We show that dynamic refractive index modulation provides a route towards non-reciprocal topological photonics. In particular, the phase of the modulation provides an effective gauge field for photons that breaks time-reversal symmetry, and can be used to create a wide range of topological effects, in both real space as well as in spaces that involve a synthetic frequency dimension. These topological effects are pointing to new capabilities for controlling the properties of light.
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