MUSIC‐Type Electromagnetic Imaging of a Collection of Small Three‐Dimensional Inclusions

Ammari, Habib; Яковлева, Екатерина; Lesselier, Dominique; Perrusson, Gae ̈le

doi:10.1137/050640655

Cited by 170 publications

(177 citation statements)

References 32 publications

Supporting

Mentioning

176

Contrasting

Unclassified

Order By: Relevance

“…The scalar case was recently considered in [13]. Our approach in this paper, combined with the ones in [7,8], opens also a door for a numerical and mathematical framework for optimal shape design of resonant nanoparticles and their superresolved imaging. The limit when t → 0 − is computed similarly and we find (4.8) for k = 0.…”

Section: Discussionmentioning

confidence: 99%

Surface Plasmon Resonance of Nanoparticles and Applications in Imaging

Ammari¹,

Deng²,

Millien³

2015

Arch Rational Mech Anal

Self Cite

138

161

View full text Add to dashboard Cite

In this paper we provide a mathematical framework for localized plasmon resonance of nanoparticles. Using layer potential techniques associated with the full Maxwell equations, we derive small-volume expansions for the electromagnetic fields, which are uniformly valid with respect to the nanoparticle's bulk electron relaxation rate. Then, we discuss the scattering and absorption enhancements by plasmon resonant nanoparticles. We study both the cases of a single and multiple nanoparticles. We present numerical simulations of the localized surface plasmonic resonances associated to multiple particles in terms of their separation distance.

show abstract

Section: Discussionmentioning

confidence: 99%

Surface Plasmon Resonance of Nanoparticles and Applications in Imaging

Ammari¹,

Deng²,

Millien³

2015

Arch Rational Mech Anal

Self Cite

138

161

View full text Add to dashboard Cite

show abstract

“…Extensions of this formula to unbounded domains have been considered in [11,28], and reconstruction methods for the corresponding inverse scattering problem in unbounded domains have been studied in [2,28,29,[31][32][33]. Assuming that the diameter of the scatterers described by ρ n is small, these methods neglect the o(ρ n 3 ) term in (5.1) and describe the measured electromagnetic fields by the leading order term in this formula.…”

Section: Examples and Applicationsmentioning

confidence: 99%

“…The asymptotic formulas for diametrically small conductivity inhomogeneities and scatterers known so far form the foundation of several efficient reconstruction methods for inverse conductivity problems (see, e.g., Ammari, Moskow, and Vogelius [7], Ammari and Seo [8] or Brühl, Hanke, and Vogelius [17]) and inverse scattering problems for Maxwell's equations (see, e.g., Ammari et al [2], Iakovleva et al [33], Volkov [42], or [28,29,31,32]). In addition the general formula for electrostatic potentials from [18] has recently been used to investigate inverse conductivity problems for wires and tubes (see Beretta et al [13] or [30]).…”

Section: Introductionmentioning

confidence: 99%

A general perturbation formula for electromagnetic fields in presence of low volume scatterers

Griesmaier

2011

ESAIM: M2AN

View full text Add to dashboard Cite

Abstract.In several practically interesting applications of electromagnetic scattering theory like, e.g., scattering from small point-like objects such as buried artifacts or small inclusions in non-destructive testing, scattering from thin curve-like objects such as wires or tubes, or scattering from thin sheet-like objects such as cracks, the volume of the scatterers is small relative to the volume of the surrounding medium and with respect to the wave length of the applied electromagnetic fields. This smallness typically causes problems when solving direct scattering problems due to the need to discretize the objects and also when solving inverse scattering problems because small objects have very little effect on electromagnetic fields. In this paper we consider an asymptotic representation formula for scattered electromagnetic waves caused by low volume objects contained in some otherwise homogeneous threedimensional bounded domain, assuming only that the scatterers are measurable and well-separated from the boundary of the domain. The formula yields a very general asymptotic model for electromagnetic scattering due to low volume objects that can either be used to simulate the corresponding electromagnetic fields or as the foundation of efficient reconstruction methods for inverse scattering problems with low volume scatterers.

show abstract

“…Using the summation convention, the relation between the stress and the displacement given by (2) can by written simply as σ ij = C ijkl ε kl , where the summation is understood to be over the repeated indexes k and l. By defining the vectors s and e as s = σ 11 , σ 22 , σ 33 , σ 23 , σ 31 , σ 12 t , (4) we can write the following relationship between the six independent components of stress and strain tensors:…”

Section: Notation and Preliminariesmentioning

confidence: 99%

Direct Elastic Imaging of a Small Inclusion

Ammari¹,

Calmon²,

Яковлева³

2008

SIAM J. Imaging Sci.

Self Cite

View full text Add to dashboard Cite

Abstract. In this paper we consider the problem of locating a small three-dimensional elastic inclusion, using arrays of elastic source transmitters and receivers. This procedure yields the multistatic response matrix that is characteristic of the elastic inclusion. We show how the eigenvalue structure of this matrix can be employed within the framework of a noniterative method of MUSIC (multiple signal classification) type in order to retrieve the elastic inclusion. We illustrate our reconstruction procedure with a variety of computational examples from synthetic, noiseless, and severely noisy data.

show abstract

MUSIC‐Type Electromagnetic Imaging of a Collection of Small Three‐Dimensional Inclusions

Cited by 170 publications

References 32 publications

Surface Plasmon Resonance of Nanoparticles and Applications in Imaging

Surface Plasmon Resonance of Nanoparticles and Applications in Imaging

A general perturbation formula for electromagnetic fields in presence of low volume scatterers

Direct Elastic Imaging of a Small Inclusion

Contact Info

Product

Resources

About