For the simulation in Figure , we chose the emitter parameters in accordance with literature. We use ϵ ∞ = 1.7, an emitter linewidth of ℏγ = 47 meV 39 together with an oscillator strength of f = 0.08 and an emitter resonance of ℏω 0 = 2.0 eV (612 nm). This resonance position is red-shifted in comparison to the resonance of TDBC in water (590 nm), which can be rationalized by the adsorption on the particle surface. The shell thickness of 3 nm was determined by TEM (see Supplementary Information). Altering these parameters, also well outside the range found in literature, does not remove the additional peak when we keep the experimentally observed mode separation. To apply the HQM, we determined the coupling strength from a series of measurements by systematic variation of the dielectric environment for each particle size (see also Supplementary Information). This additional experimental effort was required as the peak splitting directly translates to the coupling strength only when the original plasmon and exciton resonances and the respective linewidths coincide. This exact coincidence is however experimentally difficult to realize. The more appropriate way to determine the coupling strength is therefore via the anti-crossing of the polariton peaks for various detunings. This way, we obtained a value of ℏΩ 0 = 82 meV for the 18 nm rod. Using now the (only slightly deviating) value of ℏΩ = 85 meV in eq 3, the simulated extinction spectrum reproduces the experimental spectrum almost perfectly (dash-dotted blue line in Figure ), except for the previously mentioned issue with the magnitude of the transverse resonance. We use 3. The upper row shows the extinction spectra of TDBC-coated gold nanorods of different sizes as measured (solid orange lines) and simulated with to the Mie-Gans model (dash-dotted blue lines) and FEM simulations (dashed dark blue lines). Both models use the HQM. All particles have the same aspect ratio but a varying transverse diameter of 11 nm, 18 nm, 34 nm, and 37 nm (from left to right). Both models nicely reproduce the measurement data. For a comparison, the lower row presents the same measured spectra for the same particles (orange lines) with Mie-Gans-simulated (dashed red lines) and FEM-simulated (dotted dark red lines) using the classical approach. The spurious peak becomes visible for all partical sizes in both the numerical and analytical model leading to a mismatch between simulations and experiments.