Pith. sign in

REVIEW 3 major objections 4 minor 48 references

Responsivity and Stability of Nonlinear Exceptional Point Lasers with Saturable Gain and Loss

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read This paper claims that a two-resonator laser biased at a parity-time-symmetric exceptional point shifts its steady-state lasing frequency as the cube root of a frequency perturbation, with a tunable proportionality constant that can be…

desk verdict The closed-form signal scale factor (Eq. 16) that drives the paper's enhancement claims is algebraically wrong; the corrected leading-order coefficient has no f0 dependence and inverts the main design result, though the stability analysis has independent value. read the letter →

arxiv 2411.18720 v1 pith:WTWUQM6D submitted 2024-11-27 physics.optics physics.app-ph

Todd Darcie , J. Stewart Aitchison This is my paper · ORCID
classification physics.opticsphysics.app-ph
keywords exceptionalpointPTsymmetrysaturablegainandlosslasersensingcoupledmodetheorycube-rootresponsesignalscalefactorstability
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

The paper seeks to establish that a two-resonator laser biased at a parity-time-symmetric exceptional point, where both resonators exhibit saturable gain or absorption, responds to a small frequency perturbation with a steady-state lasing-frequency shift proportional to the cube root of the perturbation. The proportionality constant, called the signal scale factor, is set by designable parameters: coupling strength, passive losses, and the balance of saturable gain and absorption. The paper derives a closed form for this scale factor and shows it can be several orders of magnitude larger than in the previously studied single-nonlinear-resonator design, and that maximizing it also improves robustness against parametric errors. It then maps where the exceptional-point mode is stable, identifying mode-competition instabilities for asymmetric passive losses and a restabilization at slow gain relaxation or high coupling. A full-wave numerical laser calculation on coupled slabs reproduces the cube-root response, showing the effect survives spatially varying mode and gain profiles, at the cost of an extra geometric tuning parameter.

What carries the argument

The load-bearing identity is the saturation ansatz near the exceptional point: $g' = \kappa - b_g|\epsilon|^u$ and $f' = \kappa - b_f|\epsilon|^u$, stating that the saturated net gain and net loss both fall from their exceptional-point values as the same power of the detuning $\epsilon$. Combining this with the requirement that a steady-state lasing mode have a real eigenvalue forces $u = 2/3$ and turns the characteristic equation into a cubic in $\omega - \omega_0$, whose real root gives the cube-root scaling. A second consistency step, equating the intensity ratio from the eigenvectors with the intensity ratio from the saturation equations, produces the closed-form signal scale factor and the parameter constraints that define where the response is real and stable.

What would settle it

A numerical solution of the full saturation equations (Eqs. 2–3) without imposing the equal-exponent ansatz, for parameters where an exceptional point exists, that yields a steady-state frequency shift whose leading power is not $\epsilon^{1/3}$ would refute the central claim; equivalently, a laboratory measurement of lasing frequency versus detuning in a two-resonator laser with both resonators saturable that shows linear or square-root scaling over the asymptotic range would do so.

Watch

Extended reading notes

Core claim

The central claim is that the steady-state lasing frequency of the two-resonator system obeys $\mathrm{Re}(\omega - \omega_0) \approx (\kappa^2 \epsilon \bar b/\delta)^{1/3}$ when the system is biased at the parity-time-symmetric exceptional point and a small frequency perturbation $\epsilon$ is applied; the exponent $1/3$ is forced by the requirement that lasing eigenvalues remain real while saturable gain and loss adjust. The paper derives a closed-form signal scale factor $\tilde b = \tfrac12[\kappa/(f_0(\gamma_1+\gamma_2)T)]^{2/3}$, with $T$ given by Eq. (17), showing that the response constant depends on how saturable gain and absorption are distributed between the two resonators and on the passive-loss asymmetry. This tunability is claimed to yield several orders of magnitude larger responsivity than the case with a single nonlinear resonator coupled to a passive resonator. The paper also establishes stability boundaries: in the fast-relaxation regime the exceptional-point mode is stable except for large passive-loss asymmetry, and in the slow-relaxation regime detuning can restabilize an otherwise unstable exceptional-point mode, setting a minimum detuning below which sensing readout is not feasible.

