Realizing effective magnetic field for photons by controlling the phase of dynamic modulation

The goal to achieve arbitrary control of photon flow has motivated much of the recent research on photonic crystals and metamaterials. As a new mechanism for controlling photon flow, we introduce a scheme that generates an effective magnetic field for photons. We consider a resonator lattice in which the coupling constants between the resonators are harmonically modulated in time. With appropriate choice of the spatial distribution of the modulation phases, an effective magnetic field for photons can be created, leading to a Lorentz force for photons and the emergence of topologically protected one-way photon edge states that are robust against disorders - without the use of magneto-optical effects.