Pith. sign in

REVIEW 5 major objections 5 minor 41 references

Nonlinear synchronization through vector subharmonic entrainment

T0 review · 5 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper claims that a weak continuous-wave signal with rotating polarization can entrain the internal polarization oscillations of a passively mode-locked fiber laser, producing a stable partially mode-locked regime synchronized to the…

desk verdict A creative vectorial extension of subharmonic entrainment, but the experimental evidence is frequency coincidence rather than demonstrated phase locking. read the letter →

arxiv 2507.23596 v1 pith:6WZRBT4I submitted 2025-07-31 physics.optics nlin.AO

Dmitrii Stoliarov , Sergey Sergeyev , Hani Kbashi , Fan Wu , Qianqian Huang , Chengbo Mou This is my paper · ORCID
classification physics.opticsnlin.AO MSC 34C1534D0678A60 PACS 05.45.Xt42.55.Wd42.65.Sf
keywords vectorsubharmonicentrainmentpolarizationdynamicsmode-lockedfiberlaserQ-switchedmodelockinginjectionsynchronizationnonlinearrotationcontinuouswave
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Subharmonic entrainment, in which a weak external signal locks an oscillator at a rational fraction of its natural frequency, has been studied for scalar oscillators; this paper asks whether the same can happen through the polarization vector of light. Using a passively mode-locked erbium fiber laser, the authors inject a 1550 nm continuous-wave signal whose state of polarization rotates at about 1.67 kHz and report that this entrains the laser's internal polarization oscillations into a stable Q-switched mode-locking regime. The output then shows slow envelopes synchronized to the injection at frequencies that are multiples of ten below the fundamental cavity frequency. The authors support the claim with a vector model in which the injected signal couples only through polarization, and with a linear stability analysis that pins down the internal oscillation frequency. If correct, this would add a previously unreported vectorial degree of freedom to subharmonic entrainment and give laser users a new control knob: the polarization state of an injected signal.

What carries the argument

The load-bearing object is a vector model of the NPR mode-locked laser with an injected-signal term: two complex amplitudes $u, v$ for orthogonal polarization components evolve under the Kerr nonlinearity, gain and population equations, and an added continuous-wave injection $E_x = a\cos(\Omega t + \phi_0)$, $E_y = a\sin(\Omega t + \phi_0)e^{i\Delta\Phi}$. The injection couples entirely through polarization rather than through total power, since $|E_x|^2 + |E_y|^2 = a^2$ is constant. A linear stability analysis of the no-injection steady states identifies an internal NPR oscillation frequency near $4 \times 10^{-3} f_0$, and the full model with $a = 0.19$, $\Delta\Phi = -\pi/4$ reproduces the observed QSML dynamics. This machinery carries the argument because it is what turns the qualitative idea of polarization entrainment into a concrete mechanism.

What would settle it

Measure the phase of the slow output envelope relative to the injected polarization modulation while scanning the injection frequency across 0.5 to 3 kHz; if no interval shows a constant relative phase (an Arnold tongue), or if the same low-frequency components appear unchanged when the injection is switched off, the entrainment claim would fail.

Watch

Extended reading notes

Core claim

The paper's central claim is that vector subharmonic entrainment (VSHE) occurs when a continuous-wave signal with a rotating state of polarization is injected into a passively mode-locked fiber laser. The injected signal at $\Omega = 2\pi \cdot 0.00005$ (in normalized units) entrains the internal polarization oscillations, creating a stable Q-switched mode-locking regime in which the slow envelope repeats at $10^{-4} f_0$, a subharmonic of the round-trip frequency $f_0 = 16.67$ MHz. The authors present this as the first experimental and theoretical demonstration of VSHE in an ultrafast laser, with the mechanism being the overlap and synchronization of sidebands of the nonlinear-polarization-rotation oscillations with the low-frequency injected signal. The theoretical model reproduces the two-timescale power oscillations and the approximately $\pi$ phase slips observed experimentally.

Load-bearing premise

The load-bearing premise is that the observed coincidence between the injected 1.67 kHz modulation and a low-frequency component of the laser output is genuine phase locking; the paper does not compare with the free-running laser, scan the injection frequency, or measure the relative phase, so a passive superposition or modulation response would also produce matching peaks.

