A 2010 conformal-transformation design strategy (Aubry, Lei, Fernández-Domínguez, Sonnefraud, Maier, and Pendry, Nano Letters 10, 2574–2579) predicted that finite plasmonic nanostructures with geometric singularities — kissing (touching) cylinders and metallic crescents — harvest light efficiently over the whole visible spectrum, with a continuous plasmon spectrum, large absorption cross sections, and extreme near-field concentration at the singularity, where surface-plasmon group velocity vanishes and energy accumulates. The source work explicitly left open five coupled issues: the quantitative impact of nonlocal and quantum effects (spatial dispersion, dissipation, electron tunneling and screening) at the singularity; the fabrication tolerances (bluntness, finite gaps) needed to retain broadband behavior; the size crossover at which radiative damping and retardation degrade performance; an analytical electrodynamic theory beyond the quasistatic (near-field) approximation; and direct experimental validation on fabricated singular structures.

Background

A localized surface plasmon (LSP) is the collective oscillation of conduction electrons confined to a metallic nanoparticle; when driven at its resonance it concentrates optical fields far below the diffraction limit, which underlies surface-enhanced Raman spectroscopy (SERS) and plasmonic enhancement of photodetection, photocatalysis, and nonlinear optics. A surface plasmon polariton (SPP) is the analogous wave propagating along a metal–dielectric interface, including the metal–insulator–metal (MIM) waveguide, in which a dielectric layer is sandwiched between two metal half-spaces. Ordinary finite plasmonic particles (e.g. spheres) support discrete, spectrally narrow LSP resonances, so a small device is efficient only near discrete frequencies; extended MIM structures possess a broadband continuum of SPP modes but are physically unbounded and impractical as compact collectors. In 2010, Aubry, Lei, Fernández-Domínguez, Sonnefraud, Maier, and Pendry showed, using transformation optics (the technique of applying a coordinate change to Maxwell's equations; here a conformal, angle-preserving map in two dimensions), that the infinite MIM geometry can be mapped analytically onto finite singular structures: two touching ('kissing') nanowires (Lei, Aubry, Maier, and Pendry, New J. Phys. 12, 093030 (2010)) and crescent-shaped cylinders (Aubry, Lei, Maier, and Pendry, Phys. Rev. B 82, 125430 (2010)). In these structures the SPPs propagate toward the geometric singularity, their group velocity vanishes there, and energy accumulates, producing a continuous (broadband) plasmon spectrum with large absorption cross section relative to physical size and strong near-field concentration — an apparent route to compact light harvesters covering the whole visible band. The analytical results rest on the quasistatic (near-field) approximation, valid when the device size DD is much smaller than the wavelength λ\lambda, and on a classical, local dielectric response; radiation losses were investigated numerically when DD becomes comparable to λ\lambda. The same program was extended to three dimensions (touching spheres, Fernández-Domínguez, Maier, and Pendry, Phys. Rev. Lett. 105, 266807 (2010); nanocrescents, Fernández-Domínguez, Luo, Wiener, Pendry, and Maier, Nano Lett. 12, 5946–5953 (2012)). The 2010 source paper stated that its predictions face five unresolved issues, which define the open problem: (1) the classical local-continuum description breaks down within sub-nanometer distances of the singularity, where nonlocal dielectric response (spatial dispersion, described for instance by the hydrodynamic Drude model, in which the electron gas is treated as a compressible fluid with a characteristic nonlocal length β/ωP\beta/\omega_{P}, β\beta a velocity parameter and ωP\omega_{P} the plasma frequency), increased effective dissipation, and electron tunneling and screening are expected to reduce the extreme classical field enhancements, and their quantitative impact on the broadband absorption and peak near-field intensities remained to be established; (2) the analysis assumes idealized sharp tips or exact contact, and the tolerances on tip curvature and contact quality required experimentally were undetermined; (3) the size at which radiative losses and retardation fundamentally alter performance required systematic study; (4) a complete analytical electrodynamic theory treating retardation, radiation, and the transition to the wavelength-scale regime remained open; and (5) direct optical measurements (including SERS and absorption spectra) on fabricated crescent and kissing-cylinder particles with controlled singularity profiles were required. Progress on these issues is framed by several concepts developed in the follow-up literature: the Feibelman dd-parameters (surface-response quantities measuring the centroids of induced charge and current relative to the metal boundary, which encode quantum spill-out and surface-enabled loss in effective boundary conditions) and the Chu limit (the fundamental lower bound on the radiation quality factor QQ of any electrically small radiator, which constrains the achievable fractional bandwidth of a resonant antenna).

Problem Statement

The problem, as posed by the 2010 plasmonic light-harvesting analysis and left open by the follow-up literature, is to complete the physical description and demonstrate the performance of broadband plasmonic light-harvesting nanostructures with geometric singularities (kissing cylinders, crescents, and their three-dimensional analogues), whose common objective is a quantitatively reliable account of how singular broadband harvesting survives real materials, real sizes, and real fabrication. Specifically, the open core comprises: (1) establishing the quantitative impact of nonlocal and quantum effects — spatial dispersion, increased effective dissipation, electron spill-out, and tunnelling and screening at an exactly formed contact — on the continuous absorption spectrum, broadband absorption cross section, and peak near-field intensities of the singular structures, including the full quantum treatment of the contact point itself, beyond the hydrodynamic and Feibelman-parameter models already developed for two-dimensional geometries; (2) determining, theoretically and experimentally, the fabrication tolerances on tip curvature, bluntness, and contact quality that still realize broadband harvesting in fabricated devices, given that finite gaps and blunt tips reintroduce discrete resonances; (3) determining systematically, across materials and shapes, the crossover size at which radiative losses and retardation fundamentally alter the broadband performance, in connection with the radiation bounds (Chu-limit type constraints) now derived for nearly touching cylinders; (4) constructing the complete analytical electrodynamic theory of these singular structures that includes retardation and radiation and describes the transition from the quasistatic (near-field, D≪λD\ll\lambda) regime to the wavelength-scale regime, of which current conformal-transformation solutions of the two-cylinder problem are the quasistatic leading terms; and (5) providing direct optical experimental validation — absorption and scattering spectra, SERS, and near-field measurements — on fabricated crescent and kissing-cylinder (or analogous touching) particles with controlled singularity profiles, testing the predicted broadband harvesting, the scaling laws with size and singularity sharpness, and the role of the nonclassical effects in (1). Parts (1) and (2) have been substantially quantified for idealized two-dimensional model geometries and blunt-edge designs, and radiative bounds exist for (3); a complete answer requires these elements to be joined into a single quantitative account — quantum-corrected, retarded, and experimentally validated — of broadband light harvesting by singular plasmonic structures. These five sub-issues are jointly required for a complete resolution: the results already established for sub-issues (1)-(3) are to be integrated and extended to the actual crescent and kissing-cylinder geometries rather than re-derived in isolation, the retarded electrodynamic description of sub-issue (4) must embed the quantum, tolerance, and crossover results, and the account is complete only when the measurements of sub-issue (5) confirm its quantum-corrected and retarded predictions.

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