Stabilization and Destabilization of Multimode Solitons in Nonlinear Degenerate Multi-Pass Cavities

Bingbing Zhu; Junhan Huang; Kun Ding; Shanyue Li; Zhensheng Tao

REVIEW 3 major objections 4 minor 79 references

Stabilization and Destabilization of Multimode Solitons in Nonlinear Degenerate Multi-Pass Cavities

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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

Pith's one-line read Choosing a specific Kerr-medium thickness suppresses the multimode coupling that destabilizes femtosecond solitons in degenerate multi-pass cavities, extending stable operation to a nonlinear phase of 1.5π per pass.

desk verdict A genuinely new MCS design rule for degenerate MPCs, but the first-order derivation is asked to carry a lot of weight at b=1.5π. read the letter →

arxiv 2501.13319 v2 pith:OM2SXF4W submitted 2025-01-23 physics.optics nlin.PS

Junhan Huang , Bingbing Zhu , Shanyue Li , Kun Ding , Zhensheng Tao This is my paper · ORCID

classification physics.opticsnlin.PS

keywords multimodesolitonsmulti-passcavitymode-couplingsuppressionKerrnonlinearityFloquettheorypulsecompressiondegeneracyspatio-spectralhomogeneity

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

This paper proposes that the long-standing instability of femtosecond pulses in solid-based nonlinear multi-pass cavities can be cured by choosing a specific thickness of the Kerr medium. The authors derive a mode-coupling-suppression (MCS) length at which multimode wave components in the medium interfere destructively, making the overlap integral that drives energy transfer into higher-order spatial modes vanish. In full space-time-coupled simulations, operating a degenerate cavity at this length keeps the beam stable at a nonlinear phase of $1.5\pi$ per pass, roughly twice the limit previously thought to hold for solid MPCs, and compresses 170 fs pulses to about 12.3 fs in 9 round trips with spatio-spectral homogeneity 0.93. The paper frames gas-filled cavities as the special case where the medium fills the cavity, unifying their stability with the new design rule for solid media.

What carries the argument

The mode-coupling-suppression (MCS) condition is the central object: a set of medium half-lengths $d_{\mathrm{MCS}}$ at which destructive interference inside the Kerr medium makes the overlap integral $\Theta_{n,m}(d)$ in Eq. (5) vanish. The argument is carried by first-order perturbation theory in the Floquet basis of the linear cavity, where the amplitude $C_{n,m}$ of a degenerate higher-order mode is proportional to $\Theta_{n,m}(d)$ divided by a vanishing energy denominator; setting the numerator to zero removes the divergence and suppresses coupling. Equation (6) expresses this as a Gouy-phase condition: the phase accumulated inside the medium must be an integer multiple of $2\pi$.

What would settle it

Build a degenerate solid MPC with a chosen degeneracy index pair and compare the output after 10 round trips at $2d = 2d_{\mathrm{MCS}}$, at $1.9\,d_{\mathrm{MCS}}$, and with a thin plate, keeping the input pulse and energy fixed. If spatio-spectral homogeneity does not peak at $d_{\mathrm{MCS}}$, or the beam breaks up at $b=1.5\pi$, the MCS condition is not the controlling mechanism. A gentler test at $b=0.5$ rad, decomposing the intracavity field into Laguerre-Gaussian modes, should show the degenerate higher-order coefficients vanish at $d_{\mathrm{MCS}}$ as the perturbative formula predicts.

Watch

Extended reading notes

Core claim

The central claim is that in a degenerate multi-pass cavity, Kerr-driven multimode coupling can be suppressed entirely at discrete medium half-lengths $d_{\mathrm{MCS}}$ satisfying $4u \arctan\!\left(\frac{d_{\mathrm{MCS}}/L}{\sqrt{2F/L-1}}\right) = 2k\pi$. At these lengths the Gouy phase accumulated inside the medium makes the overlap integral $\Theta_{n,m}(d)$ vanish for every degenerate mode, so the first-order perturbation coefficient $C_{n,m}$ in the Floquet expansion vanishes and no energy leaks from the fundamental spatial mode. The paper argues that this destructive-interference mechanism explains why gas-filled MPCs, where the medium fills the cavity, are intrinsically stable, and that it can be engineered into a solid MPC. With the MCS length set for a degenerate (11,9) cavity, the simulations show stable soliton propagation at $b=1.5\pi$ per pass, more than 13-fold compression of 170 fs pulses to about 12.3 fs after 9 round trips, and spatio-spectral homogeneity 0.93.

