Pith. sign in

REVIEW 3 major objections 5 minor 43 references

Substrate matters: Coupled phonon modes of a spherical particle on a substrate probed with EELS

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read The permittivity of a thin film decides whether a supported sphere's surface phonons stay free, mix through mirror charges, or hybridize with film Fuchs-Kliewer modes.

desk verdict Solid simulation study with a clean three-regime story, but the EELS experiment cannot independently confirm the mode-resolved mechanism because the fits are seeded with the model's own peak positions. read the letter →

arxiv 2506.04395 v1 pith:SQFRQ2PQ submitted 2025-06-04 cond-mat.mtrl-sci

Ka Yin Lee , Elliot K. Beutler , Tifany Q. Crisolo , David J. Masiello , Maureen J. Lagos This is my paper
classification cond-mat.mtrl-sci
keywords vibrationalelectronenergylossspectroscopysurfacephononpolaritonsFuchs-Kliewermodesimagechargeeffectshybridizationmultipolarsphericalnanoparticlesthinfilmsubstrates
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 asks what happens to the surface-phonon resonances of a single spherical nanoparticle when it rests on a thin film, and it answers with three regimes set by the film's dielectric constant. For a film with permittivity near 1, the sphere behaves as if it were in vacuum: the film is transparent. For a dielectric film with permittivity above 1, image charges in the film mix the sphere's multipole phonon modes into new red-shifted coupled modes. For a film with negative permittivity, the sphere's modes hybridize with the film's Fuchs-Kliewer phonon modes, producing blue-shifted coupled modes, and in both coupled cases quadrupole and higher-order modes carry a substantial share of the electron-energy-loss signal. The paper validates these predictions with vibration-resolved electron energy loss spectra of individual 300 nm silica and MgO spheres, fitted with simulation-seeded Voigt profiles.

What carries the argument

The central object is the coupled multipolar surface-phonon response of a sphere–film composite, computed by solving Maxwell's equations with a boundary-element method and probed experimentally by aloof vibrational electron energy loss spectroscopy. The two active mechanisms are image-charge-mediated mode mixing, in which the film's boundaries create mirror charges that interact with the sphere's multipole modes through self- and cross-interactions, and phonon-phonon hybridization, in which the sphere's multipole modes couple to the symmetric and antisymmetric Fuchs-Kliewer slab modes of a negative-permittivity film. The analysis deliberately goes beyond dipole-dipole interactions, because quadrupolar and higher modes account for a large part of the coupled scattering. The experimental validation uses Voigt-function decomposition of the measured spectra, with peak positions, separations, and intensity ratios seeded directly from the simulations.

What would settle it

Measure the MgO-on-Si3N4 composite with energy resolution near 1 meV (or at low temperature to narrow phonon linewidths): the mirror-charge mechanism predicts resolvable substructure from Di+, Di−, Qi+, and Qi− modes around 60–76 meV with simulation-specific spacings and intensity ratios. If the high-resolution spectrum instead shows only the free-space multipolar peaks at their vacuum energies, with no splitting and no out-of-plane mode near 60 meV, the image-charge mode-mixing scenario is wrong; a second check is to refit the existing spectra with initial peak parameters offset randomly from the simulated values and see whether the simulation-seeded fits remain uniquely preferred.

Watch

Extended reading notes

Core claim

The paper's central claim is that the substrate is not a passive support: its dielectric function selects the active coupling mechanism. When the film's permittivity is close to unity (amorphous Si3N4 at the SiO2 sphere's phonon energies), the sphere's multipolar surface phonon modes—dipole, quadrupole, hexapole, and higher—are essentially unchanged from free space. When the film is a dielectric mirror (permittivity about 7.6 for Si3N4 at MgO's phonon energies), the film's two interfaces create multiple image charges, and each sphere mode interacts with its own image and with images of other multipole orders; the result is a ladder of mixed modes such as Di+, Di−, Qi+, and Qi−, with red-shifted energies. When the film is metallic-like (silica, whose permittivity is negative in the relevant spectral band), the symmetric and antisymmetric Fuchs-Kliewer modes of the film hybridize with the sphere's dipole and quadrupole modes to form coupled modes, which appear blue-shifted. In the coupled systems the EELS probability involving quadrupolar modes reaches about 40 percent of the dipolar contribution, and fits to experimental spectra fail when only dipole-dipole interactions are included.

