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arxiv: 2606.04671 · v1 · pith:BK4M5FPDnew · submitted 2026-06-03 · ⚛️ physics.optics

Higher-order exceptional points in a multimode continuum optoacoustic system

Anton Montag , Julius T. Gohsrich , Quentin Levoy , Birgit Stiller , Flore K. Kunst This is my paper

Pith reviewed 2026-06-28 05:00 UTC · model grok-4.3

classification ⚛️ physics.optics
keywords exceptional pointsstimulated Brillouin scatteringoptoacousticsnon-Hermitian systemshigher-order exceptional pointsmultimode theory
0
0 comments X

The pith

An off-resonant multimode theory for stimulated Brillouin scattering enables symmetry-induced exceptional points of any order.

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

The paper develops an off-resonant, multimode theory for stimulated Brillouin scattering to realize symmetry-induced exceptional points of arbitrary order in optoacoustic systems. Exceptional points are degeneracies where both eigenvalues and eigenvectors coalesce in non-Hermitian systems. The theory generalizes earlier second-order realizations by using continuum modes to avoid extensive fine-tuning. A sympathetic reader would care because this supplies a fabrication-free route to higher-order points and their associated sensitivity enhancements. The work also outlines potential uses in sensing and related technologies, with an experimental demonstration reported separately.

Core claim

We develop an off-resonant, multimode theory for stimulated Brillouin scattering as an avenue towards realizing symmetry-induced exceptional points of any order. We present the experimental implementation of our program in an accompanying paper. Our multimode theory could also be employed in applications in optoacoustic sensing, synthetic neuromorphic computing, microwave photonic filters, and optoacoustic quantum signal processing.

What carries the argument

Off-resonant multimode theory for stimulated Brillouin scattering, which uses continuum acoustic and optical modes to produce symmetry-protected exceptional points of arbitrary order.

If this is right

  • Higher-order exceptional points become accessible in fabrication-free optoacoustic setups.
  • The same framework supports experimental realization as described in the accompanying paper.
  • Applications open in optoacoustic sensing and synthetic neuromorphic computing.
  • Further uses appear in microwave photonic filters and optoacoustic quantum signal processing.

Where Pith is reading between the lines

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

  • The continuum-mode approach may lower the experimental barrier for studying higher-order points relative to discrete-mode fine-tuned systems.
  • Symmetry protection could allow dynamic tuning of the exceptional-point order during operation.
  • The scattering mechanism might transfer to other multimode photonic or acoustic platforms.

Load-bearing premise

The off-resonant multimode scattering framework extends from second-order to arbitrary-order exceptional points without introducing new fine-tuning requirements or instabilities.

What would settle it

An experiment that observes coalescence of three or more eigenvectors in the multimode Brillouin system under off-resonant drive, achieved without extra parameter tuning, would support the claim; failure to produce such coalescence or emergence of instabilities would refute it.

read the original abstract

Exceptional points appear in non-Hermitian systems as degeneracies, where not only eigenvalues but also eigenvectors coalesce. They are of great theoretical and experimental interest due to their exotic topological properties and enhanced sensitivity to perturbations. Experimental realizations of higher-order exceptional points, where more than two eigenvectors coalesce, rely on highly fine-tuned setups. Recently, stimulated Brillouin scattering has been employed to generate second-order exceptional points in a fabrication-free setup by leveraging off-resonant scattering. In this work we generalize this approach, and we develop an off-resonant, multimode theory for stimulated Brillouin scattering as an avenue towards realizing symmetry-induced exceptional points of any order. We present the experimental implementation of our program in an accompanying paper. Our multimode theory could also be employed in applications in optoacoustic sensing, synthetic neuromorphic computing, microwave photonic filters, and optoacoustic quantum signal processing.

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

1 major / 0 minor

Summary. The manuscript develops an off-resonant multimode theory for stimulated Brillouin scattering (SBS) in a continuum optoacoustic system. It generalizes prior second-order EP realizations to claim that symmetry constraints alone suffice for symmetry-induced exceptional points of arbitrary order, without additional fine-tuning. An accompanying experimental implementation is referenced.

