🔬 optics

Observation of topological vortex solitons on disclinations

Using fs-laser written aperiodic waveguide arrays, researchers demonstrate the formation of stable, thresholdless, and disorder-resistant topological vortex solitons on disclinations within higher-order photonic topological insulators, marking the first realization of excited soliton states with nontrivial phase structure in such systems.

Original authors: A. V. Kireev, K. Sabour, V. O. Kompanets, S. Y. Alyatkin, N. S. Kostyuchenko, S. A. Zhuravitskii, N. N. Skryabin, I. V. Dyakonov, A. A. Kalinkin, K. A. Sitnik, S. K. Ivanov, S. P. Kulik, S. V. Chekali

Published 2026-03-31

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CC BY 4.0

Original authors: A. V. Kireev, K. Sabour, V. O. Kompanets, S. Y. Alyatkin, N. S. Kostyuchenko, S. A. Zhuravitskii, N. N. Skryabin, I. V. Dyakonov, A. A. Kalinkin, K. A. Sitnik, S. K. Ivanov, S. P. Kulik, S. V. Chekalin, P. G. Lagoudakis, V. N. Zadkov, Y. V. Kartashov

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to send a message through a crowded, chaotic city. Usually, if you shout, the sound scatters in every direction, getting lost in the noise. In the world of light, this is called "diffraction." If you try to send a beam of light through a standard material, it spreads out and fades away.

To stop this, scientists use special materials called Topological Insulators. Think of these as a city with a very strict, magical traffic system. In these cities, light doesn't just wander; it is forced to travel along specific "roads" (edges or corners) that are protected by the city's very geometry. Even if there are potholes or construction (disorder), the light keeps moving forward without getting lost.

But here is the tricky part: Scientists have always struggled to make these "protected roads" carry vortex beams.

The Problem: The Spinning Top

A vortex beam is like a spinning top or a tornado. The light doesn't just move forward; it swirls around a center point, carrying a "twist" (angular momentum).

The Issue: In normal materials, these spinning tops are unstable. They wobble and fall apart unless you push them with a massive amount of energy (high power). It's like trying to balance a spinning top on a wobbly table; you need to keep pushing it hard to keep it upright.
The Goal: Scientists wanted to create a "spinning top" that is naturally stable and doesn't need a huge push to stay upright, even in a chaotic environment.

The Solution: The "Disclination" (The Missing Slice)

The researchers in this paper found a clever way to build a new kind of city. They took a standard honeycomb pattern (like a beehive) and performed a surgical operation: they removed a slice of the pie.

Imagine a pizza cut into six slices. If you take one slice away and glue the remaining five together, the center of the pizza gets distorted. This distortion is called a disclination.

The Magic: This missing slice creates a unique "core" in the center of the structure. Because of the way the geometry is twisted, this core acts like a trap for light.
The Result: In this specific "missing slice" core, the light can form a stable, spinning vortex without needing any extra power to keep it stable. It's like the spinning top is now sitting on a magnetic pedestal that holds it perfectly upright automatically.

What They Did (The Experiment)

Building the City: They used a super-fast laser (like a microscopic pen) to write these special "missing slice" patterns into a block of glass. They created tiny channels (waveguides) for the light to travel through.
The Test: They shot laser light into the center of this pattern. To make the light spin, they used a special mirror (a spatial light modulator) to twist the light into a vortex before it entered the glass.
The Comparison:
- Normal Glass (The "Trivial" City): When they tried the same thing in a normal, non-distorted honeycomb pattern, the light spread out and fell apart unless they used a huge amount of power.
- The "Disclination" Glass (The Topological City): When they used the "missing slice" pattern, the light instantly formed a tight, stable, spinning vortex. It worked even with very low power. It was thresholdless—meaning it worked immediately, no matter how weak the light was.

Why This Matters

This discovery is a big deal for a few reasons:

Super-Stable Data: Because these spinning light beams are protected by the "topology" of the material, they are immune to defects. You could send information encoded in these spinning beams through a damaged or imperfect fiber optic cable, and the message would arrive intact.
New Lasers: This could lead to "vortex lasers" that are much more efficient and stable than current ones.
Quantum Computing: These stable, spinning states of light could be used as building blocks for quantum computers, where information is stored in the "twist" of the light.

The Analogy Summary

Think of a vortex soliton as a spinning dancer.

In a normal room, the dancer needs a strong wind machine (high power) to keep spinning, and if the floor is bumpy, they stumble.
In a topological room with a disclination, the floor itself is shaped like a perfect bowl. The dancer can start spinning gently, and the shape of the room naturally keeps them in the center, spinning perfectly, no matter how bumpy the walls are.

This paper is the first time scientists have successfully built this "perfect bowl" for light and watched the dancer spin stably without needing a wind machine. It opens the door to a new era of ultra-stable, high-speed optical communication and computing.

