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A new optimization method bounds every channel amplitude of a photonic device

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-04 12:57 UTC pith:QU3DJN45

load-bearing objection New and formally sound per-index singular value bounds, but the single-device channel-count claim rests on an unenforced consistency constraint the authors themselves concede; deserves refereeing, not rejection.

arxiv 2510.01128 v2 pith:QU3DJN45 submitted 2025-10-01 physics.optics

Indexed singular value bounds on scattering operators: How many channels can a photonic device support?

Paul Virally , Pengning Chao , Alessio Amaolo , Alejandro W. Rodriguez , Sean Molesky This is my paper
classification physics.optics
keywords singular value boundschannel capacityGreen functionCourant-Fischer-Weylconvex relaxationscattering operatormetasurfaceFisher information
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper develops a general method to answer, for prescribed volumes of space filled with any linear material of known susceptibility, how large the nth singular value of the electromagnetic Green function can be. It combines the Courant-Fischer-Weyl min-max principle with convex relaxations of scattering constraints, producing computable upper bounds for each channel index n. The bounds are demonstrated on waveguide-like and metasurface-like three-dimensional systems up to 64 cubic wavelengths, and on a plane-wave angle discrimination problem where they bound the smallest singular value. If the method is correct, it gives quantitative design limits on channel counts, Shannon capacity, Fisher information, and reduced-order model errors.

Core claim

The central claim is that the ordered singular values (channel amplitudes) of the electromagnetic Green function, and related scattering operators, can be bounded from above for any arbitrarily structured linear medium by a tractable optimization. The paper's procedure selects a subspace of excluded vacuum singular vectors, then maximizes the projected response subject to real and reactive power conservation, forming a quadratically constrained quadratic program whose dual yields an upper bound. This yields indexed channel bounds: a 1×1×5 λ mediator made of a silicon-like material cannot support more than twenty-five unity-amplitude channels; increasing a metasurface's width from 2λ to 16λ r

What carries the argument

The central mechanism is the Courant-Fischer-Weyl min-max principle, which expresses the nth singular value σ_n of a compact operator as a min-max over n-dimensional subspaces: σ_n² = min_{Q_{n−1}} max_{x⊥Q_{n−1}} x†A†Ax. The paper pairs this with the T-operator expansion G = G₀ + G₀TG₀, separating free-space propagation from the scattering response of the material. The material's allowed responses are then relaxed to convex power-conservation constraints (global real and reactive power in subregions), converting the bound into a quadratically constrained quadratic program that can be solved by Lagrange duality for large volumes. A 'singular value chain' decomposition lets each channel index

Load-bearing premise

The bounds are computed by treating each channel index independently and never enforcing that a single material profile realizes all channels at once; if cross-channel tradeoffs are strong, the reported channel counts overestimate what any one structure can do.

What would settle it

Find a physical or simulated passive structure of a given size and susceptibility whose measured or computed nth singular value exceeds the paper's bound for that n (for example, a 1×1×5 λ silicon-like mediator supporting more than twenty-five unity-amplitude channels), or show via topology optimization that no structure comes close to the bound at large n, which would reveal the relaxation to be too loose.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • For any fixed device geometry and material susceptibility, the method gives a computable upper bound on how many channels can have amplitude above a chosen cutoff, directly answering the channel-count question.
  • Because the bounds apply to all major scattering operators via operator relations, they extend to power transfer and to input-output transformations relevant to multiplexing and mode conversion.
  • In detection problems, bounds on the smallest singular value translate into limits on condition number and Fisher information, so they cap how well any metasurface of a given size can distinguish a prescribed set of incident plane waves.
  • The waveguide-like example suggests that medium-distance communication with wavelength-scale structured mediators may support far more channels than free-space propagation at comparable separations.
  • The metasurface-like examples indicate that increasing non-local cell volume increases usable channel counts, but with diminishing returns as device area grows.

Where Pith is reading between the lines

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

  • A natural next test is to enforce a single-material consistency constraint across all channel indices and compare the resulting achievable channel counts with these relaxed bounds; the gap size determines whether the bounds are tight enough for device design.
  • Since the logic relies only on linear response and power conservation, the same CFW-plus-convex-relaxation recipe should transfer to acoustic, elastic, or quantum scattering where a free-space Green function and passivity are available.
  • The displayed three-dimensional bounds use a chosen rather than fully optimized excluded subspace, so at large n they likely overestimate attainable channel amplitudes; optimizing Q_{n−1} against G₀ + G₀TG₀ is an evident refinement that may tighten the predictions.