Load-bearing premise

The whole result rests on the assumption that, near the special operating point where the two modes merge, the saturated net gain and net loss both drop from their operating-point values as the same power of the frequency perturbation; if the true saturation behaviour gives different leading exponents, the cube-root scaling and the entire signal-scale-factor formalism do not follow.

Editorial extensions

If this is right

  • A practical two-resonator exceptional-point sensor can be built from two resonators using the same gain medium, pumped differently, while retaining the cube-root response and reducing the tuning burden compared with linear higher-order exceptional points.
  • The signal scale factor can be increased by lowering passive losses relative to maximum gain and optimizing coupling strength and absorption, yielding several orders of magnitude higher responsivity than the single-nonlinear-resonator baseline.
  • Parameter errors such as gain drift or coupling mismatch do not erase the advantage: the response becomes linear in a plateau regime, but the plateau level is higher for larger scale factors and scales as the inverse square of the relative coupling error.
  • Stable operation requires avoiding designs where the inter-resonator coupling rate is comparable to the gain relaxation rate; either fast relaxation or, in slow media, relaxation rates far from the coupling rate (or larger detuning) restabilizes the mode.
  • Full-wave slab simulations confirm that the cube-root shift appears even with spatially nonuniform mode and gain profiles, provided an additional geometric parameter, the inter-slab gap, is tuned to locate the exceptional point.

Reading between the lines

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

  • The paper leaves precision unaddressed; a natural extension is to analyze quantum and technical noise with saturation included, since enhanced responsivity need not imply enhanced precision if linewidth broadening grows at the exceptional point.
  • The same equal-leading-exponent saturation mechanism suggests a route to higher-order responses: staging the argument in cascaded or hidden-dimension systems might produce nth-root laws with only two resonators, beyond the cube-root case treated here.
  • The discrepancy between the coupled-mode theory and full-wave numerical scaling of the signal scale factor implies that design rules for real devices should be validated against mode-profile-aware models; low-output-coupling geometries, such as Bragg reflectors, could restore the coupled-mode prediction and are a testable extension.
  • The restabilization at slow gain relaxation with larger detuning hints that a slow-gain, high-coupling exceptional-point laser could probe very small detunings if operated just above the stability boundary, and the boundary itself might be observable as a kink in the noise spectrum.
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

3 major / 4 minor

Summary. The manuscript studies a two-resonator laser biased at a PT-symmetric exceptional point, with saturable gain in one resonator and saturable gain or absorption in the other. It derives a cube-root response of the steady-state lasing frequency to a frequency detuning, a closed-form signal scale factor, an analysis of parametric errors, linear stability maps in the class-A and class-B regimes, and SALT simulations of coupled slabs. The central claims are that the proportionality constant can be made orders of magnitude larger than in the single-nonlinear-resonator case of Ref. [18], that maximizing this scale factor also improves robustness to parametric errors, and that the behavior is supported by SALT.

Significance. If the quantitative claims hold, the paper provides a useful design framework for EP-based laser sensors, combining analytic closed forms with a more complete stability analysis than previous single-nonlinear-resonator treatments. The strengths are the explicit derivations in the appendices, the parametric-error scaling law, and the SALT validation that partially accounts for spatial effects. The paper also honestly disclaims any claim of improved sensing precision or noise performance. However, one of the central closed-form formulas and the stability appendix contain errors that must be corrected before the quantitative enhancement and stability results can be accepted.

