Hybrid Photonic-Plasmonic Cavity Design for Very Large Purcell Factors at Telecommunication Wavelengths

Hybrid photonic-plasmonic cavities can be tailored to display high $Q$ factors and extremely small mode volumes simultaneously, which ultimately results in large values of the Purcell factor, $F_P$. Amongst the different hybrid configurations, those based on a nanoparticle-on-a-mirror plasmonic cavity provide one of the lowest mode volumes, though so far their operation has been constrained to wavelengths below $1\mu \mathrm{m}$. Here, we propose a hybrid configuration consisting of a silicon photonic crystal cavity with a slot at its center in which a gold nanoparticle is introduced. This hybrid system operates at telecom wavelengths and provides high $Q$-factor values ($Q\approx {10}^5$) and small normalized mode volumes ($V_m\approx {10}^{-4}$), leading to extremely large Purcell-factor values, $F_P\approx {10}^7-{10}^8$. The proposed cavity could be used in different applications such as molecular optomechanics, bio- and chemosensing, efficient quantum emitters, or enhanced Raman spectroscopy in the relevant telecom-wavelength regime.

Figure 1

Schematics of the proposed system. (a) Geometry of the 1D slotted photonic crystal cavity. (b) A top view of the center of the cavity, where the slot of width $w$ can be distinguished. A gold spherical NP is located inside the slot. The distance between the NP and the cavity wall in the $y$ direction is $d=1\mathrm{nm}$, as shown in the close-up view and marked with a dashed-dotted line.

Figure 2

(a) The photonic band diagram of the mirror unit cell. The TE-like (TM-like) bands are depicted in blue (green). The shadowed region corresponds to the TE-like quasi–band gap where the photonic crystal cavity mode confined in the middle region is located (depicted with a red dashed line). (b) The mode profile of the electric field amplitude $|E|$ ($X$-$Y$ crosscut) normalized to its maximum value for the slotted photonic crystal cavity without the spherical gold NP.

Figure 3

The normalized LDOS, $Q$ factor, and $V_m$ for (a) the bare-silicon photonic crystal ($Q_c$, $V_c$) and (b) the hybrid plasmonic-photonic cavity ($Q_{\mathrm{Hyb}}$, $V_{\mathrm{Hyb}}$). The slot size is $w=40\mathrm{nm}$ and the radius of the gold NP is $R=19\mathrm{nm}$. The mode profile of $|E|$ ($X$-$Y$ crosscut) normalized to its maximum value in the slot for (c) the bare-silicon photonic crystal and (d) the hybrid photonic-plasmonic cavity. The inset in (b) shows a close-up view of the confined mode profile $|E|$ of the hybrid photonic-plasmonic cavity in the center of the cavity.

Figure 4

(a) The $Q$-factor (blue markers) and $V_m$ (red markers) values for the bare cavity (points) and the hybrid system (squares) as a function of the slot size $w$. The radius of the gold NP is varied accordingly to keep the gap distance between the NP and the wall of the photonic crystal to $d=1\mathrm{nm}$. (b) The $Q$-factor (blue markers) and $V_m$ (red markers) values for the hybrid system as a function of the gap size. The size of the slot is kept constant at $w=40\mathrm{nm}$. The NP is located at the center of the gap. The green circle (square) represents the $Q$ factor ($V_m$) for the hybrid system ($w=40\mathrm{nm}$ and $d=10\mathrm{nm}$) when the NP is stuck to only one of the cavity sidewalls (asymmetric cavity).

Figure 5

The normalized LDOS for gap sizes (a) $d=1\mathrm{nm}$, (c) $d=2\mathrm{nm}$, (e) $d=5\mathrm{nm}$, and (g) $d=10\mathrm{nm}$, for the hybrid system. The size of the slot is kept constant at $w=40\mathrm{nm}$. The ratio of the radiative to nonradiative LDOS for gap sizes (b) $d=1\mathrm{nm}$, (d) $d=2\mathrm{nm}$, (f) $d=5\mathrm{nm}$, and (h) $d=10\mathrm{nm}$, for the hybrid system.