Transformation Optics Approach to Plasmon-Exciton Strong Coupling in Nanocavities

We investigate the conditions yielding plasmon-exciton strong coupling at the single emitter level in the gap between two metal nanoparticles. Inspired by transformation optics ideas, a quasianalytical approach is developed that makes possible a thorough exploration of this hybrid system incorporating the full richness of its plasmonic spectrum. This allows us to reveal that by placing the emitter away from the cavity center, its coupling to multipolar dark modes of both even and odd parity increases remarkably. This way, reversible dynamics in the population of the quantum emitter takes place in feasible implementations of this archetypal nanocavity.

Figure 1

(a) QE placed at the gap between two metal spheres of permittivity $\epsilon (\omega )$ and embedded in a dielectric medium ${\epsilon }_D$. The QE dipole strength, position, and frequency are ${\mu }_E$, $z_E$, and ${\omega }_E$. (b) Normalized Purcell factor at the gap center for $R_{1,2}=R$ and $\delta =R/15$. Color dots: EM simulations for different $R$. Black line: TO prediction. Insets: induced charge distribution for the lowest 4 SP modes discernible in the spectrum (color scale is saturated for clarity).

Figure 2

(a) Normalized $J(\omega )$ at the gap center versus frequency and $\delta /R$. (b),(c) $n(t)$ versus time and gap size for $R=120\mathrm{nm}$ and ${\mu }_E=1.5e\mathrm{nm}$. The QE is at resonance with the dipolar SP mode in (b) and with the pseudomode in (c). (d) $n(t)$ for $\delta =1.5\mathrm{nm}$ (see white dashed lines) and two ${\omega }_E$: 1.7 (green) and 3.4 (red) eV. Black dotted line corresponds to ${\omega }_E=1.7\mathrm{eV}$ obtained through the fitting of $J(\omega )$ at ${\omega }_{\mathrm{PS}}$.

Figure 3

(a) $J(\omega )$ at $z_E=\delta /2$ and ${\omega }_E={\omega }_{\mathrm{PS}}$ versus $\delta$ normalized to the sum of the spectral density maxima for the spheres isolated. Inset: $J(\omega )$ for the dimer (blue) and isolated particle (green) for $\delta =8\mathrm{nm}$, $R=120\mathrm{nm}$. (b) Spectral density at the pseudomode versus $z_E/\delta$. Red solid line: $J({\omega }_{\mathrm{PS}})$ normalized to the sum of the two spheres isolated. Black dashed line: $J({\omega }_{\mathrm{PS}})$ normalized to its value at $z_E=\delta /2$. Inset: Same but versus the ratio $R_2/R_1$ for $z_E=\delta /2$. (c) $n(t)$ for ${\omega }_E={\omega }_{\mathrm{PS}}$ and three $z_E$ values (${\mu }_E=1.5e\mathrm{nm}$).

Figure 4

(a) Spectral density for $z_E=2.4\mathrm{nm}$ obtained through numerical (black dashed line), exact TO (red dotted-dashed line), and analytical TO (solid green line) calculations. The contribution to $J(\omega )$ due to even and odd modes are plotted in dark blue dotted and solid orange lines, respectively. Inset: surface charge map for the two lowest odd SPs. (b) Normalized coupling constant squared for even and odd modes versus $l$ for $z_E$: 1.2 nm (b), 2.4 nm (c), and 4 nm (d).