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arxiv: 2606.13186 · v2 · pith:4RX6JLX6new · submitted 2026-06-11 · ⚛️ physics.optics

Robustness against disorder in topological fibre lasers with explicitly broken PT symmetry

Brook Salter , Habib Rostami , Peter J Mosley , Nathan Roberts , Anton Souslov This is my paper

Pith reviewed 2026-06-27 06:07 UTC · model grok-4.3

classification ⚛️ physics.optics
keywords topological laserfibre laserPT symmetrySSH chaindisorder robustnessphotonic crystal fibrenon-Hermitian photonics
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The pith

A topological boundary mode in a fibre laser stays robust to disorder even after saturable gain is added.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper models a laser inside a photonic crystal fibre by placing a non-Hermitian Su-Schrieffer-Heeger chain with PT symmetry along the fibre length. A winding-number invariant is used to ensure that extra gain placed at the topological interface selectively amplifies only the boundary mode. Mode-coupling calculations and finite-element simulations then add saturable gain as nonlinearity and include realistic fabrication disorder; the lasing supermode continues to show the same protection. The authors also give an explicit stack-and-draw fabrication route using doped cores.

Core claim

The topological boundary mode is selectively amplified when extra gain is added at the topological interface. Even with nonlinearity added through saturable gain, the lasing supermode retains its robustness against disorder.

What carries the argument

winding-number invariant combined with a PT-symmetric SSH bulk that enforces selective amplification at the boundary

If this is right

  • Selective amplification occurs only at the designed topological interface.
  • Robustness survives both linear mode-coupling theory and full finite-element modelling with nonlinearity.
  • A practical fibre can be made with existing doped-core stack-and-draw methods.
  • The same protection principle can be applied to other non-Hermitian photonic devices.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Multi-core fibre lasers could become more stable for classical or quantum signal transmission.
  • The approach may extend to other gain media or resonator geometries where disorder is a practical limit.
  • Direct fabrication and testing of the proposed doped-core design would check whether the modelled protection survives real fabrication variations.

Load-bearing premise

The winding-number invariant and PT-symmetric SSH bulk continue to select and protect the boundary mode once saturable gain and realistic fibre disorder enter the mode-coupling and finite-element models.

What would settle it

A simulation or measurement in which the lasing supermode stops preferring the boundary location or loses its disorder robustness once the modelled disorder reaches the level expected from stack-and-draw fabrication.

Figures

Figures reproduced from arXiv: 2606.13186 by Anton Souslov, Brook Salter, Habib Rostami, Nathan Roberts, Peter J Mosley.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: b(i) and (ii). Beyond this value, delocalisation is observed, with IPR reaching a minimum at ≈ 2.5w, see output profile in Fig. 4b(iii). For disorder strength [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
read the original abstract

Fibre lasers realise a large gain medium in a compactly coiled fibre. Disorder due to fabrication can negatively impact the stability of their lasing modes, especially in multi-core fibres. Recently, topological fibres (without gain) have been experimentally demonstrated to be robust against fabrication disorder, but topological fibre lasers have not yet been designed or modelled. Here, we use a combination of mode-coupling theory and finite-element simulations to design and model a topological laser based on a non-Hermitian Su-Schrieffer-Heeger (SSH) chain embedded in a photonic crystal fibre. Our design is based on a winding-number invariant in combination with a PT-symmetric SSH bulk. We show that the topological boundary mode is selectively amplified when extra gain is added at the topological interface. Even with nonlinearity added through saturable gain, the lasing supermode retains its robustness against disorder. We present a realistic design for a topologically robust fibre laser using readily available stack-and-draw methods with doped cores. This work establishes a new approach for imbuing non-Hermitian photonic systems with topological protection, with technological implications towards generating robust quantum and classical signals.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript designs a topological fibre laser by embedding a non-Hermitian Su-Schrieffer-Heeger (SSH) chain in a photonic crystal fibre, employing a winding-number invariant together with a PT-symmetric bulk to achieve selective amplification of the topological interface mode. Using mode-coupling theory and finite-element simulations, it reports that this mode remains robust to disorder even after saturable gain is introduced to model nonlinearity, and outlines a realistic doped-core stack-and-draw fabrication route.

