Level repulsion in hybrid photonic-plasmonic microresonators for enhanced biodetection

We theoretically analyze photonic-plasmonic coupling between a high-$Q$ whispering gallery mode (WGM) resonator and a core-shell nanoparticle. Blue and red shifts of WGM resonances are shown to arise from crossing of the photonic and plasmonic modes. Level repulsion in the hybrid system is further seen to enable sensitivity enhancements in WGM sensors: maximal when the two resonators are detuned by half the plasmon linewidth. Approximate bounds are given to quantify possible enhancements. Criteria for reactive vs resistive coupling are also established.

Figure 1

Normalized extinction spectrum vs ratio of core-shell radii for a coupled WGMR-NP system illuminated to excite the $(40,1)$ WGM in a bare WGMR. Solid lines show resonance branches defined by Eq. (9). Left inset: larger scale view of resonance branches. Right inset: ratio of resonance shift, $\delta k_{0,1}^E$, to line broadening, $\delta {\Gamma }_{0,1}^E$, quantifying reactive vs resistive coupling.

Figure 2

Mode strengths of degenerate azimuthal modes in a fundamental $L=40$ WGM. Left inset: geometry of a core-shell NP. Right inset: variation of the ratio $\mathcal{D}={\sum }_{\left|m\right|\le 1}{\left|D_m\right|}^2/{\sum }_{2\le \left|m\right|\le L}{\left|D_m\right|}^2$ with polar index $L$.

Figure 3

Resonance shifts of $\left|m\right|\le 1$ quasi-TM modes for $j=1$ (blue and green) and $j=2$ (black and red). Solid (dashed) curves denote shifts calculated using Eq. (13) [Eq. (3)]. Arrows denote detunings of $\pm {\Gamma }_{0,2}/2$ [see Eq. (21)].