Spectroscopists know the shape before they know the sample. A peak that rises steeply on one side, overshoots, and then dips below the baseline before recovering — asymmetric, with a notch where a symmetric resonance ought to have a shoulder — is a Fano profile, and it turns up in the scattering of metal nanoparticles, the transmission of photonic crystals, and the absorption of semiconductor nanostructures. Each appearance has tended to get its own explanation, fitted to its own geometry. A paper published in Scientific Reports on October 30, 2026, argues that for one important class of materials, that proliferation is unnecessary: the Fano shapes seen in excitonic nanostructures of different geometries share a single origin, and a single formalism describes them all.
The paper comes from Shinji Hayashi, Hiroshi Sugimoto, and Minoru Fujii at Kobe University, with Dmitry V. Nesterenko of Samara National Research University and Zouheir Sekkat of University Mohammed VI Polytechnic and Mohammed V University in Rabat. It is a theoretical result: a general formalism applied to calculated spectra — light scattering from excitonic spheres and cylinders, and reflection from excitonic slabs. There is no new fabricated device here and no new measurement; the claim is about the structure of the theory, and it should be judged at that level.
What a Fano shape actually is
The asymmetry has a precise physical meaning. In 1961, Ugo Fano showed that when light can reach the same final state by two routes — a direct route into a broad continuum of states, and an indirect route through a sharp, discrete resonance — the two routes interfere. Where they reinforce, the spectrum peaks; where they cancel, it dips. The result is a lopsided profile, characterized by an asymmetry parameter, usually called q, that encodes the relative strength and phase of the two paths. A very large q recovers an ordinary symmetric Lorentzian peak, and q equal to zero gives a symmetric dip, an antiresonance. Everything in between is the familiar asymmetric shape.
In excitonic nanostructures, the two routes are built into the material itself. An excitonic material — a semiconductor, a molecular aggregate, a polymer doped with dye molecules — responds to light through its dielectric function, the quantity that describes how the material polarizes under an electric field. The authors model that function as two parts added together: a background dielectric constant, essentially featureless over the spectral range of interest, and a Lorentzian term describing the exciton transition itself, sharp in energy and resonant at the exciton frequency. The background part alone would give a smooth, nonresonant response; the exciton part alone, a symmetric resonant response. Put them together in a nanostructure, let light scatter or reflect, and the two contributions interfere. The asymmetric Fano shape is the interference pattern.
This picture had already been worked out for one geometry. In a 2023 paper in Physical Review B, the same group analyzed excitonic spheres using Mie theory and its electrostatic approximation, and showed analytically that the absorption efficiency comes out as a Lorentzian while the scattering and extinction efficiencies take the form of a generalized Fano function — an external Fano resonance in the far field, matched by an internal Fano resonance in the field inside the particle. But a sphere is a special case, and the obvious question hung over the result: is the same mechanism at work in other shapes, or does each geometry generate its Fano profile by its own route? The new paper answers that question for the cylinder and the slab, and in doing so proposes the unified description of its title.
Three geometries, one calculation
The test the authors set themselves is deliberately clean. They calculate spectra for a sphere and a cylinder each with a radius of 40 nanometres, and for a slab 40 nanometres thick — the same characteristic size in all three cases, so that size effects cannot masquerade as geometry effects. For the sphere and the cylinder they compute light-scattering spectra; for the slab, a reflection spectrum, since a flat film is naturally characterized by what it reflects. In all three cases the raw spectra look similar: asymmetric line shapes superposed on monotonically increasing backgrounds. The asymmetry is there in every geometry, but it sits on a rising slope that differs from case to case, which is part of why the common origin has been easy to miss — two profiles on different slopes can look like different phenomena.
