Scattering electromagnetic eigenstates of a two-constituent composite and their exploitation for calculating a physical field

Bergman, David J.; Chen, Parry Y.; Farhi, Asaf

doi:10.1103/physreva.102.063508

Cited by 9 publications

(3 citation statements)

References 21 publications

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“…Another avenue would be to develop a full-wave slender-body theory in the case where the ring diameter is comparable to the free-space wavelength; the cross-sectional scale would still be subwavelength, while the ring-scale approximation could be formed by superposition of fundamental solutions of Maxwell's equations along the centerline of the ring. Lastly, we note that it is possible but not straightforward to generalize the permittivity-eigenvalue formulation to multiconstituent photonic structures [81], e.g., hybrid metal-dielectric structures. For such ring structures, a reformulation of the theory based on quasinormal modes and complex frequency eigenvalues may be more convenient [82].…”

Section: Discussionmentioning

confidence: 99%

Plasmonic resonances of slender nanometallic rings

Ruiz

Schnitzer

2022

Phys. Rev. B

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We develop an approximate quasistatic theory describing the low-frequency plasmonic resonances of slender nanometallic rings and configurations thereof. First, we use asymptotic arguments to reduce the plasmonic eigenvalue problem governing the geometric (material-and frequency-independent) modes of a given ring structure to a one-dimensional periodic integrodifferential problem in which the eigenfunctions are represented by azimuthal voltage and polarization-charge profiles associated with each ring. Second, we obtain closed-form solutions to the reduced eigenvalue problem for azimuthally invariant rings (including torus-shaped rings but also allowing for noncircular cross-sectional shapes), as well as coaxial dimers and chains of such rings. For more general geometries, involving azimuthally nonuniform rings and noncoaxial structures, we solve the reduced eigenvalue problem using a semianalytical scheme based on Fourier expansions of the reduced eigenfunctions. Third, we used the asymptotically approximated modes, in conjunction with the quasistatic spectral theory of plasmonic resonance, to study and interpret the frequency response of a wide range of nanometallic slender-ring structures under plane-wave illumination.

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Section: Discussionmentioning

confidence: 99%

Plasmonic resonances of slender nanometallic rings

Ruiz

Schnitzer

2022

Phys. Rev. B

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“…9 that the same modes can be used to compute the effective model associated with particles having the same geometry but different materials. It should also be noted that for periodic particles made of multiple constituents, it is necessary to modify the PEP and the modal expansion as proposed in [36]. Similarly, adaptations can be made in order to deal with a spatially varying permittivity profile inside the meta-atom [37].…”

Section: From Artificially Low To Actual Losses In Metalsmentioning

confidence: 99%

Homogenized transition conditions for plasmonic metasurfaces

Lebbe

Maurel²,

Pham³

2023

Phys. Rev. B

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The present study aims to model the optical response of plasmonic metasurfaces made of a periodic arrangement of metallic particles with arbitrary shape and subwavelength dimensions. By combining homogenization with quasistatic plasmonic eigenmode expansion, the metasurface is replaced by a zero-thickness interface associated with frequency-dependent effective susceptibilities. The resulting discontinuities of the fields are responsible for strong interaction with the incoming light at the resonances when the complex permittivity of the metal passes close to the real permittivity of an eigenmode. Our modeling provides a physical picture of resonances in plasmonic metasurfaces, and it allows for a huge decrease in the numerical cost of their computations. In addition, comparisons with direct numerics in two dimensions evidence its predictive force at any incidence, particle shape, and arrangement.

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“…Here is a (non-random) projection matrix which depends only on the lattice topology and boundary conditions, and χ 1 is a diagonal (random) projection matrix which determines the geometry and component connectivity of the composite medium (Gully et al, 2015;Murphy et al, 2015). Another spectral approach to finding effective properties based on analytic continuation relies on computation of the electromagnetic eigenstates of individual inclusions (Bergman et al, 2020;Bergman, 2022).…”

Section: Spectral Measure Computations For Two-phase Compositesmentioning

confidence: 99%

Stieltjes functions and spectral analysis in the physics of sea ice

Golden,

Murphy,

Hallman

et al. 2023

Nonlin. Processes Geophys.

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Abstract. Polar sea ice is a critical component of Earth’s climate system. As a material, it is a multiscale composite of pure ice with temperature-dependent millimeter-scale brine inclusions, and centimeter-scale polycrystalline microstructure which is largely determined by how the ice was formed. The surface layer of the polar oceans can be viewed as a granular composite of ice floes in a sea water host, with floe sizes ranging from centimeters to tens of kilometers. A principal challenge in modeling sea ice and its role in climate is how to use information on smaller-scale structures to find the effective or homogenized properties on larger scales relevant to process studies and coarse-grained climate models. That is, how do you predict macroscopic behavior from microscopic laws, like in statistical mechanics and solid state physics? Also of great interest in climate science is the inverse problem of recovering parameters controlling small-scale processes from large-scale observations. Motivated by sea ice remote sensing, the analytic continuation method for obtaining rigorous bounds on the homogenized coefficients of two-phase composites was applied to the complex permittivity of sea ice, which is a Stieltjes function of the ratio of the permittivities of ice and brine. Integral representations for the effective parameters distill the complexities of the composite microgeometry into the spectral properties of a self-adjoint operator like the Hamiltonian in quantum physics. These techniques have been extended to polycrystalline materials, advection diffusion processes, and ocean waves in the sea ice cover. Here we discuss this powerful approach in homogenization, highlighting the spectral representations and resolvent structure of the fields that are shared by the two-component theory and its extensions. Spectral analysis of sea ice structures leads to a random matrix theory picture of percolation processes in composites, establishing parallels to Anderson localization and semiconductor physics and providing new insights into the physics of sea ice.

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Scattering electromagnetic eigenstates of a two-constituent composite and their exploitation for calculating a physical field

Cited by 9 publications

References 21 publications

Plasmonic resonances of slender nanometallic rings

Plasmonic resonances of slender nanometallic rings

Homogenized transition conditions for plasmonic metasurfaces

Stieltjes functions and spectral analysis in the physics of sea ice

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