Editorial analysis

A structured set of objections, weighed in public.

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

Circularity Check

0 steps flagged

No significant circularity: the QCQP relaxations give genuine upper bounds; the admitted missing structural-consistency constraint affects tightness only.

full rationale

The derivation is not circular. The bound in Eq. (16) is obtained from the exact structural optimization (14) by replacing, for each channel index, the structural variable T(ε) with any pair (q⊥,t) satisfying the passivity constraints (15). Because (15) is a necessary condition for any physical (q⊥,t), the relaxed feasible set contains every physical realization; hence the optimum is an upper bound on σ_n by construction, and no fitted quantity is later reported as a prediction. The singular-value chain (Eqs. 22–24 and 27) likewise preserves upper-bound validity: each step either removes an outer max, restricts to a subspace, or relaxes constraints, none of which can under-bound the true maximum. Most self-citations (e.g., Refs. [13,35,43] for T-operator conservation and power constraints) are parameter-free physical identities that support the constraints; they do not import the target bound. The paper explicitly flags the main caveat—cross-channel material consistency is not enforced—in Supplementary Note 2 ('there should also be cross-constraints associated with the fact that each of these responses must be realized by a single structure') and in the Outlook ('the bounds shown in §Applications do not guarantee a single structure having n singular values above a certain threshold... could well be reduced by significant factors'). This is a clear statement of looseness in the simultaneous multi-channel interpretation, not a circular reduction. Numerics are validated against topology optimization in the laser-detection example, and the RSVD and root-solving procedures are standard, so the predictions have independent content.

Axiom & Free-Parameter Ledger

2 free parameters · 5 axioms · 1 invented entities

The method rests on standard scattering identities and the authors' prior T-operator passivity constraints. The main extras introduced here are the numerical/relaxation choices (subspace selection, RSVD settings, per-channel independence), which are disclosed but not fully validated by convergence studies.

free parameters (2)
  • Silicon-like susceptibility χ = 13.6 + 0.05i
    Used in waveguide/metasurface examples to model a realistic high-index material; it is an input parameter, not fitted to the target bounds, but all reported numbers depend on it.
  • RSVD and discretization settings = rank up to 57; q=14; p=2k; 32,768 voxels/λ^3
    Chosen for computational feasibility/memory limits; the paper provides no convergence study, and the reported bounds inherit uncertainty from these choices.
axioms (5)
  • standard math Courant–Fischer–Weyl min-max principle for compact operators
    Underpins the expression of σ_n as a min-max over subspaces (Eq. 1).
  • domain assumption Lippmann-Schwinger / T-operator identity G = G0 + G0 T G0
    Standard scattering theory; assumes linear, non-magnetic media with known susceptibility (Eq. 4).
  • domain assumption Passivity: any physical T satisfies real and reactive power conservation over any subregion (Eq. 15)
    Necessary conditions from Maxwell's equations; used to relax the design optimization to a convex QCQP.
  • ad hoc to paper The relaxation from full physical constraints to only global real/reactive power conservation is sufficiently tight for the reported bounds
    The authors state that duality gaps larger than an order of magnitude are unlikely, but do not prove this; if false, the 'quantitatively predictive' claim fails.
  • ad hoc to paper The infinite-dimensional singular value problem is faithfully represented by the 32,768-voxel-per-wavelength discretization and the randomized SVD at the chosen rank
    No grid/rank convergence study is given; the paper concedes 'variations within an order of unity would not be surprising.'
invented entities (1)
  • P-operator no independent evidence
    purpose: Abstract claims indexed singular value bounds for a 'proposed P-operator' in addition to Green and W operators.
    No definition, equation, or analysis of any P-operator appears in the full text or supplementary; this is an undefined placeholder in the abstract.

