Highly directed emission from self-assembled quantum dots into guided modes in disordered photonic-crystal waveguides

We explore the dynamics and directionality of spontaneous emission from self-assembled In(Ga)As quantum dots into transverse-electric–polarized guided modes in GaAs two-dimensional photonic-crystal waveguides. The local group velocity of the guided waveguide mode is probed, with values as low as $\sim 1.5\%c$ measured close to the slow-light band edge. By performing complementary continuous-wave and time-resolved measurements with detection along and perpendicular to the waveguide axis, we probe the fraction of emission into the waveguide mode ($\beta$ factor). For dots randomly positioned within the unit cell of the photonic-crystal waveguide, our results show that the emission rate varies from $\ge 1.55\mathrm{n}{\mathrm{s}}^{-1}$ close to the slow-light band edge to $\le 0.25\mathrm{n}{\mathrm{s}}^{-1}$ within the two-dimensional photonic band gap. We measure an average Purcell factor of $\sim 2\times$ for dots randomly distributed within the waveguide and maximum values of $\beta \sim 90\%$ close to the slow-light band edge. Spatially resolved measurements performed by exciting dots at a well-controlled distance of 0–45 $\mu \text{m}$ from the waveguide facet highlight the impact of disorder on the slow-light dispersion. Although disorder broadens the spectral width of the slow-light region of the waveguide dispersion from $\delta E_d\le 0.5$ to $>6\mathrm{m}\mathrm{e}\mathrm{V}$, we find that emission is nevertheless primarily directed into propagating waveguide modes. The ability to control the rate and directionality of emission from isolated quantum emitters by placing them in a tailored photonic environment provides much promise for the use of slow-light phenomena to realize efficient single-photon sources for quantum optics in a highly integrated setting.

Figure 1

(a) Selected SEM images of one-half of the cleaved $W1$ PhC waveguide with a grating coupler on the opposite end [31], nominally identical to the sample used for the spectroscopic studies. The leftmost image shows the cleaved facet with the under-etched membrane, tilted at an angle of $60{}^{\circ }$. The rightmost images show planar views. From these images, the air-hole radius $r=79\pm 2\mathrm{n}\mathrm{m}$, lattice constant $a=250\pm 2\mathrm{n}\mathrm{m}$, and slab thickness $h=150\pm 5\mathrm{n}\mathrm{m}$ were determined. (b) Left panel: Photonic band structure calculation for the structural and geometrical parameters extracted from the SEM images shown in (a). The black and blue solid lines show the zeroth- and first-order waveguide modes, respectively. The orange dashed line marks the upper edge of the 2D photonic band and the light-blue shaded region represents the free-space light cone. In the rightmost panel, we present typical $\mu$-PL measurements of the investigated structure excited at the position of the waveguide from the top (see text) and detected from the side (green) and top (red), respectively. The blue spectrum shows typical QD emission recorded from the top using identical conditions from the unprocessed region of the sample for comparison.

Figure 2

(a) Comparison of a typical decay transient recorded at a detection energy of $\sim 1.3$ eV from dots in the unpatterned region (REF) of the samples and selected decay transients $\left(A,B,C,D\right)$ recorded at the spectral positions indicated in (b), using the measurement geometry described in the text (IRF: instrument response function). (b) Corresponding $\mu$-PL spectrum detected from the side with top excitation 10 $\mu \text{m}$ away from the facet. The slab band region is marked in blue, the photonic band gaps are green, the slow-light regions of the zeroth- and first-order mode are red, the fast-guided mode region is black, and the phonon-coupled slow-light region is brown. (c) Fast and slow spontaneous-emission rate of the QDs in the PhC waveguide as a function of the emission energy extracted from the decay transients as measured in (a) (open and closed circles, respectively). For comparison, the decay rate from QDs in the unprocessed region of the sample and on the PhC membrane away from the waveguide is shown by the orange and purple squares, respectively.

Figure 3

(a) High-power (30 $\mu \mathrm{W}/\mu {\mathrm{m}}^2)$ $\mu$-PL spectrum, detected from the side facet when exciting from the top 10 $\mu \text{m}$ from the facet. (b) Group index as a function of energy. The red circles represent the group index extracted from measured data and the black solid line is the group index derived from the photonic band structure simulations presented in Fig. 1; the inset shows a zoom of (a). (c) $Q$ factor extracted from (a) as a function of energy.

Figure 4

(a) Spectra recorded via the side channel as a function of the excitation position along the waveguide. (b) Top view SEM image from a waveguide identical to the measured one, illustrating the excitation spot scan. (c) Averaged spectrum of (a) (black curve) and a single spectrum when exciting 40 $\mu \text{m}$ away from the facet [red curve; position is indicated by the red dotted line in (a)]. The two peaks in the single spectrum arise from the zeroth- and first-order mode. The slow-light disorder window width is $\delta E_d=6\pm 1\mathrm{m}\mathrm{e}\mathrm{V}$. (d) Extracted ${\beta }_I$ factor as a function of position and energy. (e) Disorder-induced mode peak deviation of mode 1 from the average as a function of mode peak deviation of mode 0 from the average.