Load-bearing premise

The experimental validation assumes that the simulated mode structure is the correct assignment for the measured spectra, because the experimental peaks are roughly 10 meV wide while the simulated mode separations are often below 1 meV, and the fits are seeded with the simulations' peak positions, separations, and intensity ratios.

Editorial extensions

If this is right

  • Transparency can be engineered: a support whose permittivity is near 1 in the particle's Reststrahlen band leaves the particle's free-space multipolar phonon response intact, so the support does not perturb the measured spectrum.
  • For dielectric supports with permittivity above 1, the observed EELS peak is a mixture of many mixed modes, so interpreting it as the free-space dipole mode would misassign the spectrum.
  • For metallic-type supports with negative permittivity, electron spectra show blue-shifted hybrid modes rather than the red shifts typical of image-charge coupling, and the envelope blue shift grows with the contribution of higher-order coupled modes.
  • Quadrupole and higher multipoles are not negligible: their scattering strength is comparable to the dipole's in the coupled systems, so dipole-only models cannot describe sphere-film coupling.
  • Even a film thinner than 15 nm can substantially modify the infrared response of a supported nanoparticle, which matters for IR nanophotonic devices built on thin membranes.

Reading between the lines

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

  • An extension the paper leaves implicit is that the same dielectric-regime classification should transfer to other low-loss polar or metallic nanoparticles and to supports of different morphology; a systematic set of simulations and measurements on cubes, rods, or rough supports would test whether multipolar mode mixing remains the controlling mechanism.
  • Because the electron beam couples most strongly to in-plane polarizations, the measured loss spectrum is biased toward in-plane mixed modes; a polarization-resolved optical experiment could disentangle the in-plane and out-of-plane branches more cleanly than electron scattering alone.
  • The simulations use an artificially sharp silica damping of 0.05 meV rather than the physical roughly 9 meV; a high-resolution, low-temperature measurement that narrows the instrumental and thermal broadening would test whether the predicted sub-meV mode splittings survive under realistic damping.
  • For infrared photonics the paper implies that substrate selection is a tuning knob: a few nanometres of film can shift or split the phonon resonance of a supported particle, so radiative-cooling and sensing designs should treat the support as part of the resonator rather than as an inert holder.
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 / 5 minor

Summary. The paper studies vibrational EELS of a single spherical silica or MgO particle supported on a thin film, contrasting three coupling regimes: a transparent film (permittivity near unity), a dielectric mirror film (permittivity greater than unity), and a metallic-type film (permittivity negative) that hosts Fuchs-Kliewer phonons. The central claims are that mirror-charge effects cause multipolar phonon mode mixing for dielectric films, that hybridization with Fuchs-Kliewer modes governs metallic-type films, and that interactions beyond dipole-dipole are required to describe the sphere-film coupling. These claims are supported mainly by MNPBEM20 electrodynamic simulations and by Voigt-function fits to experimental EELS spectra whose initial parameters are taken directly from the simulations.

Significance. If the central mechanistic conclusions are correct, the paper provides a useful classification of substrate-induced phonon coupling in supported dielectric nanoparticles and demonstrates that high-order multipoles contribute substantially to the electron energy-loss signal in the coupled regimes. The use of an established numerical toolbox (MNPBEM20) with convergence checks and the direct comparison of simulated EELS with experimental spectra are strengths. However, the experimental validation is substantially weakened by the fitting procedure, which seeds peak positions, separations, and intensity ratios from the very simulations being validated; as the manuscript itself concedes, individual resonances are not experimentally resolved. The quantitative statement that quadrupolar EELS probability is about 40% of the dipolar contribution is also computed with an artificially reduced damping parameter, so its robustness is unclear.

