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We study the scattering of waves off a potential step in deformed honeycomblattices. For small deformations below a critical value, perfect Kleintunneling is obtained. This means that a potential step in any directiontransmits waves at normal incidence with unit transmission probability,irrespective of the details of the potential. Beyond the critical deformation,a gap in the spectrum is formed, and a potential step in the deformationdirection reflects all normal-incidence waves, exhibiting a dramatic transitionform unit transmission to total reflection. These phenomena are generic tohoneycomb lattice systems, and apply to electromagnetic waves in photoniclattices, quasi-particles in graphene, cold atoms in optical lattices.

Prefect Klein tunneling in anisotropic graphene-like photonic lattices