Figure 3: (a) The band structure of a core-shell photonic crystal arranged in square lattice for the TE polarization. The radii of the shell and core to be and . The relative permittivity of the shell and core are and . Near the point, there is a Dirac-like cone dispersion. The inset is the enlarged part near the Dirac-like point shown by blue solid region. (b)–(d) The eigenmodes of the photonic crystal at the point. (b) and (c) dipole excitations, (d) quadrupole excitation. (e) As effective medium theory cannot be applied here, the crystal cannot be mapped to a system and hence the field distributions for an incident Gaussian beam deviate from what is expected for homogeneous medium (Figure 2(a)).