• Nesterenko, Dmitry
• Hayashi, Shinji
• Fujii, Minoru
• Sekkat, Zouheir
• Sugimoto, Hiroshi

Abstract

Dielectric nanoparticles not showing distinct Mie resonances have been discarded as useful elements of resonant nanophotonics. However, the incorporation of the excitonic transition into such nanoparticles may allow us to generate sharp resonances, in particular, Fano resonances, thereby enhancing the utility of such nanoparticles. In this work, on the basis of the Mie theory and its electrostatics approximation, we analyze analytically and numerically optical responses and resonant behaviors of internal fields in spherical excitonic nanoparticles. The excitonic sphere is characterized by a dielectric constant consisting of a background dielectric constant and a Lorentzian response of the exciton excitation. From equations of the electrostatics approximation, by appropriately accounting for the background scattering, it is shown analytically that the absorption efficiency is expressed as a Lorentzian function, while the efficiencies of the scattering and extinction are expressed in the form of the generalized Fano function (external Fano resonance). From the same procedures, it is also shown that the spectra of the enhancement factor of internal fields are described by the same generalized Fano function (internal Fano resonance). Equations appearing in the derivation clearly indicate that both the external and internal Fano resonances are caused by the interference between a nonresonant component and a resonant component, corresponding to a broad background and sharp excitonic transition, respectively. Assuming a model excitonic sphere that mimics a polymer sphere doped with J-aggregates of excitonic molecules, spectra of scattering, absorption and extinction efficiencies, as well as that of the enhancement factor of internal fields, are calculated including a size range beyond the small particle limit, for which the exact Mie theory is used. The generalized Fano functions are shown to reproduce very well the calculated spectra even beyond the small particle limit, provided that the sphere radius is less than an upper bound. The results of the present paper provide a firm basis for discussing the formation of the Fano line shapes in optical responses and spectra of internal fields of excitonic nanospheres.

Topics

• nanoparticle
• impedance spectroscopy
• polymer
• theory
• dielectric constant
• laser emission spectroscopy