Analytical results regarding electrostatic resonances of surface phonon/plasmon polaritons: separation of variables with a twist

Abstract

The boundary integral equation (BIE) method ascertains explicit relations between localized surface phonon and plasmon polariton resonances and the eigenvalues of its associated electrostatic operator. We show that group-theoretical analysis of the Laplace equation can be used to calculate the full set of eigenvalues and eigenfunctions of the electrostatic operator for shapes and shells described by separable coordinate systems. These results not only unify and generalize many existing studies, but also offer us the opportunity to expand the study of phenomena such as cloaking by anomalous localized resonance. Hence, we calculate the eigenvalues and eigenfunctions of elliptic and circular cylinders. We illustrate the benefits of using the BIE method to interpret recent experiments involving localized surface phonon polariton resonances and the size scaling of plasmon resonances in graphene nanodiscs. Finally, symmetrybased operator analysis can be extended from the electrostatic to the full-wave regime. Thus, bound states of light in the continuum can be studied for shapes beyond spherical configurations.

Slender-body theory for plasmonic resonance

“…To this end, it will be convenient to adopt a modal approach based on spectral decomposition. In particular, in the quasi-static limit pertinent to subwavelength metallic nanoparticles in the visible range [33,46], the established modal approach entails solving the so-called plasmonic eigenvalue problem, a purely geometric spectral problem governing the permittivity eigenvalues and corresponding eigenfunctions of the particle [34,[47][48][49][50][51][52][53][54][55][56][57][58]. Once the latter problem is solved, the frequency response of an arbitrary lossy metallic nanostructure, for arbitrary external forcing, is explicitly provided in terms of the geometry's eigenvalues and eigenfunctions.…”

A perspective on effective medium models of thermal conductivity in (ultra) nanocrystalline diamond films

“…where l is the diameter of the circle. We recall that in 2D the depolarization factor of a circle is L k = 1/2 [20]. To check the validity of Eq.…”

Modal Approach to the Theory of Energy Transfer Mediated by a Metallic Nanosphere

“…In order to calculate the boundary Green's function one needs the knowledge of spectral properties of the electrostatic operator (11) and of its adjoint, namely χ k , u k , and v k . There are several shapes having the associated electrostatic operators with well established spectral properties [28]. One of these shapes is sphere, whose free-space Green's function (12) has a separated form in spherical coordinates given by…”

“…( 18) is a well-known expression found in any textbook treating classical electrodynamics [31]. What has been less known is the fact that this separated form allows the calculations of both the eigenfunctions and the eigenvalues of ( 11) for spherical shape [28]. Although for sphere the electrostatic operator is symmetric, the eigenfunctions u k , and v k are not identical (they differ by a constant) since they are related by Eq.…”

“…In the present work we apply the Green's function method to estimate the FRET enhancement. The approach is based on the fact that for spherical nanoparticles all spectral properties of the surface operators are known [28], hence an analytical expression of the boundary Green's function is provided. It will be further shown that the boundary Green's function allows easy calculations for any orientation of donors and acceptors.…”