Related papers: Perturbation theory for plasmonic eigenvalues
A remarkable extension of Rayleigh-Schroedinger perturbation method is found. Its (N+q) x (N+1) - dimensional Hamiltonians (as emerging, e.g., during quasi-exact constructions of bound states) are non-square matrices at q > 1. The role of…
In this paper we use the full Maxwell equations for light propagation in order to analyze plasmonic resonances for nanoparticles. We mathematically define the notion of plasmonic resonance and analyze its shift and broadening with respect…
We derive relationships between the shape deformation of an impenetrable obstacle and boundary measurements of scattering fields on the perturbed shape itself. Our derivation is rigourous by using systematic way, based on layer potential…
Plasmonic resonances of nanoparticles have drawn lots of attentions due to their interesting and useful properties such as strong field enhancements. These systems are typically studied using either classical electrodynamics or fully…
We examine here the anomalous optical response of a nanosphere composed of two conjoined hemispheres of different materials, one of them being plasmonic. At the internal resonance, we show how the light interaction becomes dramatically…
We implement Lie transform perturbation theory to second order for the planar spin-orbit problem. The perturbation parameter is the asphericity of the body, with the orbital eccentricity entering as an additional parameter. We study first…
In this paper we provide a mathematical framework for localized plasmon resonance of nanoparticles. Using layer potential techniques associated with the full Maxwell equations, we derive small-volume expansions for the electromagnetic…
This paper aims at providing a small-volume expansion framework for the scattering resonances of an open cavity perturbed by small particles. The induced shift of the scattering frequencies by the small particles is derived without…
The aim of this paper is to present a new approach, based on singular volume integral equations, in order to compute the size dependency of plasmonic resonances. The paper also provides rigorous derivations of the extinction and absorption…
The plasmonic response of nanoparticles is exploited in many subfields of science and engineering to enhance optical signals associated with probes of nanoscale and subnanoscale entities. We develop a numerical algorithm based on previous…
For all applications of plasmonics to technology it is required to tailor the resonance to the optical system in question. This chapter gives an understanding of the design considerations for nanoparticles needed to tune the resonance.…
For odd anharmonic oscillators, it is well known that complex scaling can be used to determine resonance energy eigenvalues and the corresponding eigenvectors in complex rotated space. We briefly review and discuss various methods for the…
The paper presents a new theory of unfolding of eigenvalue surfaces of real symmetric and Hermitian matrices due to an arbitrary complex perturbation near a diabolic point. General asymptotic formulae describing deformations of a conical…
In the framework of perturbation theory the reality of the perturbed eigenvalues of a class of $\PT$symmetric Hamiltonians is proved using stability techniques. We apply this method to $\PT$symmetric unperturbed Hamiltonians perturbed by…
Over the past twenty years, the field of plasmonics has been revolutionized with the isolation and utilization of two--dimensional materials, particularly graphene. Consequently there is significant interest in rapid, robust, and highly…
In the q-deformed theory the perturbation approach can be expressed in terms of two pairs of undeformed position and momentum operators. There are two configuration spaces. Correspondingly there are two q-perturbation Hamiltonians, one…
We propose a variational perturbation method based on the observation that eigenvalues of each parity sector of both the anharmonic and double-well oscillators are approximately equi-distanced. The generalized deformed algebra satisfied by…
Investigating nanoplasmonics using time-dependent approaches permits shedding light on the dynamic optical properties of plasmonic structures, which are intrinsically connected with their potential applications in photochemistry and…
Standard perturbation theory of eigenvalue problems consists of obtaining approximations of eigenmodes in the neighborhood of an operator where the corresponding eigenmode is known. Nevertheless, if the corresponding eigenmodes of several…
Many typical nanoscale structures consist of dielectric nanoparticles with an inevitable oxide-generated coating around them. Depending on the fabrication techniques, these coatings may not be homogeneous, and their distortion can cause…