Slender-body theory for plasmonic resonance

Ruiz, Matias; Schnitzer, Ory

doi:10.1098/rspa.2019.0294

Cited by 14 publications

(28 citation statements)

References 71 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is noted that the above structures are all isotropic material structures. In [12,13,21], plasmon resonance with anisotropic material structures (nanorod, slenderbody) are studied and some sophisticated observations have been investigated. In most of the aforementioned works on plasmon resonance, the spectral of so called Nuemann-Poincaré (N-P) type operators are deeply studied, since it may cause the breaking of the invertibility of an integral system derived from related physical partial differential equation.…”

Section: Introductionmentioning

confidence: 99%

On plasmon modes in multi-layer structures

Deng¹,

Fang²

2022

Preprint

View full text Add to dashboard Cite

In this paper, we consider the plasmon resonance in multi-layer structures. The conductivity problem associated with uniformly distributed background field is considered. We show that the plasmon mode is equivalent to the eigenvalue problem of a matrix, whose order is the same to the number of layers. For any number of layers, the exact characteristic polynomial is derived by a conjecture and is verified by using induction. It is shown that all the roots to the characteristic polynomial are real and exist in the span [−1, 2]. Numerical examples are presented for finding all the plasmon modes, and it is surprisingly to find out that such multi-layer structures may induce so called surface-plasmon-resonance-like band.

show abstract

Section: Introductionmentioning

confidence: 99%

On plasmon modes in multi-layer structures

Deng¹,

Fang²

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Finally, although the focus of the paper is SBT for the Stokes equations, there are similar SBTs in use in other areas. 22,23 This includes the Laplace equation, [24][25][26] which presents a simpler setting for demonstrating our methods. We include an analogous analysis of the Laplace problem in Appendix C.…”

Section: Introductionmentioning

confidence: 99%

Accuracy of slender body theory in approximating force exerted by thin fiber on viscous fluid

Mori

Ohm

2021

Stud Appl Math

View full text Add to dashboard Cite

We consider the mapping properties of the integral operator arising in nonlocal slender body theory (SBT) for the model geometry of a straight, periodic filament. It is well known that the classical singular SBT integral operator suffers from high wavenumber instabilities, making it unsuitable for approximating the slender body inverse problem, where the fiber velocity is prescribed and the integral operator must be inverted to find the force density along the fiber. Regularizations of the integral operator must therefore be used instead. Here, we consider two regularization methods: spectral truncation and the -regularization of Tornberg and Shelley (2004). We compare the mapping properties of these approximations to the underlying partial differential equation (PDE) solution, which for the inverse problem is simply the Stokes Dirichlet problem with data constrained to be constant on cross sections. For the straight-but-periodic fiber with constant radius > 0, we explicitly calculate the spectrum of the operator mapping fiber velocity to force for both the PDE and the approximations. We prove that the spectrum of the original SBT operator agrees closely with the PDE operator at low wavenumbers but differs at high frequencies, allowing us to define a truncated approximation with a wavenumber cutoff

show abstract

“…Recently, we took a first step in applying an asymptotic approach to the analysis of the plasmonic properties of slender nanometallic structures [34]. In particular, we developed an approximate theory of the longitudinal plasmonic resonances of slender bodies of revolution, with the thickness profile along the symmetry axis being essentially arbitrary.…”

Section: Introductionmentioning

confidence: 99%

“…The framework in [34] is underpinned by a spectral theory which is exact in the quasistatic approximation; it is based on the so-called plasmonic eigenvalue problem [2,[35][36][37],…”

Section: Introductionmentioning

confidence: 99%

Plasmonic resonances of slender nanometallic rings

Ruiz,

Schnitzer

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We develop an approximate quasi-static theory describing the low-frequency plasmonic resonances of slender nanometallic rings and configurations thereof. In particular, 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 1D-periodic integro-differential problem in which the eigenfunctions are represented by azimuthal voltage and polarization-charge profiles associated with each ring. 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 non-uniform rings and non-coaxial structures, the reduced eigenvalue problem is solved using a semi-analytical scheme based on Fourier expansions of the reduced eigenfunctions. In conjunction with the quasi-static spectral theory of plasmonic resonance, the geometric modes of a given nanometallic structure explicitly determine its response to external radiation. Here, we employ the asymptotically approximated modes described above to obtain comparable approximations for the frequency response of a wide range of nanometallic slenderring structures under plane-wave illumination. These examples demonstrate how the theory can be employed to interpret and geometrically tune the plasmonic properties of highly nontrivial 3D nanometallic structures.

show abstract

Slender-body theory for plasmonic resonance

Cited by 14 publications

References 71 publications

On plasmon modes in multi-layer structures

On plasmon modes in multi-layer structures

Accuracy of slender body theory in approximating force exerted by thin fiber on viscous fluid

Plasmonic resonances of slender nanometallic rings

Contact Info

Product

Resources

About