Spontaneous Emission Enhancement of Quantum Dots in a Photonic Crystal Wire

Photonic wires are the simplest extended low-dimensional systems. Photonic crystal confinement confers them a divergent density of states at zero-group-velocity points, which leads to enhancement of spontaneous emission rates [D. Kleppner, Phys. Rev. Lett. 47, 233 (1981)]. We experimentally evidence, for the first time, the spectral signature of these Purcell factor singularities, using the out-of-plane emission of InAs quantum dots buried in $\mathrm{GaAs}/\mathrm{AlGaAs}$ based photonic crystal based wire. Additionally, in-plane collection at the wire exit shows large enhancements of the signal at some of the density of states singularities.

Figure 1

Dispersion relation for 1D systems: (a) a perfectly confining waveguide, such as a metallic waveguide, (b) a dielectric wire of index $n_1$, embedded in a uniform medium of index $n_2$. Light lines are shown; (c) a dielectric wire with a periodic index variation along the direction of propagation. Dispersion relations are folded into the first Brillouin zone between $k_y=0$ and $k_y=\pi /a$.

Figure 2

(a) Scheme of a $W{3}^{\mathrm{K}}$ planar PXCW perforating a vertically guiding heterostructure. (b) Transverse mode profiles of the squared displacement field, $|\epsilon E{|}^2$, at two symmetry planes of the PXCW, for the zero-group-velocity mode at the low-frequency-edge of the mini-stopband (2D calculation). (c) Calculated dispersion relation for a $W{3}^{\mathrm{K}}$ PXCW (real part of eigenfrequencies). (d) Density of states when taking into account losses through an imaginary dielectric constant in the air holes.

Figure 3

Measurement configuration for the spontaneous emission rate measurement, for the PXCW transmission and for the edge emission modification.

Figure 4

Low-temperature measurement of the Purcell effect: (a) raw decay data for two extreme cases, fit by exponentials (early stage favored) in the inset; (b) measured spectrum of lifetime evolution; (c) calculated density of states responsible for spontaneous emission rate evolution. The mini-stopband is highlighted in both graphs and the normalized frequency axis is common to them.

Figure 5

(a) Edge-collected luminescence spectra of quantum dots (reference in arbitrary units) and transmission of a $W{3}^{\mathrm{K}}$ waveguide measured as indicated in Fig. 3, and (b) edge-collected spectrum for excitation inside the same photonic wire (solid line). The dashed line is the curve of the “filtered” density of states as explained in the text.