Hybridization and the origin of Fano resonances in symmetric nanoparticle trimers

We study the light scattering by plasmonic and dielectric symmetric trimers to investigate the existence of polarization-independent Fano resonances. Plasmonic hybridization theory is revealed to hide simple physics, and we instead provide a simplified model for hybridization to derive a plasmonic trimer's eigenmodes analytically. This approach is demonstrated to accurately recreate full wave simulations of plasmonic trimers and their Fano resonances. We are subsequently able to deduce the grounds for modal interference in plasmonic trimers and the related formation of Fano resonances. However, by generalizing our simplified hybridization approach, we are also able to investigate the eigenmodes of all-dielectric trimers. We show that bianisotropic coupling channels between high-index dielectric nanoparticles are able to increase the capacity for Fano resonances, even at normal incidence. We finally provide the first experimental measurements of sharp, polarization-independent Fano resonances from a symmetric all-dielectric trimer, with very good agreement with the predicted response from our simplified hybridization theory.

Figure 1

The eigenmodes of (a) a single particle and (b) a dimer with $D_{2h}$ symmetry, when assuming only in-plane electric dipole responses from each particle. The dimer eigenmodes are labeled according to their associated irreducible representation. We also show the location of the extra particle(s) needed to form a trimer. In (c) and (d), we depict a generalized energy-level diagram for these eigenmodes and identify the coupling channels, labeled as $A$–$D$.

Figure 2

(a) Extinction cross section from a trimer made of 100-nm silver nanospheres, simulated using (dashed line) cst microwave studio and (solid line) the analytical eigenmodes of Eq. (5). Both curves show the formation of a small Fano resonance as the gap between particles $g$ is reduced. (b) Decomposition of the extinction for the $g=20$ nm trimer in terms of the two excited eigenmodes. The eigenmode profiles depict the real components of dipole moments at 400 nm.

Figure 3

The eigenmodes of (a) a single particle and (c) a dimer with $D_{2h}$ symmetry when assuming both electric and magnetic dipole responses from each particle and neglecting the $z$ direction. (b) The $z$-oriented basis vectors of a trimer, which become doubly degenerate eigenmodes of the trimer when electric-magnetic coupling is neglected. The dimer and trimer eigenmodes are labeled according to their associated irreducible representation. (d) A generalized energy-level diagram analogous to that in Fig. 1, now with coupling channels $C$–$F$ [see Eqs. (2) and (9)]

Figure 4

(a) Experimental setup for the trimer made from MgO-${\mathrm{TiO}}_2$ spheres and (b) the measurements of extinction for both the trimer and a single sphere. The trimer exhibits a pronounced, polarization-independent Fano resonance at 4.8 GHz, in very good agreement with (c) the simulation results of extinction, which were calculated using cst microwave studio.

Figure 5

(a) Extinction of the trimer in Fig. 4 when calculated using the hybridization procedure presented in this paper. We also show the eigenmode decomposition of the extinction coming from the (b) $E^{\prime }$ and (c) $E^{\prime \prime }$ responses of the trimer. Each eigenmode's isolated contribution to the extinction is shown alongside its associated dipole moment profiles, which depict the real components of each dipole moment at 4.8 GHz. Red arrows are electric dipole moments, and blue arrows are magnetic dipole moments.