reviewed 2026-08-04 · how reviews work

0 comments
read the original abstract

Spectral properties of scattering operators, and their dependence on geometry, are of crucial importance to photonic design, enabling low-rank approximations and improved understanding of achievable power and information transfer. Here, we develop a method to bound indexed singular values (channel amplitudes) of the Green operator, $W$-operator, and proposed $P$-operator, for arbitrarily structured linear media. The approach yields computable upper bounds on the $n^{th}$ singular value, for any given $n$, that capture the complexity of multi-channel tradeoffs and competing scattering effects. As illustrations of the framework, channel bounds are provided for multi-wavelength three-dimensional ``mediating'' volumes (up to $64\,\lambda^3$, mimicking communication waveguide-like and metasurface-like configurations), power transfer between $9\,\lambda^3$ source and receiver volumes, and applied to elucidate the performance of a planewave angle discrimination problem (bounding the smallest singular value, or condition number, of a fixed input space). In addition to these exemplary uses, the approach is directly applicable to bounds on information theoretic objectives such as Shannon capacity and Fisher information, as well as computational guarantees, such as error limits for reduced-order models.

Figures

Figures reproduced from arXiv: 2510.01128 by Alejandro W. Rodriguez, Alessio Amaolo, Paul Virally, Pengning Chao, Sean Molesky.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

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Reference graph

Works this paper leans on

71 extracted references · 6 canonical work pages · cited by 1 Pith paper

  1. [1]

    Roadmap for optical metasurfaces.ACS photonics, 11 (3):816–865, 2024

    Arseniy I Kuznetsov, Mark L Brongersma, Jin Yao, Mu Ku Chen, Uriel Levy, Din Ping Tsai, Nikolay I Zhe- ludev, Andrei Faraon, Amir Arbabi, Nanfang Yu, et al. Roadmap for optical metasurfaces.ACS photonics, 11 (3):816–865, 2024

    2024

  2. [2]

    Roadmapping the next generation of silicon photonics.Nature Communications, 15(1):751, 2024

    Sudip Shekhar, Wim Bogaerts, Lukas Chrostowski, John E Bowers, Michael Hochberg, Richard Soref, and Bhavin J Shastri. Roadmapping the next generation of silicon photonics.Nature Communications, 15(1):751, 2024

    2024

  3. [3]

    Next-generation optical networks to sustain connectivity of the future: All roads lead to optical-computing-enabled network?Inter- net of Things, 29:101445, 2025

    Dao Thanh Hai and Isaac Woungang. Next-generation optical networks to sustain connectivity of the future: All roads lead to optical-computing-enabled network?Inter- net of Things, 29:101445, 2025

    2025

  4. [4]

    All linear optical devices are mode converters.Optics express, 20(21):23985–23993, 2012

    David AB Miller. All linear optical devices are mode converters.Optics express, 20(21):23985–23993, 2012

    2012

  5. [5]

    Inference in artificial intelligence with deep optics and photonics

    Gordon Wetzstein, Aydogan Ozcan, Sylvain Gigan, Shanhui Fan, Dirk Englund, Marin Soljaˇ ci´ c, Cornelia Denz, David AB Miller, and Demetri Psaltis. Inference in artificial intelligence with deep optics and photonics. Nature, 588(7836):39–47, 2020

    2020

  6. [6]

    Universal photonic processor for spatial mode decomposition.Nature Com- munications, 16(1):7982, 2025

    Varun Sharma, Dorian Brandm¨ uller, Johannes B¨ utow, J¨ org S Eismann, and Peter Banzer. Universal photonic processor for spatial mode decomposition.Nature Com- munications, 16(1):7982, 2025

    2025

  7. [7]

    End-to-end deep learn- ing of optical fiber communications.Journal of Lightwave Technology, 36(20):4843–4855, 2018

    Boris Karanov, Mathieu Chagnon, F´ elix Thouin, To- bias A Eriksson, Henning B¨ ulow, Domani¸ c Lavery, Polina Bayvel, and Laurent Schmalen. End-to-end deep learn- ing of optical fiber communications.Journal of Lightwave Technology, 36(20):4843–4855, 2018

    2018

  8. [8]

    End-to- end optimization of metasurfaces for imaging with com- pressed sensing.ACS Photonics, 11(5):2077–2087, 2024

    Gaurav Arya, William F Li, Charles Roques-Carmes, Marin Soljacic, Steven G Johnson, and Zin Lin. End-to- end optimization of metasurfaces for imaging with com- pressed sensing.ACS Photonics, 11(5):2077–2087, 2024

    2077

  9. [9]

    Neural network-assisted end- to-end design for full light field control of meta-optics

