The Harper–Hofstadter Hamiltonian and conical diffraction in photonic lattices with grating assisted tunneling

Abstract

We propose the realization of a grating assisted tunneling scheme for tunable synthetic magnetic fields in optically induced one- and two-dimensional dielectric photonic lattices. As a signature of the synthetic magnetic fields, we demonstrate conical diffraction patterns in particular realization of these lattices, which possess 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.

Keywords

• synthetic magnetic fields
• photonic lattices
• topological effects
• conical diffraction
• 42.50.Xa
• 42.82.Et