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Vortex solitons in disclination quasicrystals

This paper proposes a new class of disclination quasicrystals with tunable discrete rotational symmetry that enriches the linear spectrum to support stable, thresholdless vortex solitons with unique intensity and phase distributions, thereby expanding the theory of localization in topologically deformed photonic structures.

Original authors: Hua Zhong, Yaroslav V Kartashov, Yongdong Li, Fangwei Ye, Yiqi Zhang

Published 2026-09-04

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CC0 1.0

Original authors: Hua Zhong, Yaroslav V Kartashov, Yongdong Li, Fangwei Ye, Yiqi Zhang

Original paper dedicated to the public domain under CC0 1.0 (http://creativecommons.org/publicdomain/zero/1.0/). ✨ 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

Light usually travels in straight lines, but when it moves through special materials, it can be coaxed into twisting into spirals, carrying a kind of spinning energy known as orbital angular momentum. These twisting beams, called vortex states, are fascinating because they can carry information or power in ways that ordinary light cannot. However, keeping these delicate spirals stable is difficult; they tend to unravel or break apart as they travel. Scientists have long looked for materials that could act as a protective track for these beams. One promising candidate is a quasicrystal, a type of material that has a highly ordered structure but lacks the repeating, tiled pattern found in ordinary crystals or the total randomness of a gas. Quasicrystals are unique because they sit somewhere between perfect order and total chaos, offering a complex landscape that can trap and guide light in surprising ways.

For years, researchers have studied how light behaves in these materials, but they were limited to a specific, rigid type of pattern known as the Penrose tiling. This pattern has a fixed symmetry, meaning the material looks the same only when rotated by specific angles, like a five-pointed star. This fixed nature restricted the kinds of light spirals that could be supported. A team of researchers has now discovered a way to break this limitation. By intentionally introducing a specific type of structural flaw, known as a disclination, into the quasicrystal, they can reshape the material's symmetry. This allows them to create a new class of materials that can support stable, twisting light beams with different symmetries, opening the door to more versatile ways of controlling light.

The researchers began with a standard, aperiodic pattern of light-guiding channels, similar to a map of roads that never repeats itself exactly. In this original map, the arrangement of roads created a five-fold symmetry. To change this, the team simulated a process where they removed or added a wedge-shaped slice of the pattern and then stretched or compressed the remaining structure to fill the gap. Imagine taking a slice out of a pie and pulling the crust together, or adding an extra slice and pushing the crust apart. This simple geometric adjustment, which they call a disclination, fundamentally altered the material's properties. It allowed them to create structures with four-fold, six-fold, or even seven-fold symmetry, effectively tuning the material to match the needs of different light patterns.

When they analyzed how light moves through these new, deformed structures, they found that the material could support two distinct types of stable light spirals. In one type, the bright spots of light that make up the spiral pulse in perfect unison. In the other, these spots pulse in opposition to one another. Crucially, these light patterns could form and remain stable without needing a high-power starting point. In many other materials, creating such stable light structures requires a significant amount of energy to get started, a hurdle known as a power threshold. In these new disclination quasicrystals, the light spirals appear naturally as soon as the light enters, making them "thresholdless." This is a significant advantage because it means these devices could work with much weaker light sources.

The team also discovered that the stability of these light spirals depends on the symmetry of the material. They found that the light beams were most robust in structures with four-fold or five-fold symmetry. As the symmetry increased to six or seven-fold, the range of conditions under which the light remained stable became narrower. This suggests that while higher symmetries are possible, they are more delicate. The researchers tested how these light beams would hold up against imperfections, which are inevitable in real-world manufacturing. They simulated the presence of small errors in the position and depth of the light-guiding channels. Even with these flaws, the light spirals remained largely intact, especially when the material's natural nonlinearity—its ability to change its own properties in response to the light—was active. The nonlinearity acted as a stabilizing force, correcting the distortions caused by the imperfections and keeping the spiral shape intact.

This work demonstrates that by intentionally deforming a quasicrystal, scientists can design materials that support a wide variety of stable, twisting light beams. The ability to tune the symmetry of the material means that engineers could potentially create optical devices tailored for specific tasks, such as transmitting data or power with high efficiency. The findings suggest that these disclination quasicrystals are not just theoretical curiosities but could serve as a practical platform for future technologies that rely on the precise control of light's orbital angular momentum. The study confirms that these structures can be built using existing technologies, such as laser writing, and that the light states they support are robust enough to survive the imperfections of real-world fabrication.

Technical Summary: Vortex Solitons in Disclination Quasicrystals

Problem Statement
Quasicrystals are aperiodic materials characterized by long-range order and discrete rotational symmetry ( $C_\nu$ ), occupying a niche between periodic and disordered media. While photonic quasicrystals are known to support linear vortex-carrying beams and vortex solitons, previous research has been largely restricted to systems based on the standard Penrose tiling, which possesses a fixed $C_5$ symmetry. A fundamental gap exists in understanding how the discrete rotational symmetry $\nu$ of a quasicrystal influences the properties and stability of vortex light states. Furthermore, existing reports of vortex solitons in Penrose quasicrystals indicate they exist only above considerable power thresholds. The authors investigate whether it is possible to engineer quasicrystals with variable discrete rotational symmetry to support new types of vortex states, specifically addressing whether such structures can support stable, thresholdless vortex solitons with tailored intensity and phase distributions.