major comments (3)
  1. [Section III, Eq. (16)] The closed-form signal scale factor in Eq. (16) is inconsistent with Eq. (B3) and Eq. (14). Substituting Eq. (B3) into Eq. (14) gives \tilde b = \kappa \bar b = (1/2)[\kappa T/(f_0(\gamma_1+\gamma_2))]^{2/3}, not (1/2)[\kappa/(f_0(\gamma_1+\gamma_2)T)]^{2/3} as printed. For example, with \kappa=1, \gamma_1=\gamma_2=0.4\kappa, and f_0=\kappa, Eq. (B3) gives \delta=0.422, so \tilde b=0.701, whereas Eq. (16) gives 0.480. Since Fig. 4 and the "orders of magnitude" enhancement claim are based on Eq. (16), the optimization results and the quantitative enhancement statements need to be recomputed with the corrected expression.
  2. [Section III, Eqs. (9)-(10)] The central power-law ansatz is assumed rather than derived from the full saturation equations. The self-consistency argument shows that if both g' and f' saturate with the same leading exponent, that exponent must be 2/3, but it does not prove that solutions of Eqs. (2)-(3) realize this form, nor does it specify the range of \epsilon over which Eq. (13) captures the exact solution. Please provide an asymptotic derivation from the saturation equations and state the validity range of the cube-root law.
  3. [Appendix D, Eqs. (D2c)-(D2d)] The linearized gain and absorption equations are written incorrectly. The right-hand side of Eq. (D2c) contains no \delta g_s term, so it cannot be the linearization of Eq. (18), and the same issue appears in Eq. (D2d). As printed, these equations cannot generate the Jacobian in Eq. (D5) used for the stability eigenvalues in Figs. 6-7. Please correct the linearization and verify that the displayed eigenvalues are computed from the corrected Jacobian.
minor comments (4)
  1. [Section VI, Figs. 8-9] The SALT validation is partly circular because the CMT parameters in Fig. 8(a) are fitted to the SALT curve, and Fig. 9(a) shows an approximately linear SALT scaling versus a sub-linear CMT prediction. The paper offers plausible explanations, but the validation would be more convincing if the parameter mapping were obtained independently or if the discrepancy were quantified.
  2. [Section II / Fig. 1 caption] The caption contains a typo: "shoes" should be "shows".
  3. [Section III, after Eq. (16)] The dimensionless normalization of \bar b and \tilde b is not defined precisely; please state explicitly how \epsilon is normalized with respect to \kappa.
  4. [Section V, Fig. 6(e)] The quantity g_{th} used in the definition of R = g_c/g_{th} is not defined in the main text; please define it clearly.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the cube-root response and signal scale factor are derived from the Hamiltonian and saturation equations without fitted constants.

full rationale

The central derivation is self-contained. Equation (13) follows from the characteristic equation (Eq. 5) combined with the saturation ansatz (Eqs. 9-10); the ansatz is justified by the real-eigenvalue condition, which forces equal leading saturation exponents, and the exponent u=2/3 and scale factor are obtained by consistency between the eigenvector equations (Eq. 7) and the saturation equations (Eqs. 2-3) in Appendix B, not by fitting the response. No load-bearing self-citation is used: Refs. [28,29] appear only in a general list of nonlinear-saturation examples, and the prior single-nonlinear-resonator result [18] is external. The SALT comparison in Sec. VI calibrates CMT parameters to the SALT bifurcation data before comparing scale-factor trends, so it is a weakened, calibrated validation rather than a parameter-free test; however, this does not invert the prediction into an input or make the CMT derivation circular. The paper also explicitly disclaims sensing-precision improvement, limiting its claims to responsivity. Any algebraic error in Appendix B would be a correctness risk, not a circularity.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

No new physical entities are introduced. The main burden is carried by the saturation ansatz and the CMT modeling assumptions. The SALT comparison uses fitted CMT parameters, so its status as an external check is partial.

