Resonator-free realization of effective magnetic field for photons

We propose to create an effective magnetic field for photons in a two-dimensional waveguide network with strong scattering at waveguide junctions. The effective magnetic field is realized by imposing a direction-dependent phase along each waveguide link. Such a direction-dependent phase can be produced by dynamic modulation or by the magneto-optical effect. Compared to previous proposals for creating an effective magnetic field for photons, this scheme is resonator-free, thus potentially reduces the experimental complexity. We also show that such a waveguide network can be used to explore photonic analogue of integer quantum Hall effect for massless particles.