Resonant Zener tunneling in two-dimensional periodic photonic lattices

We study Zener tunneling in two-dimensional photonic lattices and derive, for the case of hexagonal symmetry, the generalized Landau-Zener-Majorana model describing resonant interaction between high-symmetry points of the photonic spectral bands. We demonstrate that this effect can be employed for the generation of Floquet-Bloch modes and verify the model by direct numerical simulations of the tunneling effect.