Multipole expansion of the scattering of light from a metal microspheroid

Abstract

The scattering of light by a spheroidal metal particle has been newly treated by use of the technique of the multipole expansion of radiation fields from the induced polarization and the associated current and magnetization, which are now considered as radiation sources. The relation between the polarization and the incident field is most simply obtained by using the long-wavelength approximation and a radiation-damping correction. The various orders of electricand magnetic-multipole coefficients of scattered fields have been separately calculated. Part of our calculated results confirm and thus justify the well-known features that the electric-dipole term gives the dominant contribution and that the magnitudes of multipole coefficients decrease monotonically with the increasing-order number of the multipoles. Some new features concerning the accuracy and the limitation of the radiation-damping correction are discussed against the depolarization factor of the spheroid. For a small sphere, the results reduce to the famous Rayleigh scattering, as expected. Results for larger spheres are compared with those of an exact electrodynamical calculation.

Unusual Extinction Spectra of Nanometer-Sized Silver Particles Arranged in Two-Dimensional Arrays

“…All of these features can be attributed to excitation of different spherical harmonics of the plasmon resonance for a single particle. 18 These correspond closely to the results of numerical calculations for 1000 Å silver spheres based on Mie theory by Kreibig and Zacharias. 19 The maxima at 510 and 425 nm are assigned to dipole-like and quadrupole-like oscillations, respectively, whereas the shoulders at 380 and 350 nm are probably due to excitation of higher multipoles.…”

“…Several distinct features are observed in the extinction spectrum of colloidal suspension: two maxima near 510 and 425 nm and two shoulders around 380 and 350 nm. All of these features can be attributed to excitation of different spherical harmonics of the plasmon resonance for a single particle .…”

The Effects of Mercury Adsorption on the Optical Response of Size-Selected Gold and Silver Nanoparticles

“…The UV−vis spectra for ∼51 nm colloidal Ag particles before and after Hg exposure are shown in Figure along with a calculation of a core/shell structure . An interesting observation is that the higher multiple oscillation observed near 360 nm for the Ag particles disappears after Hg adsorption. We currently do not fully understand this effect but believe it is related to a change in the polarization of the near surface region (mercury is known to lower the work function of Au and Ag surfaces by ∼0.3 eV).…”

Simulação da banda plasmônica de nanopartículas de prata utilizando o MiePlot

“…Isto corresponde a obter o campo de multipolo da distribuição de cargas da esfera em duas etapas: primeiro, o campo incidente promove o movimento oscilatório das cargas na esfera, induzindo uma polarização ⃗ ⃗ P(⃗ r, t) no material. Consequentemente, surge uma corrente de polarização ( ⃗ J p (⃗ r, t) = ∂ t ⃗ P), uma carga de polarização (ρ p (⃗ r, t) = − ⃗ ∇ • ⃗ P), além de uma magnetização ( ⃗ M p (⃗ r, t) = 1 2 ⃗ r × ⃗ J p ); segundo, estas quantidades são fontes dos campos secundários, os quais podem ser obtidos pela solução da equação de onda não homogênea através de expansão multipolar [25,26]. O modo TE de ordem (l, m), dado por…”