    Hanbin Chi, Yueqiang Hu, Xiangnian Ou, Yuting Jiang, Dian Yu, Shaozhen Lou, Quan Wang, Qiong Xie, Cheng- Wei Qiu, and Huigao Duan. Neural network-assisted end- to-end design for full light field control of meta-optics. Advanced Materials, 37(13):2419621, 2025

    2025

  10. [10]

    Singular- value decomposition for electromagnetic-scattering anal- ysis.Physical Review A, 95(5):053834, 2017

    Radius NS Suryadharma, Martin Fruhnert, Carsten Rockstuhl, and Ivan Fernandez-Corbaton. Singular- value decomposition for electromagnetic-scattering anal- ysis.Physical Review A, 95(5):053834, 2017

    2017

  11. [11]

    Generalizing normal mode expansion of electromagnetic green’s tensor to open systems.Physical Review Applied, 11(4):044018, 2018

    Parry Y Chen, David J Bergman, and Yonatan Sivan. Generalizing normal mode expansion of electromagnetic green’s tensor to open systems.Physical Review Applied, 11(4):044018, 2018

    2018

  12. [12]

    Singular value decom- position ghost imaging.Optics Express, 26(10):12948– 12958, 2018

    Xue Zhang, Xiangfeng Meng, Xiulun Yang, Yurong Wang, Yongkai Yin, Xianye Li, Xiang Peng, Wenqi He, Guoyan Dong, and Hongyi Chen. Singular value decom- position ghost imaging.Optics Express, 26(10):12948– 12958, 2018

    2018

  13. [13]

    GlobalToperator bounds on elec- tromagnetic scattering: upper bounds on far-field cross sections.Physical Review Research, 2(3):033172, 2020

    Sean Molesky, Pengning Chao, Weiliang Jin, and Alejan- dro W Rodriguez. GlobalToperator bounds on elec- tromagnetic scattering: upper bounds on far-field cross sections.Physical Review Research, 2(3):033172, 2020

    2020

  14. [14]

    Heuristic methods and performance bounds for photonic design.Optics Express, 29(2):2827–2854, 2021

    Guillermo Angeris, Jelena Vuˇ ckovi´ c, and Stephen Boyd. Heuristic methods and performance bounds for photonic design.Optics Express, 29(2):2827–2854, 2021

    2021

  15. [15]

    Many photonic design problems are sparse qcqps.Science Advances, 11(1):eadl3237, 2025

    Shai Gertler, Zeyu Kuang, Colin Christie, Hao Li, and Owen D Miller. Many photonic design problems are sparse qcqps.Science Advances, 11(1):eadl3237, 2025

    2025

  16. [16]

    Singular value decomposition and principal com- ponent analysis

    Michael E Wall, Andreas Rechtsteiner, and Luis M Rocha. Singular value decomposition and principal com- ponent analysis. InA practical approach to microarray data analysis, pages 91–109. Springer, 2003

    2003

  17. [17]

    Capacity of multi-antenna gaussian chan- nels.European Transactions on Telecommunications, 10 (6):585–595, 1999

    Emre Telatar. Capacity of multi-antenna gaussian chan- nels.European Transactions on Telecommunications, 10 (6):585–595, 1999

    1999

  18. [18]

    A randomized algorithm for the decomposition of matrices.Applied and Computational Harmonic Anal- ysis, 30(1):47–68, 2011

    Per-Gunnar Martinsson, Vladimir Rokhlin, and Mark Tygert. A randomized algorithm for the decomposition of matrices.Applied and Computational Harmonic Anal- ysis, 30(1):47–68, 2011

    2011

  19. [19]

    A tutorial on singular value decomposition with applications on image compression and dimensionality reduction

    Yousef Jaradat, Mohammad Masoud, Ismael Jannoud, Ahmad Manasrah, and Mohammad Alia. A tutorial on singular value decomposition with applications on image compression and dimensionality reduction. In2021 in- ternational conference on information technology (ICIT), pages 769–772. IEEE, 2021

    2021

  20. [20]

    In- verse design in nanophotonics via representation learn- ing.arXiv:2507.00546, 2025

    Reza Marzban, Ali Adibi, and Raphael Pestourie. In- verse design in nanophotonics via representation learn- ing.arXiv:2507.00546, 2025

    arXiv 2025

  21. [21]

