Geometrical dimensionality plays a fundamentally important role in the topological effects arising in discrete lattices. Although direct experiments are limited by three spatial dimensions, the research topic of synthetic dimensions implemented by the frequency degree of freedom in photonics is rapidly advancing. The manipulation of light in these artificial lattices is typically realized through electro-optic modulation; yet, their operating bandwidth imposes practical constraints on the range of interactions between different frequency components. Here we propose and experimentally realize all-optical synthetic dimensions involving specially tailored simultaneous short- and long-range interactions between discrete spectral lines mediated by frequency conversion in a nonlinear waveguide. We realize triangular chiral-tube lattices in three-dimensional space and explore their four-dimensional generalization. We implement a synthetic gauge field with nonzero magnetic flux and observe the associated multidimensional dynamics of frequency combs, all within one physical spatial port. We anticipate that our method will provide a new means for the fundamental study of high-dimensional physics and act as an important step towards using topological effects in optical devices operating in the time and frequency domains.

几何维数在离散晶格中产生的拓扑效应中起着至关重要的作用。尽管直接实验受到三个空间维度的限制，但光子学中通过频率自由度实现的合成维度的研究课题正在迅速推进。这些人造晶格中的光操纵通常是通过电光调制来实现的。然而，它们的工作带宽对不同频率分量之间的相互作用范围施加了实际限制。在这里，我们提出并通过实验实现了全光学合成维度，涉及由非线性波导中的频率转换介导的离散谱线之间专门定制的同时短程和长程相互作用。我们在三维空间中实现了三角形手性管晶格，并探索了它们的四维推广。我们实现了具有非零磁通量的合成规范场，并观察频率梳的相关多维动态，所有这些都在一个物理空间端口内。我们预计我们的方法将为高维物理的基础研究提供一种新方法，并成为在时域和频域运行的光学器件中使用拓扑效应的重要一步。