Methodology
The study employs a continuous model based on the dimensionless nonlinear Schrödinger equation (NLSE) to describe light propagation in a focusing nonlinear medium with an imprinted quasicrystal refractive index landscape.

Structure Design: The authors start with a "parent" $C_5$ Penrose tiling. To alter the discrete rotational symmetry, they introduce global topological defects known as disclinations. This is achieved by removing or inserting angular sectors with a Frank angle $\theta = 2\pi/5$ from the original lattice and uniformly stretching or compressing the remaining structure to fill the gap or accommodate the addition. This method generates disclination quasicrystals with symmetries ranging from $C_4$ to $C_7$ (and theoretically up to $C_\infty$ ).
Linear Analysis: The linear eigenmodes of these structures are calculated using the plane-wave expansion method. The authors analyze the linear spectrum to identify degenerate pairs of localized modes near the center of the quasicrystal, which serve as the basis for constructing vortex states with specific topological charges ( $m$ ).
Nonlinear Soliton Formation: Vortex soliton families are obtained by solving the NLSE with a focusing nonlinearity term using the Newton method. The study focuses on solitons bifurcating from the identified linear vortex states.
Stability Analysis: Stability is assessed through two methods:
- Direct Propagation: Perturbed states (with random noise up to 10% of peak amplitude) are propagated over long distances ( $z \sim 8000$ ) to observe if the vortex structure is retained.
- Linear Stability Analysis: Small perturbations are superimposed on the soliton profile to solve for the complex perturbation growth rate $\beta$ . Stability is confirmed if the real part of the growth rate ( $\beta_{re}$ ) is non-positive.
Disorder Robustness: The impact of positional and depth disorder (up to 10%) on the propagation of vortex states is simulated to evaluate experimental feasibility.

Key Contributions and Results

Engineering Disclination Quasicrystals: The paper demonstrates a method to create a broad class of quasicrystals with controllable global topological deformation, enabling the generation of structures with discrete rotational symmetries ( $C_4, C_6, C_7$ ) not accessible in standard Penrose tilings.
Linear Vortex States: The introduction of disclinations substantially enriches the linear spectrum, creating multiple mini-bands. Despite this complexity, the authors identify localized degenerate mode pairs in the center of the lattice for each symmetry. Linear combinations of these modes produce stationary vortex states with topological charges limited by the group theory of the specific symmetry (e.g., $|m| \le 1$ for $C_4$ , $|m| \le 2$ for $C_6$ ).
Thresholdless Vortex Solitons: The study reports the existence of stable vortex soliton families that bifurcate directly from these linear localized eigenstates. Crucially, these solitons are thresholdless, meaning they can exist with vanishing power as the propagation constant approaches the linear eigenvalue. This contrasts with previous findings in Penrose quasicrystals where solitons required significant power thresholds.
Soliton Classes: Two distinct classes of stable vortex solitons are identified:
1. Out-of-phase pairs: Consisting of closely located bright spots with a $\pi$ phase difference. These bifurcate from out-of-phase linear modes.
2. In-phase pairs: Consisting of closely located bright spots with zero phase difference. These bifurcate from in-phase linear modes and exhibit symmetry-breaking bifurcations at higher powers, splitting into branches where light concentrates on either inner or outer sites of the spot pairs.
Symmetry Dependence of Stability: The stability intervals of the solitons depend on the discrete rotational symmetry. The authors find that stability regions are wider for $C_4$ and $C_5$ quasicrystals compared to $C_6$ and $C_7$ structures. As the symmetry order increases, the instability domains broaden, particularly near mini-bands.
Robustness to Disorder: Simulations indicate that vortex solitons in these disclination quasicrystals are robust against weak disorder (up to ~4%). In the presence of stronger disorder (e.g., 6%), linear vortex states tend to lose their vorticity and shape. However, in the nonlinear regime, the self-focusing nonlinearity acts as a stabilizing mechanism, preserving the vortex structure and suppressing amplitude oscillations even in disordered lattices.

Significance
The paper claims to expand the theory of localization in quasicrystals to include structures with global topological deformation. By demonstrating that disclination quasicrystals can support stable, thresholdless vortex solitons with tailored symmetries and intensity distributions, the work highlights new prospects for the robust transmission of power or information in these systems. The results suggest that nonlinearity serves as a powerful tool for controlling the internal and phase structure of light beams in aperiodic materials. The authors propose that these findings could be relevant for the design of switching and transmission devices for orbital angular momentum states, as well as new classes of lasers and quantum memory, though they do not provide specific experimental proposals or detailed application scenarios beyond these general directions. The study emphasizes that the ability to alter discrete rotational symmetry makes disclination quasicrystals a versatile platform for generating vortices with tailored charges in aperiodic optical systems.

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