Significance. If the central derivation holds, the work supplies a fabrication-free route to higher-order EPs that avoids the parameter proliferation typical of such degeneracies. This would be a substantive advance in non-Hermitian optoacoustics, with the listed applications in sensing, neuromorphic computing, and quantum signal processing following directly from the multimode framework.

major comments (1)
  1. [abstract / theory section] The abstract asserts that the off-resonant multimode SBS framework extends to arbitrary-order EPs using only the symmetry constraints already employed for N=2. The manuscript must show explicitly (via the characteristic equation or scattering-matrix construction) that no new relations among acoustic or optical detunings appear for N>2; otherwise the claim that fine-tuning is eliminated is not established.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their detailed review and constructive suggestion. We address the single major comment below and will revise the manuscript accordingly to strengthen the presentation of the higher-order EP construction.

read point-by-point responses

  1. Referee: [abstract / theory section] The abstract asserts that the off-resonant multimode SBS framework extends to arbitrary-order EPs using only the symmetry constraints already employed for N=2. The manuscript must show explicitly (via the characteristic equation or scattering-matrix construction) that no new relations among acoustic or optical detunings appear for N>2; otherwise the claim that fine-tuning is eliminated is not established.

    Authors: We agree that an explicit demonstration is required to substantiate the claim for arbitrary N. In the revised manuscript we will insert a dedicated subsection in the theory section that derives the characteristic equation of the multimode scattering matrix for general N. The derivation shows that the off-resonant continuum coupling imposes the same algebraic constraints on the detuning parameters as those already used for N=2; no additional independent relations among acoustic or optical frequencies appear. The symmetry-induced coalescence of N eigenvectors therefore follows directly from the existing symmetry constraints without further fine-tuning. We will also include a brief scattering-matrix construction for N=3 and N=4 to illustrate the pattern. revision: yes

Circularity Check

0 steps flagged

No circularity: generalization presented as independent theoretical extension

full rationale

The provided abstract and context describe a multimode off-resonant SBS framework generalized from second-order to arbitrary-order EPs via symmetry constraints. No equations, fitted parameters, or self-citations appear in the load-bearing claims. The central assertion that the multimode scattering matrix permits N>2 coalescence under the same symmetry conditions used for N=2 is stated as a new construction without reduction to prior fitted inputs or self-referential definitions. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; all such elements remain unknown.

pith-pipeline@v0.9.1-grok · 5692 in / 980 out tokens · 18010 ms · 2026-06-28T05:00:56.928334+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

82 extracted references · 1 canonical work pages

  1. [1]

    NTopQuant

    By substituting As q(z) =e −2iks qzas q(z), we find (2ks i + i∂z)as i(z) = ig0P0 ωp m−ωs i=ωp n−ωs jX j,m,n h e−iz[(kp m−ks i)−(kp n−ks j)] × Ap m(Ap n)∗ 1 + iΓps nj as j(z) i .(9) Assuming linear dispersion, i.e.,k∝ω, makes thez- dependent phase factor vanish. This also shows that our previous assumptions and approximation lead to only phase-matched inte...

  2. [2]

    El-Ganainy, K

    R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, Na- ture Physics14, 11 (2018)

    2018

  3. [3]

    K.¨Ozdemir, S

    S ¸. K.¨Ozdemir, S. Rotter, F. Nori, and L. Yang, Nature Materials18, 783 (2019)

    2019

  4. [4]

    Miri and A

    M.-A. Miri and A. Al` u, Science363, eaar7709 (2019)

    2019

  5. [5]

    E. J. Bergholtz, J. C. Budich, and F. K. Kunst, Rev. Mod. Phys.93, 015005 (2021)

    2021

  6. [6]

    Ashida, Z

    Y. Ashida, Z. Gong, and M. Ueda, Advances in Physics 69, 249 (2020)

    2020

  7. [7]

    Kato,Perturbation theory of linear operators, edited by A

    T. Kato,Perturbation theory of linear operators, edited by A. Cappelli and G. Mussardo (Springer, Berlin, 1966)

    1966

  8. [8]

    W. D. Heiss, Journal of Physics A: Mathematical and Theoretical45, 444016 (2012)

    2012

  9. [9]

    M. V. Berry, Czech. J. Phys.54, 1039 (2004)

    2004

  10. [10]

    Carlstr¨ om and E

    J. Carlstr¨ om and E. J. Bergholtz, Phys. Rev. A98, 042114 (2018)

    2018

  11. [11]

    Brandstetter, M

    M. Brandstetter, M. Liertzer, C. Deutsch, P. Klang, J. Sch¨ oberl, H. E. T¨ ureci, G. Strasser, K. Unterrainer, and S. Rotter, Nature communications5, 4034 (2014)

    2014

  12. [12]

    L. Feng, X. Zhu, S. Yang, H. Zhu, P. Zhang, X. Yin, Y. Wang, and X. Zhang, Optics express22, 1760 (2013)

    2013

  13. [13]

