Grating assisted tunneling in photonic lattices: The Harper-Hofstadter Hamiltonian

We present a grating assisted tunneling scheme for creating tunable synthetic magnetic fields in optically induced one- and two-dimensional (dielectric) photonic lattices [1]. As a signature of the synthetic magnetic fields, we present conical diffraction patterns in lattices with Dirac points in k-space. We compare the light propagation in these realistic (continuous) systems with the evolution in discrete models representing the Harper-Hofstadter Hamiltonian, and obtain excellent agreement.