Editorial extensions

If this is right

  • Tuning the frequency, amplitude, or polarization modulation of an injected signal would allow selective control of the envelope timing and polarization state of a mode-locked laser output.
  • Partially mode-locked (Q-switched mode-locking) operation can be made stable and synchronized rather than drifting, which matters for applications that use structured pulse trains.
  • Subharmonic synchronization survives frequency ratios that are not exact integers, so the locking condition is more forgiving than a simple rational-ratio requirement.
  • The mechanism implies a two-dimensional synchronization: both the temporal envelope and the polarization state are locked, not just the repetition rate.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A testable extension, not reported in the paper, is to sweep the injection frequency around the 1.67 kHz component and map the Arnold tongue; the claim predicts a locking range that widens with injection amplitude.
  • If VSHE is generic, the same polarization-coupling mechanism should appear in other multi-component oscillators (for example, coupled micromechanical or spin systems), where the 'polarization' is replaced by any vector order parameter.
  • The phase-slip dynamics seen in the model suggest that quantitative comparison of the output envelope phase relative to the injected signal phase would be a sharper test than frequency coincidence alone.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. The paper reports an experimental and theoretical study of what the authors call vector subharmonic entrainment (VSHE) in a passively mode-locked erbium-doped fiber laser. In the experiment, a continuous-wave signal whose state of polarization is modulated at 1.67 kHz is injected into the cavity, and the observed polarization-resolved output contains low-frequency components at frequencies related to 10^-4 of the fundamental repetition rate. The authors interpret this as synchronization between the internal polarization oscillations and the injected signal, leading to a stable Q-switched mode-locking regime. The theory is based on an averaged vector model of an NPR mode-locked laser with an injected CW signal with rotating polarization; a linear stability analysis and numerical solutions are used to reproduce double-timescale QSML dynamics and phase slips. The central claim is that this is the first experimental and theoretical demonstration of vectorial subharmonic entrainment in an ultrafast laser.

Significance. If the synchronization claim were established, the work would be significant: it would add a vectorial degree of freedom to subharmonic entrainment and propose a new control axis for mode-locked fiber lasers. The experimental testbed and the vector model are valuable and the authors report a specific, reproducible configuration. However, the evidence presented does not currently distinguish true entrainment from a passive forced response: the injected polarization-scrambled signal will produce amplitude modulation at the scrambler frequency after any polarizer, regardless of the laser's internal dynamics. The theoretical section is also not independent, since the injection frequency and model parameters are chosen to match the observed dynamics, and one simulation drive frequency differs from the experimental one by a factor of two. The central claim therefore needs additional experimental diagnostics. The paper also contains useful modeling machinery and a clear statement of the proposed mechanism, but the load-bearing evidence is incomplete.

