Model-Based Real-Time Synthesis of Acousto-Optically Generated Laser-Beam Patterns and Tweezer Arrays

TL;DR

The paper tackles the challenge of real-time, intensity-matched 2D optical tweezer arrays created by acousto-optic deflectors, where nonlinear, frequency-dependent diffraction and cross-axis coupling hinder straightforward control. It introduces a compact, physics-based model of diffraction efficiency and a 2D decomposition that accounts for an interaction term Xi, enabling open-loop, real-time waveform synthesis on CPU/GPU/AWG hardware. Key contributions include a closed-form per-tone rf-power solution, an efficient 2D decomposition method, and a GPU-accelerated streaming system capable of handling up to 50×50 patterns with sub-millisecond latency, validated experimentally with low residual errors and manageable intermodulation. The approach promises substantial gains in parallel optical addressing for quantum information processing, high-throughput microscopy, and materials processing by enabling fast, scalable, intensity-controlled 2D beam patterning.

Abstract

Acousto-optic deflectors (AOD) enable spatiotemporal control of laser beams through diffraction at an ultrasonic grating that is controllable by radio-frequency (rf) waveforms. These devices are a widely used tool for high-bandwidth random-access scanning applications, such as optical tweezers in quantum technology. A single AOD can generate multiple optical tweezers by multitone rf input in one dimension. Two-dimensional (2D) patterns can be realized with two perpendicularly oriented AODs. As the acousto-optical response depends nonlinearly on the applied frequency components, phases, and amplitudes, and in addition experiences dimensional coupling in 2D setups, intensity regulation becomes a unique challenge. Guided by coupled-wave theory and experimental observations, we derive a compute-efficient model which we implement on a graphics processing unit. Only one-time sampling of single-tone laser-power calibration is needed for model parameter determination, allowing for straight-forward integration into optical instruments. We implement and experimentally validate an open-loop diffraction efficiency control system that enables programmable 2D multibeam trajectories with intensity control applied at every time step during digital signal generation, overcoming the limited flexibility, pattern-size constraints, and bandwidth limitations of methods using precalculation and precalibration of a predefined pattern set or closed-loop feedback. The system is capable of stable real-time waveform streaming of arrays with up to 50 x 50 tweezers with minimal time resolution of 1.4 ns (700 MS/s) and a peak latency below 257 microseconds for execution of newly requested patterns. Reactive, real-time 2D multibeam laser patterning and scanning with strict intensity matching will substantially benefit parallelization and increasing data rates in materials processing, microscopy, and optical tweezers.

Figures (7)

• Figure 1: Real-time synthesis of AOD-generated 2D beam patterns and laser spot arrays. (a) Schematic illustration of digital signal synthesis and optical setup (PM, laser power meter; PD, photodiode). The second dimension of the beam pattern is omitted for clarity. (b) Camera image (3.1mm$\times$3.1mm) of an intensity-equalized array of 50$\times$50 optical tweezers in the focal plane. For a targeted integral diffraction efficiency of 50% an efficiency of 49.5 ± 2.3% is achieved. The frequency span is 36.75MHz per dimension with a spacing of 0.75MHz between tones. (c) Two-dimensional spatiotemporal control was used to imprint the logo of TU Darmstadt depicting the Greek goddess Athene.
• Figure 2: Parameter determination for model-based diffraction efficiency control using randomly sampled single-tone data. (a) Peak diffraction efficiency $\alpha_{\text{N}}$ and (b) saturation power $\beta$ in units of the AWG power fraction were modeled for the x-axis AOD (solid blue) and the y-axis AOD (dashed yellow). (c) The interaction term $\Xi$ resolves correlations between the two crossed AODs. (d) Histogram of the residual prediction error. The measured data are modeled with an error below ± 0.7% (2$\sigma$ deviation).
• Figure 3: Measured latency between submission of a pattern to an empty data queue (t = 0) and detection of the requested light pattern on a photodiode ($10^4$ samples). A peak latency below 247µs is measured.
• Figure 4: Measured diffraction efficiency with and without efficiency control. A single tone is applied to both axes. (a) Without efficiency control, a constant AWG power fraction of 0.9 is set for the y axis while sweeping the x-axis AWG power fraction between 0.0 and 1.0. (b) Efficiency control set to 0.9 diffraction efficiency for the y axis while sampling the x-axis diffraction efficiency from 0.0 to 1.0 (i.e. $\eta_\textnormal{T}^{(\textnormal{xy})}\in[0, 0.9]$) results in a linear behavior up to saturation.
• Figure 5: Measured 2D diffraction efficiency for single-tone operation at both axes. (a) Unregulated operation with fixed AWG power fraction 0.9 for both AODs as reference. (b) Operation with the control system set to generate a flat response of 80% target diffraction efficiency. The color bar on the right holds for (a) and (b). (c) The uniformity of the controlled 2D diffraction efficiency is analyzed as a function of the 2D frequency span around $\nu_\textnormal{c}$. Mean value and variation (shaded areas) are plotted for 4080 target diffraction efficiency. (d) Mean diffraction error (i.e. the deviation from the target efficiency) and its variation visualizing the precision and accuracy for three selected target values.