Observation of the magic angle and flat band physics in dipolar photonic lattices

Evanescently coupled waveguide arrays provide a tabletop platform to realize a variety of Hamiltonians, where physical waveguides correspond to the individual sites of a tight-binding lattice. Nontrivial spatial structure of the waveguide modes enriches this picture and uncovers further possibilities. Here, we demonstrate that the effective coupling between $p$-like modes of adjacent photonic waveguides changes its sign depending on their relative orientation vanishing for a proper alignment at a so-called magic angle. Using femtosecond laser-written waveguides, we demonstrate this experimentally for $p$-mode dimers and graphene-like photonic lattices exhibiting quasi-flat bands at this angle. We observe diffraction-free propagation of corner and bulk states providing a robust experimental evidence of a two-dimensional Aharonov-Bohm-like caging in an optically switchable system.