Fundamental and high-order anapoles in all-dielectric metamaterials via Fano–Feshbach modes competition

Abstract

Abstract. One of the most fascinating possibilities enabled by metamaterials is the strong reduction of the electromagnetic scattering from nanostructures. In dielectric nanoparticles, the formation of a minimal scattering state at specific wavelengths, is associated with the excitation of photonic anapoles, which represent a peculiar type of radiationless state and whose existence has been demonstrated experimentally. In this work, we investigate the formation of anapole states in generic dielectric structures by applying a Fano-Feshbach projection scheme, a general technique widely used in the study of quantum mechanical open systems. By expressing the total scattering from the structure in terms of an orthogonal set of internal and external modes, defined in the interior and in the exterior of the dielectric structure, respectively, we show how anapole states are the result of a complex interaction among the resonances of the system and the surrounding environment. We apply our approach to a circular resonator, where we observe the formation of higher-order anapole states, which are originated by the superposition of several internal resonances of the system.

Nonradiating photonics with resonant dielectric nanostructures

“…Another approach targeted to build anapoles from general geometries was proposed by Totero and co-workers [46]. The main point in that work was to provide a fast and general approach for the computation of electromagnetic modes in arbitrary-shaped open optical structures.…”

Excitation of nonradiating magnetic anapole states with azimuthally polarized vector beams

“…Recently, the excitation of anapole states in pure dielectric nanoparticles was studied under the prism of a Weierstrass-type product expansion in terms of the resonant-state frequencies that correspond to zeros of the elements of the S-matrix of the particle in the complex frequency plane [ 26 ]. Moreover, excitation of anapole states has also been examined under a projection scheme on Fano–Feshbach resonances [ 27 ]. For our purposes, we associate any zeros of the partial scattered power of spherical harmonics with the potential of nonradiating anapole excitation.…”

Fano feature induced by a bound state in the continuum via resonant state expansion

“…Fortunately, we shall see later on that in our case we do not need the general expression for A in the second order perturabtive solution consistent with Eq. (22). By a close examination of Eq.…”

“…For the further convenience we also introduce the resonant vacuum wave number as where the complex valued α is implicitly defined by Eq. (22) and k BIC = ω BIC /c . Finally, expanding (19) into the Taylor series in φ we find the following expression for the resonant eigenmode profile within the ADL…”