1. Problem Statement

Instability of Vortex Solitons: In conventional nonlinear optical media (non-topological materials), vortex-carrying beams (solitons with orbital angular momentum) are inherently prone to azimuthal instabilities. They typically require high power thresholds to stabilize and often break up during propagation.
Limitations of Topological Solitons: While topological insulators (TIs) offer robust protection for linear edge states, previous experimental observations of topological solitons were limited to fundamental, non-vortex states. The realization of topological vortex solitons—which combine the stability of topological protection with the complex phase structure of vortices—had remained elusive.
The Challenge: Creating stable, thresholdless vortex solitons in nonlinear media that can carry high-intensity signals and information without degradation due to disorder or high-power requirements.

2. Methodology

The researchers employed a combination of theoretical modeling, numerical simulation, and experimental fabrication using ultrafast laser writing.

System Design:
- Structure: They utilized Higher-Order Topological Insulators (HOTIs) based on aperiodic waveguide arrays containing a disclination.
- Construction: Starting with a honeycomb lattice ( $C_6$ symmetry), they introduced a "Kekulé distortion" (shifting waveguides to alter intra- and inter-cell coupling) and then removed a $60^\circ$ sector to create a $C_5$ discrete rotational symmetry disclination. This defect acts as a trap for topological states.
- Fabrication: The arrays were inscribed into fused silica using femtosecond (fs) laser direct writing. To ensure isotropic coupling (crucial for degeneracy and vortex formation), they used a multiscan writing technique (6 tracks per waveguide) to create nearly circular waveguides, minimizing ellipticity-induced anisotropy.
Experimental Setup:
- Excitation: A Ti:Sapphire laser (800 nm, 1.5 ps pulses) was used. A Spatial Light Modulator (SLM) shaped the beam into five coherent spots arranged in a pentagon at the disclination core.
- Vortex Imprinting: A specific phase gradient ( $2\pi m(\ell-1)/5$ ) was imposed on the five spots to impart a total topological charge ( $m$ ) of $\pm 1$ or $\pm 2$ to the input field.
- Detection: Output intensity and phase distributions were measured using single-shot interferometry (Mach-Zehnder interferometer) and off-axis digital holography to reconstruct the phase singularities.
Theoretical Framework:
- Modeled using the Nonlinear Schrödinger Equation (NLSE) with cubic focusing nonlinearity.
- Performed linear stability analysis to determine the growth rates of perturbations for different soliton families.

3. Key Contributions

First Experimental Observation: This is the first report of topological vortex solitons existing on a disclination core within a photonic topological insulator.
Thresholdless Operation: The study demonstrates that these solitons are thresholdless, meaning they can form and remain stable at arbitrarily low power levels, unlike their non-topological counterparts which require significant power to overcome instability.
Symmetry-Topology Interplay: The work establishes a direct link between the discrete rotational symmetry of the lattice ( $C_5$ ) and the allowed topological charges of the vortex states. It shows that the $C_5$ symmetry supports stationary vortex states with $|m|=1$ and $|m|=2$ , but stability is strictly limited by the topology.
Disorder Resistance: The topological vortex solitons exhibit robustness against structural disorder (variations in waveguide depth and position), a hallmark of topological protection.

4. Key Results

Linear Spectrum Analysis:
- In the trivial phase ( $r < 1$ ), no localized states exist in the bandgap.
- In the topological phase ( $r > 1$ ), the disclination core hosts five localized modes (due to $C_5$ symmetry). Two of these are degenerate pairs that can be linearly combined to form vortex states with topological charges $m = \pm 1$ and $m = \pm 2$ .
Stability Findings:
- $m = 1$ Solitons: Theoretical and experimental results confirm that $m=1$ vortex solitons are completely stable across the entire topological gap and even inside the bulk band. They are robust against disorder.
- $m = 2$ Solitons: While theoretically allowed by symmetry, $m=2$ solitons were found to be unstable. In experiments, they spontaneously split into $m=1$ singularities due to azimuthal instability, even in the topological array.
Experimental Observations:
- Trivial Arrays ( $r=0.8$ ): Vortex formation only occurred at very high powers ( $>6$ MW) and required a semi-infinite gap, showing moderate localization.
- Topological Arrays ( $r=1.6$ ): Thresholdless formation of stable $m=1$ vortex solitons was observed starting from minimal power levels ( $P \approx 0.01$ MW).
- Phase Structure: Interferometric measurements confirmed the presence of a central phase singularity and characteristic off-center singularities in the surrounding cells, a signature of the topological nature of the vortex.
- Power Dependence: As power increased, the soliton propagation constant shifted toward the upper band edge, causing slight broadening, but the vortex structure remained intact until the soliton entered the semi-infinite gap at very high powers.

5. Significance

Fundamental Physics: The work bridges the gap between nonlinearity, angular momentum, and material topology. It proves that topological protection can stabilize excited states (vortices) that are normally unstable in nonlinear media.
Applications:
- Robust Information Transfer: The ability to transmit topological vortex states without high power thresholds or susceptibility to disorder makes them ideal for optical communication and information encoding.
- Vortex Lasers: The findings provide a blueprint for designing stable topological vortex lasers.
- Quantum Technologies: The strong confinement and stability of these states on the disclination core are promising for quantum memory and optical switching applications.
Future Directions: The study opens new avenues for exploring parametric interactions in driven-dissipative systems (like polariton condensates) and designing compact topological devices that utilize the unique interplay of symmetry and nonlinearity.