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arxiv: 2606.02265 · v1 · pith:H3L2PPQInew · submitted 2026-06-01 · ⚛️ physics.optics

Skyrmions in scalar fields of non-Hermitian optical microcavities: spontaneous formation, nonlinear control, and optical forces

Jan Wingenbach , Roman Lebs , Xuekai Ma , Ewan M. Wright , Nai H. Kwong , Rolf Binder , Harald Giessen , Stefan Schumacher This is my paper

Pith reviewed 2026-06-28 12:57 UTC · model grok-4.3

classification ⚛️ physics.optics
keywords Skyrmionspolariton condensatesnon-Hermitian opticstopological texturesmicrocavitiesnonlinear controlscalar fieldsexciton-polaritons
0
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The pith

Nonresonant excitation spontaneously generates scalar Skyrmions in non-Hermitian polariton microcavities through gain-loss phase curvature and outward flow.

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

The paper seeks to establish that topological Skyrmion textures, previously studied mainly in vector fields, can form spontaneously in two-dimensional scalar wave systems that include nonlinearities and non-Hermitian effects. In exciton-polariton condensates inside optical microcavities, simple nonresonant pumping without any imposed phase produces isolated Skyrmions and organized lattices. The mechanism is traced to phase curvature created by spatially varying gain and loss together with the radial outflow of polaritons. If this holds, it supplies a practical route to create and reconfigure topological scalar light fields using only optical control in an experimentally common platform.

Core claim

In scalar models of exciton-polariton condensates in non-Hermitian microcavities, nonresonant excitation without imposed phase produces spontaneous isolated Skyrmions and self-organized Skyrmion lattices. The textures arise from gain- and loss-induced phase curvature combined with outward polariton flow. Polariton nonlinearities then permit all-optical switching of the Skyrmion number and reconfiguration of Skyrmion moiré lattices via resonant and nonresonant drives.

What carries the argument

Gain- and loss-induced phase curvature together with outward polariton flow, which imprints the topological winding onto the scalar condensate amplitude and phase.

Load-bearing premise

The exciton-polariton system is sufficiently captured by a scalar field equation that includes the chosen gain-loss profile and nonlinear terms, allowing the reported spontaneous textures to appear without external phase imprinting.

What would settle it

Direct imaging of the condensate phase and density under nonresonant pumping that shows neither isolated Skyrmions nor lattices when the gain-loss landscape is made spatially uniform while keeping the same pumping strength and outflow.

Figures

Figures reproduced from arXiv: 2606.02265 by Ewan M. Wright, Harald Giessen, Jan Wingenbach, Nai H. Kwong, Rolf Binder, Roman Lebs, Stefan Schumacher, Xuekai Ma.

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_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: on a 1500 × 1500 µm2 grid, showing the periodic￾ity of the moir´e structure with repetitions of the central Skyrmion bag also far away from the origin. For completeness we note that similar Skyrmionic structures in the condensate can also form in non￾optically induced, external potential lattice structure ex￾cited with a spatially homogeneous nonresonant pump (not shown). In that case careful parameter opt… view at source ↗
Figure 5
Figure 5. Figure 5: compares several configurations with different relative twist angles in the linear and in the nonlinear regimes (coherent excitation). For ϕ = 17◦ , the single￾Skyrmion bag expands substantially as the nonlinearity increases [cf. Figs. 5(a) and (b)], consistent with a re￾duction of the effective in-plane wave vector magnitude. More strikingly, configurations that appear nearly identi￾cal in the linear regi… view at source ↗
read the original abstract

Topological textures of light offer powerful routes for structuring optical fields, controlling wave transport, and manipulating matter. Skyrmions, long studied as topological solitons in vector fields, have recently been extended to scalar wave systems, including acoustics, hydrodynamics, and plasmonics. However, their realization in two-dimensional scalar wave propagation with nonlinearities and in quantum fluids remains uncharted. Here, we establish such a Skyrmion framework for scalar fields in optical microcavities. With focus on exciton-polaritons, we show that nonresonant excitation without imposed phase can spontaneously generate isolated Skyrmions and self-organized Skyrmion lattices in a polariton condensate. We trace this mechanism to gain- and loss-induced phase curvature together with outward polariton flow. We further demonstrate that polariton nonlinearities provide all-optical control of these textures, enabling switching of the Skyrmion number and reconfiguration of Skyrmion moir\'e lattices through resonant and nonresonant excitation schemes. These results establish nonlinear non-Hermitian resonators as a versatile platform for the spontaneous generation and active control of scalar topological light fields.

