Coupled plasmon modes and constituent-selective refractive-index sensing in silver sphere–torus heterodimers

Attributing a confined dielectric change to one constituent of a composite nanostructure requires each plasmon resonance to be tied to its mode identity and to the region dominating its shift. We establish this link using boundary-element calculations for silver particles of 40 nm fixed outer diameter along a continuous sphere-to-torus path and the corresponding sphere–torus heterodimers. The transformation reorganizes the spherical dipole and quadrupole manifolds into toroidal modes. Mode labels follow from the symmetry of the quasistatic eigencharge distributions; the corresponding eigenvalues guide assignment of the retarded electron energy-loss spectroscopy (EELS) branches, and cathodoluminescence under matched trajectories assesses radiative character: E1u is strongly radiative, A1g is dark, and A2u is weakly radiative. As the torus aspect ratio e = R/r increases from 1 to 4, the monomer E1u and the dimer torus-parent E1u-like resonances redshift by about 1.3 eV, with wavelengths following a plasmon-ruler-inspired exponential form. In water, both E1u channels exceed 600 nm/RIU in bulk refractive-index sensitivity at quality factors of 18–20 and figures of merit near 13; the sphere-parent χ1-like branch is a second, less sensitive channel. Beam-position-resolved EELS shows preferential excitation of the E1u-like and χ1-like branches near the torus and sphere, respectively. Local dielectric perturbations quantify this constituent preference: the E1u-like shift is 9.9 times larger for torus than for sphere loading, and the χ1-like shift is 3.9 times larger for sphere loading. The two-channel response matrix reproduces all 15 pairwise wavelength differences among six simultaneously loaded states with maximum range-normalized residuals below 4.1%. A sphere–rod example shows that orientation-dependent excitation of different rod modes accompanies changes in local cross-response, illustrating the role of eigenmode assignment in interpreting the measured channels.