  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.