Load-bearing premise

The derivation of the MCS condition assumes the nonlinear phase per pass is much smaller than 1 ($b \ll 1$), yet the headline stable operation is shown at $b = 1.5\pi \approx 4.71$ rad; if the $\Theta_{n,m}=0$ cancellation fades at large $b$, the design rule would fail at its claimed operating point.

Editorial extensions

If this is right

Solid MPCs can be operated at nonlinear phases up to about $1.5\pi$ per pass without the beam breakup that normally appears at degenerate geometries, roughly doubling the single-pass nonlinear phase limit for solid media.
A cavity degeneracy that destabilizes thin-plate MPCs becomes an operating point once the medium length is set to $d_{\mathrm{MCS}}$, turning a liability into a design feature.
Gas-filled MPCs emerge as the special case $d/L=1$ of the MCS condition, giving one framework that explains both gas and solid behavior.
At the MCS length, a single-stage all-solid compressor can take 170 fs pulses to about 12.3 fs in 9 round trips with spatio-spectral homogeneity 0.93, and the design remains stable under the misalignment and fabrication perturbations tested.

Reading between the lines

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

The same destructive-interference mechanism should generalize to any resonator where the nonlinearity occupies a finite slice of a periodic transport map, making the MCS length a phase-matching knob analogous to quasi-phase-matching in nonlinear crystals.
Because the MCS condition depends only on geometry and linear propagation, it could be tuned in real time, by translating the medium or adjusting the cavity geometry, to re-stabilize a cavity as pulse energy is scaled.
The paper's own Floquet model neglects space-time coupling, which it notes perturbs the ideal $\Theta_{n,m}=0$ condition; a natural extension is to check whether the optimal length shifts or broadens when GDD, self-steepening, and Raman delay are included at even higher intensities.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Short version: this is a real contribution. The paper gives a closed-form medium length, Eq. (6), that should suppress multimode coupling in degenerate multipass cavities, with gas-filled MPCs falling out as the d/L=1 limit. The NLSE simulations and Fox-Li cross-checks at small b convince me the mechanism is not numerology. The weak spot is exactly where the stress-test note points: the perturbation derivation assumes b≪1, but the flagship demonstration runs at b=1.5π per pass. The paper is candid that discrepancies grow at large b and that space-time coupling perturbs the Θ=0 condition, but it does not quantify how much the optimal dMCS shifts with b, nor does it scan d at high b to show the stability peak actually sits at the predicted length. One stable (u,v)=(11,9) run is evidence, not a scaling law.

What is new: Eq. (6) is not in the earlier degenerate-MPC literature (refs 61–63), which flag degeneracy as a problem but do not give a suppression criterion. The Floquet reformulation and the overlap-integral cancellation are clean, and the recovery of d/L=1 as an MCS case is a nice unifying observation.

What is solid: the analytical expansion is done carefully, the Fox-Li validation at small b matches the perturbation eigenstates, and the full space-time-coupled NLSE results— robustness to a 1 cm displacement, ±5% GDD, and length errors—are the kind of evidence that makes this worth a referee's time. No code or data is shipped, which is a minor complaint given the simulation-heavy nature of the work.

Where I'd push back on the reader: the circularity burden is low, not moderate; the MCS condition is derived and then tested, not fit. The b≪1 issue is real but not disqualifying—it is a request for a convergence study or a higher-order estimate, not a demonstrated failure of the mechanism.

Bottom line: for people designing solid MPCs, this is a useful guide and a plausible path past the ~0.8π barrier. For me, it is not yet a proven design law until someone shows the suppression survives as b moves from 0.5 to 1.5π, either analytically to higher order or in a systematic d-scan in simulation. That is an addressable revision, not a fatal flaw.

Recommendation: send it to peer review. Ask the authors for either a second-order perturbative check or a b-sweep of the optimum dMCS, and make the supplementary derivations accessible. I would cite it as a proposed design rule, with the caveat noted, and I would bring it to a reading group.

Referee Report

3 major / 4 minor

Summary. The manuscript studies the stability of femtosecond pulses in degenerate solid multi-pass cavities (MPCs). It introduces a Floquet-perturbation model in which Kerr-induced coupling to higher-order Laguerre-Gaussian modes is proportional to an overlap integral Θn,m(d), and shows that choosing the medium length so that Θn,m(d)=0, the mode-coupling-suppression (MCS) length, suppresses multimode coupling. Full space-time-coupled NLSE simulations are used to map stability phase diagrams and to demonstrate stable propagation at b=1.5π per pass in a fused-silica MPC with 2d=8.47 cm, yielding compression from 170 fs to about 12.3 fs with spatio-spectral homogeneity 0.93. The paper also derives critical-power-limited maximum nonlinear phases and argues that gas-filled MPCs are a special case of the MCS condition.