major comments (3)
  1. [§5, §6, Appendix F, §7] The experimental validation is circular in a load-bearing way. Appendix F states that the initial peak positions, separations, and intensity ratios are 'directly extracted from the MNPBEM20 simulated result,' and Section 5 states that 'the individual resonances cannot be resolved due to the limited spectral resolution' (instrumental response ~10 meV versus simulated mode separations from below 0.1 meV to a few meV). The reported R^2 values above 0.98 therefore establish only that the data are consistent with a model-prescribed mixture of Voigt peaks, not that the data independently select the simulated multipolar mode structure. The summary's statement in §7 that the measurements 'validated our theoretical predictions' overstates the evidential force of these fits. The authors should either present the experiments as consistency checks rather than validation, or provide a non-circular test (e.g., fitting without seeding, model comparison criteria, or resolving modes with better energy resolution).
  2. [§2 and §6] The quantitative claim that 'the EELS probability involving quadrupolar modes is about 40% of that of the dipolar modes' depends on the unphysically low silica damping of 0.05 meV used in the simulations, while the physical value is 9 meV as acknowledged in Section 2. This artificially sharpens the simulated peaks and changes their relative heights, so the 40% ratio is not a robust prediction for the real system. The authors should show how the quadrupole/dipole ratio and the overall spectral assignments change when the physical damping is used, and clarify whether the central 'beyond dipole-dipole' conclusion survives with physical broadening.
  3. [§5] The claim that fits fail without quadrupole components ('if one considers only the low-energy mode contributions... it is not possible to fit satisfactorily the experimental data') is presented as experimental evidence for the importance of higher-order modes. Because the fit is initialized with the full simulated mode set including quadrupole terms, this test does not independently demonstrate that the data require quadrupole modes; a model with fewer modes might fit comparably if positions and widths were freely optimized. The authors should quantify the comparison (e.g., F-test or reduced chi-square) and show the best fit obtainable without quadrupole contributions.
minor comments (5)
  1. [§3 and Appendix A] The film thickness is inconsistent: Section 3 states the a-Si3N4 film is 15 nm thick, while Appendix A states the purchased membranes are 10 nm thick. Section 5 also says 15 nm for the MgO-on-nitride sample, while Appendix A again says 10 nm. Please clarify which thicknesses were actually used and whether the simulations used the same values.
  2. [Appendix D] The equations in Appendix D are garbled in the manuscript text; the expressions for A_lm and B_lm are unreadable. Since this appendix is meant to document the free-space sphere calculation, the authors should provide clean, correctly typeset formulas so readers can verify the implementation.
  3. [§4] The energy-level diagrams in Figs. 2b and 2d are not referenced in sufficient detail in the text; in particular, the notation for the coupled dipole-FK and quadrupole-FK modes in Fig. 2d is introduced only later in §6. A brief explanation of the diagram axes and level ordering would improve readability.
  4. [§6] The inset of Fig. 4a is said to highlight the quadrupole-FK modes, but the labeling of the two close resonances is hard to read. Please enlarge the inset or add explicit markers for 2l_sym_iD^- and 2l_anti_zD^-.
  5. [Appendix E] There are typographical errors in the appendix, e.g., 'compos e' and an unmatched closing brace in the EELS probability expression. These should be corrected.

Circularity Check

1 steps flagged · score 6.0 of 10

Experimental validation is partially circular: fits are seeded with simulated peak positions, separations, and intensity ratios, so R²>0.98 cannot independently confirm the mode-resolved phonon-coupling claims.

  1. fitted input called prediction [Appendix F: Fitting analysis; Section 5: Image charge effects]
    "The initial input parameters, e.g. the peak positions and separations, intensity ratios, are directly extracted from the MNPBEM20 simulated result. ... Notice that the individual resonances cannot be resolved due to the limited spectral resolution."

    The validation loop is: MNPBEM20 simulates the coupled-mode spectrum; the Voigt least-squares fit is initialized with the simulated peak positions, separations, and intensity ratios; the fit returns parameter families anchored at those simulation values; and the resulting R²>0.98 is quoted as confirming the simulated mode structure. Because each resonance is not individually resolved (instrumental response ~10 meV, mode separations from below 0.1 to a few meV), the fit cannot independently select the multipolar composition. The claim that dipole-only components cannot fit the data is also inherited from the seeded decomposition, since the fit already contains quadrupole and higher-mode components chosen from the simulation.

