Figure 1

(Color online) (a) A cut through a coated ellipsoidal nanoparticle. The principal semiaxes perpendicular to the paper are $a_y$ and $b_y$, respectively. The relevant dielectric functions ${ϵ}_{\mathit{in}}\left(\omega \right)$, ${\epsilon }_{c\Vert }\left(\omega \right)$, ${\epsilon }_{c\perp }\left(\omega \right)$, and ${\epsilon }_m$ are also indicated. (b) Extinction spectrum, where ${\sigma }_{vv}=\omega \mathrm{Im}\left[{\alpha }_{vv}\right]$, $v=x,y,z$. The dash-dotted curves are for an uncoated metallic ellipsoid, where the red (blue) curve is for the external field along the $x$ axis ($z$ axis). The red solid ($x$ direction) and blue solid ($z$ direction) curves correspond to the case of an ellipsoidal molecular layer (without an interior metallic region; i.e., we set ${ϵ}_i=1$) with a resonance parallel to the layer normal. Here, this situation is modeled by taking ${\gamma }_{0\Vert }∕v_0=0.2$, ${\gamma }_{\infty \Vert }∕v_0=0.02$, and ${\gamma }_{0\perp }∕v_0={\gamma }_{\infty \perp }∕v_0=0.01$ (corresponding to effective oscillator strength $c_{0\Vert }\approx 2.26$ and large frequency refractive index $n_{\Vert }\approx 1.06$; see text). The red dashed ($x$ direction) and blue dashed ($z$ direction) curves are for the case that the molecular layer has a resonance perpendicular to the layer normal. We take ${\gamma }_{0\perp }∕v_0=0.1$ and ${\gamma }_{\infty \perp }∕v_0={\gamma }_{0\Vert }∕v_0={\gamma }_{\infty \Vert }∕v_0=0.01$ (so that $c_{0\perp }\approx 1.13$ and $n_{\perp }\approx 1.07$). The following parameters were used: $e_o^2=0.8$, $s=1$, ${\Delta }_V=0.08$, ${\Gamma }_p∕{\omega }_p=0.05$, ${\omega }_{0\Vert }∕{\omega }_p={\omega }_{0\perp }∕{\omega }_p=0.5$, ${\Gamma }_{\Vert }∕{\omega }_p={\Gamma }_{\perp }∕{\omega }_p=0.03$, and ${\epsilon }_m=1$. The extinction cross sections are shown in units of the total volume $V_o$. The solid and dashed vertical bars indicate the plasmon and molecular resonance frequencies, respectively. Notice the small peak heights of the molecular layer resonances (here enlarged by a factor of 50) compared with the plasmon resonance heights.Reuse & Permissions

Figure 2

(Color online) Extinction spectrum for a coated prolate spheroid with different orientations of the molecules on the surface. The spectrum is in units of the total volume $V_o$ of the coated spheroid. ${\sigma }_{vv}^{\mu }=\omega \mathrm{Im}\left[{\alpha }_{vv}\right]$ ($\mu =\Vert ,\perp$ and $v=x,z$) and $\lambda =2\pi c∕\omega$ is the wavelength of the external electromagnetic field. (a) The external field is along the $z$ axis (short axis) of the spheroid. The molecules have their resonant axes perpendicular to the metallic particle normal. (b) The external field is along the $x$ axis (long axis), and the molecules are perpendicular to the layer normal. (c) The field is along the $z$ axis, and the molecules have their resonant axis parallel to the layer normal. (d) The field is along the $x$ axis, and the molecules are oriented parallel to the layer normal. The different colors are the spectra for different molecular resonant wavelengths; the upper vertical bars indicate these resonance wavelengths ${\lambda }_{0\mu }=2\pi c∕{\omega }_{0\mu }$. Here, we chose the following values for ${\omega }_{0\mu }$: $0.35{\omega }_p$, $0.4{\omega }_p$, $0.6{\omega }_p$, $0.7{\omega }_p$, $0.9{\omega }_p$. The lower vertical bar is the particle plasmon resonance wavelengths ${\lambda }_{pv}=2\pi c∕{\omega }_{pv}$ $(v=x,z)$. The same parameters as in Fig. 1 were used. Notice the strong hybridization when ${\lambda }_{0\mu }\approx {\lambda }_{pv}$ and increased peak height (surface enhanced absorption) for the molecular resonance, compared with Fig. 1b.Reuse & Permissions

Figure 3

(Color online) Scaled peak height for the coupled resonances in a coated prolate metal spheroid for the case (a) when the coating molecules have their resonant axis parallel to the surface normal and (b) for a perpendicular resonance. The resonance frequencies ${\omega }_{v\mu }^{\pm }$ and peak heights ${\sigma }_{vv}\left({\omega }_{v\mu }^{\pm }\right)$, see Figs. 2, 4, for different ${\omega }_{0\mu }$ were numerically determined and used to calculate the scaled peak height $T_{v\mu }^{\pm }=4\pi {\sigma }_{vv}\left({\omega }_{v\mu }^{\pm }\right)∕\left[V_o{\left({\omega }_{v\mu }^{\pm }\right)}^2\right]$ ($v=x,z$ and $\mu =\Vert ,\perp$); see Eq. (A7). The peak heights were normalized by the molecular layer peak heights $T_{v\mu }({\epsilon }_i=1)$ obtained from Fig. 1. The vertical solid lines correspond to the two plasmon resonances ${\omega }_{px}$ and ${\omega }_{pz}$, Eq. (7). The dash-dotted horizontal lines correspond to the plasmon peak heights as given in the text right after Eq. (17). The solid and dashed curves are the approximate results given in Eq. (17). The same parameters as in Fig. 1 were used. Notice the different ranges of the ordinates and that the abscissas are in frequency units.Reuse & Permissions

Figure 4

(Color online) Illustration of strong coupling and “avoided crossing” between the plasmonic and molecular resonances of a coated prolate metal spheroid for the case (a) when the molecules have their resonant axis parallel to the surface normal and (b) for a perpendicular resonance. The horizontal dashed lines correspond to the two plasmon resonances ${\omega }_{px}$ and ${\omega }_{pz}$, and the diagonal dashed lines denotes $\omega ={\omega }_{0\mu }$. The solid white curves are the approximate results for the coupled resonances as given in Eq. (10). The same parameters as in Fig. 1 were used. Notice that the axes are in frequency units.Reuse & Permissions

Figure 5

(Color online) Difference in averaged extinction cross section, $\Delta \sigma ∕V_o=({\sigma }^{\Vert }-{\sigma }^{\perp })∕V_o$ (indicated by the different colors), between the parallel and perpendicular cases as shown in Figs. 4a, 4b, as a function molecular resonance frequency ${\omega }_0={\omega }_{0\Vert }={\omega }_{0\perp }$ and external field frequency $\omega$. Note that the axes are in frequency units.Reuse & Permissions