major comments (5)
  1. [§2 Experimental demonstration, Fig. 3c and Discussion] The central claim of entrainment is not supported because the experiment does not distinguish synchronization from passive forced modulation. A polarization-scrambled CW signal at 1.67 kHz passing through the polarizer-based cavity will produce an amplitude-modulated output at the scrambler frequency even in the absence of any internal oscillator. The manuscript reports no no-injection control recorded at the same polarization-controller settings as Fig. 3, no scan of the injection frequency, and no measurement of the phase of the output envelope relative to the injected modulation or of phase-error statistics. Without these, the observed peak at 10^-4 f0 is equally consistent with a forced response. Please provide a locking-range (Arnold tongue) measurement and/or a phase-locking diagnostic.
  2. [§2 Theoretical Analysis, Eq. (4) and Fig. 4] The simulation uses Omega = 2π·0.00005, which is 5×10^-5 f0, whereas the experimental injection frequency is 1.67 kHz = 10^-4 f0. The text claims agreement of the low-frequency scales of 10^-4 and 10^-3, but the drive frequency used in the numerics is a factor of two lower than the experimental drive. This discrepancy needs to be reconciled; otherwise the theoretical 'prediction' is not actually computed at the experimental drive frequency.
  3. [§2 Theoretical Analysis, linear stability analysis and Figs. 1e, 2d, 3c] The text states that the linear stability analysis predicts fNPR = 4×10^-3 f0 and that this 'closely matches' the experimental results, but the measured high-frequency components are at 2×10^-3 f0 in Figs. 1e, 2d, and 3c. Please clarify whether fNPR refers to a different quantity or correct the factor-of-two discrepancy between the predicted and measured high-frequency oscillation.
  4. [§2 Theoretical Analysis, Eq. (4) and Figs. 4-5] The parameters of the injected signal (a, Omega, phi0, DeltaPhi) and the model coefficients are tuned to reproduce the observed dynamics, and no scan of detuning or injection amplitude is presented. The numerical results therefore demonstrate that the model can produce QSML-like dynamics for a chosen drive, but they do not by themselves establish entrainment. A plot of the synchronization region versus detuning and amplitude would make the entrainment claim testable and would connect the results to the Arnold-tongue framework invoked in the Introduction.
  5. [§3 Discussion, paragraph on increased amplitude] The Discussion states that with increased injected amplitude the authors observe phase- and frequency-locking towards high-power oscillations, but immediately adds that 'to obtain experimentally such dynamics, it is necessary to adjust the power and wavelength... and will be published elsewhere.' This is an explicit admission that the strong-injection regime is not experimentally demonstrated. Please either provide the corresponding experiment or clearly restrict the claim of experimental demonstration to the weak-injection regime shown in Fig. 3.
minor comments (5)
  1. [§2 Theoretical Analysis, text near Figs. 4-5] The sentence 'As follows from Fig.5 c and d, the QSML dynamics...' appears to refer to Fig. 4 rather than Fig. 5, since Fig. 5a,b is the ∆Φ = -π/2 case and Fig. 5c,d is the high-amplitude case; please correct the figure references.
  2. [Abstract and §2] The acronym is inconsistently spelled: 'VHSE' appears once in the text while 'VSHE' is used elsewhere; please standardize.
  3. [§2 Experimental demonstration] The phrase 'seeded an optical power of 15 dBm at 1.67 kHz' should be reworded to indicate that a signal with 15 dBm power was modulated at 1.67 kHz, not that 15 dBm is a frequency-dependent quantity.
  4. [Reference [41] and Supplementary Material] Reference [41] is listed as 'Unpublished (2025)' and no URL for the supplementary material is given; the supplementary stability analysis and model details should be made accessible for the claims to be verifiable.
  5. [§2 Experimental demonstration, Fig. 1e vs Fig. 2d] The frequency labels in the text and figures should be made internally consistent: Fig. 1e reports fCW = 2×10^-3 f0, but Fig. 2d reports fHQ = 2×10^-3 f0 with sidebands; please define whether these are the same physical component and explain the appearance of the additional low-frequency components in Fig. 2d.

Circularity Check

1 steps flagged · score 6.0 of 10

The theoretical 'prediction' of the low-frequency VSHE peak reduces to the second harmonic of the injected modulation; the experimental claim lacks detuning/phase-locking evidence.

  1. fitted input called prediction [Theoretical Analysis, Eq. (4) and Fig. 4; Methods Eqs. (5)-(6)]
    "By adding a CW signal into the cavity with parameters a = 0.19, Ω = 2π · 0.00005, φ0 = π/4, and ∆Ψ = −π/4, the QSML dynamics emerge, as shown in Fig. 4. ... the QSML dynamics ... similar to the experimentally observed ... in the context of the shape of pulses, the two-scale oscillations in the range of frequencies with 10−4 · f0 and 10−3 · f0, and the number of sidebands (Fig.4 b), and the phase difference slips of about π radians."