full rationale

The paper's numerical theory is largely non-circular: the free-space and sphere-film EELS spectra are computed with MNPBEM20 boundary-element electrodynamics using independent material dielectric data and standard electron-energy-loss theory, and those simulations contain genuine predictive content. The self-citations to the authors' earlier work (e.g., Refs. [12] and [25–30]) provide context, published analytical limits, and methodological precedent rather than the load-bearing derivation, so they do not by themselves constitute circularity. The circularity is confined to the experimental-validation leg. Appendix F states that the fitting parameters are directly extracted from the MNPBEM20 simulated result, and Section 5 concedes that the individual resonances cannot be resolved at the ~10 meV instrumental resolution. A Voigt fit seeded at the simulated peak positions, separations, and intensity ratios cannot independently establish the multipolar mode structure; its R²>0.98 only shows that a model-prescribed decomposition is consistent with the broad measured envelope. Consequently, the claim that the EELS experiments validate the mode-resolved mechanisms (mirror-charge mode mixing, Fuchs-Kliewer hybridization, and the ~40% quadrupole weight) is partially circular. The additional modeling choice of using a silica damping of 0.05 meV instead of the physical 9 meV sharpens simulated peaks and changes relative intensities, which weakens quantitative comparisons but is a modeling approximation rather than a circular step. Overall score 6: the central simulated physics retains independent content, but a key 'prediction-versus-experiment' confirmation reduces by construction to the simulation-seeded fit.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

No new physical entities are introduced; the 'mixed modes' (Di+, Di-, Qi+, and so on) and the coupled modes are linear combinations of classical multipole and Fuchs-Kliewer basis states, not new degrees of freedom. The ledger's fitted parameters are concentrated in the Voigt decomposition of the experimental spectra and in two modeling choices: the reduced silica damping and the nominal geometry (diameter, thickness, impact parameters).

free parameters (6)
  • silica damping gamma = 0.05 meV (physical value 9 meV)
    Section 2: a damping of 0.05 meV was used for the silica dielectric function instead of the actual 9 meV to reduce peak overlap; this changes simulated linewidths and relative peak intensities, and all silica simulation results inherit this choice.
  • Voigt amplitudes A_l per mode = not reported numerically
    Appendix F: a scaling parameter for each Voigt component, fit to experimental EELS data; the fitted values are not listed.
  • mode relative contributions c_l = not reported numerically
    Appendix F: a parameter representing the relative contribution of each mode or mode group, fit to the experimental EELS data.
  • peak positions and separations = initialized from MNPBEM20 simulation, then minimized by interior point algorithm
    Appendix F: initial input parameters are directly extracted from the simulation; the fit then varies them, so the final positions are effectively fitted values with simulation priors. This makes the reported R2 a measure of internal consistency.
  • sphere diameter = 300 nm nominal
    Sections 3, 5, 6 and Appendix A: sphere size from vendor or synthesis; surface phonon energies red-shift with size (Fig. S1), so the nominal diameter enters the comparison between simulation and experiment.
  • film thickness = 15 nm in text, 10 nm in Appendix A
    The silicon nitride film is stated as 15 nm in Sections 3 and 5 but Appendix A lists a 10 nm thick Norcada membrane; the discrepancy is unexplained and affects FK mode dispersion and image-charge spacing.
assumptions (5)
  • standard math Mie theory and the relativistic inelastic scattering formalism of de Abajo describe the free-space sphere EELS probability
    Appendix D, equation (1) from ref [33]; used to simulate the isolated sphere reference spectra.
  • domain assumption The reflected Green's function for stratified media, implemented in MNPBEM20, correctly models the finite-thickness film
    Appendix E: the film is modeled with the Paulus et al. [37] reflected Green's function as implemented by Waxenegger et al. [38]; this is a classical electrodynamics approximation with no explicit validation against experiment for this geometry.
  • standard math The Lorentz-gauge boundary element solution of the full Maxwell equations computes the induced field along the electron trajectory
    Appendix E, following Hohenester [32]; convergence is checked by varying the sphere surface discretization from 2000 to 6000 elements.
  • domain assumption The reference subtraction isolates the composite response by superposition
    Appendix C: sample spectrum minus film-only spectrum 'imposed by the principle of superposition [12]'; assumes the film response is identical with and without the sphere at the reference position.
  • domain assumption The literature dielectric functions are accurate in the Reststrahlen bands
    Sections 3, 5, 6 and Fig. S4 use Palik [23] for silica and MgO and Luke et al. [24] for Si3N4; the transparency, mirror, and metallic classifications all follow from these data.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Substrate matters: Coupled phonon modes of a spherical particle on a substrate probed with EELS." pith.science (2026). https://pith.science/paper/SQFRQ2PQ

@misc{pith2026250604395,
  author       = {Pith},
  title        = {Pith review of: Substrate matters: Coupled phonon modes of a spherical particle on a substrate probed with EELS},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SQFRQ2PQ}},
  note         = {Machine review of arXiv:2506.04395}
}
read the original abstract

Using vibrational electron energy loss spectroscopy (vib-EELS) combined with numerical modeling, we investigate the physical mechanisms governing the phonon coupling between a spherical particle sustaining multipolar surface phonon modes and an underlying thin film. Depending upon their dielectric composition, a variety of hybrid phonon modes arise in the EEL spectrum due to the interaction between polarization charges in the particle and film. Mirror charge effects and phonon mode hybridization are the active mechanisms acting on dielectric and metallic-type films, respectively. Processes beyond dipole-dipole interactions are required to describe the sphere-film coupling.