    Wei Sun and Chongchong Zhang. Analysis and forecast- ing of the carbon price using multi—resolution singular value decomposition and extreme learning machine opti- mized by adaptive whale optimization algorithm.Applied Energy, 231:1354–1371, 2018

    2018

  22. [22]

    Minute-ahead stock price forecasting based on singular spectrum analysis and support vector 14 regression.Applied Mathematics and Computation, 320: 444–451, 2018

    Salim Lahmiri. Minute-ahead stock price forecasting based on singular spectrum analysis and support vector 14 regression.Applied Mathematics and Computation, 320: 444–451, 2018

    2018

  23. [23]

    Singular value decomposition based recom- mendation using imputed data.Knowledge-Based Sys- tems, 163:485–494, 2019

    Xiaofeng Yuan, Lixin Han, Subin Qian, Guoxia Xu, and Hong Yan. Singular value decomposition based recom- mendation using imputed data.Knowledge-Based Sys- tems, 163:485–494, 2019

    2019

  24. [24]

    How complicated must an optical com- ponent be?JOSA A, 30(2):238–251, 2013

    David AB Miller. How complicated must an optical com- ponent be?JOSA A, 30(2):238–251, 2013

    2013

  25. [25]

    Establishing optimal wave commu- nication channels automatically.Journal of Lightwave Technology, 31(24):3987–3994, 2013

    David AB Miller. Establishing optimal wave commu- nication channels automatically.Journal of Lightwave Technology, 31(24):3987–3994, 2013

    2013

  26. [26]

    Waves, modes, communications, and optics: a tutorial.Advances in Optics and Photonics, 11 (3):679–825, 2019

    David AB Miller. Waves, modes, communications, and optics: a tutorial.Advances in Optics and Photonics, 11 (3):679–825, 2019

    2019

  27. [27]

    Determining the optimal communication channels of arbitrary optical systems using integrated photonic processors.Nature Photonics, 18(2):149–155, 2024

    SeyedMohammad SeyedinNavadeh, Maziyar Mi- lanizadeh, Francesco Zanetto, Giorgio Ferrari, Marco Sampietro, Marc Sorel, David AB Miller, Andrea Mel- loni, and Francesco Morichetti. Determining the optimal communication channels of arbitrary optical systems using integrated photonic processors.Nature Photonics, 18(2):149–155, 2024

    2024

  28. [28]

    Unitary control of multiport wave transmission.Physical Review A, 111(2):023507, 2025

    Cheng Guo, David AB Miller, and Shanhui Fan. Unitary control of multiport wave transmission.Physical Review A, 111(2):023507, 2025

    2025

  29. [29]

    Communicating with waves between volumes: evaluating orthogonal spatial channels and lim- its on coupling strengths.Applied Optics, 39(11):1681– 1699, 2000

    David A B Miller. Communicating with waves between volumes: evaluating orthogonal spatial channels and lim- its on coupling strengths.Applied Optics, 39(11):1681– 1699, 2000

    2000

  30. [30]

    Fundamental bounds on mimo antennas.IEEE Antennas and Wireless Propagation Letters, 17(1):21–24, 2017

    Casimir Ehrenborg and Mats Gustafsson. Fundamental bounds on mimo antennas.IEEE Antennas and Wireless Propagation Letters, 17(1):21–24, 2017

    2017

  31. [31]

    Capacity bounds and degrees of freedom for mimo antennas constrained by q-factor.IEEE Trans- actions on Antennas and Propagation, 69(9):5388–5400, 2021

    Casimir Ehrenborg, Mats Gustafsson, and Miloslav Capek. Capacity bounds and degrees of freedom for mimo antennas constrained by q-factor.IEEE Trans- actions on Antennas and Propagation, 69(9):5388–5400, 2021

    2021

  32. [32]

    Rodriguez

    Sean Molesky, Pengnging Chao, Jewel Mohajan, Wes- ley Reinhart, Heng Chi, and Alejandro W. Rodriguez. T-operator limits on optical communication: Metaop- tics, computation, and input-output transformations. Physical Review Research, 4:013020, Jan 2022. doi: 10.1103/PhysRevResearch.4.013020

    work page doi:10.1103/physrevresearch.4.013020 2022

  33. [33]

