Temporal coherence of a photonic crystal nanocavity laser with high spontaneous emission coupling factor

Temporal coherence of a continuous-wave photonic crystal nanocavity laser is investigated in detail using interference experiments at room temperature. The nanocavity laser operates at $1.3\mu \mathrm{m}$ with InAs quantum dot gain material and has a very high spontaneous emission coupling factor $\beta =0.9$ with a threshold absorbed pump power of $\sim 375\mathrm{nW}$. The coherence around the laser threshold of such a high-$\beta$ laser is not obvious because spontaneous emission efficiently couples to the lasing mode. The output power dependence of the coherence length shows linearity at and above threshold. This result indicates that the first-order coherence is not greatly reduced even at threshold, where the cumulative power of spontaneous emission of other wavelengths cannot be negligible when compared with the laser power. This can be attributed to the fact that the lasing mode of a high-$\beta$ laser has a relatively large portion of the total power compared to lasers with lower $\beta$’s due to efficient coupling of the spontaneous emission to the cavity mode.

Figure 1

(Color online) Diagram of the photonic crystal slab structure. An air hole array confines photons in the nanocavity consisting of three missing air holes located at the middle of the hexagon-shaped pattern.

Figure 2

(Color online) Light-in versus light-out curve of the PhC nanocavity laser. The laser threshold excitation power is $\sim 2.5\mu \mathrm{W}$, corresponding to $375\mathrm{nW}$ absorbed excitation power. The inset is the lasing spectrum at $1330\mathrm{nm}$, where the PL peak of the ground state is observed.

Figure 3

(Color online) Time-resolved PL measurements performed at RT (upper) and $4\mathrm{K}$ (lower) with $120\mathrm{fs}$ pulses. (Upper) The PL was measured for QDs at the PL peak of the ground state at $1330\mathrm{nm}$ to obtain the nonradiative recombination time. The QDs were located outside of the cavity region but within the PhC membrane. (Lower) Time evolution of the PL of the cavity mode of another nanocavity with $a=328\mathrm{nm}$ at $1257\mathrm{nm}$ to obtain the radiative recombination time, which is shortened by the Purcell effect. The time evolution of PL of QDs located outside of the PhC region is also shown.

Figure 4

(Color online) Experimental $L\text{−}L$ plots of the PhC nanocavity laser and the simulation curves with various values of $\beta$ with logarithmic scales in both axes. The best fit has been found for $\beta =0.9$.

Figure 5

(Color online) (a) Interference fringe produced by the cw-laser beam from the PhC nanocavity. The interference fringe is observed by superposing the two split beams of zero time-delayed replica on a multichannel detector array. The horizontal axis is the position along the pixel array. The inset is the experimental setup. (b) Interference fringes at various optical delay path lengths. The visibility of the interference fringe decreases as the delay path length becomes longer due to the finite temporal coherence.

Figure 6

(Color online) The output power dependence of the coherence length. The linear increase of the coherence length follows the Schawlow-Townes law above the threshold. The excitation powers are shown in the figure, and the inset shows the $L\text{−}L$ curve in log-log scale.