Significance. If the MCS mechanism is quantitatively valid at the high nonlinear phases claimed, the paper provides a simple design rule for solid MPCs and a unified explanation of why gas-filled MPCs tolerate higher single-pass nonlinear phases than thin-solid-medium MPCs. The work combines an analytical Floquet-perturbation framework, Fox-Li eigenmode checks, and full space-time-coupled NLSE simulations with realistic fused-silica parameters, including GDD compensation, Raman response, self-steepening, and robustness tests against medium-length, displacement, and dispersion perturbations. The predicted operating point, 1.5π per pass in a solid MPC with high spatio-spectral homogeneity, is specific and falsifiable, which makes the manuscript of considerable interest to the ultrafast-optics community. The main deficit, discussed below, is that the analytical derivation of the MCS length is explicitly small-b while the headline result uses b=4.71 rad, and the paper does not yet provide a quantitative bridge between these two regimes.

major comments (3)

[Methods, after Eq. (23); Eq. (4); Eq. (6)] The perturbation expansion that produces Eq. (4) and hence the MCS condition Eq. (6) is introduced in Methods with the statement “we introduce the perturbation terms by assuming b ≪ 1”, whereas the headline demonstration in Fig. 4 operates at b=1.5π. The paper acknowledges that discrepancies with the Fox-Li iteration grow when b is large and that space-time coupling perturbs the ideal Θn,m=0 condition, but it does not provide a quantitative bound on the neglected higher-order terms or a check that Eq. (6) still gives the suppression-optimal length at b=1.5π. Please add a scaling test, such as scanning b and comparing the NLSE-optimal medium length with Eq. (6) at several b values, or computing second-order corrections to C̃n,m, so that the MCS design rule is secured at the claimed operating point.
[Methods, Eq. (4); Sec. 3] At exact cavity degeneracy the denominator ε0,0−εn,m in Eq. (4) vanishes, so the nondegenerate perturbative expression for Cn,m diverges. The paper uses this divergent coefficient to explain beam destabilization at degenerate geometries, but nondegenerate perturbation theory is not valid at the degeneracy point itself. Although the Fox-Li and NLSE results independently support the qualitative destabilization trend, the divergent-coefficient argument should be replaced or supplemented by a degenerate-perturbation treatment or by a controlled detuning scan near the degeneracy condition, so that the mechanism invoked in the phase-diagram discussion is internally consistent.
[Sec. 3; Fig. 4] The analytical model neglects space-time coupling, and the paper explicitly states that space-time coupling modifies the details of the stability landscape and perturbs the ideal destructive-interference condition Θn,m=0. The main simulation in Fig. 4 includes space-time coupling at a single operating point (u,v)=(11,9), d=dMCS, b=1.5π, but the paper does not quantify how much the effective MCS length shifts when temporal effects are included. Please provide a quantitative estimate of this shift, for example by comparing the NLSE-optimal d with Eq. (6) over a range of pulse durations and intensities, or by showing that the MCS length remains optimal across such a range.

minor comments (4)

[Methods, after Eq. (27)] The sentence “Equation (25) is an alias for Eq. (5)” appears to be a typo: Eq. (25) is the matrix element ⟨Φn,m|Vk|Φ0,0⟩, while the definition of Θn,m that corresponds to Eq. (5) in the main text is Eq. (26).
[Methods, Floquet theory] In the sentence “We use Floquet theory to analyze the linear contribution in Eq. (8)”, the reference should be to Eq. (11), the simplified NLSE, rather than Eq. (8).
[Reference list] References [78] and [79] appear in the reference list but I could not find in-text citations for them in the main text; if they are not cited in the Supplementary Material, they should be removed or cited explicitly.
[Eq. (6)] For the reader’s convenience, Eq. (6) could be explicitly solved for dMCS: dMCS = L √(2F/L−1) tan(kπ/(2u)); the current implicit form is correct but less immediately usable as a design rule.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the MCS length is derived analytically from a first-order Floquet perturbation calculation and then validated against independent NLSE simulations; no fitted parameter is renamed as a prediction.

