Subwavelength resonant dielectric nanoparticles with high refractive indices

Ammari, Habib; Dabrowski, Alexander; Fitzpatrick, Brian; Millien, Pierre; Sini, Mourad

doi:10.1002/mma.5760

Cited by 18 publications

(29 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In our context, the contrast comes from the fact that the density of the bubble is moderate while its bulk is still small. At the mathematical level, our formulas in (11) extend those in [5] to the case of the acoustic model, i.e. a divergence form model, with heterogeneous background.…”

Section: •)mentioning

confidence: 94%

“…The body-wave resonances have been characterized already in [5,21] in the framework of dielectric nanoparticles, in the scalar model related to the TM regime of the electromagnetic scattering, with a homogeneous background. There, the contrast comes from the dielectric nanoparticles with high permittivity and moderate permeability.…”

Section: •)mentioning

confidence: 99%

“…Here, G ω stands for the Green's functions related to (5). More precisely, G ω is solution, in the distributional sense, of…”

mentioning

confidence: 99%

See 2 more Smart Citations

Mathematical analysis of the acoustic imaging modality using bubbles as contrast agents at nearly resonating frequencies

Dabrowski¹,

Ahcene²,

Sini³

2021

IPI

Self Cite

View full text Add to dashboard Cite

We analyze mathematically the acoustic imaging modality using bubbles as contrast agents. These bubbles are modeled by mass densities and bulk moduli enjoying contrasting scales. These contrasting scales allow them to resonate at certain incident frequencies. We consider two types of such contrasts. In the first one, the bubbles are light with small bulk modulus, as compared to the ones of the background, so that they generate the Minnaert resonance (corresponding to a local surface wave). In the second one, the bubbles have moderate mass density but still with small bulk modulus so that they generate a sequence of resonances (corresponding to local body waves).We propose to use as measurements the far-fields collected before and after injecting a bubble, set at a given location point in the target domain, generated at a band of incident frequencies and at a fixed single backscattering direction. Then, we scan the target domain with such bubbles and collect the corresponding far-fields. The goal is to reconstruct both the, variable, mass density and bulk modulus of the background in the target region.

show abstract

Section: •)mentioning

confidence: 94%

Section: •)mentioning

confidence: 99%

See 1 more Smart Citation

Mathematical analysis of the acoustic imaging modality using bubbles as contrast agents at nearly resonating frequencies

Dabrowski¹,

Ahcene²,

Sini³

2021

IPI

Self Cite

View full text Add to dashboard Cite

show abstract

“…But as (β − αρ ε /k ε ) ∼ ε −2 1, suitable choices of ω allow to excite the eigenvalues of the Newtonian operators N 0 and create singularities in (1.10). This gives us a sequence of resonances with volumetric-modes which were observed in [5] and [21].…”

Section: Resonant Frequencies Generated By a Micro-bubblementioning

confidence: 95%

On the Origin of Minnaert Resonances

Mantile¹,

Posilicano²,

Sini³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

It is well known that the presence, in a homogeneous acoustic medium, of a small inhomogeneity (of size ε), enjoying a high contrast of both its mass density and bulk modulus, amplifies the generated total fields. This amplification is more pronounced when the incident frequency is close to the Minnaert frequency ωM . Here we explain the origin of such a phenomenon: at first we show that the scattering of an incident wave of frequency ω is described by a self-adjoint ω-dependent Schrödinger operator with a singular δ-like potential supported at the inhomogeneity interface. Then we show that, in the low energy regime (corresponding in our setting to ε 1) such an operator has a non-trivial limit (i.e., it asymptotically differs from the Laplacian) if and only if ω = ωM . The limit operator describing the non-trivial scattering process is explicitly determined and belongs to the class of point perturbations of the Laplacian. When the frequency of the incident wave approaches ωM , the scattering process undergoes a transition between an asymptotically trivial behaviour and a non-trivial one. As a by-product, we get the existence of a local maximum of the scattering amplitude occurring at the Minnaert frequency. It is this last property that is experimentally observed and used in the applications.

show abstract

“…Two solutions feature a positive imaginary frequency. Causality imposes negative imaginary parts of the eigen-frequencies and these 2 solutions can be safely removed [43][44][45][46][47][48][49]. The only two solutions with negative imaginary parts satisfy the causality principle and correspond to the first and second electric poles.…”

Section: Polesmentioning

confidence: 99%

Poles, physical bounds, and optimal materials predicted with approximated Mie coefficients

et al. 2021

View full text Add to dashboard Cite

Resonant electromagnetic scattering with particles is a fundamental problem in electromagnetism that has been thoroughly investigated through the excitation of localized surface plasmon resonances (LSPR) in metallic particles or Mie resonances in high refractive index dielectrics. The interaction strength between electromagnetic waves and scatterers is limited by maximum and minimum physical bounds. Predicting the material composition of a scatterer that will maximize or minimize this interaction is an important objective but its analytical treatment is challenged by the complexity of the functions appearing in the multipolar Mie theory. Here, we combine different kinds of expansions adapted to the different functions appearing in Mie scattering coefficients to derive simple and accurate expressions of the scattering electric and magnetic Mie coefficients in the form of rational functions. We demonstrate the accuracy of these expressions for metallic and dielectric homogeneous particles before deriving the analytical expressions of the complex eigen-frequencies (poles) for both cases. Approximate Mie coefficients can be used to derive in a simple but accurate expressions the complex dielectric permittivities that will yield a pole of the dipolar Mie coefficient and to ideal absorption conditions. The same expressions also predict the real dielectric permittivities that maximize (unitary limit) or minimize (anapole) electromagnetic scattering.

show abstract

Subwavelength resonant dielectric nanoparticles with high refractive indices

Cited by 18 publications

References 18 publications

Mathematical analysis of the acoustic imaging modality using bubbles as contrast agents at nearly resonating frequencies

Mathematical analysis of the acoustic imaging modality using bubbles as contrast agents at nearly resonating frequencies

On the Origin of Minnaert Resonances

Poles, physical bounds, and optimal materials predicted with approximated Mie coefficients

Contact Info

Product

Resources

About