arXiv subjects

Doo Sung Choi

Publications and source records attributed to Doo Sung Choi.

2 recordsLinked to original sources

arXiv2018

A mathematical and numerical framework for near-field optics

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 analyze 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.

math.AP↗

arXiv2018

Corner effects on the perturbation of an electric potential

We consider the perturbation of an electric potential due to an insulating inclusion with corners. This perturbation is known to admit a multipole expansion whose coefficients are linear combinations of generalized polarization tensors. We define new geometric factors of a simple planar domain in terms of a conformal mapping associated with the domain. The geometric factors share properties of the generalized polarization tensors and are the Fourier series coefficients of a kind of generalized external angle of the inclusion boundary. Since the generalized external angle contains the Dirac delta singularity at corner points, we can determine the criterion for the existence of corner points on the inclusion boundary in terms of the geometric factors. We illustrate and validate our results with numerical examples computed to a high degree of precision using integral equation techniques, Nyström discretization, and recursively compressed inverse preconditioning.

math.AP↗