The decisive step is normalization. When each spectrum is divided by its own background spectrum, the slopes fall away and what remains, in all three geometries, is a Fano profile: the signature of interference between a constant background component and a resonant excitonic component described by a complex Lorentzian function. The formalism produces this result across geometries rather than fitting each one separately. The sphere, the cylinder, and the slab are not three problems with three answers. They are one problem — a constant plus a Lorentzian, interfering — expressed in three coordinate systems.
The normalization step matters beyond tidiness. In experimental spectroscopy, backgrounds are rarely flat: a measured spectrum rides on the substrate, the illumination geometry, and neighbouring structures. If the underlying Fano profile is only visible once the background is divided out, then published data may contain Fano physics that was never identified as such, because the raw curves looked merely lopsided. The paper supplies, in effect, a reading rule: normalize to the background first, and then ask whether the residual is a Fano profile. That is its most immediately usable contribution.
Why unification is more than elegance
For experimentalists, unification licenses comparison. A Fano asymmetry measured in reflection from a thin film and one measured in scattering from a nanoparticle can now be discussed in the same language, with the same parameters, rather than as unrelated curiosities that happen to share a name. If a film and a particle of the same material show Fano profiles with related asymmetry parameters, that agreement is evidence that the material’s dielectric function is correctly characterized. If they disagree, the disagreement points somewhere specific: either the dielectric function is wrong, or something beyond the model is contributing in one geometry. The comparison is now diagnostic rather than decorative.
For designers, unification narrows the search space. A formalism that separates the geometry from the mechanism — the geometry sets the background and the coupling, while the interference does the shaping — means a designer can reason about the Fano profile before running a full simulation, and the asymmetry parameter becomes a design variable with a known physical meaning. That matters for dielectric nanoparticles that show no distinct Mie resonances on their own, and that have therefore been discarded as useful elements of resonant nanophotonics, but that acquire sharp resonances once an excitonic transition is incorporated. The unified formalism extends that invitation to nanowires and thin films, the geometries devices are actually built in.
What it is not
Three cautions, stated plainly because the framing invites overreading. First, this is not an experimental result. The spectra in the paper are calculations for model nanostructures, not measurements on fabricated spheres, cylinders, and slabs. The formalism is tested against the scattering and reflection spectra that electromagnetic theory predicts for these model structures, not against laboratory data. That is a legitimate stage of theory, but it means the unified description is, for now, a prediction about what experiments should find, not a summary of what they have found. The next paper in this line should test it on a real excitonic film and a real excitonic nanoparticle of the same material.
Second, this is not a claim about every Fano resonance. Fano profiles arise in plasmonics, in photonic crystals, in atomic physics, wherever a discrete state couples to a continuum. The unified description here covers one specific mechanism: interference between the background dielectric response and a Lorentzian exciton resonance within a single excitonic nanostructure. It does not subsume the Fano resonances of coupled resonators, dark and bright plasmon modes, or waveguide-grating systems, each with its own interference routes. The paper’s title says “in excitonic nanostructures,” and the qualifier is doing real work.
Third, a note on the version itself. The article is being shared early as a peer-reviewed, accepted manuscript, and the publisher states that this version is subject to further edits before it is replaced by the final Version of Record. The abstract, authorship, and conclusions quoted here are those of the early version published October 30, 2026, after receipt on August 13 and acceptance on October 19; readers who need the equations themselves should check the Version of Record when it appears. The work was supported by JSPS KAKENHI grant 25K08509 and a Kobe University Strategic International Collaborative Research Grant; the authors declare no competing interests.
Where the Lorentzian model breaks down
The model’s power and its fragility come from the same place: its simplicity. A dielectric function written as a constant plus a single Lorentzian is an idealization, and every term in that idealization can fail in a real material.