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

43 extracted references · 43 canonical work pages

  1. [1]

    Curtin, N.W

    W.A. Curtin, N.W. Ashcroft, Theory of far-infrared absorption in small-metal-particle--insulator composites, Phys. Rev. B 31 (1985) 3287–3295. https://doi.org/10.1103/PhysRevB.31.3287

    work page doi:10.1103/physrevb.31.3287 1985

  2. [2]

    Lee, T.W

    S.-I. Lee, T.W. Noh, J.R. Gaines, Effect of an oxide layer on the far-infrared absorption of small silver particles, Phys. Rev. B 32 (1985) 3580–3585. https://doi.org/10.1103/PhysRevB.32.3580

    work page doi:10.1103/physrevb.32.3580 1985

  3. [3]

    Ruppin, Far-infrared absorption in small metallic particles, Phys

    R. Ruppin, Far-infrared absorption in small metallic particles, Phys. Rev. B 19 (1979) 1318–1321. https://doi.org/10.1103/PhysRevB.19.1318

    work page doi:10.1103/physrevb.19.1318 1979

  4. [4]

    Ruppin, Infrared active modes of dielectric crystallites on a substrate, Surface Science 58 (1976) 550 –556

    R. Ruppin, Infrared active modes of dielectric crystallites on a substrate, Surface Science 58 (1976) 550 –556. https://doi.org/10.1016/0039-6028(76)90488-X

    work page doi:10.1016/0039-6028(76)90488-x 1976

  5. [5]

    Ruppin, Surface modes and optical absorption of a small sphere above a substrate, Surface Science 127 (1983) 108–118

    R. Ruppin, Surface modes and optical absorption of a small sphere above a substrate, Surface Science 127 (1983) 108–118. https://doi.org/10.1016/0039-6028(83)90402-8

    work page doi:10.1016/0039-6028(83)90402-8 1983

  6. [6]

    Gentle, G.B

    A.R. Gentle, G.B. Smith, Radiative heat pumping from the earth using surface phonon resonant nanoparticles, Nano Letters 10 (2010) 373

    work page 2010

  7. [7]

    Tamagnone, A

    M. Tamagnone, A. Ambrosio, K. Chaudhary, L.A. Jauregui, P. Kim, W.L. Wilson, F. Capasso, Ultra -confined mid-infrared resonant phonon polaritons in van der Waals nanostructures, Science Advances 4 (2018) eaat7189

    work page 2018

  8. [8]

    Dubrovkin, B

    A.M. Dubrovkin, B. Qiang, T. Salim, D. Nam, N.I. Zheludev, Q.J. Wang, Resonant nanostructures for highly confined and ultra-sensitive surface phonon-polaritons, Nat Commun 11 (2020) 1863. https://doi.org/10.1038/s41467-020-15767-y

    work page doi:10.1038/s41467-020-15767-y 2020

Show all 43 references
  1. [9]

    Berte, C.R

    R. Berte, C.R. Gubbin, V.D. Wheeler, A.J. Giles, V. Giannini, S.A. Maier, S. De Liberato, J.D. Caldwell, Sub-nanometer thin oxide film sensing with localized surface phonon polaritons, ACS Photonics 5 (2018) 2807

    2018

  2. [10]

    Lourenço-Martins, M

    H. Lourenço-Martins, M. Kociak, Vibrational Surface Electron-Energy-Loss Spectroscopy Probes Confined Surface-Phonon Modes, Phys. Rev. X 7 (2017) 041059. https://doi.org/10.1103/PhysRevX.7.041059

    2017 doi

  3. [11]

    Lagos, A

    M.J. Lagos, A. Trügler, V. Amarasinghe, L.C. Feldman, U. Hohenester, P.E. Batson, Excitation of long - wavelength surface optical vibrational modes in films, cubes and film/cube composite system using an atom - sized electron beam, Microscopy 67 (2018) i3–i13. https://doi.org/...

