Spontaneous Emission Suppression via Quantum Path Interference in Coupled Microcavities

We examine theoretically the spontaneous emission rate in optical microstructures with cavity resonances that overlap in both position and frequency. Using projection techniques, we show that the spontaneous emission in such structures can be accurately described by the direct emission and quantum path interference of emission into a few discrete resonant modes, even though the exact infinite-dimensional problem involves a coupling to the continuum of radiation states. Moreover, we obtain an efficient numerical time-domain method for determining the spontaneous emission rate that incorporates these effects, including the suppression of spontaneous emission into some modes.

Figure 1

Index of refraction and intensity profile for the two modes in the lowest band gap. As the modes are symmetric about $y=0$, $|{\mathbf{M}}_1(\mathbf{r}){|}^2$ ($|{\mathbf{M}}_2(\mathbf{r}){|}^2$) is only shown for $y>0$ ($y<0$). Small circles denote the rods, while the large circle encloses volume, $V_s$, and denotes the hard boundary used to calculate the quasimodes.

Figure 2

LDOS for the structure of Fig. 1 evaluated at $y=0$ as a function $x$ and $\omega$.

Figure 3

(a) Quantities ${\rho }_1(\omega )$, ${\rho }_2(\omega )$, and $\mathrm{Im}\{C_{12}(\omega )\}$ for the two modes in Fig. 1 calculated using FDTD (solid lines) and Eq. (5) (dotted lines). (b) SE ratio [$R_{\mathrm{SE}}(\omega ,\mathbf{r})$], the reduced SE ratio [$R_{\mathrm{SE}}^{(2)}(\omega ,\mathbf{r})$], and the reduced SE ratio without the interference term [$R_{\mathrm{SE}}^{(NI)}(\omega ,\mathbf{r})$] at the centers of the two defects as a function of frequency. For comparison purposes, $R_{\mathrm{SE}}^{(2)}(\omega ,\mathbf{r})$ has been frequency-shifted by the frequency difference found in Fig. 3a.