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Asymptotic approximations for the plasmon resonances of nearly touching spheres
摘要： Excitation of surface-plasmon resonances of closely spaced nanometallic structures is a key technique used in nanoplasmonics to control light on subwavelength scales and generate highly confined electric-field hotspots. In this paper, we develop asymptotic approximations in the near-contact limit for the entire set of surface-plasmon modes associated with the prototypical sphere dimer geometry. Starting from the quasi-static plasmonic eigenvalue problem, we employ the method of matched asymptotic expansions between a gap region, where the boundaries are approximately paraboloidal, pole regions within the spheres and close to the gap, and a particle-scale region where the spheres appear to touch at leading order. For those modes that are strongly localised to the gap, relating the gap and pole regions gives a set of effective eigenvalue problems formulated over a half space representing one of the poles. We solve these problems using integral transforms, finding asymptotic approximations, singular in the dimensionless gap width, for the eigenvalues and eigenfunctions. In the special case of modes that are both axisymmetric and odd about the plane bisecting the gap, where matching with the outer region introduces a logarithmic dependence upon the dimensionless gap width, our analysis follows Schnitzer [Singular perturbations approach to localized surface-plasmon resonance: nearly touching metal nanospheres. Phys. Rev. B 92(23), 235428 (2015)]. We also analyse the so-called anomalous family of even modes, characterised by field distributions excluded from the gap. We demonstrate excellent agreement between our asymptotic formulae and exact calculations.
关键词： asymptotic analysis,eigenvalue problems,Surface plasmons
更新于2025-09-23 15:22:29
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Homogenization of plasmonic crystals: seeking the epsilon-near-zero effect
摘要： By using an asymptotic analysis and numerical simulations, we derive and investigate a system of homogenized Maxwell’s equations for conducting material sheets that are periodically arranged and embedded in a heterogeneous and anisotropic dielectric host. This structure is motivated by the need to design plasmonic crystals that enable the propagation of electromagnetic waves with no phase delay (epsilon-near-zero effect). Our microscopic model incorporates the surface conductivity of the two-dimensional (2D) material of each sheet and a corresponding line charge density through a line conductivity along possible edges of the sheets. Our analysis generalizes averaging principles inherent in previous Bloch-wave approaches. We investigate physical implications of our ?ndings. In particular, we emphasize the role of the vector-valued corrector ?eld, which expresses microscopic modes of surface waves on the 2D material. We demonstrate how our homogenization procedure may set the foundation for computational investigations of: effective optical responses of reasonably general geometries, and complicated design problems in the plasmonics of 2D materials.
关键词： asymptotic analysis,homogenization,plasmonic crystals,Maxwell’s equations,surface plasmon-polariton,graphene
更新于2025-09-12 10:27:22