free parameters (2)
  • CMT parameters fitted to SALT data = κ=1, g0=4.75, γ1=γ2=3.55
    Used in Section VI to match the SALT bifurcation curve; the subsequent scale-factor comparison is a fit, not a parameter-free prediction.
  • Optimized coupling and absorption/gain = optimal κ and f0 from Fig. 4(b,c)
    Chosen by hand to maximize the signal scale factor for a given passive loss and maximum gain; the 'several orders of magnitude' comparison depends on these choices.
assumptions (5)
  • domain assumption Coupled-mode Hamiltonian (Eq. 1) with conservative real coupling, no dissipative coupling, and uniform spatial mode profiles.
    Used throughout the analytic derivation; the SALT section shows this assumption is violated in inhomogeneous slabs and requires additional tuning.
  • domain assumption Homogeneously broadened saturable gain and absorption with g_s=g0/(1+|ψ1|^2) and f_s=f0/(1+|ψ2|^2) (Eqs. 2-3), i.e., class-A adiabatic elimination.
    Basis for the cube-root derivations and the steady-state response; class-B dynamics are added later only for stability.
  • ad hoc to paper The saturated net gain and loss follow the same leading power law near the EP (Eqs. 9-10).
    Central ansatz; the paper argues by consistency that exponents must match for real eigenvalues, but does not prove this from the full saturation equations.
  • domain assumption Dynamic gain equations (Eqs. 18-19) with a single inversion relaxation rate γ|| and no transverse intensity variation describe the class-B regime.
    Used for the Lyapunov stability analysis; may fail for media with significant spatial hole burning or multiple relaxation rates.
  • domain assumption SALT (Eq. 21) with a two-level gain medium, Lorentzian line shape, and conductivity loss is a valid benchmark for the CMT predictions.
    The SALT comparison is one-dimensional-slab specific and covers only the f0<0 (both-gain) configuration.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Responsivity and Stability of Nonlinear Exceptional Point Lasers with Saturable Gain and Loss." pith.science (2026). https://pith.science/paper/WTWUQM6D

@misc{pith2026241118720,
  author       = {Pith},
  title        = {Pith review of: Responsivity and Stability of Nonlinear Exceptional Point Lasers with Saturable Gain and Loss},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WTWUQM6D}},
  note         = {Machine review of arXiv:2411.18720}
}
read the original abstract

The responsivity of perturbation sensing can be effectively enhanced by using higher-order exceptional points (HOEPs) due to their nonlinear response to frequency perturbations. However, experimental realization can be difficult due to the stringent parameter conditions associated with these points. In this work, we study an EP laser composed of two coupled nonlinear resonators that uses nonlinearity to simplify these tuning requirements. This system demonstrates a distinct cube-root response in the steady-state lasing frequency, with a constant of proportionality that depends on the distribution of linear and saturable gain and loss. This design freedom enables several orders of magnitude higher responsivity than systems with a single nonlinear resonator, which have been previously explored. Maximizing responsivity also improves the robustness of sensing performance against parametric errors. These features are derived from coupled mode theory and further supported by steady-state ab initio laser theory (SALT) results at several nonlinear EPs. Through linear stability analysis, we also identify regions of instability within the class-A regime that arise due to mode competition, which can be induced by asymmetric passive losses. In the class-B regime, we show that the interplay between gain dynamics and detuning can lead to restabilization at slow relaxation rates or higher inter-resonator coupling rates. This regime could be used to increase the maximum achievable responsivity of the system.

Figures

Figures reproduced from arXiv: 2411.18720 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Schematic of the coupled resonator system un [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Phase map of the coupled resonator system. (a) [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Stability map of the EP mode under variation of (a) [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Maximum signal scale factor [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Signal enhancement factor [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Lyapunov exponents Re( [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Trajectories of the stability eigenvalues [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. (a) Lasing frequency [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. (a) Signal scale factor (in SALT units) extracted from Fig. [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

48 extracted references · 30 canonical work pages

  1. [18]

    K. Bai, L. Fang, T.-R. Liu, J.-Z. Li, D. Wan, and M. Xiao, Natl. Sci. Rev. 10, nwac259 (2022)

    work page 2022

  2. [1]

    L. Feng, R. El-Ganainy, and L. Ge, Nat. Photonics 11, 752 (2017)

    2017

  3. [2]

    El-Ganainy, K

    R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, Nat. Phys. 14, 11 (2018)

    2018

  4. [3]

    Miri and A

    M.-A. Miri and A. Al` u, Science363, 77090 (2019)

    work page 2019

  5. [4]

    Wiersig, Phys

    J. Wiersig, Phys. Rev. Lett. 112, 203901 (2014)

    2014

  6. [5]

    Wiersig, Phys

    J. Wiersig, Phys. Rev. A 93, 033809 (2016)

    work page 2016

  7. [6]