    The injected field in Eq. (4) is a sinusoidal polarization modulation at frequency Ω. After projection through the polarizer/isolator and intensity detection, the output power necessarily contains a 2Ω component (since |cos Ωt|² contains cos 2Ωt). With Ω = 2π·0.00005 (normalized to f0), 2Ω = 10⁻⁴ f0, so the low-frequency peak at 10⁻⁴ f0 in Fig. 4b is the second harmonic of the drive, not an independently emerging entrainment frequency. The 'prediction' of this peak is therefore built into the chosen Ω. Moreover, ΔΦ and a are explicitly tuned ('the case of ∆Φ = −π/4 ... provides better correspondence') until the simulation resembles Fig. 3, so the agreement is a fit rather than a parameter-free prediction.

full rationale

The experimental observation of a QSML regime with an injected polarization-modulated signal is not itself circular: there is a real injected signal, a real output spectrum, and a reproducible regime. However, the paper's theoretical 'confirmation' is not an independent prediction. The drive frequency Ω = 2π·0.00005 is chosen so that the second harmonic of the modulated injection is 10⁻⁴ f0, exactly the low-frequency component that is then presented as the signature of VSHE; detecting such a harmonic is a mathematical consequence of intensity detection of a sinusoidally polarization-modulated field. Model parameters a and ΔΦ are manually adjusted to improve correspondence with the measured spectra, so the match with Fig. 3 is a fit. The experimental section does not report a no-injection control at identical settings, nor does it vary the injection frequency to map an Arnold tongue or measure the output-envelope phase relative to the drive, so the central synchronization claim is underdetermined. That underdetermination is a validity problem rather than circularity, but the theoretical 'prediction' of the key low-frequency peak does reduce by construction to the drive harmonic. No load-bearing self-citation chain was found: the vector model from Sergeyev and co-workers is used as a modeling tool, not as a uniqueness proof, and the paper explicitly critiques and extends the earlier ansatz. Overall, one central theoretical prediction reduces to its input, giving partial circularity; the experimental content prevents the score from being higher.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central theoretical contribution rests on a vector model inherited from prior work of the same authors, with several control parameters (injection amplitude, frequency, phase, model coefficients) selected so that the simulations match the measured spectra. No new physical entities are introduced. The main additional assumption is the interpretation of sideband overlap as entrainment.

free parameters (7)
  • Injected signal amplitude a = a = 0.19 (also 0.5 for spiking regime)
    Chosen to reproduce the experimentally observed QSML dynamics; no independent measurement of the intracavity coupling coefficient is provided.
  • Injected modulation frequency Omega = Omega = 2*pi*0.00005 (normalized to round-trip time)
    Set equal to the observed low-frequency component fLQ1 = 10^-4 f0, so the locked frequency is present in the simulation by construction.
  • Injected signal phase difference DeltaPhi = DeltaPhi = -pi/4 (with -pi/2 tested and rejected)
    Tuned to match the measured phase-slip behavior of the polarization phase difference.
  • Injected signal initial phase phi0 = phi0 = pi/4
    Chosen ad hoc; the paper gives no constraint or sensitivity analysis.
  • Pump power in simulations Ip = Ip = 45 (normalized)
    Selected to place the laser in the regime where linear stability gives an NPR oscillation; experimental pump power was 72 mW.
  • Model coefficients alpha1, alpha2, Delta, chi, gamma, epsilon, delta = 10.131, 2.3, 0.015, 2.3, 2e-6, 0.6e-5, 1
    Parameter values listed in Fig. 6 caption; they are chosen to reproduce the approximately 4e-3 f0 NPR oscillation and are not measured for this specific cavity.
  • Polarizer angle and birefringence angles = theta = -pi/4; phi1 = phi2 = xi1 = xi2 = 0
    Chosen to yield the steady-state solution with non-equal amplitudes; the paper states 'no birefringence in the cavity' as an initial case.
assumptions (5)
  • domain assumption Erbium dipole moments lie in the plane orthogonal to the propagation direction
    Invoked in Methods to justify truncating the angular distribution to n0, n12, n21 and obtaining the finite-dimensional system (Eq. 5).
  • domain assumption The lasing field can be modeled by complex amplitudes u and v averaged over the pulse width, with polarization dynamics on the slow time scale
    The vector model (Eq. 5) describes SOP evolution rather than full pulse propagation; this is the standard approximation used in the cited prior work.
  • domain assumption The injected signal is continuous wave with constant total power and a rotating polarization state as in Eq. (4)
    The experimental injection uses a polarization scrambler; the model assumes perfect sinusoidal polarization rotation with a fixed phase difference.
  • ad hoc to paper Observed low-frequency components are sidebands of the NPR-driven oscillation and can synchronize through overlap
    This is the central mechanism asserted in the Discussion; it is not derived from the equations and is the basis for calling the regime entrainment rather than forced response.
  • standard math Standard Jones calculus for polarization controllers and polarizer
    Used for transfer matrix A in Eq. (6).

