Dielectric GaAs Antenna Ensuring an Efficient Broadband Coupling between an InAs Quantum Dot and a Gaussian Optical Beam

We introduce the photonic trumpet, a dielectric structure which ensures a nearly perfect coupling between an embedded quantum light source and a Gaussian free-space beam. A photonic trumpet exploits both the broadband spontaneous emission control provided by a single-mode photonic wire and the expansion of this mode within a conical taper. Numerical simulations highlight the performance and robustness of this concept. As a first application in the field of quantum optics, we report the realization of an ultrabright single-photon source. The device, a high aspect ratio GaAs photonic trumpet containing a few InAs quantum dots, demonstrates a first-lens external efficiency of $0.75\pm 0.1$ and an external coupling efficiency to a Gaussian beam as high as $0.58\pm 0.08$.

Figure 1

Fundamental guided mode in a tapered wire. (a) Effective surface ($S_{\mathrm{eff}}$) of the mode ${\mathrm{HE}}_{11}$ guided by a cylindrical wire of diameter $d$ (double log scale, operation wavelength $\lambda =950\mathrm{nm}$). The dashed lines are guides for the eye, indicating the slope of $\log (S_{\mathrm{eff}})$ vs ($\log d$) in the “small” and “large” diameter range. (b) Modal transmission of ${\mathrm{HE}}_{11}$ ($T_{{\mathrm{HE}}_{11}}$), plotted against the tapering angle $\alpha$ for two representative tapers. For the photonic trumpet, $d_2$ is set to $1.5\mu \mathrm{m}$; in the needle taper, $d_3=166\mathrm{nm}$ is chosen to ensure the same collection of the mode using a $\mathrm{NA}=0.75$ lens. Typical electrical field profiles are also shown (amplitude of the discontinuous component). The dots appearing in (a) correspond to $d_1$, $d_2$, and $d_3$.

Figure 2

Far-field emission. (a) Calculated total transmission $T$ (dashed line) into a $\mathrm{NA}=0.75$ lens and transmission to a Gaussian beam $T_g$ (solid line). The evaluation is conducted for a $12\mu \mathrm{m}$ high photonic trumpet with various taper angle $\alpha$ (and thus different top diameter $d_2$). The same quantities for a needle taper are shown in (b). Experimental realizations: needle tapers, upward open triangles (Ref. 5); upward solid triangles (Ref. 22); and photonic trumpet, downward open triangles (this work).

Figure 3

Single-photon trumpets. (a) Scanning electron microscope view of a large field of devices, illustrating the reproducibility of the fabrication process. Scale bar: $15\mu \mathrm{m}$. (b) Zoom on a representative device (false colors online); note the excellent control over the structure geometry. Vertical and horizontal scale bars: $1\mu \mathrm{m}$. (c) Zoom on the connection between the trumpet and the integrated mirror. Scale bar: 200 nm.

Figure 4

Optical characterization. (a) Spatial distribution of the intensity in the top facet plane. At the location of the QD, only ${\mathrm{HE}}_{11}$ is guided by the structure and all the QDs contribute to the signal. Two diameter cuts and their fit to a Gaussian profile are also shown. The circle represents the facet circumference. (b) Microphotoluminescence spectrum, measured at $T=5\mathrm{K}$ for an excitation power $P=20\mu \mathrm{W}$. (c) Spectrally integrated intensity of the lines 1, 2, and 3, extracted from a fit to a Lorentzian line shape, as a function of $P$. The solid lines are theory, assuming an excitonic emission (lines 1 and 3) and biexcitonic emission (line 2). For each transition, the luminescence decay time $T_1$, the raw and background-corrected intensity autocorrelation values $g_2(0)$ and $g_2^{\star }(0)$ are also shown.