    A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett.103, 093902 (2009)

    2009

  14. [14]

    C. E. R¨ uter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nature physics 6, 192 (2010)

    2010

  15. [15]

    Feng, Y.-L

    L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, Nature materials12, 108 (2013)

    2013

  16. [16]

    B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S.-L. Chua, J. D. Joannopoulos, and M. Soljaˇ ci´ c, Nature525, 354 (2015)

    2015

  17. [17]

    Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett.106, 213901 (2011)

    2011

  18. [18]

    Peng, S ¸

    B. Peng, S ¸. K. ¨Ozdemir, M. Liertzer, W. Chen, J. Kramer, H. Yılmaz, J. Wiersig, S. Rotter, and L. Yang, Proceedings of the National Academy of Science113, 6845 (2016)

    2016

  19. [19]

    Goldzak, A

    T. Goldzak, A. A. Mailybaev, and N. Moiseyev, Phys. Rev. Lett.120, 013901 (2018)

    2018

  20. [20]

    Delplace, T

    P. Delplace, T. Yoshida, and Y. Hatsugai, Phys. Rev. Lett.127, 186602 (2021)

    2021

  21. [21]

    Sayyad and F

    S. Sayyad and F. K. Kunst, Phys. Rev. Res.4, 023130 (2022)

    2022

  22. [22]

    Montag and F

    A. Montag and F. K. Kunst, Phys. Rev. Res.6, 023205 (2024)

    2024

  23. [23]

    Montag and F

    A. Montag and F. K. Kunst, Journal of Mathematical Physics65(2024)

    2024

  24. [24]

    Montag, J

    A. Montag, J. Isaacs, M. St˚ alhammar, and F. K. Kunst, Phys. Rev. Res.7, 043199 (2025)

    2025

  25. [25]

    Hodaei, A

    H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Kha- javikhan, Nature548, 187 (2017)

    2017

  26. [26]

    Jahangiri, G.-M

    M. Jahangiri, G.-M. Parsanasab, and L. Hajshahvaladi, Scientific Reports15, 4823 (2025)

    2025

  27. [27]

    W. Tang, X. Jiang, K. Ding, Y.-X. Xiao, Z.-Q. Zhang, C. T. Chan, and G. Ma, Science370, 1077 (2020)

    2020

  28. [28]

    W. Tang, K. Ding, and G. Ma, Nature Communications 14, 6660 (2023)

    2023

  29. [29]

    Y. S. Patil, J. H¨ oller, P. A. Henry, C. Guria, Y. Zhang, L. Jiang, N. Kralj, N. Read, and J. G. E. Harris, Nature 607, 271 (2022)

    2022

  30. [30]

    K. Yin, X. Hao, Y. Huang, J. Zou, X. Ma, and T. Dong, Physical Review Applied20, L021003 (2023)

    2023

  31. [31]

    K. Wang, L. Xiao, H. Lin, W. Yi, E. J. Bergholtz, and P. Xue, Science Advances9, eadi0732 (2023)

    2023

  32. [32]

    Y. Wu, Y. Wang, X. Ye, W. Liu, Z. Niu, C.-K. Duan, Y. Wang, X. Rong, and J. Du, Nature Nanotechnology 19, 160 (2024)

    2024

  33. [33]

    C. Wang, N. Li, J. Xie, C. Ding, Z. Ji, L. Xiao, S. Jia, B. Yan, Y. Hu, and Y. Zhao, Physical Review Letters 132, 253401 (2024)

    2024

  34. [34]

    P.-R. Han, W. Ning, X.-J. Huang, R.-H. Zheng, S.-B. Yang, F. Wu, Z.-B. Yang, Q.-P. Su, C.-P. Yang, and S.- B. Zheng, Nature Communications15, 10293 (2024)

    2024

  35. [35]

    Zhang, T

    H. Zhang, T. Liu, Z. Xiang, K. Xu, H. Fan, and D. Zheng, PRX Quantum6, 020328 (2025)

    2025

  36. [36]

    Zhang, P.-R

    H.-L. Zhang, P.-R. Han, F. Wu, W. Ning, Z.-B. Yang, and S.-B. Zheng, Phys. Rev. Lett.135, 230203 (2025)

    2025

  37. [37]

    Y.-Y. Chen, K. Li, L. Zhang, Y.-K. Wu, J.-Y. Ma, H.- X. Yang, C. Zhang, B.-X. Qi, Z.-C. Zhou, P.-Y. Hou, Y. Xu, and L.-M. Duan, Nature Communications16, 7478 (2025)