full rationale

The paper's central prediction, the mode-coupling-suppression length dMCS, is obtained by setting the overlap integral Θn,m(d) in Eq. (5) to zero, which yields Eq. (6) as a closed-form expression in terms of the cavity geometry (u, v, F, L). This is an analytical derivation from the linear-cavity LG/Floquet basis, not a fit to the simulation output. The full space-time-coupled NLSE simulations (Figs. 2 and 4) are independent checks: they use the derived dMCS value for a different degeneracy pair (u,v)=(11,9) and observe stable propagation and compression, with no parameter of the NLSE tuned to force the MCS result. The paper is also benchmarked externally against previous experimental spectral data (SM S1) and against Fox-Li iteration for the eigenstates. The only in-text caveats—that the perturbation expansion assumes b≪1 (Methods: 'we introduce the perturbation terms by assuming b ≪ 1') and that space-time coupling perturbs the ideal Θn,m=0 condition—are validity/robustness limitations, not circularity: they concern whether the first-order condition survives at b=1.5π, not whether the prediction reduces to its inputs. No load-bearing self-citation is present: references to prior MPC work (e.g., Refs. 63, 68) supply standard formulas and numerical algorithms rather than the MCS condition itself. The claim that gas-filled MPCs are a special case (d/L=1 ⇒ k=v) follows algebraically from Eqs. (2) and (6), not from an imported uniqueness result. Therefore the derivation chain is self-contained, and the appropriate circularity score is 0.

Assumptions & free parameters 1 free parameters · 7 assumptions · 0 invented entities

No free parameters are fitted to the central claim. The simulation operating points (b, dMCS, GDD) are chosen by design rather than calibrated to reproduce the headline compression. The main assumptions are the small-b perturbation basis, neglect of space-time coupling in the analytic model, the equivalent-lens mirror treatment, and literature values for Raman and self-focusing parameters. No new physical entities are introduced; the MCS length is a derived geometric condition, not a new object.

free parameters (1)

Single-pass nonlinear phase b = 1.5pi in headline; scanned 0-2pi in phase diagrams
Chosen by hand through input pulse energy via Eq. (1), not fitted to data. It is the control parameter of the study.

assumptions (7)

ad hoc to paper First-order perturbation theory with b much less than 1 remains predictive at b=1.5pi
Methods state 'assuming b much less than 1'; the headline simulation uses b about 4.71 rad. The paper acknowledges discrepancies at large b but does not justify the extrapolation of the MCS condition to this regime.
domain assumption Space-time coupling can be neglected in the analytic Floquet and perturbation model
The model neglects space-time coupling, and the paper states it 'does modify the details of the stability landscape' in the Floquet and Perturbation Model Analysis section.
domain assumption Cavity mirrors are accurately represented by thin lenses in an equivalent-lens sequence
Used throughout Methods; standard for paraxial MPC modeling but an approximation that ignores mirror aberrations and finite aperture effects.
domain assumption The Kerr response is captured by the instantaneous plus single-Lorentzian Raman model with parameters from Ref. 65
NLSE Eqs. (9)-(10) use chiK=0.2, tau1=20 fs, tau2=40 fs from literature; no sensitivity study is shown for these Raman parameters.
domain assumption Effective medium length deff = z0 arctan(d/z0) relates intensity to SNLP
Used in Eq. (1) and Methods; valid for weakly focused beams and affects all quoted b values.
domain assumption Marburger empirical self-focusing formula provides the self-focusing length
Eq. (34) from Ref. 77 is used to derive the relaxed bmax in Eq. (8); the constants are empirical.
standard math Floquet theorem and orthogonality of Floquet eigenstates in the periodic cavity
Foundation of Eq. (3) and the perturbation expansion; standard mathematical framework.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Stabilization and Destabilization of Multimode Solitons in Nonlinear Degenerate Multi-Pass Cavities." pith.science (2026). https://pith.science/paper/OM2SXF4W

@misc{pith2026250113319,
  author       = {Pith},
  title        = {Pith review of: Stabilization and Destabilization of Multimode Solitons in Nonlinear Degenerate Multi-Pass Cavities},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OM2SXF4W}},
  note         = {Machine review of arXiv:2501.13319}
}

read the original abstract

Optical solitons in multimode nonlinear optical systems offer a unique platform for exploring the interplay of nonlinearity, dispersion, and spatial mode coupling, offering insights into complex nonlinear wave phenomena. Multi-pass cavities (MPCs) incorporating nonlinear Kerr media serve as prototypical systems, enabling high-efficiency supercontinuum generation and pulse compression. However, stabilizing femtosecond laser pulses in solid-medium-based MPCs (solid MPCs) under strong Kerr nonlinearity remains a significant challenge due to multimode coupling, which disrupts beam stability. In this work, we address this challenge by investigating the stability of laser pulses in MPCs using Floquet and perturbation model. We identify novel mode-coupling-suppression (MCS) medium lengths, where destructive interference among multimode wave components suppresses coupling and facilitates soliton stabilization. Under MCS conditions, our simulations demonstrate stable beam propagation in solid MPCs with nonlinear phases up to 1.5{\pi} per pass, achieving >13-fold pulse compression with excellent spatio-spectral homogeneity. Our findings offer valuable guidance for designing advanced MPCs with tailored Kerr media.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

