear vortex corner states, which evolve into self-sustained corner vortex solitons under nonlinearity.

A series of experiments confirmed the unique advantages of these new solitons. They maintain stable performance across an extremely broad input power window, showing strong resistance to structural imperfections. Most notably, the vortex solitons form without any minimum power threshold, a stark contrast to vortex solitons in ordinary trivial lattices that rely on high power to emerge. Phase-resolved interference measurements directly captured the phase singularity characteristic of optical vortices at the lattice corners, verifying the successful coexistence of topological corner confinement and orbital angular momentum.

This work introduces orbital angular momentum as a new degree of freedom to topological corner mode research. It eliminates core technical limitations that once separated topological protection and vortex light fields. Moving forward, the findings lay a solid foundation for developing topologically protected vortex photonic chips, high-dimensional optical encryption hardware, and robust on-chip information transmission systems.

The international research team published their full experimental and theoretical findings in Science Bulletin, titled “Thresholdless corner vortex solitons in fractal Sierpiński topological insulators”.