Fano resonances in core-shell particles with high permittivity covers

Abstract

In this paper, an approximate model is presented to understand Fano resonances observed in the Mie scattering from a core-shell particle with high permittivity cover. The scattering coefficients of a core-shell particle with high permittivity cover can be described by the superposition of narrow resonance and slow varying background. The slow varying background part is the same as scattering coefficient of a perfect electric conductor with same radius as the outer radius of shell, which is independent of material parameter. The narrow resonance part is a symmetrical Lorenz resonance which is affected by both sizes and material parameters of the core and shell. The interference of narrow resonance and slow varying background brings about a typical asymmetric Fano profile. Hence, the Mie scattering coefficients of core-shell particles can be presented through cascades of Fano resonances. The Fano parameter and resonance width of a core-shell particle with given material and size can be perfectly predicted by using this model. We discover that the Fano parameter is only related to the outer radius of the shell when incident wave frequency is fixed while the resonance width is determined by both sizes and material parameters. An analytic condition for the occurrence of Fano resonance can also be shown in the approximate model. As a function of size and material parameter, the variation of resonance positions are shown in the text. We find that the sensitivity of resonance to core materials is different in different orders of resonances, which may help to manipulate scattering waves by core-shell particles.