79 extracted references · 78 canonical work pages

[1]

Haus, H. A. & Wong, W. S. Solitons in optical communications. Rev. Mod. Phys. 68, 423–444 (1996)

work page 1996
[2]

& Akhmediev, N

Grelu, P. & Akhmediev, N. Dissipative solitons for mode-locked lasers. Nat. Photonics 6, 84–92 (2012)

work page 2012
[3]

& Wise, F

Kieu, K., Renninger, W., Chong, A. & Wise, F. W. Sub-100-fs pulses at watt- level powers from a dissipative-soliton fiber laser. Opt. Lett. 34, 593–595 (2009)

work page 2009
[4]

W., Gaeta, A

Boyd, R. W., Gaeta, A. L. & Giese, E. Nonlinear Optics. in Springer Handbook of Atomic, Molecular, and Optical Physics 1097–1110 (Springer International Publishing, 2023)

work page 2023
[5]

G., CHRISTODOULIDES, D

LIU, Z., WRIGHT, L. G., CHRISTODOULIDES, D. N. & WISE, F. W. Kerr self-cleaning of femtosecond-pulsed beams in graded-index multimode fiber. Opt. Lett. 41, 3675–3678 (2016)

work page 2016
[6]

Safaei, R. et al. High-energy multidimensional solitary states in hollow-core fibres. Nat. Photonics 14, 733–739 (2020)

work page 2020
[7]

Krupa, K. et al. Spatial beam self-cleaning in multimode fibres. Nat. Photonics 28 11, 237–241 (2017)

work page 2017
[8]

G., Renninger, W

Wright, L. G., Renninger, W. H., Christodoulides, D. N. & Wise, F. W. Spatiotemporal dynamics of multimode optical solitons. Opt. Express 23, 3492–3506 (2015)

work page 2015

Show all 79 references

[9]

Zitelli, M. et al. High-energy soliton fission dynamics in multimode GRIN fiber. Opt. Express 28, 20473 (2020)

2020
[10]

& Columbo, L

Brambilla, M., Maggipinto, T., Patera, G. & Columbo, L. Cavity light bullets: Three-dimensional localized structures in a nonlinear optical resonator. Phys. Rev. Lett. 93, 203901 (2004)

2004
[11]

Collapse of optical pulses

Silberberg, Y. Collapse of optical pulses. Opt. Lett. 15, 1282–1284 (1990)

1990
[12]

Parra-Rivas, P. et al. Pure quartic three-dimensional spatiotemporal Kerr solitons in graded-index media. Phys. Rev. A 109, 033516 (2024)

2024
[13]

& Wabnitz, S

Parra-Rivas, P., Sun, Y. & Wabnitz, S. Dynamics of three-dimensional spatiotemporal solitons in multimode waveguides. Opt. Commun. 546, 129749 (2023)

2023
[14]

Renninger, W. H. & Wise, F. W. Optical solitons in graded-index multimode fibres. Nat. Commun. 4, 1719 (2013)

2013
[15]

Sun, Y. et al. Multimode soliton collisions in graded-index optical fibers. Opt. Express 30, 21710 (2022)

2022
[16]

SUN, Y. et al. Multimode solitons in optical fibers: a review. Photonics Res. 12, 2581 (2024)

2024
[17]

Lilienfein, N. et al. Temporal solitons in free-space femtosecond enhancement 29 cavities. Nat. Photonics 13, 214–218 (2019)

2019
[18]

G., Renninger, W

Wright, L. G., Renninger, W. H., Christodoulides, D. N. & Wise, F. W. Nonlinear multimode photonics: nonlinear optics with many degrees of freedom. Optica 9, 824–841 (2022)

2022
[19]

Russbueldt, P. et al. Scalable 30 fs laser source with 530 W average power. Opt. Lett. 44, 5222–5225 (2019)

2019
[20]

Pfaff, Y. et al. Nonlinear pulse compression of a 200 mJ and 1 kW ultrafast thin-disk amplifier. Opt. Express 31, 22740–22756 (2023)

2023
[21]

Daniault, L. et al. Sub-2-cycle post-compression of multi-mJ energy Ti : sapphire laser pulses in a gas-filled multi-pass cell. Opt. Lett. 49, 6833–6836 (2024)