    Maximum shannon capacity of pho- tonic structures.arXiv preprint arXiv:2409.02089, 2024

    Alessio Amaolo, Pengning Chao, Benjamin Strekha, Ste- fan Clarke, Jewel Mohajan, Sean Molesky, and Alejan- dro W Rodriguez. Maximum shannon capacity of pho- tonic structures.arXiv preprint arXiv:2409.02089, 2024

    Pith/arXiv arXiv 2024

  34. [34]

    Bounds on the coupling strengths of communication channels and their information capacities.IEEE Trans- actions on Antennas and Propagation, 2025

    Zeyu Kuang, David AB Miller, and Owen D Miller. Bounds on the coupling strengths of communication channels and their information capacities.IEEE Trans- actions on Antennas and Propagation, 2025

    2025

  35. [35]

    Fundamental limits to ra- diative heat transfer: theory.Physical Review B, 101(3): 035408, 2020

    Sean Molesky, Prashanth S Venkataram, Weiliang Jin, and Alejandro W Rodriguez. Fundamental limits to ra- diative heat transfer: theory.Physical Review B, 101(3): 035408, 2020

    2020

  36. [36]

    Maximum electromagnetic local density of states via material structuring.Nanophotonics, 12(3):549–557, 2023

    Pengning Chao, Rodrick Kuate Defo, Sean Molesky, and Alejandro Rodriguez. Maximum electromagnetic local density of states via material structuring.Nanophotonics, 12(3):549–557, 2023

    2023

  37. [37]

    Trace expressions and associated limits for nonequilibrium casimir torque.Physical Review A, 106(4):042222, 2022

    Benjamin Strekha, Sean Molesky, Pengning Chao, Matthias Kr¨ uger, and Alejandro W Rodriguez. Trace expressions and associated limits for nonequilibrium casimir torque.Physical Review A, 106(4):042222, 2022

    2022

  38. [38]

    Physical bounds and radiation modes for mimo antennas.IEEE Transactions on Antennas and Propagation, 68(6):4302– 4311, 2020

    Casimir Ehrenborg and Mats Gustafsson. Physical bounds and radiation modes for mimo antennas.IEEE Transactions on Antennas and Propagation, 68(6):4302– 4311, 2020

    2020

  39. [39]

    Information- driven design of imaging systems.arXiv preprint arXiv:2405.20559, 2025

    Henry Pinkard, Leyla Kabuli, Eric Markley, Tiffany Chien, Jiantao Jiao, and Laura Waller. Information- driven design of imaging systems.arXiv preprint arXiv:2405.20559, 2025

    arXiv 2025

  40. [40]

    Coupled-mode theory for general free-space resonant scattering of waves.Physical Review A, 75(5):053801, 2007

    Rafif E Hamam, Aristeidis Karalis, John D Joannopou- los, and Marin Soljaˇ ci´ c. Coupled-mode theory for general free-space resonant scattering of waves.Physical Review A, 75(5):053801, 2007

    2007

  41. [41]

    Trace formulas for nonequilibrium casimir interactions, heat radiation, and heat transfer for arbitrary objects.Physical Review B, 86(11):115423, 2012

    Matthias Kr¨ uger, Giuseppe Bimonte, Thorsten Emig, and Mehran Kardar. Trace formulas for nonequilibrium casimir interactions, heat radiation, and heat transfer for arbitrary objects.Physical Review B, 86(11):115423, 2012

    2012

  42. [42]

    Trace formulation for photonic inverse design with incoherent sources.Structural and Multidisciplinary Optimization, 65(11):336, 2022

    Wenjie Yao, Francesc Verdugo, Rasmus E Christiansen, and Steven G Johnson. Trace formulation for photonic inverse design with incoherent sources.Structural and Multidisciplinary Optimization, 65(11):336, 2022

    2022

  43. [43]

    Physical lim- its in electromagnetism.Nature Reviews Physics, 4(8): 543–559, 2022

    Pengning Chao, Benjamin Strekha, Rodrick Kuate Defo, Sean Molesky, and Alejandro W Rodriguez. Physical lim- its in electromagnetism.Nature Reviews Physics, 4(8): 543–559, 2022

    2022

  44. [44]

    Nonlocal metasurfaces for optical signal processing.Physical Review Letters, 121(17):173004, 2018

