Synthetic dimensions in photonics have attracted broad interest in recent years.1^–4 They promise new ways to study fundamental physical phenomena with exotic artificial connectivities5^–9 and manipulate light in various ways,10^–18 pointing toward exploration of higher-dimensional physics, beyond three dimensions.19^–21 Among recent experimental achievements, different degrees of freedom of light, including arrival times of pulses,10^,11 frequencies,22^–24 and modal dimensions,8 have been used to construct synthetic dimensions. Hence, a variety of novel physics have been demonstrated in synthetic dimensions, such as the photonic topological insulator,8 the Hall ladder with effective magnetic flux,25 the trajectory of dynamic band structures,26 and the topological funneling with non-Hermitian physics,27 physical models of which are hard to build in structures with only spatial dimensions.