2018/07/04 by Ory Schnitzer, Schnitzer, Ory
Engineering · Materials Science · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Near-Field Optical Microscopy #Optical Coatings and Gratings #Optics (physics.optics) #Plasmonic and Surface Plasmon Research
paper · pdf · doi:10.48550/arxiv.1807.01636
openalex publication_date 2018/07/04 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28
Excitation of surface-plasmon resonances of closely spaced nanometallic\nstructures is a key technique used in nanoplasmonics to control light on\nsubwavelength scales and generate highly confined electric-field hotspots. In\nthis paper we develop asymptotic approximations in the near-contact limit for\nthe entire set of surface-plasmon modes associated with the prototypical sphere\ndimer geometry. Starting from the quasi-static plasmonic eigenvalue problem, we\nemploy the method of matched asymptotic expansions between a gap region, where\nthe boundaries are approximately paraboloidal, pole regions within the spheres\nand close to the gap, and a particle-scale region where the spheres appear to\ntouch at leading order. For those modes that are strongly localised to the gap,\nrelating the gap and pole regions gives a set of effective eigenvalue problems\nformulated over a half space representing one of the poles. We solve these\nproblems using integral transforms, finding asymptotic approximations, singular\nin the dimensionless gap width, for the eigenvalues and eigenfunctions. In the\nspecial case of modes that are both axisymmetric and odd about the plane\nbisecting the gap, where matching with the outer region introduces a\nlogarithmic dependence upon the dimensionless gap width, our analysis follows\n[O. Schnitzer, \Physical Review B, \92 235428 2015]. We also\nanalyse the so-called anomalous family of even modes, characterised by field\ndistributions excluded from the gap. We demonstrate excellent agreement between\nour asymptotic formulae and exact calculations.\n