    2018 doi

  4. [12]

    Beutler, M.J

    E.K. Beutler, M.J. Lagos, D.J. Masiello, Infrared surface phonon nanospectroscopy of an interacting dielectric-particle–dielectric-substrate dimer using fast electrons, Physical Review B 103 (2021) 165418

    2021

  5. [13]

    Beutler, J.P

    E.K. Beutler, J.P. Camden, D.J. Masiello, Resonance energy transfer in the presence of a spherical cavity and dispersive substrate, Physical Review B 110 (2024) 155435

    2024

  6. [14]

    Genzel, T.P

    L. Genzel, T.P. Martin, Infrared Absorption in Small Ionic Crystals, Physica Status Solidi (b) 51 (1972) 91 –

    1972

  7. [15]

    Lagos, A

    M.J. Lagos, A. Trügler, U. Hohenester, P.E. Batson, Mapping vibrational surface and bulk modes in a single nanocube, Nature 543 (2017) 529–532. https://doi.org/10.1038/nature21699

    2017 doi

  8. [16]

    Lagos, I.C

    M.J. Lagos, I.C. Bicket, S.S. Mousavi M., G.A. Botton, Advances in ultrahigh -energy resolution EELS: phonons, infrared plasmons and strongly coupled modes, Microscopy 71 (2022) i174 –i199. https://doi.org/10.1093/jmicro/dfab050

    2022 doi

  9. [17]

    Fuchs, K.L

    R. Fuchs, K.L. Kliewer, Optical modes of vibration in an ionic crystal sphere, Journal of the Optical Society of America 58 (1968) 319

    1968

  10. [18]

    Fuchs, K.L

    R. Fuchs, K.L. Kliewer, Optical Modes of Vibration in an Ionic Crystal Slab, Phys. Rev. 140 (1965) A2076 – A2088. https://doi.org/10.1103/PhysRev.140.A2076. 13

    1965 doi

  11. [19]

    Hohenester, A

    U. Hohenester, A. Trügler, MNPBEM – A Matlab toolbox for the simulation of plasmonic nanoparticles, Computer Physics Communications 183 (2012) 370–381. https://doi.org/10.1016/j.cpc.2011.09.009

    2012 doi

  12. [20]

    Ferrell, P.M

    T.L. Ferrell, P.M. Echenique, Generation of surface excitations on dielectric spheres by an external electron beam, Physical Review Letters 55 (1985) 1526

    1985

  13. [21]

    Fuchs, F

    R. Fuchs, F. Claro, Multipolar response of small metallic spheres: Nonlocal theory, Phys. Rev. B 35 (1987) 3722–3727. https://doi.org/10.1103/PhysRevB.35.3722

    1987 doi

  14. [22]

    Cherqui, N

    C. Cherqui, N. Thakkar, G. Li, J.P. Camden, D.J. Masiello, Characterizing Localized Surface Plasmons Using Electron Energy-Loss Spectroscopy, Annual Review of Physical Chemistry 67 (2016) 331–357. https://doi.org/10.1146/annurev-physchem-040214-121612

    2016 doi

  15. [23]

    Palik, Handbook of Optical Constants of Solids, Academic Press, 1998

    E.D. Palik, Handbook of Optical Constants of Solids, Academic Press, 1998

    1998

  16. [24]

    K. Luke, Y. Okawachi, M.R.E. Lamont, A.L. Gaeta, M. Lipson, Broadband mid -infrared frequency comb generation in a Si 3 N 4 microresonator, Optics Letters 40 (2015) 4823

    2015

  17. [25]

    Cherqui, G

    C. Cherqui, G. Li, J.A. Busche, S.C. Quillin, J.P. Camden, D.J. Masiello, Multipolar nanocube plasmon mode-mixing in finite substrates, The Journal of Physical Chemistry Letters 9 (2018) 504

    2018

  18. [26]

    G. Li, C. Cherqui, N.W. Bigelow, G. Duscher, P.J. Straney, J.E. Millstone, D.J. Masiello, J.P. Camden, Spatially Mapping Energy Transfer from Single Plasmonic Particles to Semiconductor Substrates via STEM/EELS, Nano Lett. 15 (2015) 3465–3471. https://doi.org/10.1021/acs.nanol...

