Figure 2: Numerical simulation that demonstrates the property of the alumina photonic crystal with Dirac-like cone dispersion at the Brillouin zone center. (a) An block of a hypothetical homogeneous medium is placed inside a waveguide with a tightly focused (waist equal to ) Gaussian beam incident at the surface of the homogeneous medium. As the medium only allows plane wave with to propagate, we expect only plane wave can exit, which can be clearly seen. The Gaussian wave front is transformed to a plane wave. (b) By replacing the homogeneous medium with the alumina photonic crystal, very similar wavefront transformation can be observed. Here, is the lattice constant of the photonic crystal.