    Hoyeong Kwon, Dimitrios Sounas, Andrea Cordaro, Al- bert Polman, and Andrea Al` u. Nonlocal metasurfaces for optical signal processing.Physical Review Letters, 121(17):173004, 2018

    2018

  45. [45]

    Multifunctional nonlocal metasurfaces.Physical Review Letters, 125(1):017402, 2020

    Adam C Overvig, Stephanie C Malek, and Nanfang Yu. Multifunctional nonlocal metasurfaces.Physical Review Letters, 125(1):017402, 2020

    2020

  46. [46]

    Nonlocal metamaterials and meta- surfaces.Nature Reviews Physics, pages 1–14, 2025

    Yi Chen, Romain Fleury, Pierre Seppecher, Gengkai Hu, and Martin Wegener. Nonlocal metamaterials and meta- surfaces.Nature Reviews Physics, pages 1–14, 2025

    2025

  47. [47]

    Li, Gaurav Arya, Charles Roques-Carmes, Zin Lin, Steven G

    William F. Li, Gaurav Arya, Charles Roques-Carmes, Zin Lin, Steven G. Johnson, and Marin Soljaˇ ci´ c. Tran- scending shift-invariance in the paraxial regime via end- to-end inverse design of freeform nanophotonics.Optics Express, 31(15):24260, July 2023. ISSN 1094-4087. doi: 10.1364/OE.492553

    work page doi:10.1364/oe.492553 2023

  48. [48]

    American Mathematical Soc., 2014

    Gerald Teschl.Mathematical methods in quantum me- chanics, volume 157. American Mathematical Soc., 2014

    2014

  49. [49]

    Freeform metagratings based on complex light scattering dynamics for extreme, high efficiency beam steering.Annalen der Physik, 530(1):1700302, 2018

    Jianji Yang, David Sell, and Jonathan A Fan. Freeform metagratings based on complex light scattering dynamics for extreme, high efficiency beam steering.Annalen der Physik, 530(1):1700302, 2018

    2018

  50. [50]

    Design of metasurface polarization converter from linearly po- larized signal to circularly polarized signal.Optik, 161: 12–19, 2018

    Oguzhan Akgol, Emin Unal, Olcay Altintas, Muharrem Karaaslan, Faruk Karadag, and Cumali Sabah. Design of metasurface polarization converter from linearly po- larized signal to circularly polarized signal.Optik, 161: 12–19, 2018

    2018

  51. [51]

    Topology optimized mode multiplexing in silicon-on-insulator photonic wire waveguides.Optics Express, 24(15):16866–16873, 2016

    Louise F Frellsen, Yunhong Ding, Ole Sigmund, and Lars H Frandsen. Topology optimized mode multiplexing in silicon-on-insulator photonic wire waveguides.Optics Express, 24(15):16866–16873, 2016

    2016

  52. [52]

    Why optics needs thickness.Science, 379(6627):41–45, 2023

    David AB Miller. Why optics needs thickness.Science, 379(6627):41–45, 2023

    2023

  53. [53]

    Wenchao Ma, Rapha¨ el Pestourie, Zin Lin, and Steven G. Johnson. Inverse design for robust inference in in- tegrated computational spectrometry.arXiv preprint arXiv:2506.02194, June 2025

    arXiv 2025

  54. [54]

    Passivity constraints on the relations between transmission, reflection, and ab- sorption eigenvalues.Physical Review B, 110(20):205431, 2024

    Cheng Guo and Shanhui Fan. Passivity constraints on the relations between transmission, reflection, and ab- sorption eigenvalues.Physical Review B, 110(20):205431, 2024. 15

    2024

  55. [55]

    Bounds as blueprints: To- wards optimal and accelerated photonics inverse design

    Pengning Chao, Alessio Amaolo, Sean Molesky, and Alejandro W Rodriguez. Bounds as blueprints: To- wards optimal and accelerated photonics inverse design. arXiv:2504.10469, 2025

    Pith/arXiv arXiv 2025

  56. [56]

    Owen D Miller, Chia Wei Hsu, M. T. Homer Reid, Wenjun Qiu, Brendan G DeLacy, John D Joannopou- los, Marin Soljaˇ ci´ c, and Steven G Johnson. Fundamental limits to extinction by metallic nanoparticles.Physical Review Letters, 112(12):123903, 2014

