41 research outputs found
Analysis of surface polariton resonance for nanoparticles in elastic system
This paper is concerned with the analysis of surface polariton resonance for
nanoparticles in linear elasticity. With the presence of nanoparticles, we
first derive the perturbed displacement field associated to a given elastic
source field. It is shown that the leading-order term of the perturbed elastic
wave field is determined by the Neumann-Poinc\'are operator associated to the
Lam\'e system. By analyzing the spectral properties of the aforesaid
Neumann-Poinc\'are operator, we study the polariton resonance for the elastic
system. The results may find applications in elastic wave imaging.Comment: 18 pages, comments are welcom
A review of anomalous resonance, its associated cloaking, and superlensing
We review a selected history of anomalous resonance, cloaking due to
anomalous resonance, cloaking due to complementary media, and superlensing.Comment: 15 pages and 1 figur
Shape reconstructions by using plasmon resonances with enhanced sensitivity
This paper investigates the shape reconstructions of sub-wavelength objects
from near-field measurements in transverse electromagnetic scattering. This
geometric inverse problem is notoriously ill-posed and challenging. We develop
a novel reconstruction scheme using plasmon resonances with significantly
enhanced sensitivity and resolution. First, by spectral analysis, we establish
a sharp quantitative relationship between the sensitivity of the reconstruction
and the plasmon resonance. It shows that the sensitivity functional blows up
when plasmon resonance occurs. Hence, the signal-to-noise ratio is
significantly improved and the robustness and effectiveness of the
reconstruction are ensured. Second, a variational regularization method is
proposed to overcome the ill-posedness, and an alternating iteration method is
introduced to automatically select the regularization parameters. Third, we use
the Laplace approximation method to capture the statistical information of the
target scattering object. Both rigorous theoretical analysis and extensive
numerical experiments are conducted to validate the promising features of our
method