Monolithic Polarizing Circular Dielectric Gratings on Bulk Substrates for Improved Photon Collection from InAs Quantum Dots

Abstract

III-V semiconductor quantum dots (QDs) are near-ideal and versatile single-photon sources. Because of the capacity for monolithic integration with photonic structures as well as optoelectronic and optomechanical systems, they are proving useful in an increasingly broad application space. Here, we develop monolithic circular dielectric gratings on bulk substrates - as opposed to suspended or wafer-bonded substrates - for greatly improved photon collection from InAs quantum dots. The structures utilize a unique two-tiered distributed Bragg reflector (DBR) structure for vertical electric field confinement over a broad angular range. Opposing "openings" in the cavities induce strongly polarized QD luminescence without harming collection efficiencies. We describe how measured enhancements depend on the choice of collection optics. This is important to consider when evaluating the performance of any photonic structure that concentrates farfield emission intensity. Our cavity designs are useful for integrating QDs with other quantum systems that require bulk substrates, such as surface acoustic wave phonons.

FIG. 4.

Calculated angle-dependent reflectance spectra from two distinct DBRs (top images) and the composite two-tiered DBR used in our fabricate devices (bottom image).

FIG. 5.

(a) Schematic setup for collecting emitted photons into a single-mode optical fiber. The fiber-coupling optics were optimized for collection from an emitter without a photonic structure. With a photonic structure, emitted light is concentrated within a cone corresponding to divergence angle θ_p (designated by dotted red contours). The objective collimates this collected light into a beam with radius r_p, and a fiber-coupling lens focuses it to a diameter d_p that should coincide with the fiber’s mode field diameter for optimal fiber coupling. (b) Numerically calculated first-lens collection enhancement from an optimized bullseye grating as a function of the objective’s NA (black). The enhancement is relative to a bare GaAs substrate. Results for a single conventional DBR are also shown (dotted gray). (c) Collection efficiency for the system as a function of θ_p (black). Objective (dotted gray) and fiber-coupling (dashed gray) components are also shown. The objective NA (0.7) and fiber-coupling optics are held constant. Fiber coupling was optimized around 44°, corresponding to NA=0.7. Each component has been individually normalized to unity.

FIG. 1.

(a) Cross-sectional schematic (x-z plane) of the device. Etched grooves (white regions), “normal DBR” (dark blue) and “oblique DBR” (light blue) regions are designated. Red lines illustrate how light emitted from a QD (red star) at various angles interacts with the structure. (b) In-plane (x-y) structure of the center of the device, illustrated to scale. Gray corresponds to etched regions. Several design parameters are designated in panels a and b. (c) Full in-plane structures of four devices, illustrated to scale, differing only by a cavity enclosure angle θ. (d) Cross-sectional SEM of the wafer structure. White regions: GaAs. Gray regions: AlAs. Distinct normal DBR and oblique DBR regions are designated. A single etched groove is apparent. QDs are grown at the center of the top GaAs slab (black dotted line). (e) Plan-view SEM images of four distinct devices, corresponding to the four devices in panel c. The 10 μm scale bar applies to panels e and c.

FIG. 2.

(a,b) Calculated field magnitude (∣E∣) in the (a) x-y plane and (b) y-z plane when driving a fully enclosed cavity with an x-oriented electric dipole on resonance at 945 nm. In a, edges of the etched regions are designated by white circles. In b, boundaries between the DBRs and GaAs slab regions are designated by white horizontal lines and etched regions by gray rectangles. (c) Farfield intensity ∣E∣² calculated in vacuum (above the device) under the same conditions as in panels a and b. Dotted white circles indicate increments of NA=0.25. (d) Purcell spectra calculated for y-oriented (top panel) and x-oriented (bottom panel; dashed curves) dipoles. Different colors correspond to different cavity enclosure angles θ according to the legend. The system geometry (illustrated in each panel) is the same as in Fig. 1c. (e) Photon collection enhancements calculated for 5 different systems (illustrated at right and below), all with respect to a dipole emitting from within an unpatterned bulk GaAs substrate. ‘System 1’ is our optimized monolithic bullseye grating. “Total rate” includes both Purcell and geometrical enhancements. “Scattering only” excludes changes due to the Purcell factor. (More complete explanations of these terms are provided in the main text.) In all cases, collected photons correspond to power contained in the farfield within an NA of 0.5.

FIG. 3.

(a) PL spectra recorded from QDs inside a θ=90° cavity (black) and from a bare region immediately outside the same cavity (light blue; multiplied by 10). The differential reflection spectrum ∣ΔR∣/R (red filled region; right axis) from the same θ=90° cavity is also shown. (b) Estimated collection enhancement for a variety of cavities with different cavity enclosure angles θ (horizontal axis). All spectra in panels a and b were recorded with y polarization. Enhancements are calculated by comparing the peak PL counts from a QD inside each cavity to characteristic peak PL counts from QDs immediately outside the cavity. Error bars represent uncertainties arising from the random brightness of each QD in the ensemble; specifically, they were derived by taking 10 distinct estimates for QD count rates outside the cavity within a 10 nm spectral range of the cavity’s peak PL. (c) Experimental PL counts (open markers) of single QD emission lines as a function of collection polarization angle ϕ for cavities with different enclosure angles θ (specified in the legend). (One device of each θ was measured and plotted.) Fits to a sinusoidal angular variation are shown by solid curves. Data for θ=60°, 90°, and 120° cavities are normalized to the fit value at polarization angle ϕ=0°; data for the θ=180° cavity is normalized independently.