Automatic differentiation accelerated shape optimization approaches to photonic inverse design on rectilinear simulation grids

Shape optimization approaches to inverse design offer low-dimensional, physically-guided parameterizations of structures by representing them as combinations of shape primitives. However, on discretized rectilinear simulation grids, computing the gradient of a user objective via the adjoint variables method requires a sum reduction of the forward/adjoint field solutions and the Jacobian of the simulation material distribution with respect to the structural shape parameters. These shape parameters often perturb large or global parts of the simulation grid resulting in many non-zero Jacobian entries, which are typically computed by finite-difference in practice. Consequently, the gradient calculation can be non-trivial. In this work we propose to accelerate the gradient calculation by invoking automatic differentiation (AutoDiff) in instantiations of structural material distributions. In doing so, we develop extensible differentiable mappings from shape parameters to shape primitives and differentiable effective logic operations (denoted AutoDiffGeo). These AutoDiffGeo definitions may introduce some additional discretization error into the field solutions because they relax notions of sub-pixel smoothing along shape boundaries. However, we show that some mappings (e.g. simple cuboids) can achieve zero error with respect to volumetric averaging strategies. We demonstrate AutoDiff enhanced shape optimization using three integrated photonic examples: a multi-etch blazed grating coupler, a non-adiabatic waveguide transition taper, and a polarization-splitting grating coupler. We find accelerations of the gradient calculation by AutoDiff relative to finite-difference often exceed 50x, resulting in total wall time accelerations of 4x or more on the same hardware with little or no compromise to final device performance. Our code is available open source at https://github.com/smhooten/emoptComment: 29 pages, 15 figure

Generating single photons at gigahertz modulation-speed using electrically controlled quantum dot microlenses

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Appl. Phys. Lett. 108, 021104 (2016) and may be found at https://doi.org/10.1063/1.4939658.We report on the generation of single-photon pulse trains at a repetition rate of up to 1 GHz. We achieve this speed by modulating the external voltage applied on an electrically contacted quantum dot microlens, which is optically excited by a continuous-wave laser. By modulating the photoluminescence of the quantum dot microlens using a square-wave voltage, single-photon emission is triggered with a response time as short as (281 ± 19) ps, being 6 times faster than the radiative lifetime of (1.75 ± 0.02) ns. This large reduction in the characteristic emission time is enabled by a rapid capacitive gating of emission from the quantum dot, which is placed in the intrinsic region of a p-i-n-junction biased below the onset of electroluminescence. Here, since our circuit acts as a rectifying differentiator, the rising edge of the applied voltage pulses triggers the emission of single photons from the optically excited quantum dot. The non-classical nature of the photon pulse train generated at GHz-speed is proven by intensity autocorrelation measurements with g(2)(0) = 0.3 ± 0.1. Our results combine optical excitation with fast electrical gating and thus show promise for the generation of indistinguishable single photons at rates exceeding the limitations set by the intrinsic radiative lifetime.BMBF, 03V0630, Entwicklung einer Halbleiterbasierten Einzelphotonenquelle für die Quanteninformationstechnologie (QSOURCE)DFG, 43659573, SFB 787: Halbleiter - Nanophotonik: Materialien, Modelle, Bauelement

Accessing the dark exciton spin in deterministic quantum-dot microlenses

The dark exciton state in semiconductor quantum dots (QDs) constitutes a long-lived solid-state qubit which has the potential to play an important role in implementations of solid-state-based quantum information architectures. In this work, we exploit deterministically fabricated QD microlenses which promise enhanced photon extraction, to optically prepare and read out the dark exciton spin and observe its coherent precession. The optical access to the dark exciton is provided via spin-blockaded metastable biexciton states acting as heralding states, which are identified by deploying polarization-sensitive spectroscopy as well as time-resolved photon cross-correlation experiments. Our experiments reveal a spin-precession period of the dark exciton of (0.82 ± 0.01) ns corresponding to a fine-structure splitting of (5.0 ± 0.7) μeV between its eigenstates ↑⇑±↓⇓. By exploiting microlenses deterministically fabricated above pre-selected QDs, our work demonstrates the possibility to scale up implementations of quantum information processing schemes using the QD-confined dark exciton spin qubit, such as the generation of photonic cluster states or the realization of a solid-state-based quantum memory

Bright Single-Photon Sources Based on Anti-Reflection Coated Deterministic Quantum Dot Microlenses

We report on enhancing the photon-extraction efficiency (PEE) of deterministic quantum dot (QD) microlenses via anti-reflection (AR) coating. The AR-coating deposited on top of the curved microlens surface is composed of a thin layer of Ta2O5, and is found to effectively reduce back-reflection of light at the semiconductor-vacuum interface. A statistical analysis of spectroscopic data reveals, that the AR-coating improves the light out-coupling of respective microlenses by a factor of 1.57 ± 0.71, in quantitative agreement with numerical calculations. Taking the enhancement factor into account, we predict improved out-coupling of light with a PEE of up to 50%. The quantum nature of emission from QDs integrated into AR-coated microlenses is demonstrated via photon auto-correlation measurements revealing strong suppression of two-photon emission events with g(2)(0) = 0.05 ± 0.02. As such, these bright non-classical light sources are highly attractive with respect to applications in the field of quantum cryptography