    2025

  38. [38]

    Y. Li, Y. Wu, Y. Zhou, M. Zhang, X. Zhao, Y. Yuan, X. Cheng, Y. Li, X. Qin, X. Rong,et al., Quantum Fron- tiers4, 16 (2025)

    2025

  39. [39]

    Bergman, R

    A. Bergman, R. Duggan, K. Sharma, M. Tur, A. Zadok, and A. Al` u, Nature communications12, 486 (2021)

    2021

  40. [40]

    Ippen and R

    E. Ippen and R. Stolen, Applied Physics Letters21, 539 (1972)

    1972

  41. [41]

    Nikl` es, L

    M. Nikl` es, L. Th´ evenaz, and P. A. Robert, Optics Letters 21, 758 (1996)

    1996

  42. [42]

    Hasegawa and K

    T. Hasegawa and K. Hotate, inFiber Optic Sensor Tech- nology and Applications, Vol. 3860 (SPIE, 1999) pp. 306– 316

    1999

  43. [43]

    Geilen, A

    A. Geilen, A. Popp, D. Das, S. Junaid, C. G. Poul- ton, M. Chemnitz, C. Marquardt, M. A. Schmidt, and B. Stiller, Nature Physics , 1 (2023)

    2023

  44. [44]

    Marpaung, J

    D. Marpaung, J. Yao, and J. Capmany, Nature Photonics 13, 80 (2019)

    2019

  45. [45]

    Kabakova, J

    I. Kabakova, J. Zhang, Y. Xiang, S. Caponi, A. Bi- lenca, J. Guck, and G. Scarcelli, Nature Reviews Methods Primers4, 8 (2024)

    2024

  46. [46]

    Prevedel, A

    R. Prevedel, A. Diz-Mu˜ noz, G. Ruocco, and G. An- tonacci, Brillouin microscopy: an emerging tool for mechanobiology (2019)

    2019

  47. [47]

    N. T. Otterstrom, R. O. Behunin, E. A. Kittlaus, Z. Wang, and P. T. Rakich, Science360, 1113 (2018)

    2018

  48. [48]

    Gundavarapu, G

    S. Gundavarapu, G. M. Brodnik, M. Puckett, T. Huff- man, D. Bose, R. Behunin, J. Wu, T. Qiu, C. Pinho, N. Chauhan,et al., Nature Photonics13, 60 (2019)

    2019

  49. [49]

    X. Zeng, P. S. J. Russell, Y. Chen, Z. Wang, G. K. L. Wong, P. Roth, M. H. Frosz, and B. Stiller, Laser & Photonics Reviews17, 2200277 (2023)

    2023

  50. [50]

    Z. Zhu, D. J. Gauthier, and R. W. Boyd, Science318, 1748 (2007)

    2007

  51. [51]

    Geilen, S

    A. Geilen, S. Becker, and B. Stiller, ACS Photonics11, 4524 (2024)

    2024

  52. [52]

    Merklein, B

    M. Merklein, B. Stiller, K. Vu, S. J. Madden, and B. J. 10 Eggleton, Nature Communications8, 574 (2017)

    2017

  53. [53]

    Saffer, J

    O. Saffer, J. H. Marines Cabello, S. Becker, A. Geilen, and B. Stiller, APL Photonics10, 060802 (2025)

    2025

  54. [54]

    Stiller, M

    B. Stiller, M. Merklein, C. Wolff, K. Vu, P. Ma, S. J. Madden, and B. J. Eggleton, Optica7, 492 (2020)

    2020

  55. [55]

    Becker, D

    S. Becker, D. Englund, and B. Stiller, Nature Communi- cations15, 3020 (2024)

    2024

  56. [56]

    Slinkov, S

    G. Slinkov, S. Becker, D. Englund, and B. Stiller, Nanophotonics14, 2711 (2025)

    2025

  57. [57]

    Stiller, S

    B. Stiller, S. M. Foaleng, J.-C. Beugnot, M. W. Lee, M. Delqu´ e, G. Bouwmans, A. Kudlinski, L. Th´ evenaz, H. Maillotte, and T. Sylvestre, Optics Express18, 20136 (2010)

    2010

  58. [58]

    Godet, A

    A. Godet, A. Ndao, T. Sylvestre, V. Pecheur, S. Lebrun, G. Pauliat, J.-C. Beugnot, and K. P. Huy, Optica4, 1232 (2017)

    2017

  59. [59]

    B. J. Eggleton, C. G. Poulton, P. T. Rakich, M. J. Steel, and G. Bahl, Nature Photonics13, 664 (2019)

    2019

  60. [60]

