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Timestamp: 2019-04-22 00:54:20+00:00

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We report coupling of the excitonic photon emission from photoexcited PbSe colloidal quantum dots (QDs) into an optical circuit that was fabricated in a silicon-on-insulator wafer using a CMOS-compatible process. The coupling between excitons and sub-μm sized silicon channel waveguides was mediated by a photonic crystal microcavity. The intensity of the coupled light saturates rapidly with the optical excitation power. The saturation behaviour was quantitatively studied using an isolated photonic crystal cavity with PbSe QDs site-selectively located at the cavity mode antinode position. Saturation occurs when a few μW of continuous wave HeNe pump power excites the QDs with a Gaussian spot size of 2 μm. By comparing the results with a master equation analysis that rigorously accounts for the complex dielectric environment of the QD excitons, the saturation is attributed to ground state depletion due to a non-radiative exciton decay channel with a trap state lifetime ∼ 3 μs.
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Fig. 1 (A) Schematic and scanning electron micrograph of an “L3” microcavity. (B) Fundamental in-gap cavity mode electric field intensity at the silicon-air interface, with etched holes outlined. Axes originate at the L3 slab centroid, and ẑ is perpendicular to x̂ and ŷ.
Fig. 2 (A) Close-up scanning electron micrograph of the photonic crystal cavity, photonic crystal waveguide, and channel waveguide region. (B) An optical image of the entire cavity, waveguides, and grating structure, with excitation spot (centered on the cavity) and collection spot (centered on the grating coupler) indicated. (C) Example ŷ-polarization-filtered PL spectrum for the excitation/collection geometry indicated in (B), and a plot of the cavity-enhanced, waveguide-coupled PL versus pump power.
Fig. 3 Experimental setup and resulting data modeled in this article. (A) Schematic of excitation/collection geometry: excitation (at 633 nm) and collection performed with a common 100 X microscope objective. Red-filled circle indicates 1/e excitation spot intensity. Shaded square indicates span of grafted PbSe QDs. (B) Example PL spectrum with cavity-coupled emission indicated, and cavity-coupled PL versus pump power.
Fig. 4 Minimal Hilbert space necessary to accommodate observed saturation behaviour: four states for the QD subspace and two for the cavity subspace. Significant decay paths indicated by solid blue arrows, of which squiggly lines are radiative and the remainder non-radiative. Laser field of Rabi coupling frequency Ω “pumps” the |P〉 state. The cavity is “fed” by coupling to the |X〉 ↔ |G〉 transition with electric-dipole coupling strength g.
Fig. 5 Model dielectric environment ε(r,ω) = εL3(r,ω) +εQDs(r,ω). Nanocrystal array εQDs(r,ω) on left, centered on the L3 cavity surface. The computational volume for FDTD calculations (see text) is restricted to the 3 μm cube centered about the centroidal QD. The intrinsic “test” dipole is located at the center of centroidal QD, position rQD. The device silicon slab is surrounded by vacuum above and below, with backing silicon 1.2 μm below.
Fig. 6 Spontaneous emission rate of a point dipole source of frequency ωcav + δω, for positions along the ẑ-axis of the L3 cavity, excluding the cavity mode and QD array, for electric dipole orientations along axes x̂, ŷ, or ẑ (see text and orientation definitions in Fig. 1). All values normalized to the free-space spontaneous emission rate γXG,0.
Fig. 7 Intensity profiles of HeNe excitation field, as modulated by the L3 cavity εL3(r). Gaussian laser field was injected along the ẑ axis towards increasingly negative z, indicated by black arrow. Air-silicon interfaces lined in black. (left) Profile several nanometers above the slab surface, the plane containing the PbSe QDs. (right) Profile in the x = 0 plane.
Fig. 8 Best (minimum χ2) fits to cavity-enhanced photoluminescence for only three electronic levels (left), i.e. without a non-radiative state, and for four electronic levels (right), i.e. including a non-radiative “trap” state.
Fig. 9 Trap state lifetime τ trap = γ YG − 1 required to fit the data. Parameterization of τtrap is in terms of the “effective depolarization”, DPF, which is defined in-text (see Eq. (18)) and is equal to the laser field inside the QD in the full model dielectric environment relative to the laser field inside the same QD in vacuum. Variation of τtrap with DPF is dominated by uncertainties in parameters specific to our dielectric environment (photonic crystal cavity, QD array), whereas variation of τtrap for a particular DPF is dominated by parameter uncertainty not specific to our dielectric environment (e.g. solvent permittivity from solvent-based QD properties). Points are sampled from the model parameter space.

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