Effective magnetic fields have enabled unprecedented manipulation of neutral particles including photons. In most studied cases, the effective gauge fields are defined through the phase of mode coupling between spatially discrete elements, such as optical resonators and waveguides in the case for photons. Here, in the paradigm of Bloch-wave modulated photonic crystals, we show creation of effective magnetic fields for photons in conventional dielectric continua for the first time, via Floquet band engineering. By controlling the phase and wavevector of Bloch waves, we demonstrated anomalous quantum Hall effect for light with distinct topological band features due to delocalized wave interference. Based on a cavity-free architecture, in which Bloch-wave modulations can be enhanced using guided-resonances in photonic crystals, the study here opens the door to the realization of effective magnetic fields at large scales for optical beam steering and topological light-matter phases with broken time-reversal symmetry.
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