A mathematical and numerical framework for near-field optics. (30th September 2018)

• Record Type: Journal Article
• Authors: Ammari, Habib; Sung Choi, Doo; Yu, Sanghyeon
• Is Part Of: Proceedings. Volume 474:Number 2217(2018)
• Publication Date: 2018-09-30
• Subjects: near-field optics -- plasmonic sensing -- super-resolution -- Möbius transformation -- generalized polarization tensors -- plasmonic resonances; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2018.0150
• Languages: English
• ISSNs: 1364-5021

Abstract

Abstract : This paper is concerned with the inverse problem of reconstructing small and local perturbations of a planar surface using the field interaction between a known plasmonic particle and the planar surface. The aim is to perform a super-resolved reconstruction of these perturbations from shifts in the plasmonic frequencies of the particle-surface system. In order to analyse the interaction between the plasmonic particle and the planar surface, a well-chosen conformal mapping, which transforms the particle-surface system into a coated structure, is used. Then the even Fourier coefficients of the transformed domain are related to the shifts in the plasmonic resonances of the particle-surface system. A direct reconstruction of the perturbations of the planar surface is proposed. Its viability and limitations are documented by numerical examples.