2024
[22]

Barbiero, G. et al. Efficient nonlinear compression of a thin-disk oscillator to 8.5 fs at 55 W average power. Opt. Lett. 46, 5304–5307 (2021)

2021
[23]

Silletti, L. et al. Dispersion-engineered multi-pass cell for single-stage post- compression of an ytterbium laser. Opt. Lett. 48, 1842–1845 (2023)

2023
[24]

Gierschke, P. et al. Nonlinear pulse compression to 51-W average power GW- class 35-fs pulses at 2-µ m wavelength in a gas-filled multi-pass cell. Opt. Lett. 47, 3511–3514 (2022)

2022
[25]

& Limpert, J

Mü ller, M., Buldt, J., Stark, H., Grebing, C. & Limpert, J. Multipass cell for high-power few-cycle compression. Opt. Lett. 46, 2678–2681 (2021)

2021
[26]

& Karsch, S

Kaumanns, M., Kormin, D., Nubbemeyer, T., Pervak, V. & Karsch, S. Spectral broadening of 112 mJ, 1.3 ps pulses at 5 kHz in a LG10 multipass cell with 30 compressibility to 37 fs. Opt. Lett. 46, 929–932 (2021)

2021
[27]

& Limpert, J

Grebing, C., Mü ller, M., Buldt, J., Stark, H. & Limpert, J. Kilowatt-average- power compression of millijoule pulses in a gas-filled multi-pass cell. Opt. Lett. 45, 6250–6253 (2020)

2020
[28]

Viotti, A.-L. et al. Temporal pulse quality of a Yb:YAG burst-mode laser post- compressed in a multi-pass cell. Opt. Lett. 46, 4686–4689 (2021)

2021
[29]

Balla, P. et al. Postcompression of picosecond pulses into the few-cycle regime. Opt. Lett. 45, 2572–2575 (2020)

2020
[30]

Ueffing, M. et al. Nonlinear pulse compression in a gas-filled multipass cell. Opt. Lett. 43, 2070–2073 (2018)

2018
[31]

Lavenu, L. et al. Nonlinear pulse compression based on a gas-filled multipass cell. Opt. Lett. 43, 2252–2255 (2018)

2018
[32]

Kaumanns, M. et al. Multipass spectral broadening of 18 mJ pulses compressible from 13 ps to 41 fs. Opt. Lett. 43, 5877–5880 (2018)

2018
[33]

Rueda, P., Videla, F., Witting, T., Torchia, G. A. & Furch, F. J. 8 fs Laser Pulses From a Compact Gas-Filled Multi-Pass Cell. Opt. Express 29, 27004– 27013 (2021)

2021
[34]

Kramer, P. L. et al. Enabling high repetition rate nonlinear THz science with a kilowatt-class sub-100 fs laser source. Opt. Express 28, 16951–16967 (2020)

2020
[35]

Guo, J. et al. Spatial mode cleaning and efficient nonlinear pulse compression to sub-50 fs in a gas-filled multipass cell. Opt. Lett. 49, 4385–4388 (2024)

2024
[36]

& 31 RUSSBUELDT, P

SCHULTE, J., SARTORIUS, T., WEITENBERG, J., VERNALEKEN, A. & 31 RUSSBUELDT, P. Nonlinear pulse compression in a multipass cell. Opt. Lett. 41, 4511–4514 (2016)

2016
[37]

Russbueldt, P., Mans, T., Weitenberg, J., Hoffmann, H. D. & Poprawe, R. Compact diode-pumped 11 kW Yb:YAG Innoslab femtosecond amplifier. Opt. Lett. 35, 4169–4171 (2010)

2010
[38]

Eisenbach, L. et al. Highly efficient nonlinear compression of mJ pulses at 2 μm wavelength to 20 fs in a gas-filled multi-pass cell. J. Phys. Photonics 6, 035015 (2024)

2024
[39]

Heyl, C. M. et al. High-energy bow tie multi-pass cells for nonlinear spectral broadening applications. J. Phys. Photonics 4, 014002 (2022)

2022
[40]

Daher, N. et al. Multipass cells: 1D numerical model and investigation of spatio-spectral couplings at high nonlinearity. J. Opt. Soc. Am. B 37, 993–999 (2020)

2020
[41]

SCHÖNBERG, A. et al. Compact, folded multi-pass cells for energy scaling of post-compression. arXiv:2409.02542 (2024)

2024 arXiv
[42]

Khatri, D. et al. Carrier-envelope phase-stabilized ultrashort pulses from a gas- filled multi-pass cell. Appl. Phys. Lett. 125, 094103 (2024)

