Mie scattering as a cascade of Fano resonances

Abstract

We reveal that the resonant Mie scattering by high-index dielectric nanoparticles can be presented through cascades of Fano resonances. We employ the exact solution of Maxwell's equations and demonstrate that the Lorenz-Mie coefficients of the Mie problem can be expressed generically as infinite series of Fano functions as they describe interference between the background radiation originated from an incident wave and narrow-spectrum Mie scattering modes that lead to Fano resonances.

Fano resonances and band structure of two-dimensional photonic structures

“…For the case of individual dielectric cylinder, Fano resonances were observed as a result of the coupling of Mie resonant states [10,11] with an incident electromagnetic wave in spherical [12] and cylindrical dielectric object [13]. Fano resonances play an important role in design of metamaterials [14,15] and influence considerably the transport proper- (Color online) (a) Frequency spectrum of the square array of dielectric cylinders with radius R = 0.4a (a is the spatial periodicity in x and y directions) and permittivity ε = 12 calculated by the plane wave expansion method [1].…”

Fano resonances and fluorescence enhancement of a dipole emitter near a plasmonic nanoshell

“…The interference between the sphere and cavity plasmon modes gives rise to a Fano line-shape response in the scattering cross section and a Lorentzian (Breit-Wigner) line-shape response in the absorption cross section [9]. It is worth mentioning that one could also achieve Fano resonances in the total scattering cross section of a homogeneous high-permittivity dielectric sphere [15,16], which is not the focus of our study.…”

Switchable invisibility of dielectric resonators

“…Here, we consider the TE-polarization, at which the Mie resonances excited in the infinite cylinder are denoted as TE nk , (n is integer and k is positive integer) where n is the multipole order, and k is the resonance number. Figure 2(a) demonstrates the total Mie scattering efficiency Q 0 = 2 χ ∞ n=−∞ |a n | 2 (χ = rω/c = 2πr/λ) for the infinite cylinder in the low-frequency part of the spectrum at ε 1 = 60 where the resonant modes TE 01 , TE 11 , TE 21 , and TE 02 are observed 29 . For a reference scattering intensity we choose standard scattering efficiency Q 0 PEC for the infinite cylinder made from perfect conducting metal (PEC, ε 1 → ∞).…”

“…As a result of the interference of the nonresonant and resonant scattering, the spectra of the squared Lorenz-Mie scattering coefficients |a n | 2 demonstrate asymmetric profiles with either sharp increase or drop at the resonance frequencies of the cylinder eigenmodes. The scattering coefficients |a n | 2 can be presented in the form of infinite cascades of resonances each of which is described by the conventional Fano formula (1) as was shown for the first time numerically 14,29 and then analytically for the cases of infinite cylinder 30 and sphere 31 .…”