    Wiersig, Photon

    J. Wiersig, Photon. Res. 8, 1457 (2020)

    2020

  8. [7]

    B.-B. Li, W. R. Clements, X.-C. Yu, K. Shi, Q. Gong, and Y.-F. Xiao, Proc. Natl. Acad. Sci. 111, 14657 (2014)

    work page 2014

Show all 48 references
  1. [8]

    Kato, Perturbation Theory for Linear Operators (Springer Science & Business Media, 2012)

    T. Kato, Perturbation Theory for Linear Operators (Springer Science & Business Media, 2012)

    2012

  2. [9]

    Hodaei, A

    H. Hodaei, A. U. Hassan, J. Ren, W. E. Hayenga, M.-A. Miri, D. N. Christodoulides, and M. Khajavikhan, IEEE J. Sel. Topics Quantum Electron. 22, 12 (2016)

    2016

  3. [10]

    Chen, S ¸

    W. Chen, S ¸. K. ¨Ozdemir, G. Zhao, J. Wiersig, and L. Yang, Nature 548, 192 (2017)

    2017

  4. [11]

    H. Zhao, Z. Chen, R. Zhao, and L. Feng, Nat. Commun. 9, 1764 (2018)

    2018

  5. [12]

    M. P. Hokmabadi, A. Schumer, D. N. Christodoulides, and M. Khajavikhan, Nature 576, 70 (2019)

    2019

  6. [13]

    Lai, Y.-K

    Y.-H. Lai, Y.-K. Lu, M.-G. Suh, Z. Yuan, and K. Vahala, Nature 576, 65 (2019)

    2019

  7. [14]

    Kononchuk, J

    R. Kononchuk, J. Cai, F. Ellis, R. Thevamaran, and T. Kottos, Nature 607, 697 (2022)

    2022

  8. [15]

    Zhang, L

    M.-N. Zhang, L. Dong, L.-F. Wang, and Q.-A. Huang, Microsystems & Nanoengineering 10, 12 (2024)

    2024

  9. [16]

    Hodaei, A

    H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Kha- javikhan, Nature 548, 187 (2017)

    2017

  10. [17]

    C. Zeng, Y. Sun, G. Li, Y. Li, H. Jiang, Y. Yang, and H. Chen, Opt. Express 27, 27562 (2019)

    2019

  11. [19]

    Zhong, J

    Q. Zhong, J. Ren, M. Khajavikhan, D. N. Christodoulides, S ¸. K. ¨Ozdemir, and R. El-Ganainy, Phys. Rev. Lett. 122, 153902 (2019)

    2019

  12. [20]

    H. Zhou, J. Y. Lee, S. Liu, and B. Zhen, Optica 6, 190 (2019)

    2019

  13. [21]

    Zhang, K

    X. Zhang, K. Ding, X. Zhou, J. Xu, and D. Jin, Phys. Rev. Lett. 123, 237202 (2019)

    2019

  14. [22]

    Qin, R.-R

    G.-Q. Qin, R.-R. Xie, H. Zhang, Y.-Q. Hu, M. Wang, G.-Q. Li, H. Xu, F. Lei, D. Ruan, and G.-L. Long, Laser Photonics Rev. 15, 2000569 (2021)

    2021

  15. [23]

    H. Yang, X. Mao, G.-Q. Qin, M. Wang, H. Zhang, D. Ruan, and G.-L. Long, Opt. Lett. 46, 4025 (2021)

    2021

  16. [24]

    Kullig, D

    J. Kullig, D. Grom, S. Klembt, and J. Wiersig, Photon. Res. 11, A54 (2023)

    2023

  17. [25]

    A. U. Hassan, H. Hodaei, M.-A. Miri, M. Khajavikhan, and D. N. Christodoulides, Phys. Rev. A 92, 063807 (2015)

    2015

  18. [26]

    Ge and R

    L. Ge and R. Elganainy, Sci. Rep. 6, 10.1038/srep24889 (2016). 14

    2016 doi

  19. [27]

