Purcell enhancement of fast-dephasing spontaneous emission from electron-hole droplets in high-$Q$ silicon photonic crystal nanocavities

We have observed electron-hole droplet emission enhanced by silicon photonic crystal nanocavities with different $Q$ values and simulated their Purcell effect using a semiclassical theory considering the temporal dephasing of the emission. When the photon loss rate of the nanocavities is smaller than the dephasing rate of the emission, the cavity-enhanced integrated photoluminescence (PL) intensity is unchanged by the cavity $Q$ value. This is because the Purcell enhancement of the spontaneous emission rate is saturated in a high-$Q$ region. In contrast, the peak intensity of the cavity-enhanced PL is proportional to the cavity $Q$ value without saturation. These results suggest that a high-$Q$ nanocavity is suitable for fabricating bright narrowband light emitting devices that concentrate the broadband emission energy of fast-dephasing emitters in a narrowband cavity resonance.

Figure 1

(a) Dimensions of a fabricated $L3$ cavity with surface oxide and an EHD consisting of electrons and holes. The typical diameter of the EHD is comparable with a length of the $L3$ cavity. (b) Snapshot of the spatial distribution of a cavity-confined electric field directed towards the $y$ axis $\left(E_y\right)$. This mode is a fundamental cavity mode. (c) Setup for photoluminescence measurements. DM: dichroic mirror; L: objective; LPF: optical low-pass filter; P: polarizer; BPF: bandpass filter. (d) Typical PL spectra of the surface-oxidized Si PhC nanocavities with lattice periods of 307 and 308 nm and no end-hole shift. The spectral resolution is 0.1 nm and the sample temperature is 4 K.

Figure 2

Cavity-enhanced components of the PL spectra for Si PhC nanocavities with $Q$ values of (a) 7900, (b) 14 000, and (c) 26 000. In each graph, the spectra of nanocavities with different lattice periods are overlaid. The spectral resolution is 0.06 nm. The average excitation laser power and repetition frequency are 30 μW and 8 MHz, respectively. The exposure time is 60 s.

Figure 3

Normalized PL decays for resonant PhC nanocavities with different $Q$ values of (a) 7900, (b) 14 000, and (c) 26 000. The detection wavelengths of the resonant cavity are 1161, 1163, and 1162 nm for (a–c), respectively. The detection bandwidth is 1 nm. The graph for $Q=7900$ shows the PL decay at a wavelength detuned by −2 nm from the cavity resonance. The PL lifetime is 22 ns, which is defined as the time it takes for the normalized PL intensity to reach $e^{-1}$. The data accumulation times for on- and off-resonant emissions are 120 and 3600 s, respectively. The average excitation laser power and repetition frequency are 30 μW and 8 MHz, respectively.

Figure 4

(a) Integrated PL intensity and (b) peak PL intensity of the cavity-enhanced components of the EHD as a function of the cavity $Q$ value. They are calculated from Fig. 2. The plotted data are taken at the spectral detuning of less than 5 nm between the cavity resonance and the center wavelength of the EHD emission (1165 nm). The broken lines are fitted to the data as a guide to the eye.

Figure 5

(a) Calculated SE rate enhancement ratios with and without considering the dephasing of a single emitter as a function of $\kappa /{\gamma }_d$. (b) Integrated and (c) peak emission intensity of a cavity-enhanced single emitter calculated with the semiclassical model. Each graph shows the results calculated with different three mode volumes. The typical mode volume of the fabricated PhC nanocavities is around $0.026\mu {\mathrm{m}}^3$.

Figure 6

Simulated intensities of the cavity-enhanced PLs with the inhomogeneous broadening and three different dephasing times. The experimental integrated PL intensities are also shown. The simulated data agree well with the experimental data assuming a dephasing time of 1 ps.