Super-resolution in recovering embedded electromagnetic sources in high contrast media

Ammari, Habib; Li, Bowen; Zou, Jun

doi:10.48550/arxiv.2001.07116

Cited by 1 publication

(5 citation statements)

References 32 publications

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“…with an appropriate boundary condition at infinity; see [5,Lemma 3.1]. Then the nontrivial solution E automatically satisfies the following transmission boundary condition for its normal trace:…”

Section: Problem Setting and Definitionmentioning

confidence: 99%

“…This allows us to see the clear asymptotic properties of T δω B on different components of an L 2 -vector field and the impact of the parameters δ and τ . We adopted the same technique earlier in [5] for the spectral analysis of the integral operator T ω D beyond the quasi-static regime.…”

Section: Dielectric Subwavelength Resonancementioning

confidence: 99%

“…We shall analyze the dielectric subwavelength resonances ω according to the above definition. It has been shown in [24,5] that the essential spectrum of T ω B for any ω ∈ C is given by…”

Section: A Priori Estimatementioning

confidence: 99%

“…To further analyze the dielectric resonant frequencies ω, we now write the operator function A(τ, ω) as an analytic family of operator matrices by the Helmholtz decomposition. In contrast to the statement in [5], we provide a more general perspective for this procedure here, by using the concept of global equivalence from [30] . It generalizes the concept of similarity for the linear operator and is applied to a nonlinear eigenproblem.…”

Section: A Priori Estimatementioning

confidence: 99%

“…In [23,24,25], the authors gave a complete characterization of the essential spectrum of various integral operators arising from the EM scattering problems for both smooth and non-smooth (Lipschitz) domains. Along this direction, we showed in [5] that the spectrum of T ω D is a disjoint union of the essential spectrum on the real axis and the eigenvalues of finite type in the upper-half plane with the essential spectrum being its possible accumulation points, and derived the pole-pencil decomposition of the resolvent (λ − T ω D ) −1 near its poles. We emphasize that all the aforementioned results concern the linear eigenproblem of the operator T ω D and the corresponding research is far from being complete.…”

Section: Introductionmentioning

confidence: 99%

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Mathematical analysis of electromagnetic scattering by dielectric nanoparticles with high refractive indices

Ammari¹,

Li²,

Zou³

2020

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In this work, we are concerned with the mathematical modeling of the electromagnetic (EM) scattering by arbitrarily shaped non-magnetic nanoparticles with high refractive indices. When illuminated by visible light, these particles can exhibit a very strong isotropic magnetic response, in addition to the electric resonance, resulting from the coupling of the incident wave with the circular displacement currents of the EM fields. We shall first introduce the mathematical concept of dielectric (subwavelength) resonances, then perform the asymptotic analysis in terms of the small particle size and the high contrast parameter. This enables us to derive the a priori estimates for the leading-order terms of dielectric resonances and the associated resonant modes, by making use of a Helmholtz decomposition for divergence-free vector fields. It turns out that these dielectric resonant fields are almost transverse electric in the quasi-static and high contrast regime, and hence present the feature of the magnetostatic fields. To address the existence of resonances, we apply the Gohberg-Sigal theory under a physical condition for the contrast, and show that there exist finitely many physically meaningful resonances in the fourth quadrant. The second part of this work is for the quantitative investigation of the enhancement of the scattered field and the cross sections when the dielectric resonance occurs. In doing so, we develop a novel multipole radiation framework that directly separates the electric and magnetic multipole moments and allows us to clearly see their orders of magnitude and blow-up rates. We show that at the dielectric subwavelength resonant frequencies, the nanoparticles with high refractive indices behave like the coupling of an electric dipole with a resonant magnetic dipole. By using the spherical multipole expansion, we further show how to explicitly calculate the quasi-static dielectric resonance and the approximate scattered field which helps validate our general results and formulas.

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Section: Problem Setting and Definitionmentioning

confidence: 99%

Section: Dielectric Subwavelength Resonancementioning

confidence: 99%

Section: A Priori Estimatementioning

confidence: 99%

Section: A Priori Estimatementioning

confidence: 99%