2024
[43]

Carlson, D. et al. Nonlinear post-compression in multi-pass cells in the mid-IR region using bulk materials. Opt. Lett. 47, 5289–5292 (2022)

2022
[44]

JARGOT, G. et al. Self-compression in a multipass cell. Opt. Lett. 43, 5643– 5646 (2018)

2018
[45]

& Pronin, O

Fritsch, K., Poetzlberger, M., Pervak, V., Brons, J. & Pronin, O. All-solid-state 32 multipass spectral broadening to sub-20 fs. Opt. Lett. 43, 4643–4646 (2018)

2018
[46]

Grö bmeyer, S. et al. Self-compression at 1 µ m wavelength in all-bulk multi- pass geometry. Appl. Phys. B Lasers Opt. 126, 159 (2020)

2020
[47]

Song, J. et al. Generation of 601 fs pulse from an 8 kHz Nd:YVO4 picosecond laser by multi-pass-cell spectral broadening. Chinese Opt. Lett. 19, 093201 (2021)

2021
[48]

Zhang, X. et al. Milli-Joule pulses post-compressed from 14 ps to 475 fs in bulk-material multi-pass cell based on cylindrical vector beam. Chinese Phys. B 32, 104206 (2023)

2023
[49]

Barbiero, G. et al. Broadband terahertz solid-state emitter driven by Yb:YAG thin-disk oscillator. J. Phys. B At. Mol. Opt. Phys. 53, 125601 (2020)

2020
[50]

& Pronin, O

Grö bmeyer, S., Brons, J., Seidel, M. & Pronin, O. Carrier-Envelope-Offset Frequency Stable 100 W-Level Femtosecond Thin-Disk Oscillator. Laser Photonics Rev. 13, 1800256 (2019)

2019
[51]

Vicentini, E. et al. Nonlinear pulse compression to 22 fs at 15.6 µ J by an all- solid-state multipass approach. Opt. Express 28, 4541–4549 (2020)

2020
[52]

TSAI, C.-L. et al. Efficient nonlinear compression of a mode-locked thin-disk oscillator to 27 fs at 98 W average power. Opt. Lett. 44, 4115–4118 (2019)

2019
[53]

NATILE, M. et al. CEP-stable high-energy ytterbium-doped fiber amplifier. Opt. Lett. 44, 3909–3912 (2019)

2019
[54]

Raab, A.-K. et al. Multi-gigawatt peak power post-compression in a bulk multi-pass cell at a high repetition rate. Opt. Lett. 47, 5084–5087 (2022). 33

2022
[55]

Viotti, A.-L. et al. Few-cycle pulse generation by double-stage hybrid multi- pass multi-plate nonlinear pulse compression. Opt. Lett. 48, 984–987 (2023)

2023
[56]

Song, J. et al. Generation of 172 fs pulse from a Nd: YVO4 picosecond laser by using multi-pass-cell technique. Appl. Phys. B Lasers Opt. 127, 50 (2021)

2021
[57]

Weitenberg, J. et al. Multi-pass-cell-based nonlinear pulse compression to 115 fs at 75 µ J pulse energy and 300 W average power. Opt. Express 25, 20502– 20510 (2017)

2017
[58]

Seidel, M. et al. Factor 30 Pulse Compression by Hybrid Multipass Multiplate Spectral Broadening. Ultrafast Sci. 2022, 9754919 (2022)

2022
[59]

& Brabec, T

Milosevic, N., Tempea, G. & Brabec, T. Optical pulse compression: bulk media versus hollow waveguides. Opt. Lett. 25, 672–674 (2000)

2000
[60]

Direct Amplification of Femtosecond Pulses

Ueffing, M. Direct Amplification of Femtosecond Pulses. (Ludwig- Maximilians-Universitä t, 2018)

2018
[61]

& Schulte, J

Russbueldt, P., Weitenberg, J., Vernaleken, A., Sartorius, T. & Schulte, J. Method and Arrangment for Spectral Broadening of Laser Pulses for Non- linear Pulse Compression. (2017)

2017
[62]

Hanna, M. et al. Nonlinear Optics in Multipass Cells. Laser Photonics Rev. 15, 2100220 (2021)

2021
[63]

Viotti, A.-L. et al. Multi-pass cells for post-compression of ultrashort laser pulses. Optica 9, 197–216 (2022)

2022
[64]

& Fujimoto, J

Sennaroglu, A. & Fujimoto, J. Design criteria for Herriott-type multi-pass cavities for ultrashort pulse lasers. Opt. Express 11, 1106–1113 (2003). 34

