Non-diffracting optical Bloch oscillations in hexagonal photonic lattices

Light beams undergoing optical Bloch oscillations (OBOs) in two-dimensional (2D) photonic lattices suffer from severe diffraction along the perpendicular direction to the oscillation plane. In this paper, we propose and demonstrate that such diffraction could be suppressed in hexagonal photonic lattices via sophisticated managements of the discrete diffraction. By positioning the Fourier spectrum of the beam to a special region in the Brillouin zone, the light driven by the OBO experiences normal and anomalous diffractions alternatively, leading to a non-diffracting propagation for a long distance. We show that non-diffracting OBOs can be implemented not only for Gaussian beam but also for other complex 2D beams including self-accelerating Airy beams and vortex beams. Our results provide novel insights into the diffraction or dispersion engineering of waves in periodic structures.