    E. A. Kittlaus, H. Shin, and P. T. Rakich, Nature Pho- tonics10, 463 (2016)

    2016

  61. [61]

    Kobyakov, M

    A. Kobyakov, M. Sauer, and D. Chowdhury, Advances in Optics and Photonics2, 1 (2010)

    2010

  62. [62]

    Neijts, C

    G. Neijts, C. K. Lai, M. K. Riseng, D.-Y. Choi, K. Yan, D. Marpaung, S. J. Madden, B. J. Eggleton, and M. Merklein, APL Photonics9, 106114 (2024)

    2024

  63. [63]

    C. C. Rodrigues, N. J. Schilder, R. O. Zurita, L. S. Ma- galh˜ aes, A. Shams-Ansari, F. J. L. dos Santos, O. M. Paiano, T. P. M. Alegre, M. Lonˇ car, and G. S. Wieder- hecker, Physical Review Letters134, 113601 (2025)

    2025

  64. [64]

    K. Ye, H. Feng, R. te Morsche, C. Wei, Y. Klaver, A. Mishra, Z. Zheng, A. Keloth, A. T. I¸ sık, Z. Chen, C. Wang, and D. Marpaung, Science Advances11, eadv4022 (2025)

    2025

  65. [65]

    W. Xu, A. Iyer, L. Jin, S. Y. Set, and W. H. Renninger, Optica10, 206 (2023)

    2023

  66. [66]

    Y. Chu, P. Kharel, W. H. Renninger, L. D. Burkhart, L. Frunzio, P. T. Rakich, and R. J. Schoelkopf, Science 358, 199 (2017)

    2017

  67. [67]

    W. H. Renninger, P. Kharel, R. O. Behunin, and P. T. Rakich, Nature Physics14, 601 (2018)

    2018

  68. [68]

    H. M. Doeleman, T. Schatteburg, R. Benevides, S. Vol- lenweider, D. Macri, and Y. Chu, Phys. Rev. Res.5, 043140 (2023)

    2023

  69. [69]

    Bl´ azquez Mart´ ınez, P

    L. Bl´ azquez Mart´ ınez, P. Wiedemann, C. Zhu, A. Geilen, and B. Stiller, Physical Review Letters132, 023603 (2024)

    2024

  70. [70]

    E. A. Cryer-Jenkins, A. C. Leung, H. Rathee, A. K. C. Tan, K. D. Major, and M. R. Vanner, APL Photonics 10, 010805 (2025)

    2025

  71. [71]

    Enzian, M

    G. Enzian, M. Szczykulska, J. Silver, L. D. Bino, S. Zhang, I. A. Walmsley, P. Del’Haye, and M. R. Vanner, Optica6, 7 (2019)

    2019

  72. [72]

    Enzian, J

    G. Enzian, J. J. Price, L. Freisem, J. Nunn, J. Janousek, B. C. Buchler, P. K. Lam, and M. R. Vanner, Phys. Rev. Lett.126, 033601 (2021)

    2021

  73. [73]

    C. Zhu, C. Genes, and B. Stiller, Physical Review Letters 133, 203602 (2024)

    2024

  74. [74]

    Zhang, C

    J. Zhang, C. Zhu, C. Wolff, and B. Stiller, Physical Re- view Research5, 013010 (2023)

    2023

  75. [75]

    L. B. Mart´ ınez, C. Zhu, and B. Stiller, arXiv:2507.08673 (2025)

    work page arXiv 2025

  76. [76]

    Wolff, M

    C. Wolff, M. J. A. Smith, B. Stiller, and C. G. Poulton, JOSA B38, 1243 (2021), publisher: Optica Publishing Group

    2021

  77. [77]

    Boyd,Nonlinear Optics–3rd Edition(Springer, New York, 2007)

    R. Boyd,Nonlinear Optics–3rd Edition(Springer, New York, 2007)

    2007

  78. [78]

    Kozii and L

    V. Kozii and L. Fu, Phys. Rev. B109, 235139 (2024)

    2024

  79. [79]

    H. Zhou, C. Peng, Y. Yoon, C. W. Hsu, K. A. Nelson, L. Fu, J. D. Joannopoulos, M. Soljaˇ ci´ c, and B. Zhen, Science359, 1009 (2018)

    2018

  80. [80]

    J. L. K. K¨ onig, K. Yang, J. C. Budich, and E. J. Bergholtz, Phys. Rev. Res.5, L042010 (2023)

    2023

Showing first 80 references.