    2014

  57. [57]

    Tun- nelling escape of waves.Nature Photonics, 19(3):284–290, 2025

    David AB Miller, Zeyu Kuang, and Owen D Miller. Tun- nelling escape of waves.Nature Photonics, 19(3):284–290, 2025

    2025

  58. [58]

    Sean Molesky, Weiliang Jin, Prashanth S Venkataram, and Alejandro W Rodriguez.T-operator bounds on angle-integrated absorption and thermal radiation for ar- bitrary objects.Physical Review Letters, 123:257401, 2019

    2019

  59. [59]

    Owen D Miller, Athanasios G Polimeridis, M. T. Homer Reid, Chia Wei Hsu, Brendan G DeLacy, John D Joannopoulos, Marin Soljaˇ ci´ c, and Steven G Johnson. Fundamental limits to optical response in absorptive sys- tems.Optics Express, 24(4):3329–3364, 2016

    2016

  60. [60]

    Actual communication also requires encoding the source current and decoding the received field

    Note1. Actual communication also requires encoding the source current and decoding the received field. These ad- ditional conversions must be composed with the Green function to properly model physical systems

  61. [61]

    General heuristics for nonconvex quadratically constrained quadratic program- ming.arXiv:1703.07870, 2017

    Jaehyun Park and Stephen Boyd. General heuristics for nonconvex quadratically constrained quadratic program- ming.arXiv:1703.07870, 2017

    Pith/arXiv arXiv 2017

  62. [62]

    Ro- driguez

    Sean Molesky, Pengning Chao, and Alejandro W. Ro- driguez. Hierarchical mean-fieldToperator bounds on electromagnetic scattering: Upper bounds on near-field radiative purcell enhancement.Physi- cal Review Research, 2:043398, Dec 2020. doi: 10.1103/PhysRevResearch.2.043398

    work page doi:10.1103/physrevresearch.2.043398 2020

  63. [63]

    Upper bounds on absorption and scat- tering.New Journal of Physics, 22(7):073013, September

    Mats Gustafsson, Kurt Schab, Lukas Jelinek, and Miloslav Capek. Upper bounds on absorption and scat- tering.New Journal of Physics, 22(7):073013, September

  64. [64]

    Zeyu Kuang and Owen D. Miller. Computational bounds to light–matter interactions via local conservation laws. Physical Review Letters, 125:263607, Dec 2020. doi: 10.1103/PhysRevLett.125.263607

    work page doi:10.1103/physrevlett.125.263607 2020

  65. [65]

    Zeyu Kuang, Lang Zhang, and Owen D. Miller. Maximal single-frequency electromagnetic response.Optica, 7(12): 1746–1757, Dec 2020. doi:10.1364/OPTICA.398715

    work page doi:10.1364/optica.398715 2020

  66. [66]

    Inferring structure via duality for photonic inverse design.arXiv:2504.14083, 2025

    Sean Molesky, Pengning Chao, Alessio Amaolo, and Ale- jandro W Rodriguez. Inferring structure via duality for photonic inverse design.arXiv:2504.14083, 2025

    Pith/arXiv arXiv 2025

  67. [67]

    Note2. Although eachs k represents an orthogonal excita- tion of the design, there should also be cross-constraints associated with the fact that each of these responses must be realized by a single structure [32]

  68. [68]

    Note3. At a higher level of sophistication, this loose es- timate can be improved by tracking what portion ofU rd has already been covered, and then optimizingd k over the remaining subspace

  69. [69]

    In the simplest implementation, these additional vectors may be ignored in bounding the second term—the previous value of max k>n ξkγ◦ds k is simply repeated

    Note4. In the simplest implementation, these additional vectors may be ignored in bounding the second term—the previous value of max k>n ξkγ◦ds k is simply repeated

  70. [70]

    Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decom- positions.SIAM Review, 53(2):217–288, 2011

    Nathan Halko, Per-Gunnar Martinsson, and Joel A Tropp. Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decom- positions.SIAM Review, 53(2):217–288, 2011

    2011

  71. [2020]

    doi:10.1088/1367-2630/ab83d3

    ISSN 1367-2630. doi:10.1088/1367-2630/ab83d3

    work page doi:10.1088/1367-2630/ab83d3

This paper was first reviewed by deepseek-v4-flash on August 4, 2026.