how reviews work

0 comments
Cite this review

Pith. "Pith review of Nonlinear synchronization through vector subharmonic entrainment." pith.science (2026). https://pith.science/paper/6WZRBT4I

@misc{pith2026250723596,
  author       = {Pith},
  title        = {Pith review of: Nonlinear synchronization through vector subharmonic entrainment},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6WZRBT4I}},
  note         = {Machine review of arXiv:2507.23596}
}
read the original abstract

Synchronization is ubiquitous across a wide range of fields. Subharmonic entrainment (SHE) is a nonlinear synchronization phenomenon that results in a locking oscillator at a frequency of an external periodic forcing signal with a fraction of the oscillator frequency. Beyond the fundamentals of nonlinear dynamics, SHE has a range of practical applications from stabilizing ultrafast laser pulses to optimizing control in various engineering and natural systems. However, the vectorial nature of SHE remains elusive. Here, we present the results of a theoretical and experimental study of a vector type of subharmonic entrainment (VSHE) using a passively mode-locked fiber laser as a testbed. We unveil the mechanism of vectorial SHE, in which weak external signals can entrain internal laser dynamics through vectorial coupling. Vectorial SHE presents in the form of synchronization between the subharmonic of mode-locking-driven oscillations and continuous wave (CW) signal through an evolving state of polarization. This CW signal, driven by the internal dynamics of the injected signal, causes VSHE with the frequencies ratios of multiples of ten, resulting in a partially mode-locking regime operation. Our findings offer new control techniques over mode-locking and additional dimension such as polarization states.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

41 extracted references · 41 canonical work pages

  1. [1]

    PNAS 109, 4786 (2012)

    Bialek, W., Cavagna, A., Giardina, I., Mora, T., Silvestri, E., Viale, M., Walczak, A.M.: Statistical mechanics for natural flocks of birds. PNAS 109, 4786 (2012)

    work page 2012

  2. [2]

    Papo, D., Buld´ u, J.M., Boccaletti, S., Bullmore, E.T.: Complex network theory and the brain. Philos. Trans. Roy. Soc. B, Biol. Sci. 369, 20130520 (2014)

    work page 2014

  3. [3]

    Schintler, L.A., Gorman, S.P., Reggiani, A., Patuelli, R., Gillespie, A., Nijkamp, P., Rutherford, J.: Complex network phenomena in telecommunication systems. Netw. Spatial Econ. 5, 351 (2005)

    work page 2005

  4. [4]

    Complex Adapt

    Batool, K., Niazi, M.A.: Modeling the internet of things: A hybrid modeling approach using complex networks and agent-based models. Complex Adapt. Syst. Model. 5, 4 (2017)

    work page 2017

  5. [5]

    Nature Commun

    O’Keeffe, K.P., Hong, H., Strogatz, S.H.: Oscillators that sync and swarm. Nature Commun. 8, 1504 (2017)

    work page 2017

  6. [6]

    Mancini, H., Vidal, G.: Dynamics of two coupled chaotic systems driven by external signals. Eur. Phys. J. D 62, 57 (2010)

    work page 2010

  7. [7]

    IEEE Access 7, 174793 (2019)

    Minati, L., Ito, H., Perinelli, A., Ricci, L., Faes, L., Yoshimura, N., Koike, Y., Frasca, M.: Connectivity influences on nonlinear dynamics in weakly-synchronized networks: Insights from r¨ ossler systems, electronic chaotic oscillators, model and biological neurons. IEEE Access 7, 174793 (2019)

    work page 2019

  8. [8]

    Arenas, A., D ´ ıaz-Guilera, A., Kurths, J., Moreno, Y., Zhou, C.: Synchronization in complex networks. Phys. Rep. 469, 93 (2008)

    work page 2008

Show all 41 references
  1. [9]

    Cambridge University Press, Cambridge, England (2001) 14

    Pikovsky, A., Rosenblum, M., Kurths, J.: Synchronization: A Universal Concept in Nonlinear Science. Cambridge University Press, Cambridge, England (2001) 14