2003
[65]

& Wolf, J

Bergé , L., Skupin, S., Nuter, R., Kasparian, J. & Wolf, J. P. Ultrashort filaments of light in weakly ionized, optically transparent media. Reports Prog. Phys. 70, 1633–1713 (2007)

2007
[66]

Lu, C. et al. Generation of intense supercontinuum in condensed media. Optica 1, 400–406 (2014)

2014
[67]

Liu, Y. Y. et al. High-Efficiency Generation of 0.12 mJ, 8.6 Fs Pulses at 400nm Based on Spectral Broadening in Solid Thin Plates. Chinese Phys. Lett. 34, 074204 (2017)

2017
[68]

Zhang, S. et al. Solitary beam propagation in periodic layered Kerr media enables high-efficiency pulse compression and mode self-cleaning. Light Sci. Appl. 10, 53 (2021)

2021
[69]

& Kompfner, R

Herriott, D., Kogelnik, H. & Kompfner, R. Off-Axis Paths in Spherical Mirror Interferometers. Appl. Opt. 3, 523–526 (1964)

1964
[70]

Rudner, M. S. & Lindner, N. H. The Floquet Engineer’s Handbook. arXiv:2003.08252 (2020)

2020 arXiv
[71]

Fox, A. G. & Li, T. Resonant Modes in a Maser Interferometer. Bell Syst. Tech. J. 40, 453–488 (1961)

1961
[72]

Boyd, R. W. Nonlinear Optics. (Academic Press, Inc., 2008)

2008
[73]

Tan, C. Z. Determination of refractive index of silica glass for infrared wavelengths by IR spectroscopy. J. Non. Cryst. Solids 223, 158–163 (1998)

1998
[74]

Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica

Milam, D. Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica. Appl. Opt. 37, 546–550 (1998). 35

1998
[75]

& Lin, W

Ma, C. & Lin, W. Parallel simulation for the ultra-short laser pulses’ propagation in air. arXiv:1507.05988 (2015)

2015 arXiv
[76]

& Gaeta, A

Fibich, G. & Gaeta, A. L. Critical power for self-focusing in bulk media and in hollow waveguides. Opt. Lett. 25, 335–337 (2000)

2000
[77]

Marburger, J. H. Self-focusing: theory. Prog. Quantum Electron. 4, 35–110 (1975)

1975
[78]

Kevrekidis, P. G. The Discrete Nonlinear Schrö dinger Equation. (Springer Berlin, Heidelberg, 2009)

2009
[79]

Many Manda, B., Carretero-Gonzá lez, R., Kevrekidis, P. G. & Achilleos, V. Skin modes in a nonlinear Hatano-Nelson model. Phys. Rev. B 109, 094308 (2024)

2024

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

Haus, H. A. & Wong, W. S. Solitons in optical communications. Rev. Mod. Phys. 68, 423–444 (1996)

work page 1996

[2] [2]

& Akhmediev, N

Grelu, P. & Akhmediev, N. Dissipative solitons for mode-locked lasers. Nat. Photonics 6, 84–92 (2012)

work page 2012

[3] [3]

& Wise, F

Kieu, K., Renninger, W., Chong, A. & Wise, F. W. Sub-100-fs pulses at watt- level powers from a dissipative-soliton fiber laser. Opt. Lett. 34, 593–595 (2009)

work page 2009

[4] [4]

W., Gaeta, A

Boyd, R. W., Gaeta, A. L. & Giese, E. Nonlinear Optics. in Springer Handbook of Atomic, Molecular, and Optical Physics 1097–1110 (Springer International Publishing, 2023)

work page 2023

[5] [5]

G., CHRISTODOULIDES, D

LIU, Z., WRIGHT, L. G., CHRISTODOULIDES, D. N. & WISE, F. W. Kerr self-cleaning of femtosecond-pulsed beams in graded-index multimode fiber. Opt. Lett. 41, 3675–3678 (2016)

work page 2016

[6] [6]

Safaei, R. et al. High-energy multidimensional solitary states in hollow-core fibres. Nat. Photonics 14, 733–739 (2020)

work page 2020

[7] [7]

Krupa, K. et al. Spatial beam self-cleaning in multimode fibres. Nat. Photonics 28 11, 237–241 (2017)

work page 2017

[8] [8]

G., Renninger, W

Wright, L. G., Renninger, W. H., Christodoulides, D. N. & Wise, F. W. Spatiotemporal dynamics of multimode optical solitons. Opt. Express 23, 3492–3506 (2015)

work page 2015