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The synthetic dimension opens new horizons in quantum physics and topologicalphotonics by enabling new dimensions for field and particle manipulations. Themost appealing property of the photonic synthetic dimension is its ability toemulate high-dimensional optical behavior in a unitary physical system. Here weshow that the photonic synthetic dimension can transform technical problems inphotonic systems between dimensionalities, providing unexpected solutions totechnical problems that are otherwise challenging. Specifically, we propose andexperimentally demonstrate a photonic Galton board (PGB) in the temporalsynthetic dimension, in which the temporal high-speed challenge is convertedinto a spatial fiber-optic length matching problem, leading to the experimentalgeneration of tera-sample-per-second arbitrary waveforms. Limited by the speedof the measurement equipment, waveforms with sampling rates of up to 341.53GSa/s are recorded. Our proposed PGB operating in the temporal syntheticdimension breaks the speed limit in a physical system, bringing arbitrarywaveform generation into the terahertz regime. The concept of dimensionconversion offers possible solutions to various physical dimension-relatedproblems, such as super-resolution imaging, high-resolution spectroscopy, timemeasurement, etc.

Tera-sample-per-second arbitrary waveform generation in the synthetic dimension