Conical diffractions in Kagome lattice

We investigate the conical diffraction in Kagome lattice (KL) theoretically and numerically. According to the plane wave expansion method, we obtain the band structure of KL, in which there are Dirac cones and a flat band. The band structure of KL with pointy edges is also discussed, in which the edge state is around the boundary of the first Brillouin zone. The approximate Dirac cone state which is between the bulk states and the edge states is used to observe the linear and nonlinear conical diffractions during propagation. Both the Kerr nonlinearity and the saturable nonlinearity have been considered, and we find that the profile of conical diffraction will be deformed from circular to triangular. Last but not least, we find that the profile of nonlinear conical diffraction is strongly affected by the nonlinearity type, which is self-focusing or self-defocusing.