Significance. If the numerical evidence is confirmed, the work would demonstrate a concrete route to topological protection in non-Hermitian fibre lasers, offering a fabrication-tolerant platform for stable classical and quantum light sources.

major comments (2)
  1. [Nonlinear simulations (mode-coupling and FEM sections)] The central claim that the linear winding-number invariant continues to enforce selective amplification and disorder robustness once saturable gain is added rests entirely on the specific numerical implementations chosen for the mode-coupling equations and the finite-element discretizations. No analytic continuation or independent cross-validation (e.g., comparison of gain-saturation effects on inter-core coupling between the two models) is supplied, so any mismatch would remove the reported nonlinear robustness.
  2. [Finite-element model description] Details of how disorder is implemented (random perturbations to core positions, refractive indices, or gain), the convergence criteria for the finite-element mesh, and the precise functional form of the saturable-gain term are not visible; without these, the quantitative robustness statements cannot be reproduced or stress-tested.
minor comments (2)
  1. [Abstract and introduction] The title states 'explicitly broken PT symmetry' while the abstract and body refer to a 'PT-symmetric SSH bulk'; a brief clarification of how the explicit breaking is introduced would remove ambiguity.
  2. [Figure captions] Figure captions should explicitly state the disorder strength (standard deviation) and the saturation intensity used in each panel so that the robustness curves can be compared directly to the linear case.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed and constructive comments on our manuscript. We address each of the major comments below and outline the revisions we plan to make to strengthen the paper.

read point-by-point responses

  1. Referee: [Nonlinear simulations (mode-coupling and FEM sections)] The central claim that the linear winding-number invariant continues to enforce selective amplification and disorder robustness once saturable gain is added rests entirely on the specific numerical implementations chosen for the mode-coupling equations and the finite-element discretizations. No analytic continuation or independent cross-validation (e.g., comparison of gain-saturation effects on inter-core coupling between the two models) is supplied, so any mismatch would remove the reported nonlinear robustness.

    Authors: We agree that providing cross-validation between the mode-coupling theory and finite-element simulations in the nonlinear regime would strengthen the central claim. In the revised manuscript, we will include a direct comparison of the gain-saturation effects on the inter-core coupling coefficients as obtained from both numerical approaches. This will serve as an independent check on the consistency of the reported robustness. revision: yes

  2. Referee: [Finite-element model description] Details of how disorder is implemented (random perturbations to core positions, refractive indices, or gain), the convergence criteria for the finite-element mesh, and the precise functional form of the saturable-gain term are not visible; without these, the quantitative robustness statements cannot be reproduced or stress-tested.

    Authors: We acknowledge that the current manuscript lacks sufficient detail on the numerical implementation. In the revised version, we will expand the methods section to explicitly describe: the implementation of disorder through random perturbations to core positions and refractive indices (with the specific ranges and distributions used), the finite-element mesh convergence criteria (including element size and residual error thresholds), and the exact functional form of the saturable-gain term (including any parameters such as saturation intensity). These additions will enable reproducibility of the results. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's central claims rest on explicit numerical implementations of mode-coupling theory and finite-element simulations that incorporate saturable gain and disorder into a PT-symmetric SSH model. These simulations are independent of the target robustness result and do not reduce any prediction to a fitted parameter or self-citation by construction. The winding-number invariant is applied from linear theory to the nonlinear regime via direct modeling, with no quoted step showing self-definitional equivalence or load-bearing self-citation chain. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of the winding-number invariant to the non-Hermitian fibre geometry with gain; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption Winding-number invariant protects the boundary mode in the non-Hermitian PT-symmetric SSH chain
    Invoked to guarantee selective amplification and disorder robustness

pith-pipeline@v0.9.1-grok · 5737 in / 1056 out tokens · 21619 ms · 2026-06-27T06:07:53.467800+00:00 · methodology

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