Perturbation theory for plasmonic eigenvalues

Grieser, Daniel; Uecker, Hannes; Biehs, Svend‐Age; Huth, Oliver; Rüting, Felix; Holthaus, Martin

doi:10.1103/physrevb.80.245405

Cited by 13 publications

(17 citation statements)

References 24 publications

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“…and A 2 also satisfies the attenuation condition (24). Just as in the previous order, we find a forced variant of the homogeneous O(1) problem.…”

Section: E Slow Variation Of Amplitude and Phasesupporting

confidence: 63%

“…The same spectral problem arises in several other areas, such as in the theory of composite media [9]; the plasmonic spectrum is also closely linked to the specturm of the Neumann-Poincaré integral operator [10][11][12]. There is an enormous body of literature on this problem, with recent developments including analyses of strongly interacting particles using separation of variables [13,14], transformation optics [15], multipole methods [16], matched asymptotic expansions [17,18] and layer-potential techniques [12,19]; analysis of corners [20,21]; application to stimulated emission [22] and second-harmonic generation [23]; regular shape perturbations [24,25]; extensions incorporating nonlocality [26][27][28][29] and retardation [30][31][32][33][34]; and high-mode-number asymptotics [35,36].…”

Section: Introductionmentioning

confidence: 99%

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Geometric quantization of localized surface plasmons

Schnitzer

2019

IMA Journal of Applied Mathematics

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We consider the quasi-static problem governing the localized surface plasmon modes and permittivity eigenvalues ǫ of smooth, arbitrarily shaped, axisymmetric inclusions. We develop an asymptotic theory for the dense part of the spectrum, i.e., close to the accumulation value ǫ = −1 at which a flat interface supports surface plasmons; in this regime, the field oscillates rapidly along the surface and decays exponentially away from it on a comparable scale. With τ = −(ǫ + 1) as the small parameter, we develop a surface-ray description of the eigenfunctions in a narrow boundary layer about the interface; the fast phase variation, as well as the slowly varying amplitude and geometric phase, along the rays are determined as functions of the local geometry. We focus on modes varying at most moderately in the azimuthal direction, in which case the surface rays are meridian arcs that focus at the two poles. Asymptotically matching the diverging ray solutions with expansions valid in inner regions in the vicinities of the poles yields the quantization rulewhere n ≫ 1 is an integer and Θ a geometric parameter given by the product of the inclusion length and the reciprocal average of its cross-sectional radius along its symmetry axis. For a sphere, Θ = π, whereby the formula returns the exact eigenvalues ǫ n = −1 − 1/n. We also demonstrate good agreement with exact solutions in the case of prolate spheroids.

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“…and A 2 also satisfies the attenuation condition (24). Just as in the previous order, we find a forced variant of the homogeneous O(1) problem.…”

Section: E Slow Variation Of Amplitude and Phasesupporting

confidence: 63%

Section: Introductionmentioning

confidence: 99%

Geometric quantization of localized surface plasmons

Schnitzer

2019

IMA Journal of Applied Mathematics

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“…The existence of v ℓ and w ℓ , their density properties, and (4.18) and (4.19) can be considered as the existence of surface plasmons for complementary media, a fact which can be used elsewhere; see e.g., [11,12,19] for discussions on surface plasmons and their applications. The choice of a 1 is to ensure such properties.…”

Section: Separation Of Variables Approach For Cauchy Problems In a Gementioning

confidence: 99%

Cloaking via anomalous localized resonance for doubly complementary media in the quasistatic regime

Nguyên¹

2015

J. Eur. Math. Soc.

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Cloaking a source via anomalous localized resonance (ALR) was discovered by Milton and Nicorovici in [14]. A general setting in which cloaking a source via ALR takes place is the settting of doubly complementary media. This was introduced and studied in [19] for the quasistatic regime. In this paper, we study cloaking a source via ALR for doubly complementary media in the finite frequency regime as a natural continuation of [19]. We establish the following results: 1) Cloaking a source via ALR appears if and only if the power blows up; 2) The power blows up if the source is "placed" near the plasmonic structure; 3) The power remains bounded if the source is far away from the plasmonic structure. Concerning the analysis, we extend ideas from [19] and add new insights on the problem which allows us to overcome difficulties related to the finite frequency regime and to obtain new information on the problem. In particular, we are able to characterize the behaviour of the fields far enough from the plasmonic shell as the loss goes to 0 for an arbitrary source outside the core-shell structure in the doubly complementary media setting.

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“…h is a small dimensionless parameter, common to all sides. The formalism of resonance shifting due to such shape perturbation of a plasmonic particle was developed in [27] resulting in:…”

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confidence: 99%

Resonances On-Demand for Plasmonic Nano-Particles

et al. 2011

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A method for designing plasmonic particles with desired resonance spectra is presented. The method is based on repetitive perturbations of an initial particle shape while calculating the eigenvalues of the various quasistatic resonances. The method is rigorously proved, assuring a solution exists for any required spectral resonance location. Resonances spanning the visible and the near-infrared regimes, as designed by our method, are verified using finite-difference time-domain simulations. A novel family of particles with collocated dipole-quadrupole resonances is designed, demonstrating the unique power of the method.Such on-demand engineering enables strict realization of nano-antennas and metamaterials for various applications requiring specific spectral functions.

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Perturbation theory for plasmonic eigenvalues

Cited by 13 publications

References 24 publications

Geometric quantization of localized surface plasmons

Geometric quantization of localized surface plasmons

Cloaking via anomalous localized resonance for doubly complementary media in the quasistatic regime

Resonances On-Demand for Plasmonic Nano-Particles

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