Fast, reprogrammable control over the transverse structure of light beams plays an essential role in applications such as structured illumination microscopy, optical trapping, and quantum information processing. Existing technologies, such as liquid-crystal-on-silicon spatial light modulators or digital micromirror devices, suffer from limited refresh rates, low damage thresholds, and high insertion loss. Acousto-optic modulators (AOMs) address these limitations and enable rapid phase and amplitude modulation controlled by the amplitude and frequency of the rf waveform. By effectively mapping the temporal rf waveforms onto the spatial diffraction patterns of the optical field, individual AOMs have been shown to generate one-dimensional spatial modes at a pixel refresh rate of nearly 20 MHz. Here we extend this concept to enable fast modulation in a two-dimensional (2D) space using a double-AOM scheme and show the generation of 2D Hermite-Gaussian (${\mathrm{HG}}_{nm}$) modes. Numerical simulations demonstrate that one can improve the fidelity to a desired amplitude and phase pattern for the diffracted beam by optimizing the amplitude and frequency of the input rf waveform. With optimized rf input, our experimentally generated HG modes have an average mode fidelity of 81%, while the highest-order mode generated, ${\mathrm{HG}}_{53}$, maintains a fidelity of 56%.

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• Light-matter interaction
• Spatial profiles of optical beams
• Structured light
• Optical materials & elements
• Spatial light modulators
• Acoustic techniques
• Optical techniques
• Radio frequency techniques