    2001

  2. [10]

    Buczek, C.J., Freiberg, R.J., Skolnick, M.L.: Laser injection locking. Proc. IEEE 61, 1411 (1973)

    1973

  3. [11]

    Lang, R.: Injection locking properties of a semiconductor laser. IEEE J. Quantum Electron. 18, 976 (1982)

    1982

  4. [12]

    Gat, O., Kielpinski, D.: Frequency comb injection locking of mode locked lasers. New J. Phys. 15, 033040 (2013)

    2013

  5. [13]

    Yu, T., Jiang, S., Fang, J., Liu, T., Wu, X., Yan, M., Huang, K., Zeng, H.: Passive repetition-rate stabilization for a mode-locked fiber laser by electro-optic modulation. Opt. Lett. 47, 1178 (2022)

    2022

  6. [14]

    Mao, D., Wang, H., Zhang, H., Zeng, C., Du, Y., He, Z., Sun, Z., Zhao, J.: Synchro- nized multi-wavelength soliton fiber laser via intracavity group delay modulation. Nat. Commun. 12, 1 (2021)

    2021

  7. [15]

    Sergeyev, S.V., Eliwa, M., Kbashi, H.: Polarization attractors driven by vector soliton rain. Opt. Express 30, 35663 (2022)

    2022

  8. [16]

    Chang, Z., Kong, L., Cao, Y., Liu, A., Li, Z., Wu, Q., Huang, J., Gao, L., Zhu, T.: Real-time dynamics of optical controlling for bound states of mode-locked fiber laser with short-range interaction. Opt. Laser Technol. 149, 107859 (2022)

    2022

  9. [17]

    Optica 9, 1307 (2022)

    Zou, D., Song, Y., Gat, O., Hu, M., Grelu, P.: Synchronization of the internal dynamics of optical soliton molecules. Optica 9, 1307 (2022)

    2022

  10. [18]

    Kielpinski, D., Gat, O.: Phase-coherent repetition rate multiplication of a mode- locked laser from 40 mhz to 1 ghz by injection locking. Opt. Express 20, 2717 (2012)

    2012

  11. [19]

    Ribenek, V.A., Stoliarov, D.A., Korobko, D.A., Fotiadi, A.A.: Mitigation of the supermode noise in a harmonically mode-locked ring fiber laser using optical injection. Opt. Lett. 46, 5747–5750 (2021)

    2021

  12. [20]

    Ribenek, V.A., Stoliarov, D.A., Korobko, D.A., Fotiadi, A.A.: Pulse repetition rate tuning of a harmonically mode-locked ring fiber laser using resonant optical injection. Opt. Lett. 46, 5687 (2021)

    2021

  13. [21]

    Korobko, D.A., Ribenek, V.A., Stoliarov, D.A., M´ egret, P., Fotiadi, A.A.: Res- onantly induced mitigation of supermode noise in a harmonically mode-locked fiber laser: revealing the underlying mechanisms. Opt. Express 30, 17243 (2022)

    2022

  14. [22]

    Korobko, D.A., Ribenek, V.A., Itrin, P.A., Stoliarov, D.A., Fotiadi, A.A.: Polarization maintaining harmonically mode-locked fiber laser with suppressed supermode noise due to continuous wave injection. Opt. Laser Technol. 162, 109284 (2023) 15

    2023

  15. [23]

    Th´ evenin, J., Romanelli, M., Vallet, M., Brunel, M., Erneux, T.: Resonance assisted synchronization of coupled oscillators: frequency locking without phase locking. Phys. Rev. Lett. 107, 104101 (2011)

    2011

  16. [24]

    Xian, T., Zhan, L., Wang, W., Zhang, W.: Subharmonic entrainment breather solitons in ultrafast lasers. Phys. Rev. Lett. 125, 163901 (2020)

    2020

  17. [25]

    Wu, X., Peng, J., Boscolo, S., Finot, C., Zeng, H.: Synchronization, desynchro- nization, and intermediate regime of breathing solitons and soliton molecules in a laser cavity. Phys. Rev. Lett. 131, 263802 (2023)