    2015 doi

  19. [27]

    G. Li, C. Cherqui, Y. Wu, N.W. Bigelow, P.D. Simmons, P.D. Rack, D.J. Masiello, J.P. Camden, Examining Substrate-Induced Plasmon Mode Splitting and Localization in Truncated Silver Nanospheres with Electron Energy Loss Spectroscopy, J. Phys. Chem. Lett. 6 (2015) 2569–2576. htt...

    2015 doi

  20. [28]

    Y. Wu, G. Li, C. Cherqui, N.W. Bigelow, N. Thakkar, D.J. Masiello, J.P. Camden, P.D. Rack, Electron Energy Loss Spectroscopy Study of the Full Plasmonic Spectrum of Self-Assembled Au–Ag Alloy Nanoparticles: Unraveling Size, Composition, and Substrate Effects, ACS Photonics 3 (...

    2016 doi

  21. [29]

    Thakkar, N.P

    N. Thakkar, N.P. Montoni, C. Cherqui, D.J. Masiello, Plasmonic Landau damping in active environments, Phys. Rev. B 97 (2018) 121403. https://doi.org/10.1103/PhysRevB.97.121403

    2018 doi

  22. [30]

    Beutler, V

    E.K. Beutler, V. Kumar, G.H.K. Duddy, M.R. Bourgeois, B.R. Srijanto, J.A. Hachtel, D.J. Masiello, J.P. Camden, Localizing Low-Grade Heat Using Hybrid Photonic-Phononic Materials, ACS Energy Lett. 9 (2024) 941–947. https://doi.org/10.1021/acsenergylett.3c02573

    2024 doi

  23. [31]

    Jackson, Classical Electrodynamics, 1962

    J.D. Jackson, Classical Electrodynamics, 1962

    1962

  24. [32]

    Hohenester, Plasmon excitation by fast electrons, in: World Scientific Handbook of Metamaterials and Plasmonics, 2017

    U. Hohenester, Plasmon excitation by fast electrons, in: World Scientific Handbook of Metamaterials and Plasmonics, 2017

    2017

  25. [33]

    de Abajo, Relativistic energy loss and induced photon emission in the interaction of a dielectric sphere with an external electron beam, Physical Review B 59 (1999) 3095

    F.J.G. de Abajo, Relativistic energy loss and induced photon emission in the interaction of a dielectric sphere with an external electron beam, Physical Review B 59 (1999) 3095

    1999

  26. [34]

    Mie, Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen, Annalen Der Physik 330 (1908) 377

    G. Mie, Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen, Annalen Der Physik 330 (1908) 377

    1908

  27. [35]

    Womersley, I.H

    R.S. Womersley, I.H. Sloan, How good can polynomial interpolation on the sphere be?, Advances in Computational Mathematics 14 (2001) 195

    2001

  28. [36]

    Sloan, R.S

    I.H. Sloan, R.S. Womersley, Extremal systems of points and numerical integration on the sphere, Advances in Computational Mathematics 21 (2004) 107

    2004

  29. [37]

    Paulus, P

    M. Paulus, P. Gay-Balmaz, O.J.F. Martin, Accurate and efficient computation of the Green’s tensor for stratified media, Physical Review E 62 (2000) 5797

    2000

  30. [38]

    Waxenegger, A

    J. Waxenegger, A. Trügler, U. Hohenester, Plasmonics simulations with the MNPBEM toolbox: Consideration of substrates and layer structures, Computer Physics Communications 193 (2015) 138

    2015

  31. [39]

    Dahan, J.J

    N. Dahan, J.J. Greffet, Enhanced scattering and absorption due to the presence of a particle close to an interface, Optics Express 20 (2012) A530

    2012

  32. [40]

    Lytle, P.S

    D.R. Lytle, P.S. Carney, J.C. Schotland, E. Wolf, Generalized optical theorem for reflection, transmission, and extinction of power for electromagnetic fields, Physical Review E 71 (2005) 056610

    2005

  33. [41]

    Byrd, J.C

    R.H. Byrd, J.C. Gilbert, J. Nocedal, A trust region method based on interior point techniques for nonlinear programming, Mathematical Programming 89 (2000) 149

    2000

  34. [42]

    Waltz, J.L

    R.A. Waltz, J.L. Morales, J. Nocedal, D. Orban, An interior algorithm for nonlinear optimization that combines line search and trust region steps, Mathematical Programming 107 (2006) 391

    2006

  35. [99]

    https://doi.org/10.1002/pssb.2220510107

    doi

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.