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 / 0 minor

Summary. The manuscript establishes a Skyrmion framework for scalar fields in non-Hermitian optical microcavities, with focus on exciton-polariton condensates. It claims that nonresonant excitation without imposed phase spontaneously generates isolated Skyrmions and self-organized Skyrmion lattices, traced to gain- and loss-induced phase curvature together with outward polariton flow. Polariton nonlinearities are shown to enable all-optical control, including switching of Skyrmion number and reconfiguration of moiré lattices via resonant and nonresonant schemes.

Significance. If the numerical results hold under the stated modeling, the work provides a new platform for spontaneous formation and active control of scalar topological textures in nonlinear non-Hermitian resonators, extending Skyrmion concepts from vector fields to scalar wave systems in quantum fluids with potential implications for structured light and optical forces.

major comments (2)
  1. The central claim that nonresonant excitation produces Skyrmions via gain-loss-induced phase curvature and outward flow rests on numerical observation for specific gain/loss profiles and nonlinear coefficients; no analytical derivation is supplied showing that the phase curvature must arise generically from the non-Hermitian terms independent of parameter choice or discretization (see the mechanism tracing in the abstract and associated simulation sections).
  2. The modeling premise that the exciton-polariton system can be treated as a scalar field with the chosen gain-loss and nonlinear terms is sufficient to produce the reported spontaneous formation; this enters directly into the claim but receives limited justification or comparison to vectorial treatments.

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 indicate the revisions made to the manuscript.

read point-by-point responses

  1. Referee: [—] The central claim that nonresonant excitation produces Skyrmions via gain-loss-induced phase curvature and outward flow rests on numerical observation for specific gain/loss profiles and nonlinear coefficients; no analytical derivation is supplied showing that the phase curvature must arise generically from the non-Hermitian terms independent of parameter choice or discretization (see the mechanism tracing in the abstract and associated simulation sections).

    Authors: The demonstration of the mechanism is indeed based on numerical simulations for the chosen parameters, as the work focuses on establishing the Skyrmion formation in this non-Hermitian optical system through computational modeling. While a general analytical derivation would be valuable, it is not provided here, and the claim is supported by the consistent observation across simulations. We have revised the manuscript to include additional discussion on the parameter sensitivity and numerical convergence to strengthen the presentation of the mechanism. revision: partial

  2. Referee: [—] The modeling premise that the exciton-polariton system can be treated as a scalar field with the chosen gain-loss and nonlinear terms is sufficient to produce the reported spontaneous formation; this enters directly into the claim but receives limited justification or comparison to vectorial treatments.

    Authors: We have expanded the justification in the methods section for using the scalar model, explaining that it captures the essential dynamics for the intensity and phase textures studied, with references to prior works where scalar approximations are validated for polariton condensates. A direct comparison to full vectorial treatments is not included as it would require a separate study, but we note the limitations and potential differences in the revised text. revision: yes

Circularity Check

0 steps flagged

No circularity; spontaneous formation shown via direct numerical integration of the model equations.

full rationale

The paper reports numerical solutions of a scalar non-Hermitian Gross-Pitaevskii-type equation for exciton-polaritons under nonresonant pumping. The claimed mechanism (gain-loss phase curvature plus outward flow) is identified by inspecting the simulated fields rather than being presupposed by any fitted parameter, self-definition, or self-citation chain. No equation is shown to reduce to its own input by construction, and the modeling premise is stated explicitly as an ansatz whose consequences are then computed. The result is therefore an independent numerical observation within the chosen model, not a tautology.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit model equations, fitted parameters, or background axioms; the central claim rests on the unstated premise that the polariton condensate can be treated as a scalar field whose dynamics are dominated by gain-loss-induced phase curvature and outward flow.

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discussion (0)

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Reference graph

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