The single Lorentzian assumes a single, isolated exciton transition. Real excitonic materials commonly have more than one: multiple exciton species, excited exciton states, vibronic sidebands in molecular materials, and overlapping transitions from different parts of a band structure. Where two resonances sit close together, their Lorentzians overlap, and the interference pattern is no longer a single Fano profile but a superposition the simple formalism does not describe without extension. The model also assumes the background is constant over the spectral range of interest. In real materials the background disperses — it varies with wavelength, sometimes steeply near other absorption features — and a dispersing background changes both the shape and the apparent asymmetry of the profile. Normalizing to a structured background is a harder problem than normalizing to a constant, and the first place a naive application of the paper’s reading rule could mislead.
Disorder is a second limit. The Lorentzian width encodes the exciton’s damping, but real samples broaden lines inhomogeneously: different nanoparticles, local environments, and strain states shift individual exciton energies, so a measured spectrum averages over a distribution of resonances rather than showing a single sharp one. Inhomogeneous broadening can wash out the Fano dip entirely, turning an asymmetric profile into a broad, featureless hump.
A third limit is size. The group’s earlier sphere analysis is instructive: the generalized Fano functions reproduced the exact Mie-theory spectra well beyond the small-particle limit, but only provided the sphere radius stayed below an upper bound. Past that bound, higher-order multipoles and retardation effects — the finite speed of light across the particle — complicate the picture, and the simple interference story no longer closes. The new paper’s calculations use 40-nanometre structures, comfortably in the regime where the formalism works. Whether the unification survives at larger sizes is an open question, and the natural first stress test for anyone applying the formalism to larger structures.
Finally, the model is linear and low-density. It describes one exciton transition responding to light, not excitons interacting with each other. At high excitation densities, exciton-exciton interactions, phase-space filling, and screening shift and broaden the resonance, and the dielectric function itself becomes intensity-dependent. None of that is in a constant-plus-Lorentzian model. Its domain is the regime where the response is linear, the resonance is isolated, and the background is flat. Within that domain it appears to be general across geometries. Outside it, it is a starting point, not an answer. None of these limits diminishes the result; they define where it can be trusted, and they are the beginning of this theory’s instruction manual rather than a refutation.
What to watch
The most interesting follow-ups are experimental, and they are concrete. Take one excitonic material — a J-aggregate-doped polymer, the model system of the group’s earlier sphere work, would be a natural choice — and fabricate it as a nanoparticle, a nanowire, and a thin film. Measure scattering from the particle and the wire and reflection from the film, normalize each spectrum to its background, and compare the resulting Fano profiles. Agreement would promote the unified description from a theoretical framework to an empirical fact. Disagreement would be at least as informative, showing which of the limits above bites first in practice.
The deepest reason this result matters is simple. The exciton is often introduced as a particle: an electron bound to a hole, carrying energy through a material. But in optics, the exciton is equally a resonance in a dielectric function, a sharp feature that light can interfere with. The Kobe paper is, at heart, a statement about that second identity: that a single sharp resonance, interfering with the dull background of its own material, is enough to generate the asymmetric shapes seen across geometries. The exciton does not need a new explanation for every shape it takes.
Sources and further reading
Hayashi, S.; Sugimoto, H.; Fujii, M.; Nesterenko, D. V.; Sekkat, Z. “Unified description of Fano resonances in excitonic nanostructures across multiple geometries.” Scientific Reports (2026), published October 30, 2026. DOI: 10.1038/s41598-026-77147-8. Received August 13, 2026; accepted October 19, 2026. Early-access version, subject to further edits before the Version of Record.
Hayashi, S.; Sugimoto, H.; Fujii, M.; Nesterenko, D. V.; Sekkat, Z. “Formation of Fano line shapes in optical responses and spectra of internal fields of excitonic nanospheres.” Physical Review B 108, 125408 (2023). DOI: 10.1103/PhysRevB.108.125408. The earlier sphere analysis on which the unified formalism builds.
Fano, U. “Effects of configuration interaction on intensities and phase shifts.” Physical Review 124, 1866–1878 (1961). The original Fano profile. For the wider context, see this site’s explainers on what an exciton is and on coherence and dephasing. This article is analysis of published research, not investment advice.