    K. Ji, Q. Zhong, L. Ge, G. Beaudoin, I. Sagnes, F. Raineri, R. El-Ganainy, and A. M. Yacomotti, Nature Communications 14, 8304 (2023)

    2023

  20. [28]

    Darcie and J

    T. Darcie and J. S. Aitchison, in 2023 Photonics North (PN) (2023) pp. 1–2

    2023

  21. [29]

    Darcie and J

    T. Darcie and J. S. Aitchison, in 2024 Photonics North (PN) (2024) pp. 1–2

    2024

  22. [30]

    T. Chen, Z. Xiao, S. Jiang, W. Li, J. Li, Y. Wang, X. Wang, A. Huang, and H. Zhang, J. Appl. Phys. 131, 10.1063/5.0094917 (2022)

    2022 doi

  23. [31]

    Bai, J.-Z

    K. Bai, J.-Z. Li, T.-R. Liu, L. Fang, D. Wan, and M. Xiao, Phys. Rev. Lett. 130, 266901 (2023)

    2023

  24. [32]

    Esterhazy, D

    S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. G. Makris, A. D. Stone, J. M. Melenk, S. G. Johnson, and S. Rotter, Phys. Rev. A 90, 023816 (2014)

    2014

  25. [33]

    W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, Nat. Commun. 8, 15389 (2017)

    2017

  26. [34]

    Benzaouia, A

    M. Benzaouia, A. D. Stone, and S. G. Johnson, APL Photonics 7, 121303 (2022)

    2022

  27. [35]

    Peng, S ¸

    B. Peng, S ¸. K. ¨Ozdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, Science 346, 328 (2014)

    2014

  28. [36]

    Z. Lu, H. Yun, Y. Wang, Z. Chen, F. Zhang, N. Jaeger, and L. Chrostowski, Opt. Express 23, 3795 (2015)

    2015

  29. [37]

    Wang, Y.-H

    H. Wang, Y.-H. Lai, Z. Yuan, M.-G. Suh, and K. Vahala, Nat. Commun. 11, 1610 (2020)

    2020

  30. [38]

    Burkhardt, M

    S. Burkhardt, M. Liertzer, D. O. Krimer, and S. Rotter, Phys. Rev. A 92, 013847 (2015)

    2015

  31. [39]

    Zhou and Y

    X. Zhou and Y. D. Chong, Opt. Express 24, 6916 (2016)

    2016

  32. [40]

    Assawaworrarit, X

    S. Assawaworrarit, X. Yu, and S. Fan, Nature 546, 387 (2017)

    2017

  33. [41]

    A. M. Yacomotti, Z. Denis, A. Biella, and C. Ciuti, Laser Photonics Rev. 17, 2200377 (2023)

    2023

  34. [42]

    A. E. Siegman, Lasers (University Science Books, 1986)

    1986

  35. [43]

    Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, Phys. Rev. Lett. 105, 053901 (2010)

    2010

  36. [44]

    C. Chen, L. Jin, and R.-B. Liu, New journal of physics 21, 083002 (2019)

    2019

  37. [45]

    N. A. Mortensen, P. A. D. Gon¸ calves, M. Khajavikhan, D. N. Christodoulides, C. Tserkezis, and C. Wolff, Optica 5, 1342 (2018)

    2018

  38. [46]

    Zhang, B

    J. Zhang, B. Peng, S ¸. K. ¨Ozdemir, K. Pichler, D. O. Krimer, G. Zhao, F. Nori, Y.-x. Liu, S. Rotter, and L. Yang, Nature Photonics 12, 479 (2018)

    2018

  39. [47]

    J. M. Silver, L. D. Bino, M. T. M. Woodley, G. N. Gha- lanos, A. Ø. Svela, N. Moroney, S. Zhang, K. T. V. Grat- tan, and P. Del’Haye, Optica 8, 1219 (2021). Supplementary Material: Responsivity and Stability of Nonlinear Exceptional Point Lasers with Saturable Gain and Loss To...

    2021 arXiv

  40. [48]

    Hodaei, A

    H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, Enhanced sensitivity at higher-order exceptional points, Nature 548, 187 (2017)

    2017

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.