    2023

  18. [26]

    (eds.): Polarization Dynamics of Mode-locked Fiber Lasers: Science, Technology and Applications

    Sergeyev, S., Mou, C. (eds.): Polarization Dynamics of Mode-locked Fiber Lasers: Science, Technology and Applications. CRC Press, London, New York (2023)

    2023

  19. [27]

    Laser Phys

    Kbashi, H.J., Sergeyev, S.V., Araimi, M.A., Tarasov, N., Rozhin, A.: Vector soliton rain. Laser Phys. Lett. 16, 035103 (2019)

    2019

  20. [28]

    Kbashi, H., Sergeyev, S.V., Mou, C., Garcia, A.M., Araimi, M.A., Rozhin, A., Kolpakov, S., Kalashnikov, V.: Bright-dark rogue waves. Ann. Phys.530, 1700362 (2018)

    2018

  21. [29]

    Sergeyev, S., Kolpakov, S., Loika, Y.: Vector harmonic mode-locking by acoustic resonance. Photon. Res. 9, 1432 (2021)

    2021

  22. [30]

    Sergeyev, S.V.: Fast and slowly evolving vector solitons in mode-locked fibre lasers. Phil. Trans. R. Soc. A 372, 20140006 (2014)

    2014

  23. [31]

    Light Sci

    Sergeyev, S.V., Mou, C., Turitsyna, E.G., Rozhin, A., Turitsyn, S.K., Blow, K.: Spiral attractor created by vector solitons. Light Sci. Appl. 3, 131 (2014)

    2014

  24. [32]

    invisible

    Wang, Q., Wang, P., Xu, Q., Shi, Z., He, J., Wang, Z., Liu, Y.: Observation of the “invisible” pulsation of soliton molecules in a bidirectional ultrafast fiber laser. Opt. Express 31, 19036 (2023)

    2023

  25. [33]

    Wu, Q., Gao, L., Cao, Y., Wabnitz, S., Chang, Z., Liu, A., Huang, J., Huang, L., Zhu, T.: Single-shot measurement of wavelength-resolved state of polarization dynamics in ultrafast lasers using dispersed division-of-amplitude. Photon. Res. 11, 35 (2023)

    2023

  26. [34]

    Nanoscale 15, 7566 (2023)

    Wang, Q., Li, Z., Wang, P., Xu, Q., Zhang, Z., Wang, Z., Huang, Y., Liu, Y.: Q- switched and vector soliton pulses from an er-doped fiber laser with high stability based on a γ-graphyne saturable absorber. Nanoscale 15, 7566 (2023)

    2023

  27. [35]

    Science Advances 11(12), 3660 (2025)

    Wu, X., Peng, J., Yuan, B., Boscolo, S., Finot, C., Zeng, H.: Unveiling the com- plexity of arnold’s tongues in a breathing-soliton laser. Science Advances 11(12), 3660 (2025)

    2025

  28. [36]

    JOSA B 26, 2290 (2009)

    Ding, E., Kutz, J.N.: Operating regimes, split-step modeling, and the haus master 16 mode-locking model. JOSA B 26, 2290 (2009)

    2009

  29. [37]

    Dengra, A., G´ omez-Alcal´ a, R.: Multisoliton generation and control in fibre ring lasers including two linear polarizers. J. Opt. 14, 055204 (2012)

    2012

  30. [38]

    Zeghlache, H., Boulnois, A.: Polarization instability in lasers. i. model and steady states of neodymium-doped fiber lasers. Phys. Rev. A 52, 4229 (1995)

    1995

  31. [39]

    Quantum Semiclass

    Leners, R., St´ ephan, G.: Rate equation analysis of a multimode bipolarization nd3+ doped fibre laser. Quantum Semiclass. Opt. 7, 757 (1995)

    1995

  32. [40]

    Sergeyev, S.V.: Spontaneous light-polarization symmetry breaking for an anisotropic ring-cavity dye laser. Phys. Rev. A 59, 3909 (1999)

    1999

  33. [41]

    Unpublished (2025) 17

    Authors: See Supplementary Material at [URL] for more details on the experi- mental setup and linear stability analysis. Unpublished (2025) 17

    2025

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.